diff --git a/research/vocal-source-grounding/README.md b/research/vocal-source-grounding/README.md new file mode 100644 index 0000000..5dbd8f7 --- /dev/null +++ b/research/vocal-source-grounding/README.md @@ -0,0 +1,206 @@ +# Vocal Source Grounding + +This packet grounds the next cut to Aqua's graph tissue-valve source law. The +trigger was the Warbling White-eye audition: a low-drive, smooth single-labium +candidate finally sounded birdlike, but the route there was suspicious. The +question is whether low drive and harmonic suppression are legitimate source +controls or compensators that should instead fall out of morphology, pressure, +tissue loss, aperture geometry, and acoustic load. + +Downloaded/captured source files live in `sources/`. + +## Decision Pressure + +The current graph valve lowering still gives `drive` too much authority: + +- it scales reservoir pressure, so it changes energy input; +- it participates in oscillation gating, so it changes phonation threshold; +- it scales modal/displacement contribution into flow, so it changes brightness; +- it sits beside `pressure`, `damping`, `saturation`, `load_coupling`, and + `rest_opening`, which already have clearer physical meanings. + +That is not one organ. That is a desk drawer full of half-labeled teeth. + +## Literature Anchors + +### Myoelastic-Aerodynamic Ownership + +Elemans et al. 2015 provide the cleanest cross-species authority map: bird +syrinxes and mammal larynxes both use the myoelastic-aerodynamic mechanism. +Airflow supplies energy; tissue elasticity/restoring forces, tissue-wave phase, +and aerodynamic asymmetry sustain oscillation. The paper explicitly ties +frequency and mode of oscillation to mechanical tissue properties plus +aerodynamic driving forces, not a standalone timbre-gain parameter. + +Implementation implication: `pressure` or `reservoir_pressure` is the energy +input. `mass`, `stiffness`, `damping`, layered phase, aperture geometry, and +load decide what that energy becomes. A single `drive` knob should not also own +spectral aggression. + +### Syrinx Models Use Pressure/Tension Paths, Not Timbre Rescues + +Mindlin/Laje-style syrinx work models syllables as trajectories through +physiological parameter space, especially pressure and stiffness/tension. Their +review emphasizes that the syrinx itself can be a source of complex acoustical +behavior, and that smooth excursions in pressure/stiffness parameter space can +produce recognizable syllables. The same review highlights that source-tract and +source-source coupling can create subharmonics, period-doubling, and complex +periodic/aperiodic behavior. + +Implementation implication: the higher-level controller can own motif gestures, +but the lower-level source law must expose meaningful physical coordinates. +Harmonic behavior should arise from nonlinear source dynamics and coupling +regimes, not from a spectral smoothing knob. + +### Mechanical Syrinx Experiments Separate Bronchial Pressure And Tension + +Elemans et al. 2009 modeled the syrinx as a collapsible-tube/starling-resistor +style mechanical system with separately controlled bronchial pressure and +membrane tension. The captured abstract reports high-frequency self-sustained +oscillations, tension-dependent frequency, mass-dependent lower frequency +limits, and strong coupling to distal tube resonance. + +Implementation implication: source morphology needs separate controls for +tension/stiffness, mass, damping/tissue loss, and tract load. Pressure should +drive the system; distal tube/reflection should perturb it. A generic low-drive +value is not the correct way to make a small bird source less harsh. + +### Two-Mass Vocal Fold Modeling Keeps Flow, Tissue, And Tract Separate + +Ishizaka and Flanagan's classic two-mass model approximates the vocal folds as +two stiffness-coupled masses, uses Bernoulli flow through the glottis, and +represents the tract as a transmission line. It calculates glottal area, glottal +volume velocity, mouth pressure, and relationships among subglottal pressure, +cord tension, glottal area, and duty ratio. + +Implementation implication: our layered valve law should move toward explicit +upper/lower masses and aperture/flow equations. It should not hide duty ratio, +open quotient, or source spectral tilt behind `drive`. + +### Self-Oscillating Fold Reviews Point To Coupled Nonlinear Physics + +The 2024 review of synthetic self-oscillating vocal fold models frames phonation +as coupled flow dynamics, tissue motion, and acoustics. It calls out turbulence, +flow separation, large deformation/strain, collision, acoustic coupling, and +radiated acoustics as difficult but central nonlinear phenomena. It also +emphasizes that stiffness and geometry are meaningful experimental controls. + +Implementation implication: if the current valve needs harmonic suppression, +candidate owners are damping/tissue loss, collision stiffness/damping, aperture +geometry, flow separation/loss, and radiation/load. A musical-synth style drive +stage is the wrong default owner. + +### Vocal-Tract Loss Work Makes Area-Dependent Flow Loss A First-Class Actor + +Birkholz and Haesner 2024 propose unified viscous and kinetic pressure losses in +discrete tube vocal-system models, including the glottis. Their measurements +support area-dependent viscous losses and partial pressure recovery at +expansions; the losses affect formant bandwidths, airflow, and turbulent source +power. + +Implementation implication: some of the "harmonic suppression" we wanted by +turning drive down should instead come from source/tract loss and radiation +loading. For small apertures and narrow passages, area-dependent loss is not a +post-EQ trick; it is pressure-flow physics. + +### Faust Can Express The Clean Version + +Faust has first-class tools for this lane: recursive state with `~`, filters, +fractional delays, bidirectional waveguide primitives, mode filters, tube +models, reed tables, and nonlinear functions. We do not need to keep a fake +drive authority because of Faust. The hard part is choosing a source law that is +simple enough to inspect and stable enough for realtime. + +Implementation implication: the next cut can stay Faust-friendly if it is a +small set of named locals: reservoir/downstream pressure, pressure drop, +flow-resistance/loss, upper/lower displacement and velocity, aperture, +collision/contact, load pressure, volume velocity, and radiation flow. + +## Authority Map For The Next Cut + +Owner: `AcousticSourcePort` source morphology owns local valve dynamics; +`AcousticNetwork` owns incident pressure/load and radiation; gesture/controller +layers own time-varying physiological inputs. + +Inputs: + +- Controller/gesture: `pressure`, `opening`, `tension`, left/right activation. +- Source morphology: `mass`, `upper_mass`, `lower_mass`, `stiffness`, + `upper_stiffness`, `lower_stiffness`, `coupling_stiffness`, `damping`, + `tissue_loss`, `collision_stiffness`, `collision_damping`, + `rest_opening`, `aperture_shape`, `flow_loss`. +- Graph load: incident/downstream pressure, tract impedance, tube losses, + radiation opening/reflection/loss. + +Outputs: + +- Source volume velocity/flow injection. +- Optional debug locals for aperture, pressure drop, contact, tissue energy, + load pressure, and radiated flow. + +Derived state: + +- Dominant pitch, harmonic richness, phonation threshold, breathiness, + brightness, and biphonation are outcomes of the above. They are not owned by + `freq=` or a generic `drive`. + +Forbidden writers: + +- No hidden fixed oscillator floor when stiffness exists. +- No direct displacement-as-audio lane except as a tiny diagnostic/legacy term. +- No "harmonic suppression" or "bird smoothness" scalar. +- No source-owned spectral EQ pretending to be morphology. + +## Proposed Cut, Not Yet Implemented + +1. Split `drive` into physical pieces: + - keep `pressure`/`reservoir_pressure` as the energy input; + - introduce or repurpose `flow_scale` only as a unit/calibration factor; + - move threshold/ease-of-oscillation into pressure drop, aperture, damping, + and load; + - move spectral harshness into aperture/contact/flow-loss/radiation. + +2. Add explicit morphology fields only if they name physics: + - `tissue_loss` or `viscous_loss` for dissipative tissue/flow losses; + - `aperture_shape` for the nonlinear mapping from displacement to area; + - `flow_loss` or `flow_resistance` for area-dependent pressure-flow loss; + - keep `collision_stiffness`/`collision_damping` as the contact owner. + +3. Change the source law shape: + - compute `pressure_drop = reservoir_pressure - downstream/load pressure`; + - compute aperture from rest opening + controlled opening + displacement; + - compute flow from a pressure-flow relation damped by aperture-dependent + resistance, not from arbitrary modal gain into `tanh`; + - use modal/two-mass tissue state to modulate aperture and flow, not as a + parallel oscillator output; + - let tract/radiation losses shape brightness before any post-source + normalization. + +4. Keep a compatibility path only as explicit legacy: + - `drive` can remain parsed for now, but it should lower to `flow_scale` or a + deprecated alias with warnings/tests, not retain secret timbre authority. + +## Open Questions + +- Do we want `flow_scale` exposed in DSL at all, or should it be a patch + calibration constant hidden behind morphology presets? +- Should `aperture_shape` be a continuous scalar first, or should we jump + directly to named aperture laws such as `slot`, `wedge`, `membrane`, and + `reed`? +- How aggressive should the v1 area-dependent pressure-flow loss be before we + have a calibration set for birds? +- Should one-mass law remain the default for realtime, with two-mass/body-cover + reserved for richer source patches, or should syrinx defaults move directly to + two-mass because MEAD phase asymmetry is central? + +## Source Index + +- `pmc-elemans-2015-universal-mechanisms.html` and + `elemans-2015-universal-mechanisms.pdf` +- `pmc-new-perspectives-birdsong-physics.html` +- `wur-elemans-mechanical-model.html` +- `nokia-ishizaka-flanagan-two-mass.html` +- `pmc-self-oscillating-vocal-fold-review.html` +- `vocaltractlab-birkholz-2024-losses.pdf` and `.txt` +- `faust-physmodels-doc.html`, `faust-filters-doc.html`, + `faust-noises-doc.html` diff --git a/research/vocal-source-grounding/SOURCES.md b/research/vocal-source-grounding/SOURCES.md new file mode 100644 index 0000000..b578d39 --- /dev/null +++ b/research/vocal-source-grounding/SOURCES.md @@ -0,0 +1,22 @@ +# Sources + +Downloaded or captured on 2026-05-28 for the vocal-source grounding pass. + +| Local file | Source | Use | +| --- | --- | --- | +| `sources/pmc-elemans-2015-universal-mechanisms.html` | | Cross-species MEAD evidence for birds and mammals. | +| `sources/elemans-2015-universal-mechanisms.pdf` | | Local PDF copy of the same paper. | +| `sources/pmc-new-perspectives-birdsong-physics.html` | | Mindlin/Laje birdsong physics review: pressure/tension parameter trajectories, nonlinear syrinx, source-tract/source-source coupling. | +| `sources/pubmed-mindlin-birdsong-nonlinear-dynamics.html` | | PubMed metadata for Mindlin's nonlinear dynamics of birdsong review. | +| `sources/pubmed-fee-nonlinear-dynamics-birdsong.html` | | PubMed metadata for Fee et al. nonlinear dynamics in birdsong. | +| `sources/wur-elemans-mechanical-model.html` | | Mechanical syrinx model metadata and abstract. | +| `sources/nokia-ishizaka-flanagan-two-mass.html` | | Classic two-mass model summary from Bell Labs/Nokia. | +| `sources/pubmed-titze-1988-small-amplitude.html` | | PubMed metadata for Titze's small-amplitude vocal fold oscillation paper. | +| `sources/pmc-self-oscillating-vocal-fold-review.html` | | 2024 review of synthetic self-oscillating vocal fold models. | +| `sources/vocaltractlab-birkholz-2024-losses.pdf` | | Birkholz/Haesner 2024 vocal-system pressure-loss model. | +| `sources/faust-physmodels-doc.html` | | Faust physical modeling primitives. | +| `sources/faust-filters-doc.html` | | Faust filters for loss/radiation/source shaping. | +| `sources/faust-noises-doc.html` | | Faust noise primitives for turbulence. | + +Note: two attempted URLs resolved to unrelated pages during collection and were +removed from the packet. diff --git a/research/vocal-source-grounding/sources/elemans-2015-universal-mechanisms.pdf b/research/vocal-source-grounding/sources/elemans-2015-universal-mechanisms.pdf new file mode 100644 index 0000000..8fdf2f1 Binary files /dev/null and b/research/vocal-source-grounding/sources/elemans-2015-universal-mechanisms.pdf differ diff --git a/research/vocal-source-grounding/sources/elemans-2015-universal-mechanisms.txt b/research/vocal-source-grounding/sources/elemans-2015-universal-mechanisms.txt new file mode 100644 index 0000000..0f8f8b4 --- /dev/null +++ b/research/vocal-source-grounding/sources/elemans-2015-universal-mechanisms.txt @@ -0,0 +1,2128 @@ +University of Southern Denmark + +Universal mechanisms of sound production and control in birds and mammals +Elemans, Coen; Rasmussen, Jeppe Have; Herbst, Christian T.; Düring, Daniel Normen; +Zollinger, Sue Anne; Brumm, Henrik ; Srivastava, K.; Svane, Niels; Ding, Ming; Larsen, Ole +Næsbye; Sober, Sam J. ; Svec, Jan G. +Published in: +Nature Communications +DOI: +10.1038/ncomms9978 +Publication date: +2015 +Document version: +Final published version +Document license: +CC BY +Citation for pulished version (APA): +Elemans, C., Rasmussen, J. H., Herbst, C. T., Düring, D. N., Zollinger, S. A., Brumm, H., Srivastava, K., Svane, +N., Ding, M., Larsen, O. N., Sober, S. J., & Svec, J. G. (2015). Universal mechanisms of sound production and +control in birds and mammals. Nature Communications, 6, Article 8978. https://doi.org/10.1038/ncomms9978 + +Go to publication entry in University of Southern Denmark's Research Portal + +Terms of use +This work is brought to you by the University of Southern Denmark. +Unless otherwise specified it has been shared according to the terms for self-archiving. +If no other license is stated, these terms apply: +• You may download this work for personal use only. +• You may not further distribute the material or use it for any profit-making activity or commercial gain +• You may freely distribute the URL identifying this open access version +If you believe that this document breaches copyright please contact us providing details and we will investigate your claim. +Please direct all enquiries to puresupport@bib.sdu.dk + +Download date: 28. May. 2026 + + ARTICLE +Received 24 Mar 2015 | Accepted 22 Oct 2015 | Published 27 Nov 2015 + +DOI: 10.1038/ncomms9978 + +OPEN + +Universal mechanisms of sound production +and control in birds and mammals +C.P.H Elemans1,2,3, J.H. Rasmussen1,*, C.T. Herbst4,*, D.N. Düring1,*, S.A. Zollinger5, H. Brumm5, K. Srivastava6,7, +N. Svane1, M. Ding8, O.N. Larsen1, S.J. Sober6 & J.G. Švec4 + +As animals vocalize, their vocal organ transforms motor commands into vocalizations for +social communication. In birds, the physical mechanisms by which vocalizations are produced +and controlled remain unresolved because of the extreme difficulty in obtaining in vivo +measurements. Here, we introduce an ex vivo preparation of the avian vocal organ that allows +simultaneous high-speed imaging, muscle stimulation and kinematic and acoustic analyses to +reveal the mechanisms of vocal production in birds across a wide range of taxa. Remarkably, +we show that all species tested employ the myoelastic-aerodynamic (MEAD) mechanism, +the same mechanism used to produce human speech. Furthermore, we show substantial +redundancy in the control of key vocal parameters ex vivo, suggesting that in vivo vocalizations +may also not be specified by unique motor commands. We propose that such motor +redundancy can aid vocal learning and is common to MEAD sound production across birds +and mammals, including humans. + +1 Department of Biology, University of Southern Denmark, Campusvej 55, 5230 Odense, Denmark. 2 QuanTM program, Emory University, Atlanta, Georgia +30322, USA. 3 Université de Saint-Etienne/Lyon, ENES/CNPS CNRS UMR8195, Saint-Etienne 42023, France. 4 Faculty of Science, Department of Biophysics, +Voice Research Lab, Palacky University, Olomouc 77146, Czech Republic. 5 Communication and Social Behaviour Group, Max Planck Institute for Ornithology, +Seewiesen 82319, Germany. 6 Department of Biology, Emory University, Atlanta, Georgia 30332, USA. 7 Coulter Department of Biomedical Engineering, +Georgia Institute of Technology, Atlanta, Georgia 30332, USA. 8 Department of Orthopaedic Surgery & Traumatology, Odense University Hospital, University +of Southern Denmark, Odense 5230, Denmark. * These authors contributed equally to this work. Correspondence and requests for materials should be +addressed to C.P.H.E. (email: coen@biology.sdu.dk). + +NATURE COMMUNICATIONS | 6:8978 | DOI: 10.1038/ncomms9978 | www.nature.com/naturecommunications + +1 + + ARTICLE + +NATURE COMMUNICATIONS | DOI: 10.1038/ncomms9978 + +n contrast to laryngeally vocalizing mammals, B10,000 +species of extant birds vocalize with a uniquely avian vocal +organ, the syrinx, located at the tracheobronchial junction and +suspended in an air sac of the respiratory system1. The syrinx is +structurally highly diverse across species1, but how morphological +diversity reflects functional diversity remains unexplored. In +addition, while songbirds are a widely used experimental animal +model for neural mechanisms underlying vocal imitation +learning2,3, we lack the empirical evidence to precisely map +motor function onto neural circuitry4. Addressing these questions +requires empirical quantification of syringeal dynamics as a +function of control parameters in different species under +physiologically realistic, controlled conditions. However, +imaging the syrinx in vivo remains a challenge5,6, and we thus +still lack this quantification of syringeal dynamics and control +parameters. +Earlier endoscopic imaging identified syringeal vibratory +tissues in songbirds and non-songbirds5,6, arguing against +purely aerodynamical whistle mechanisms in which sound is +produced without periodic movement of the vocal apparatus. +Many mathematical models for birdsong7–11 assume that +syringeal sound production is based on a myoelasticaerodynamic (MEAD) system12–15. However, conclusive +empirical evidence for MEAD is lacking4,16. The MEAD +framework explains the physical mechanism underlying +laryngeal sound production in mammals12–15,17. In brief, +self-sustaining laryngeal vocal fold oscillations are maintained +through fluid-tissue interactions and (myo)elastic restoring +forces generated within the tissues12–15, preventing the +need for muscle contractions at the rate of tissue vibration or +other periodic input18. Expiratory airflow is mechanically +converted by vocal folds into pulse-like airflow, which +causes air pressure disturbances constituting the acoustic +excitation of the system13. The mechanical properties and +recruitment of different layers of vibrating tissues affect +their resonance properties, which in combination with +aerodynamic driving forces determine the frequency and mode +of oscillation19–22. +According to MEAD theory, the medio-lateral vibration of the +inner vocal fold surface (vibrational component 1 (VC1)) that +gates airflow23 can only be self-sustaining if moving around a +stable equilibrium position and if no net energy loss occurs per +oscillation cycle13,24. The latter requires the presence of an +aerodynamic force that changes magnitude with direction of +vocal fold motion and thus is asymmetric over the oscillation +cycle13. One possibility is that during self-sustained vocal fold +vibration the required asymmetric aerodynamic force is produced +by time-varying supraglottal pressure due to inertia of air in +the vocal tract23. Such a mechanism would result in uniform +medio-lateral vibration of the vocal folds24. However, models +suggest that this mechanism limits the range of fundamental +frequencies (F0) produced14. Another, more robust possibility is +that the asymmetric aerodynamic force during self-sustained +vocal fold vibration is produced by out-of-phase motion of the +superior and inferior edge of the vibrating tissue (vibrational +component 2 (VC2))13,25. VC1 and VC2 are the respective +medio-lateral and caudo-cranial components of a tissue surface +wave, or mucosal wave, that travels on the inner vocal fold surface +along the expiratory air stream and facilitates aerodynamic energy +transfer into tissue24. The wave phase changes cause the vocal +folds to change shape from convergent during opening to +divergent during closing parts of the cycle24. Because the +intraglottal pressure is higher for the convergent shape than for +the divergent shape26,27, the vocal folds are pushed apart during +opening and pulled together during closing14,24,25. VC2 presence +thus indicates that intraglottal pressure forms the asymmetric + +I + +2 + +forcing function over opening and closing phases of vibration25 +essential to self-sustained oscillation. Sound excitation events in +mammals occur mainly at glottal closure and/or opening, when +airflow abruptly stops or starts28–30. +Although isolated aspects of syringeal dynamics have been +studied in birds5,6,31–35, the asymmetric forcing function essential +to maintain self-sustained oscillation has not yet been identified, +and the caudo-cranial tissue-wave component VC2—a crucial +underlying assumption in modelling studies7,9,36—has not been +demonstrated experimentally in the intact syrinx under +appropriate physiological conditions16. Furthermore, it is +unknown how syringeal dynamics relate to sound generating +events within a single oscillatory cycle. These essential features of +syringeal dynamics required to confirm MEAD have yet to be +established16. +The translation of vocal motor commands into acoustic output +depends on neural activity, musculature, morphology and +physical mechanism of sound production4,16,37. These variables +define a multi-dimensional parameter space that the brain needs +to explore and navigate to control vocal output. In birds, these +control variables have been studied in vivo by correlating +acoustical parameters, for example, F0, with physiological +parameters, for example, lung pressure or muscle activity, +taking advantage of the highly stereotyped vocal patterns +employed by adult birds38. This approach can inform us about +a particular solution an individual uses to control its vocal output. +However, if the control space is redundant (that is, there is more +than one possible solution to achieve a specific vocal target, for +example, F0), as commonly observed in motor control systems39, +studying stereotyped in vivo behaviour provides limited insight in +the behaviour of the entire system as we only observe the final +solution the individual uses that may not be unique. Furthermore +if vocal control parameters covary it may be difficult to establish +causal relationships. To understand how the brain controls vocal +behaviour therefore requires systematic quantification of the +system’s behaviour across its multi-dimensional parameter space. +However, we currently lack an experimental paradigm to +systematically study physiological control of the vocal system +in birds. +Here, we present a novel ex vivo paradigm of the syrinx, which +allows unprecedented experimental control and high-resolution +imaging during sound production. First, to investigate if the +MEAD physical mechanism of self-sustained oscillations as +observed in mammals is applicable to birds, we test the +hypotheses that a caudo-cranial travelling tissue surface wave is +present and that this tissue wave is associated with sound +production events. Second, to determine whether vocalizations +are encoded by unique motor commands we test the hypothesis +that the physiological control space of the syrinx ex vivo is +redundant for key acoustic parameters. We show that birds +employ the MEAD mechanism for sound production and that +key vocal parameters exhibit redundant control ex vivo. We +propose that motor redundancy may accelerate vocal learning +and is common to MEAD sound production across birds and +mammals. +Results +Physical mechanism of sound production. We developed an +experimental paradigm that allows imaging of syringeal dynamics +under controlled conditions ex vivo (Methods section; +Supplementary Fig. 1). To test our first hypothesis, if the +MEAD physical mechanism of self-sustained oscillations is +applicable to birds (Fig. 1a), we took advantage of the diversity in +syringeal morphology across species and first studied the +domestic pigeon syrinx (Fig. 1b) because of its relatively simple + +NATURE COMMUNICATIONS | 6:8978 | DOI: 10.1038/ncomms9978 | www.nature.com/naturecommunications + + ARTICLE + +NATURE COMMUNICATIONS | DOI: 10.1038/ncomms9978 + +VC1 + +VC2 + +Trachea +ICAS membrane + +psupra + +Muscle + +pICAS + +T4 +Lateral vibratory +mass (LVM) + +T2 +psub +Larynx + +Closing + +Syrinx + +Right +LVM + +T1 +Opening + +Bronchus +Cranial + +Left +LVM + +T4 +Ch B + +DKG1 +T2 + +Δy + +DKG2 + +T1 +Ch A + +1 mm +Closing/divergent + +Caudal + +Collision + +Opening/convergent + +DKG1 + +Syringeal opening + +Left + +ΔtDKG + +Right + +DKG2 + +Left + +Right + +μEGG + +Ch A +Ch B + +Position + +2 + +1 mm + +Cranial +Min + +VC2 mucosal wave + +2 +2 ms + +4 +0 + +6 + +LVM displacement +(mm) + +ΔtEGG + +Glottovibrogram +GVG + +3 +Opening / closing / opening cranial edge + +2 + +Cranial edge + +1 + +Caudal edge + +0 + +Syringeal opening +(mm) + +Caudal + +Closing/opening caudal edge +Right + +Sound (Pa) + +Tracheal +VKG + +Closing caudal edge +Mediolateral mucosal wave + +Left + +Opening/closing cranial edge + +0 + +5 + +0 +Excitation +10 + +15 + +20 + +25 + +30 + +35 + +Time (ms) + +morphology. We found self-sustained syringeal oscillations when +both bronchial and air sac pressures were 40.5 kPa (N ¼ 12). +The lateral vibratory masses (LVMs)7 were visualized using +transillumination of the syrinx (Fig. 1c). Within an oscillation + +cycle the LVM inner wall changed shape from divergent +during closing, rectangular during full collision and to +convergent during opening (Fig. 1c, Supplementary Movie 1). +A consistent phase shift in LVM position, confirmed by + +NATURE COMMUNICATIONS | 6:8978 | DOI: 10.1038/ncomms9978 | www.nature.com/naturecommunications + +3 + + ARTICLE + +NATURE COMMUNICATIONS | DOI: 10.1038/ncomms9978 + +simultaneous micro-electroglottography (mEGG) recordings +(Methods section), was present along the caudo-cranial +axis (Fig. 1d). Spatiotemporal analysis of the LVM inner wall +displacement and syringeal opening identified both components +VC1 and VC2 of a tissue travelling wave along the caudo-cranial +axis (Fig. 1e). Furthermore, we observed medio-lateral, that is, +laterally travelling, tissue waves on the cranial surface of the +LVMs (Fig. 1f), which are continuations of the caudo-cranial +waves accompanying the LVM opening, and commonly observed +on mammalian vocal folds (Supplementary Fig. 2). Sound +pressure excitation occurred both during opening and closing +events (Fig. 1g). The presence of both VC1 and VC2 components +confirms our hypotheses that a caudo-cranial travelling tissue +surface wave is present and that this wave is associated with +sound producing events in pigeons. +To test whether the presence of a tissue surface wave is a shared +trait across birds, we studied syringeal oscillatory behaviour in six +additional bird species from five orders. We selected species +ranging in size (B15 g–200 kg) and vocal complexity, each with +highly divergent syrinx morphologies, containing one or two +paired oscillators and controlled by zero to seven pairs of intrinsic +syringeal muscles (Figs 2 and 3). We reconstructed threedimensional geometries including bone, soft tissue and muscle +based on micro-computed tomography (CT) scans (Figs 2a +and 3a). Our study species included the largest extant bird +(ostrich), a phylogenetically basal paleognathid bird (elegantcrested tinamou) and several neognathids: a parrot (cockatiel), +dove (Barbary dove) and two songbirds (zebra finch and +Bengalese finch). Medio-lateral vibration components (VC1) +were observed in each species using tracheal endoscopy (Figs 2c +and 3c). These VC1 vibrations resulted in complete syringeal +closure within an oscillatory cycle in each species except for the +ostrich, where full closure was never observed, more closely +resembling human breathy phonation40. +In each species, regardless of syringeal morphology, we +confirmed the presence of the caudo-cranial component (VC2) +of a travelling tissue wave using spatiotemporal analysis of +syringeal inner wall displacement, syringeal opening and/or +mEGG (Figs 2d and 3d, Supplementary Movies 1–6). To further +test if the tissue wave was present over a range of fundamental +frequencies, we subjected the syrinx to bronchial pressure ramps +and measured the direction and speed of the tissue wave when +present (Methods section). During self-sustained oscillations over +a range of F0 values, the tissue wave was always present (Fig. 4) +and running from caudal to cranial (indicated by all velocities +being positive in Fig. 4). The wave speed did either not vary +(pigeon and tinamou; linear regression, P ¼ 0.56 (n ¼ 10) and +P ¼ 0.26 (n ¼ 10), respectively) or increased significantly with +F0 (zebra finch and cockatiel; linear regression, Po0.001 +(n ¼ 11) and Poo0.001 (n ¼ 118) respectively) within a range of +0.5–4.0 m s  1. + +Furthermore, to investigate the relationship between tissue +motion dynamics and sound generation events within a single +oscillatory cycle, we quantified the delay between sound +excitation events and first opening and closing events of the +syringeal passage over a range of F0 values (Fig. 5). In the pigeon, +both opening and closing events were precisely accompanied by +an acoustic excitation at very short delays of 170 and 90 ms, +respectively (Fig. 5a), which are both below the 250 ms temporal +accuracy of the opening and closing event timing (that is, one +frame duration of high-speed video). The tinamou showed a +strong acoustic excitation on syringeal opening, with a delay of +100 ms, also below the 250 ms temporal accuracy of the opening +and closing event timing (Fig. 5b). A second, often weaker, +excitation occurred 1.63 ms after closing. The zebra finch showed +a very precisely timed strong acoustic excitation on syringeal +closing at a delay of 40 ms (at a temporal accuracy of 33 ms; +Fig. 5c). +In conclusion, these data confirm our first hypothesis that a +caudo-cranial travelling tissue surface wave is present across a +range of syringeal morphologies and sizes. Furthermore, our data +confirm a close association between opening/closing event timing +and sound generation events within single oscillatory cycles +across a range of species. Collectively, our data thus provide the +essential lacking demonstrations of syringeal dynamics and sound +generation events required to conclusively show that MEAD +theory is applicable to sound production in birds. +Vocal control redundancy ex vivo. To test our second hypothesis +that the physiological control space of the vocal organ is +redundant for key acoustic parameters, we systematically +investigated the relationship between syringeal control parameters and acoustic output ex vivo. In mammals, the brain can +control bronchial pressure and laryngeal muscle activity to +modulate aerodynamic forces and vocal fold tissue properties (for +example, geometry and elasticity) and attain a target fundamental +frequency (F0)12–15. In birds, in addition to bronchial pressure, +pressure in the interclavicular air sac (ICAS) enclosing the syrinx +also affects F0, as suggested by models7,9,10 and experimental +manipulations10. We first quantified syringeal oscillatory +behaviour in different species as a function of bronchial and air +sac pressure (Figs 6 and 7a–c). For each species the F0 ranges +produced ex vivo corresponded well to the lower-end distribution +of spontaneous vocalizations (Figs 6 and 7b,c). We further found +that in each investigated species, multiple different combinations +of bronchial and ICAS pressures could achieve the same target +frequency (iso-F0 contours in Figs 6 and 7c), indicating that F0 +control is redundant within the pressure control space. To +investigate how much two other important vocal parameters, that +is, sound pressure level (SPL) and sound quality, changed with F0, +we quantified the SPL and Wiener entropy (WE) along evenly + +Figure 1 | The MEAD theory explains sound production in the domestic pigeon (Columba livia) syrinx. (a) Schematic illustration of vocal organs in +mammals (larynx) and birds (syrinx) showing the two vibrational components essential to MEAD theory: medio-lateral oscillation (VC1), and caudo-cranial +phase differences (VC2). The latter are related to a tissue surface wave moving cranially and cause the inner wall of the vibratory tissue to be divergent during +closing (solid line, black arrows) and convergent during opening motion (dashed line, white arrows). The syrinx is suspended in the ICAS. Three pressures act +on the syrinx: subsyringeal (psub), suprasyringeal (psupra) and ICAS pressure (pICAS). (b) Annotated micro-CT scan of the pigeon syrinx showing LVM (yellow) +and their inner edges (right, green; left, red), muscle (pink) and tracheal rings (T1–4). (c) Transilluminated syrinx filmed at 4 kHz with traced outlines of right +(green) and left (red) LVM during closing, collision and opening phases of oscillation. The region shown is indicated by the dotted box in b. White +arrows indicate movement. Circles indicate mEGG electrode pairs channel A (cyan fill) and B (black fill). (d) Two DKG (compiled at dotted lines in c) and +simultaneous mEGG recordings show consistent caudo-cranial time delay of syringeal closure between the caudal line DKG2 and cranial line DKG1 (DtDKG) as +well as between the caudal and cranial mEGG signals (DtmEGG). (e) Spatiotemporal displacement analysis of the left LVM (top) shows a caudo-cranial travelling +tissue wave (dashed line), which is also present in the glottovibrogram of syringeal opening (bottom). (f) Simultaneous tracheal endoscopic VKG confirms +opening and closing event timing of the cranial LVM edge, and reveals tissue waves (arrowheads) travelling mediolaterally over the epithelia. (g) Abrupt +positive and negative excitation of the acoustic waveform aligns with opening and closing of the LVM cranial edge. +4 + +NATURE COMMUNICATIONS | 6:8978 | DOI: 10.1038/ncomms9978 | www.nature.com/naturecommunications + + ARTICLE + +NATURE COMMUNICATIONS | DOI: 10.1038/ncomms9978 + +Ostrich + +Tinamou +Muscle +ICAS + +1m + +Tracheal view + +LVM + +10 mm + +ventral + +Muscle + +LVM +100 mm + +1 mm + +Ventral + +1 + +Tracheal VKG + +Right + +Left + +Pa + +Left + +Opening cranial edge + +GVG + +DKG + +VC2 wave + +Caudal (pos 1) + +Sound + +Closing + +3 + +Cranial + +Cranial (pos 2) + +VC2 + +Right + +VC2 wave + +2 ms + +Caudal + +F0 = 150 Hz + +0.4 + +1 mm + +Tracheal VKG + +VC1 + +DKG + +0.2 + +0 + +Syringeal opening +(mm) + +2 +Dorsal + +Left +LVM + +Right +LVM +VKG + +F0 = 310 Hz + +0 + +0 + +2 ms + +5 ms + +–0.4 + +–0.2 +Time + +Time + +Figure 2 | MEAD theory explains syringeal sound production in paleognaths. (a) Three-dimensional syrinx geometry of the ostrich (Struthio camelus) and +elegant-crested tinamou (Eudromia elegans) showing bone (grey), LVM (yellow) and muscles (pink). Both views are ventral. Muscle is rendered transparent +in tinamou syrinx to show vibratory tissue. (b) High-speed imaging stills of endoscopic tracheal (ostrich) and transilluminated frontal views (tinamou) of +the syrinx at two different phases during the oscillatory cycle. The region and location of these stills is indicated with a dotted box in a. For the ostrich the +position of VKG analysis (dotted horizontal line) and DKG analysis (solid white line from point 1–2) presented in panel c is indicated. Transillumination +provides sufficient detail to identify inner edges of right (green) and left (red) LVM in tinamou. (c) Evidence for medio-lateral vibrations (VC1) using +tracheal endoscopic VKG. In the ostrich predominantly the right side vibrated. Full opening and closure of the cranial edge can be observed in tinamou. +(d) Evidence for the caudo-cranial component (VC2) of the tissue wave as demonstrated by DKG for ostrich, and glottovibrogram for tinamou. +(e) Synchronised acoustic waveforms. + +spaced iso-F0 contours. A point on the iso-F0 contour was +considered to be redundant in all three acoustic parameters if +neither SPL nor WE changed along the iso-F0 contour (Methods +section). The percentage of the explored control space that +demonstrated redundancy for the three vocal parameters +measured 79.8±21.4% (mean±s.d.) for pigeon (N ¼ 7), +83.0±7.7% for Barbary dove (N ¼ 3), 67.8±4.7% for tinamou +(N ¼ 3), 71.4±18.9% for cockatiel (N ¼ 2), 44.3% for zebra finch +right hemisyrinx, 62.4±13.3% for Bengalese finch left hemisyrinx +(N ¼ 6) and 71.6±18.6% for Bengalese finch left hemisyrinx +(N ¼ 6). These results demonstrate that F0 control by pressure +ex vivo is redundant in subspaces within the pressure control +space, and that this redundancy is conserved across species +exhibiting a wide range of syringeal morphologies. Therefore, in +the ex vivo preparation redundant acoustic output can be +achieved by modulating air pressure, without any active control +of syringeal muscles. +We furthermore examined whether muscular control +introduced an additional source of redundancy and quantified +the effect of syringeal muscle recruitment on F0 using local +micro-stimulation (Fig. 7d). Muscle stimulation caused an F0 +increase of 300–750 Hz and 75–200 Hz for tinamou and zebra +finch, respectively (Fig. 7e). The F0 range achieved by pressure + +and muscle recruitment overlapped within each species (tinamou +(N ¼ 1) and zebra finch (N ¼ 5)) and multiple different +combinations of muscle recruitment and bronchial pressure +resulted in the same F0. These results thus demonstrate that +muscular control of F0 is redundant in the ex vivo preparation. +Taken together, the above data confirm our second hypothesis +that the physiological control space of the vocal organ ex vivo is +redundant for key acoustic parameters across a range of syringeal +morphologies and sizes. +Discussion +Our data establish that birds use MEAD as the primary physical +mechanism for sound production with strong similarities to +mammalian MEAD systems: First, we demonstrate the presence +of a tissue wave that travels from the caudal to cranial end of the +syringeal vibratory tissue (Figs 1–4). This tissue wave thus causes +the syringeal vibratory tissue shape to be convergent when +opening, and divergent when closing during expiratory sound +production, and can be considered analogous to the caudo-cranial +mucosal wave observed in mammalian vocal folds. Our data +therefore strongly suggest that in birds, just as in mammals, the +dominant asymmetric forcing function over the opening and + +NATURE COMMUNICATIONS | 6:8978 | DOI: 10.1038/ncomms9978 | www.nature.com/naturecommunications + +5 + + ARTICLE + +NATURE COMMUNICATIONS | DOI: 10.1038/ncomms9978 + +Zebra finch + +Cockatiel + +Muscle +Muscle + +Medial +Labia +Lateral +Labia + +B3 +LVM +100 mm + +10 mm + +1 mm + +1 mm + +B3 +Ch B + +Ch B + +Right +LL + +Ch A + +Right + +Left + +Closing + +Opening cranial edge + +Right + +Closing +Midline +Opening cranial edge + +Left + +μEGG + +μEGG + +ΔtEGG + +ΔtEGG +1 + +F0 = 1450 Hz + +Sound +Pa + +0.5 + +GVG + +Ch A +Ch B + +VC2 + +0.4 + +VC2 wave + +0 + +Syringeal opening +(mm) + +VC1 + +Tracheal VKG + +Tracheal VKG + +Ch A + +6 +F0 = 420 Hz + +0 + +0 + +2 ms + +1 ms +–0.4 + +–1 +Time + +Time + +Figure 3 | MEAD theory explains syringeal sound production in neognaths. (a) Three-dimensional syrinx geometry of the cockatiel (Nymphicus hollandicus, +ventral view) and zebra finch (Taeniopygia guttata, dorsal view) showing bone (grey), LVM (yellow) and muscles (pink). Muscle is rendered transparent in +zebra finch right hemisyrinx to show vibratory tissue. (b) High-speed imaging stills of frontal transilluminated frontal views of the syrinx at two different phases +during the oscillatory cycle at view and location indicated with a dotted box in a. While transillumination does not provide detail on motion in the cockatiel +syrinx, it provides sufficient detail to identify inner edges of vibratory tissue in female zebra finches (green). Circles indicate location of mEGG electrodes (cyan, +channel A; black, channel B). (c) Tracheal endoscopic VKG shows opening and closing events and thus evidence for medio-lateral vibrations (VC1). In the +zebra finch sound production was induced in the right hemisyrinx. (d) Evidence for caudo-cranial component (VC2) of the tissue wave as demonstrated by +mEGG phase delays for cockatiel and zebra finch and glottovibrogram analysis for zebra finch. (e) Synchronised acoustic waveforms. + +closing phases of vibration essential to maintain self-sustained +oscillation is not formed by the mass inertance of the air column +in the vocal tract23,24, but by the tissue-wave-induced intraglottal +pressure changes. This mechanism reduces the dependency of the +self-sustained syringeal oscillations on acoustic resonances of the +vocal tract and allows for an expanded F0 range of vocalization14, +which in addition to labial morphology41 could aid birds in +extending their F0 range. Second, the magnitude range of the +tissue-wave speed measured (0.5–3.0 m s  1) is in excellent +agreement with values reported for the mammalian larynx30,41– +46 (human41,43–45, 0.5–2.0 m s  1; dog42,46,47, 0.5–2 m s  1; calf45, +0.4 m s  1; and an African elephant30, 1.2 m s  1) suggesting that +no scaling effects occur. Third, our data show that in some species +(zebra finch, cockatiel) the tissue-wave speed increased with F0, +similar to what has been observed in humans47, whereas in other +species (pigeon, tinamou) the tissue-wave remained constant with +respect to F0 (Fig. 4). The different relationships are possibly +related to biomechanical properties of the tissue layers involved in +the vibrations or varying aerodynamic forces acting on the +vibrating structures. Future work will be required to establish the +respective causality. Last, our findings demonstrate that acoustic +excitation occurs at opening and/or closing of the syringeal +passage (Fig. 5), which strongly suggests a causal relation between +6 + +tissue vibration and generation of acoustic energy by modulating +the glottal airflow as found in the mammalian larynx28–30. While +in humans the maximum acoustic excitation has been shown to +occur mainly at the instant of glottal closure28,29, a recent study +reported that in an excised elephant larynx the maximum +acoustic excitation occurred at the instant of glottal opening30. +The mammalian larynx thus exhibits more diversity than +previously thought in what movements cause the predominant +acoustic excitation. Our work demonstrates that this diversity is +also present in birds and that more comparative studies are +needed to explain the causal link between airflow, tissue vibration +and acoustic excitation. +In conclusion, we find that despite the large diversity present in +syringeal morphology of the bird species included in this study, +all use MEAD as the primary physical mechanism of sound +production, supporting MEAD-based approaches to modelling +avian sound production7–11. Moreover, our findings suggest that +despite their different evolutionary origins1, laryngeally vocalizing +mammals and syringeally vocalizing birds have converged on the +same physical mechanism for vocalization. +Furthermore, our data show that key acoustic parameters, such +as particular F0 values, can be achieved by multiple distinct +combinations of respiratory pressure and syringeal muscle + +NATURE COMMUNICATIONS | 6:8978 | DOI: 10.1038/ncomms9978 | www.nature.com/naturecommunications + + ARTICLE + +NATURE COMMUNICATIONS | DOI: 10.1038/ncomms9978 + +vVC2 (m s–1) + +1.0 + +Pigeon + +0.8 +0.6 +0.4 +0.2 +0 + +vVC2 (m s–1) + +4 + +190 + +200 + +210 + +220 + +230 + +240 + +250 + +260 + +270 + +Tinamou + +3 +2 +1 +0 + +2 +vVC2 (m s–1) + +P = 0.56 +180 + +P = 0.26 +230 + +240 + +250 + +260 + +270 + +280 + +290 + +300 + +310 + +320 + +330 + +Zebra finch + +1 + +P < 0.001 +0 + +240 + +260 + +280 + +300 + +320 + +340 + +360 + +380 + +400 + +Cockatiel +vVC2 (m s–1) + +3 +2 +1 +P << 0.001 +0 + +1,650 + +1,700 1,750 1,800 1,850 1,900 +Fundamental frequency (Hz) + +1,950 + +2,000 + +Figure 4 | The caudo-cranial tissue wave is present across a range of +fundamental frequencies. Magnitude of the caudo-cranial component +(vVC2) of the travelling tissue-wave’s velocity in (a) pigeon and (b) tinamou, +(c) zebra finch and (d) cockatiel. The positive velocity values indicate that +the wave travelled from caudal to cranial. Wave speed remained constant +with F0 in pigeon and tinamou (Linear regression, P ¼ 0.56 (n ¼ 10) and +P ¼ 0.26 (n ¼ 10), respectively), but increased significantly with F0 in zebra +finch and cockatiel (linear regression, Po0.001 (n ¼ 11) and Poo0.001 +(n ¼ 118), respectively). + +recruitment ex vivo (Figs 6 and 7). This finding thus supports the +hypothesis that subspaces within the entire physiological control +space of the vocal organ ex vivo are redundant for acoustic +parameters. +Our work represents the first systematic exploration of +syringeal behaviour in a controlled environment using pressure +differentials up to 2 kPa. Although it remains unresolved to what +degree birds can independently control bronchial pressure and +ICAS air sac pressure in vivo, ventilation flow across the lungs +requires the existence of pressure differences between different +parts of the respiratory system48–50. Especially in dynamic +situations such as vocal behaviour, the passive geometry of the +air sac system can lead to substantial pressure differences between +air sacs51,52 and indeed transient pressure differences up to +1.0 kPa occur during vocalizations in Barbary doves7,53. These +pressure fluctuations can result in local transmural pressure +differentials over the syringeal walls and thus in transmural forces +on the vibrating tissues7,37. The individual bird can either avoid +or exploit such regimes during vocalization. However, regardless + +of pressure differentials, only bronchial pressure in combination +with different levels of recruitment in a single vocal muscle leads +to redundancy in F0 (Fig. 7e). +How acoustic redundancy of the vocal organ ex vivo reflects the +functional motor redundancy in vivo remains to be explored. The +speed at which consecutive motor commands can be executed +in vivo (either on the same side of the syrinx or when vocal +production switches rapidly from one side to the other within a +complex syllable) may cause a significant reduction of the +available functional redundancy, especially because at least some +songbirds possess superfast syringeal muscles that produce peak +force in o5 ms (refs 54,55). Here, we did not investigate the rapid +time-varying pressure and muscle recruitment patterns that occur +in vivo, and indeed for most species more detailed experimental +in vivo data are required to meaningfully explore the highdimensional control space ex vivo. On the other hand, we show +that redundancy emerges when only varying the activity level of a +single vocal muscle. Redundancy can thus be expected to +increase when the brain can produce a given acoustic output by +choosing from a large set of redundant motor commands when +coordinating the B16 syringeal muscles56 with several thousand +motor units57. +A recent study used zebra finch song acoustics to infer lowdimensional motor commands11, which were then used to +generate synthetic songs that closely resembled the acoustic +output of natural vocal behaviour, and evoked auditory responses +that closely resembled the pattern of premotor activity. These +results led the authors to suggest that premotor area HVC +encodes a low-dimensional forward model of gesture dynamics11. +In contrast, our data indicate that particular acoustic outputs can +be specified by multiple motor states, suggesting that motor +commands cannot be uniquely inferred from acoustics. It will +therefore be important for future studies to investigate whether +the method used in ref. 11 to infer motor commands from +acoustic data yields the actual combination of control parameters +employed by the bird to generate the sound, rather than a +different set of control parameters that redundantly produces the +same acoustic output. Similarly, future ex vivo studies employing +time-varying stimulus patterns across multiple muscles will allow +us to explore the limits of vocal redundancy during sophisticated +motor trajectories similar to those in behaving animals. Despite +the apparent conflict between our findings and elements of +ref. 11, it is important to note that the instantiation of a lowdimensional forward model within HVC—which is multiple +synapses upstream from the vocal and respiratory muscles—is +not incompatible with a redundant vocal organ. Indeed, one +strength of low-dimensional encoding in HVC is that it would +allow HVC to represent control parameters (for example, vocal +fold tension) without regard to the details of the redundant +combinations of muscle contraction states required to achieve +that tension. +In many fine motor control systems such as arm reaching, the +brain must negotiate the so-called motor redundancy problem39, +in which a particular behavioural target can be achieved by vast +numbers of motor commands. However, one potential advantage +to a redundant control space is that it allows the brain to find +subspaces of possible motor commands (for example, along the +iso-F0 contours in Figs 6 and 7c in our ex vivo paradigm) rather +than searching for unique motor commands to achieve the target. +Crucially, redundant control spaces allow variability in taskirrelevant directions58,59. In vocal production, the brain may +select from within this motor command space to meet other +demands, such as acoustic targets in future and/or past syllables. +Consequently, we speculate that vocal motor redundancy may +simplify trial-and-error learning during song acquisition by +allowing the brain to rapidly discover one of many motor + +NATURE COMMUNICATIONS | 6:8978 | DOI: 10.1038/ncomms9978 | www.nature.com/naturecommunications + +7 + + ARTICLE + +NATURE COMMUNICATIONS | DOI: 10.1038/ncomms9978 + +Acoustic excitation with syringeal +Rock pigeon + +Opening + +350 + +150 + +50 +0 +180 + +200 + +220 + +240 + +Opening + +100 + +No. observations per bin + +200 + +Closing + +Closed + +250 + +Open + +Phase ϕ (deg) + +–90 μs + +10 + +300 + +8 +8 +6 + +6 +4 + +4 + +2 + +2 + +0 +–1 + +260 + +Tinamou + +0 + +0 +–1 + +1 + +14 + +350 + +0 + +10 + +–100 μs + +1 + +1.63 ms + +250 +200 +Opening Closing + +150 +100 +50 +0 +220 + +240 + +260 + +280 + +300 + +No. observations per bin + +12 + +300 +Phase ϕ (deg) + +Closing +10 + +–170 μs + +8 + +6 + +6 + +4 + +4 +2 + +2 +0 +–1 + +320 + +8 + +10 + +0 + +0 + +1 + +0 + +1 + +2 + +3 + +Time after opening (ms) +Zebra finch + +250 +200 +150 +100 +Opening + +Phase ϕ (deg) + +300 + +50 +0 +240 260 280 300 320 340 360 380 400 +Fundamental frequency (Hz) + +18 +No. observations per bin + +Closing + +350 + +–40 μs + +16 +14 +12 +10 +8 +6 +4 +2 +0 +–1 +0 +1 +Time after closing (ms) + +Figure 5 | Sound excitation is associated with syringeal opening and closing events. The relative duration of the syrinx in open (white bar starting at +phase j ¼ 0°) and closed (grey bar) state within a single oscillatory cycle (full oscillation equals 360°) over a range of fundamental frequencies in +(a) pigeon, (b) tinamou and (c) zebra finch (left) based on transillumination data (Methods section). Sound excitation events are associated with opening +(red circles: mean±s.d.) and/or closing (blue circles: mean±s.d.) of the syrinx. The thick vertical black line at the base of each column indicates the +duration of a single movie frame relative to the cycle duration and thus the timing accuracy for determining a syringeal closing or opening event. Note that +in zebra finch the lines are short due to high frame-rates used (25 kHz). The histograms (right) show that timing of sound excitation is closely associated +with syringeal opening (red) and closing (blue) events. + +solutions60 before learning how to further improve performance +by exploiting motor redundancy39. Vocal redundancy may +therefore have aided, or even been necessary for, the +evolutionary development of vocal learning. Future studies +might evaluate this speculation by quantifying whether learned +vocalizations exploit vocal redundancy. Furthermore, because +many species do not learn their vocalizations and many vocal +learners produce innate vocalizations in addition to learned ones, +future work might also determine whether innate vocal motor +programs similarly exploit redundancy to improve performance. +8 + +Our ex vivo results suggest that the redundant control of key +vocal parameters represents a significant aspect of avian vocal +control, and one that merits further investigation. Because +redundancy in F0 control by pressure and muscle recruitment +is also observed in various simplified computational models of the +human larynx13, and songbird syrinx9 as well as in ex vivo dog +larynx preparations61,62, we propose that vocal control +redundancy is a typical feature of MEAD sound production +systems and hence a common feature of vocal production and +control in mammals and birds. + +NATURE COMMUNICATIONS | 6:8978 | DOI: 10.1038/ncomms9978 | www.nature.com/naturecommunications + + ARTICLE + +NATURE COMMUNICATIONS | DOI: 10.1038/ncomms9978 + +Airsac pressure (kPa) + +Frequency (kHz) + +Rock pigeon +0.8 + +0.4 + +0 + +Airsac pressure (kPa) + +Frequency (kHz) + +Barbary dove + +0.5 + +0 +500 ms + +Airsac pressure (kPa) + +Frequency (kHz) + +Cockatiel +4 + +2 + +0 +500 ms + +2 +R +1 +0 + +Airsac pressure (kPa) + +Frequency (kHz) + +L + +0.2 + +180 + +1 + +0.1 + +0 +0 + +1 + +3 + +2 + +500 + +0.4 + +450 + +2 + +400 + +0.2 + +1 +0 + +0 + +F0 (kHz) + +3 + +0 + +1 + +2 + +3 + +0 + +F0 (kHz) +2 + +3 + +1,100 +2 +1 + +1,500 +1,800 + +1 +0 +0 + +Left hemisyrinx + +Bengalese finch +3 + +230 +220 + +2 + +500 ms + +1 + +F0 (kHz) +0.3 + +3 + +3 + +1 + +2 + +3 + +0 + +Right hemisyrinx +F0 (kHz) +900 + +2,350 +1,900 +1,500 + +2 +1 +0 +0 + +1 + +2 + +800 +1 + +700 + +1 +2 +2 +30 +Bronchial pressure (kPa) + +3 + +0 + +200 ms + +Frequency (kHz) + +0.2 +0.1 +0 + +500 ms + +0.3 +0.2 +0.1 + +pb (kPa) + +Frequency (kHz) + +Ostrich +0.3 + +0 + +2 + +Sound +500 ms + +0 + +Figure 6 | Pressure control of F0 in sound production is redundant across avian taxa. Spectrograms and oscillograms of spontaneous vocalisation (left) +and representative pressure control spaces ex vivo (right) of (a) pigeon (Columba livia), (b) Barbary dove (Streptopelia risoria), (c) cockatiel and +(d) Bengalese finch (Lonchura striata domestica). The F0 ranges of sounds produced ex vivo (grey vertical bar right of spectrogram) correspond well to the +lower range of spontaneous vocalizations. Pressure control may allow higher F0 values, as indicated by the grey bar fading out. Iso-F0 contours (values in +Hz) are overlaid on the pressure control spaces and shown in white when redundant for all three acoustics parameters (F0, SPL and WE), or black when +not. In the Bengalese finch, the left hemisyrinx produces higher F0 than the right hemisyrinx, corroborating earlier in vivo studies70. (e) Spectrogram and +oscillogram (left) of ostrich mating call, and ex vivo sound production including bronchial pressure (pb) patterns underlying phonation (right). A complete +pressure control space was not obtained for this species. + +NATURE COMMUNICATIONS | 6:8978 | DOI: 10.1038/ncomms9978 | www.nature.com/naturecommunications + +9 + + ARTICLE + +NATURE COMMUNICATIONS | DOI: 10.1038/ncomms9978 + +Tinamou + +Zebra finch +ICAS +membrane + +M. syringealis + +Right +M. syringealis +ventralis + +pICAS + +Frequency (kHz) + +psub +2 + +2 + +1 + +1 + +0 + +0 +100 ms + +200 ms + +Time (s) +F0 (kHz) +Airsac pressure (kPa) + +F0 (kHz) +0.6 + +2 + +3 + +450 + +0.4 +2 + +450 +350 + +1 + +0.4 + +400 +1 +0.2 + +0.2 + +300 +300 + +Frequency (kHz) + +0 + +0 + +1 + +2 + +0 + +0 + +3 +0 +Bronchial pressure (kPa) + +2 + +2 + +1 + +1 + +0 + +0 + +1 + +2 + +0 + +F0stim + +F0pre +100 ms + +100 ms +Time (s) + +1,200 +F0stim + +800 +F0 (Hz) + +1,000 +700 + +800 +600 + +600 +F0Pre + +400 +1.6 + +2.0 + +500 +1.0 +2.4 +Bronchial pressure (kPa) + +2.0 + +Figure 7 | Motor control of F0 in sound production is redundant. (a) Three-dimensional geometry of the tinamou and zebra finch syrinx with pressure +control parameters; bronchial or subsyringeal (psub), and ICAS pressure (pICAS). Stimulated muscles are indicated. (b) Sound spectrogram (top) and +oscillogram (bottom) of a tinamou honksqueal call and zebra finch song motif. (c) Representative pressure control spaces ex vivo of one individual. Iso-F0 +contour as in previous figure (values in Hz). (d) Sound spectrogram (top) and muscle stimulus (bottom) during syringeal muscle stimulation. Black dots +indicate measurements points. (e) Fundamental frequency (F0) is affected by muscle stimulation (blue dots, no stimulation; red dots, maximal stimulation) +and pressure. The grey bar indicates the individuals’ frequency range achieved by varying only pressure. Pressure control may allow higher F0 values, as +indicated by the grey bar fading out. Multiple different combinations result in the same frequency, for example, 500 and 650 Hz in tinamou and zebra finch, +respectively, (green horizontal line). + +10 + +NATURE COMMUNICATIONS | 6:8978 | DOI: 10.1038/ncomms9978 | www.nature.com/naturecommunications + + ARTICLE + +NATURE COMMUNICATIONS | DOI: 10.1038/ncomms9978 + +Methods +Subjects. To study sound production mechanisms and the effect of muscle stimulation on sound production, we used 12 adult domestic pigeons (Columba livia; +order Columbiformes; nine males, three females), four domestic Barbary doves +(Streptopelia risoria; order Columbiformes; three males, one female), three elegantcrested tinamous (Eudromia elegans; order Tinamiformes; two males, one female), +two ostriches (Struthio camelus; order Struthioniformes; sex unknown), three +cockatiels (Nymphicus hollandicus; order Psittaciformes; two males, one female), +six Bengalese finches (Lonchura striata domestica; order Passeriformes; six males) +and 19 zebra finches (Taenopygia guttata, order Passeriformes; five adult males; +two juvenile males (B40 dph); 12 females). Ostrich syrinxes were obtained from a +local breeding farm. They were transferred to ice immediately after extraction, flash +frozen in liquid nitrogen and stored at  80 °C. Bengalese finches were kept in +indoor aviaries on a 14-h light:10-h dark light cycle with food and water ad libitum +(Emory University, Atlanta, GA, USA). Zebra finches were kept in indoor aviaries +on a 12-h light:dark photoperiod with food and water ad libitum (University of +Southern Denmark (SDU), Odense, Denmark). All other animals were kept +in 3  6  2 m outdoor aviary with food and water ad libitum (SDU, Odense, +Denmark). Pigeons, doves, cockatiels and tinamous were obtained from local +breeders. Bengalese finch experiments were carried out at Emory University, and +all other experiments at SDU, Denmark. All experiments were conducted in +accordance with the Institutional Animal Care and Use Committee of Emory +University and of SDU. +Surgical and mounting procedures. Animals were euthanized with isoflurane and +cooled on ice or icepacks. The syrinx and associated blood vessels were dissected +out using a stereoscope (M165-FC, Leica Microsystems) through a ventral incision +to the sternum while regularly flushing with oxygenated Ringers solution (5 °C, +recipe cf. refs 54–56), and transferred to a Sylgard-covered petri dish on ice +containing oxygenated Ringer solution. The syrinx was cleaned of fat and +connected to species–specific tubing assemblies of non-reactive polyethylene tubing +(Instech Salomon, PA, USA) in the experimental chamber with 10/0 nylon suture +(S&T, Neuhausen, Switzerland). Special care was taken to mount the syrinx of each +species in its natural position by leaving structural elements, such as bronchidesmus and collagen tissue strands, intact. Two pairs of mEGG electrodes (see +below) were inserted in tissue and fixed with 10/0 suture at locations indicated in +Figs 1 and 2. For muscle stimulation experiments ex vivo, perfusion pathways were +established in the zebra finch that allowed perfusion through the original syringeal +vasculature. All arteriole capillaries were localized and closed using 10/0 suture +immediately after exposure of the syrinx by a ventral incision to the sternum. The +syrinx was then transferred to a Sylgard-covered petri dish on ice and connected to +micro-perfusion lines, gravity fed with oxygenated Ringers. Perfusion pressure was +kept at 2–4 kPa until patent perfusion was observed and immediately reduced to +1–2 kPa. The syrinx was typically mounted ventral side up in the experimental +chamber to two bronchial and one tracheal connector (Supplementary Fig. 1). +Experimental chamber design. To study syringeal sound production, we +developed an experimental chamber that allowed for study of the syrinx ex vivo +(that is, intact perfused organ) under controlled conditions. This experimental +chamber was milled out of aluminium (temperature controlled) or PVC and +covered by an airtight glass lid that allowed pressurization and a clear view +(Supplementary Fig. 1). The glass was either coated with nano-particles (Percenta +AG, Germany) or heated to 10 °C above chamber temperature by a 18-mm +diameter Formvar coated Nichrome wire assembly (A-M Systems, Sequim, WA, +USA), to prevent droplet forming fogging up the glass. In the floor centre of the +chamber, a 1-mm raised edge with glass bottom covered in Sylgard allowed +transillumination of the syrinx. We separately controlled pressure in the bronchial +connectors (pb) and chamber (pICAS) with dual valve differential pressure PID +controllers (model PCD, 0–10 kPa, Alicat Scientific, AZ, USA), referenced to +atmospheric pressure, and a response time of 1 ms. Bronchial mass flow was +measured with micro-electro-mechanical system (MEMS) flow sensors of various +ranges (PMF series, Posifa Microsystems, San Jose, USA) and a response time of +1 ms. The supply of pressurized air to the controllers was heated and humidified +with deionised water in a pressure cooker. Excess vapour condensed in a downstream second pressure cooker. The pressure controllers were temperature controlled at 37 °C (HD4034 with PT100 sensor, Hotek Technologies, WA, USA) +ensuring pre-heated, fully humidified air to the syrinx. The temperature of the +aluminium experimental chamber was controlled with a recirculating water bath +(Julebo F12-ED, Seelbach, Germany) and logged at 1 s intervals with a 1-mm +diameter J-type miniature temperature probe (USBTC01, National Instruments, +TX, USA) 1–2 mm away from the syrinx. Perfusion fluids attained the same +temperature as the chamber due to physical contact with a platform in the chamber +(labelled ‘Perfusate platform’ in Supplementary Fig. 1). During the mounting +process the temperature of the chamber was kept at 7 °C. +Image acquisition and analysis. The syrinx was imaged through the chamber lid +with a high-speed camera (MotionPro-X4, 12 bit CMOS sensor, Integrated Design +Tools, Inc.; 4,000–25,000 frames s–1) mounted on a stereomicroscope (M165-FC, +Leica Microsystems). For the zebra finch, we also used a more light-sensitive 16 bit + +high-speed camera (Fastcam SA1, Photron, San Diego, CA, USA; 20,000–35,000 +frames s  1). We used a 1.2-mm (Schölly Fiberoptics, Denzlingen, Germany) and +300-mm (Advanced Inspection Technologies, Melbourne, FL, USA) diameter +flexible fiberscope for endoscopic imaging. The low-light images obtained with the +endoscopes were captured with a videokymographic (VKG) system (model 2156, +Cymo B.V., Groningen, The Netherlands), which combines a high-speed linescan +camera (7,200 line images s  1) with a full frame CMOS camera (25 frames s  1). +The analogue video output from the VKG was captured together with the +microphone and a synchronization signal using a capturing device (Intensity +Extreme, Black Magic Design, Australia). Light for transillumination was provided +by a 1,700 lumen LED (Luxeon S, Philips, The Netherlands) powered by a stable +power source (PS23023, HQ Power, Belgium) or plasma light source (HPLS200, +Thorlabs, Germany) through liquid light guides and reflected of a 45° angled silver +coated prism (MRA series, Thorlabs) to absorb heat. +Kymography. A kymogram displays pixel intensity over time along a set line in an +image. The VKG system used here generates a kymogram at the fixed position of +the linescan camera63. Digital kymograms (DKG) are kymograms along any +arbitrary line in a digital image64 and were extracted from high-speed image +recordings using Matlab (The Mathworks). Two kymograms in Supplementary +Fig. 2 were previously published: human from ref. 40, and elephant from ref. 30. +Micro-electroglottography. As an independent proxy for kinematics of the +syringeal vibratory tissues, we used EGG. This non-invasive technique measures +electrical impedance between electrodes and is commonly used to quantify vocal +fold contact area in the larynx65. mEGG electrodes consisting of single stranded +25 mm diameter Formvar coated Nichrome wires (A-M Systems) were inserted as +described above and connected to a modified two-channel electroglottograph +(model EG2, Glottal Enterprises Inc. NY, USA). +Data acquisition and synchronisation. Sound was recorded with a ½ inch +pressure microphone-pre-amplifier assembly (model 46AD with preamplifier type +26AH, G.R.A.S., Denmark), amplified and high-pass filtered (10 Hz, 3-pole +Butterworth filter, model 12AQ, G.R.A.S.). The microphone sensitivity was +measured before each experiment (sound calibrator model 42AB, G.R.A.S.). +The microphone was placed at 2–3 cm from the tracheal connector outlet in the +acoustic near field, and on a 45° angle to avoid the air jet from the tracheal outlet. +The sound signal was time shifted for the travelling distance from vibratory +membranes to microphone. Microphone, mEGG, pressure and flow signals were +low-pass filtered at 10 kHz (custom-built filter). These signals together with +synchronization signals from camera systems and muscle stimulators were +digitized at 50 kHz (USB 6259, 16 bit, National Instruments, Austin, TX, USA). +These signals were synchronized with all imaging systems with an accuracy of +o21 ms before each experiment. All control and analysis software was written in +Labview (National Instruments) or Matlab. +Tissue-wave imaging protocol and analysis. Transillumination successfully +visualized the inside outlines of vibratory tissues in the domestic pigeon, Barbary +dove, elegant-crested tinamou and zebra finch. High optical density of the ostrich +and cockatiel syrinx did not allow transillumination. In the tinamou, we dissected +apart M. syringealis to allow LVMs imaging using transillumination. In zebra finch +transillumination was successful in adult females and juvenile males, but attempts +in adult males were unsuccessful due to the high optical density of M. syringealis +ventralis (VS) muscles. In the zebra finch sound production was induced in the +right hemisyrinx. Substantially different requirements in lighting conditions did +not allow for simultaneous transillumination and tracheal endoscopy in zebra +finches. +To image syringeal oscillatory behaviour we subjected the syrinx to a single +bronchial pressure ramps at constant air sac pressure, while filming from 5,000 to +35,000 frames s  1. Our system could acquire and save a maximum of 2–10 s of +data depending on frame rates, which comprised (tens of) thousands of frames. +Due to the image complexity of the data, analysis could not be automatized, and +required frame-by-frame manual analysis. On selected sequences of high-speed +images, the left and right LVM or labia were traced manually in Amira (Visage +Imaging GmbH, Berlin, Germany) and processed in Matlab. We calculated +displacement (for example, Fig. 1e top panel) as current position minus the most +lateral position during oscillation (indicated by the green line ‘min’ on the top left +in Fig. 1e). With both left and right LVM shapes quantified we could then compute +the syringeal opening as a function of position and time, a graph also known as the +glottovibrogram30 as can be seen in Figs 1e,2d and 3d. +To quantify syringeal dynamics over a range of F0 values, full glottovibrogram +reconstructions over several cycles were not suitable due to the labour intensive +manual tracing required. Therefore we used an alternative approach to determine +the presence of the VC2 component and speed of the tissue wave across a range of +F0 values. For pigeon, tinamou and zebra finch we used transilluminated frontal +views of the syrinx and calculated one DKG at the caudal edge and one DKG at the +cranial edge of the LVM or labia (top two panels in Fig. 1d) at distance Dy +(indicated in middle panel Fig. 1c). DKG’s contain many periodic traces as many +structures move with each oscillation. By tracing selected LVM and labial inner + +NATURE COMMUNICATIONS | 6:8978 | DOI: 10.1038/ncomms9978 | www.nature.com/naturecommunications + +11 + + ARTICLE + +NATURE COMMUNICATIONS | DOI: 10.1038/ncomms9978 + +edges in video stills over five oscillation cycles, we could identify the wave +representing the motion of the LVM or labial inner edge in the DKG’s and as such +measure the time difference between maximal lateral position of LVM or labium on +the two DKG’s (DtDKG in Fig. 1d). The wave speed equalled vVC2 ¼ Dy/DtDKG and +was averaged over five consecutive cycles. Because in the cockatiel syrinx +transillumination was not successful, we used cross-correlation between two +mEGG electrode pairs located at distance Dy to calculate time delay (DtmEGG) and +wave speed vVC2. The ostrich was not included in this analysis because both +transillumination was not successful and mEGG did not resolve vibrations due to +lack of syringeal closure. We did not estimate wave speed from the tracheal +endoscopic view because the VC2 velocity component was almost normal to the +imaging plane, leading to large inaccuracies. +In these five consecutive oscillations, we quantified the timing of syringeal +opening and closing from the transilluminated frontal views as the first frame in +which the entire syringeal passage was open or closed, respectively. The minimal +precision for these measurements equals the duration of one frame as indicated by +the black vertical line at the base of each column in Fig. 5. In addition, we +quantified the timing of acoustic excitations in the sound pressure signal. The +timing of the sound signals was corrected for the time needed for the sound to +propagate from the oscillators through trachea and tubing to the microphone, +assuming a sound speed of 340 m s  1. With these parameters we quantified the +timing of acoustic excitation with respect to syringeal opening and closing events +within single oscillatory cycles. +Pressure control space protocol. To explore syringeal oscillatory behaviour in +the pressure control space we subjected the syrinx to a set of bronchial pressure +ramps at randomized and variable air sac pressure, and one additional ramp where +pb equalled pICAS. Ramp speed was 1 kPa s  1. Depending on species, we used +pressures o2.0–4.0 kPa and |pb  pICAS|o2.0 kPa to avoid regimes of high flow +(that is, combinations of high pb and low pICAS) and/or mechanical failure of +syringeal oscillatory structures. These sets were performed without transillumination imaging. SPL and WE were calculated on 100 ms segments by applying a +sliding window with 50 ms steps. If the SPL of these segments were above the 60 dB +re. 20 mPa threshold, segments were zero-padded to the next power of two, and a +4,096 point power spectral density estimate was computed (periodogram method +in Matlab). Additional filtering was used to extract the fundamental frequency (F0) +reliably from the spectral density estimate. WE was calculated as the geometric +mean of the power spectrum over the arithmetic mean of the power spectrum. +We extracted iso-F0 contours in pb, pICAS control space. SPL and WE were +evaluated along the iso-F0 contours at a resolution of 10 Pa (Supplementary Fig. 3). +To evaluate whether points on these iso-F0 contour lines were redundant for all +three quantified acoustic parameters (F0, SPL and WE) we computed acoustic +parameters at a fixed distance of 100 Pa both before and after each point along the +iso-F0 contour line locations in pb, pICAS control space (Supplementary Fig. 3). For +the 100 Pa start and end sections of the contour, only forward and backward values +could be computed. A point along the iso-F0 contour was considered redundant for +all the three parameters if the WE and SPL variation within the 100 Pa interval +was below 0.2 units of WE and 1 dB SPL (ref. 66). This resulted in a logical (1/0) +redundancy array for each iso-F0 contour. The iso-F0 contour is plotted +white when redundant and black when not in the pb, pICAS control spaces in +Figs 6a–d and 7c. +We computed iso-F0 contours at fixed intervals (Columba, 10 Hz; Streptopelia, +50 Hz Eudromia, 50 Hz; Nymphicus, 100 Hz; Lonchura, 100 Hz; Taenopygia, 50 Hz) +within the F0 range observed in the preparation. The percentage redundancy +of a pressure control space was expressed as the ratio of redundant points to +the total amount of points on all iso-F0 contours computed in the pb, pICAS +control space. +Muscle stimulation protocol. Muscles were stimulated with 50 mm diameter +Teflon-coated twisted silver wire electrodes (A-M Systems) that were fixed with +10/0 suture. We used a stimulus isolator (model A395, WPI, Sarasota, FL, USA) to +apply variable currents (0–10 mA) when limited compliance voltage was sufficient +to contract muscles (tinamou). For zebra finches and Bengalese finches, we used +two stimulators (model 14E11, DISA, Herlev, Denmark and model 2100, A-M +Systems, respectively). To ensure muscle specificity, we placed carbon microspheres +(20–40 mm diameter) at regular intervals on the muscles and surrounding tissues +and filmed contractions at 1 kHz. We stimulated the single syringeal muscle +present in tinamous, M. syringealis. In songbirds, activity of the M. syringealis +ventralis correlates to F0 (ref. 67). Therefore we focussed on this muscle to study F0 +control in zebra finches (N ¼ 5 adult males). F0 of the sound was determined +30 ms prior (control) and 30 ms after stimulation. We computed 512-point fast +Fourier transforms and used parabolic interpolation around the peak power to +determine F0. +Statistics. Linear regressions were calculated to test the significance of wave speed +as a function of F0 in Matlab. All values are presented as mean±1 s.d. +Morphome reconstruction. We constructed three-dimensional annotated syrinx +morphologies, that is, morphomes, based on IKI contrasted CT scans56. All +12 + +specimens were scanned at Odense University Hospital with a mCT scanner +(VivaCT 40, Scanco Medical AG, Switzerland) with 10 mm resolution, except the +ostrich syrinx which was scanned with 80 mm resolution on a XtremeCT (Scanco +Medical AG). These scans were annotated manually in Amira for bone, soft tissue +and muscle using protocols cf. ref. 56. +Natural vocalizations. Sound recordings of natural vocalizations were obtained in +previous studies for domestic Barbary dove7, elegant-crested tinamou68 and zebra +finch69. 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Comparative Hearing: Birds and Reptiles +13, 308–359 (Springer, 2000). +67. Goller, F. & Suthers, R. A. Role of syringeal muscles in controlling the +phonology of bird song. J. Neurophysiol. 76, 287–300 (1996). +68. Schuster, S., Zollinger, S. A., Lesku, J. A. & Brumm, H. On the evolution of +noise-dependent vocal plasticity in birds. Biol. Lett. 8, 913–916 (2012). +69. Elemans, C. P. H., Laje, R., Mindlin, G. B. & Goller, F. Smooth operator: +avoidance of subharmonic bifurcations through mechanical mechanisms +simplifies song motor control in adult zebra finches. J. Neurosci. 30, +13246–13253 (2010). +70. Secora, K. R. et al. Syringeal specialization of frequency control during song +production in the Bengalese finch (Lonchura striata domestica). PLoS ONE 7, +e34135 (2012). + +Acknowledgements +We thank T. Christensen, P. Martensen, F. Mortensen, F. Andreasen, A. Chandler, V. +Shanbogue and N. Ditzel for technical assistance, J. Brewer for optics advice, L. Jakobsen +for use of equipment, S. Pedersen for ostrich access, A. Qiu for videokymography advice +and M. Rothenberg for EGG advice. H. Mehaffey, J.M. Ratcliffe and A. Surlykke commented on the manuscript. This study was funded by grants from the Danish Research +Council (FNU), Carlsberg Foundation, visiting professorship (Université de Saint-Etienne) and QuanTM fellowship (Emory University) to C.P.H.E., a Heisenberg Fellowship +of the German Research Foundation (Br 2309/8-1) to H.B., US National Institutes of +Health grants F31DC013753 to K.S., P30NS069250 and R01NS084844 to S.J.S., European +Social Fund and the state budget of the Czech Republic, project numbers OPVK CZ.1.07/ +2.3.00/30.0004 ‘POST-UP’ to C.T.H. and J.G.Š., the institutional fund of Palacký University Olomouc to C.T.H. and OPVK CZ.1.07/2.3.00/20.0057 to J.G.Š. + +Author contributions +C.P.H.E. conceived the study and built the set-up. All authors contributed to data +acquisition: pigeon (C.P.H.E., J.H.R., C.T.H., D.N.D., J.G.Š.), Barbary dove (C.P.H.E.), +ostrich (N.S., C.P.H.E.), tinamou (S.A.Z., H.B., C.P.H.E.), cockatiel (O.N.L., C.P.H.E.), +Bengalese finch (K.S., S.J.S., C.P.H.E.) and zebra finch (D.N.D., C.P.H.E.). CT scans were +performed by D.N.D. and M.D., data annotation by D.N.D. All authors contributed to +data analysis and the manuscript. All authors read and approved the final manuscript. + +Additional information +Supplementary Information accompanies this paper at http://www.nature.com/ +naturecommunications +Competing financial interests: The authors declare no competing financial interests. +Reprints and permission information is available online at http://npg.nature.com/ +reprintsandpermissions/ +How to cite this article: Elemans, C. P. H. et al. Universal mechanisms of +sound production and control in birds and mammals. Nat. Commun. 6:8978 +doi: 10.1038/ncomms9978 (2015). +This work is licensed under a Creative Commons Attribution 4.0 +International License. The images or other third party material in this +article are included in the article’s Creative Commons license, unless indicated otherwise +in the credit line; if the material is not included under the Creative Commons license, +users will need to obtain permission from the license holder to reproduce the material. +To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ + +NATURE COMMUNICATIONS | 6:8978 | DOI: 10.1038/ncomms9978 | www.nature.com/naturecommunications + +13 + + \ No newline at end of file diff --git a/research/vocal-source-grounding/sources/faust-filters-doc.html b/research/vocal-source-grounding/sources/faust-filters-doc.html new file mode 100644 index 0000000..ee7de8b --- /dev/null +++ b/research/vocal-source-grounding/sources/faust-filters-doc.html @@ -0,0 +1,3416 @@ + + + + + + + + + + + filters - Faust Libraries + + + + + + + + + + + + + + + + + +
+
+
+ +

filters.lib

+

Filters library. Its official prefix is fi.

+

This library provides a comprehensive collection of linear and nonlinear +filters used in audio and signal processing. It includes low-pass, high-pass, +band-pass, allpass, shelving, equalizer, and crossover filters, as well as advanced +analog and digital filter design sections for both educational and production use.

+

The Filters library is organized into 23 sections:

+ +

References

+ +

Basic Filters

+
+

(fi.)zero

+

One zero filter. Difference equation: .

+

Usage

+
_ : zero(z) : _
+
+

Where:

+
    +
  • z: location of zero along real axis in z-plane
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+zero_test = src : fi.zero(0.5);
+
+

References

+ +
+

(fi.)pole

+

One pole filter. Could also be called a "leaky integrator". +Difference equation: .

+

Usage

+
_ : pole(p) : _
+
+

Where:

+
    +
  • p: pole location = feedback coefficient
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+pole_test = src : fi.pole(0.9);
+
+

References

+ +
+

(fi.)integrator

+

Same as pole(1) [implemented separately for block-diagram clarity].

+

Usage

+
_ : integrator : _
+
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+integrator_test = src : fi.integrator;
+
+
+

(fi.)dcblockerat

+

DC blocker with configurable "break frequency". +The amplitude response is substantially flat above fb, +and sloped at about +6 dB/octave below fb. +Derived from the analog transfer function: + +(which can be seen as a 1st-order Butterworth highpass filter) +by the low-frequency-matching bilinear transform method +(i.e., using the typical frequency-scaling constant 2*SR).

+

Usage

+
_ : dcblockerat(fb) : _
+
+

Where:

+
    +
  • fb: "break frequency" in Hz, i.e., -3 dB gain frequency (see 2nd reference below)
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+dcblockerat_test = src : fi.dcblockerat(30);
+
+

References

+ +
+

(fi.)dcblocker

+

DC blocker. Default dc blocker has -3dB point near 35 Hz (at 44.1 kHz) +and high-frequency gain near 1.0025 (due to no scaling). +dcblocker is as standard Faust function.

+

Usage

+
_ : dcblocker : _
+
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+dcblocker_test = src : fi.dcblocker;
+
+
+

(fi.)lptN

+

One-pole lowpass filter with arbitrary dis/charging factors set in dB and +times set in seconds.

+

Usage

+
_ : lptN(N, tN) : _
+
+

Where:

+
    +
  • N: is the attenuation factor in dB
  • +
  • tN: is the filter period in seconds, that is, the time for the +impulse response to decay by N dB
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+lptN_test = src : fi.lptN(60, 0.1);
+
+

References

+ +
+

(fi.)lptau

+

One-pole lowpass with a tau time constant (1/e attenuation after tN seconds).

+

Usage

+
_ : lptau(tN) : _
+
+

Where:

+
    +
  • tN: tau time constant in seconds (1/e attenuation after tN seconds)
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+lptau_test = src : fi.lptau(0.1);
+
+
+

(fi.)lpt60

+

One-pole lowpass with a T60 time constant (60 dB attenuation after tN seconds).

+

Usage

+
_ : lpt60(tN) : _
+
+

Where:

+
    +
  • tN: T60 time constant in seconds (60 dB attenuation after tN seconds)
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+lpt60_test = src : fi.lpt60(0.3);
+
+
+

(fi.)lpt19

+

One-pole lowpass with a T19 time constant (approx. 19 dB attenuation after tN seconds).

+

Usage

+
_ : lpt19(tN) : _
+
+

Where:

+
    +
  • tN: T19 time constant in seconds (approximately 19 dB attenuation after tN seconds)
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+lpt19_test = src : fi.lpt19(0.2);
+
+

Comb Filters

+
+

(fi.)ff_comb

+

Feed-Forward Comb Filter. Note that ff_comb requires integer delays +(uses delay internally). +ff_comb is a standard Faust function.

+

Usage

+
_ : ff_comb(maxdel,intdel,b0,bM) : _
+
+

Where:

+
    +
  • maxdel: maximum delay (a power of 2)
  • +
  • intdel: current (integer) comb-filter delay between 0 and maxdel
  • +
  • del: current (float) comb-filter delay between 0 and maxdel
  • +
  • b0: gain applied to delay-line input
  • +
  • bM: gain applied to delay-line output and then summed with input
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+ff_comb_test = src : fi.ff_comb(2048, 64, 1, 0.7);
+
+

References

+ +
+

(fi.)ff_fcomb

+

Feed-Forward Comb Filter. Note that ff_fcomb takes floating-point delays +(uses fdelay internally). +ff_fcomb is a standard Faust function.

+

Usage

+
_ : ff_fcomb(maxdel,del,b0,bM) : _
+
+

Where:

+
    +
  • maxdel: maximum delay (a power of 2)
  • +
  • del: current (float) comb-filter delay between 0 and maxdel
  • +
  • b0: gain applied to delay-line input
  • +
  • bM: gain applied to delay-line output and then summed with input
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+ff_fcomb_test = src : fi.ff_fcomb(2048, 64.5, 1, 0.7);
+
+

References

+ +
+

(fi.)ffcombfilter

+

Typical special case of ff_comb() where: b0 = 1.

+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+ffcombfilter_test = src : fi.ffcombfilter(2048, 64, 0.7);
+
+
+

(fi.)fb_comb_common

+

A generic feedback comb filter.

+

Usage

+
_ : fb_comb_common(dop,N,b0,aN) : _
+
+

Where

+
    +
  • dop: delay operator, e.g. @ or de.fdelay4a(2048)
  • +
  • N: current delay
  • +
  • b0: gain applied to input
  • +
  • aN: gain applied to delay-line output
  • +
+

Example test program

+
process = fb_comb_common(@,N,b0,aN);
+
+

implements the following difference equation:

+
y[n] = b0 x[n] + aN y[n - N]
+
+

See more examples in filters.lib below.

+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+fb_comb_common_test = src : fi.fb_comb_common(@, 64, 0.8, 0.6);
+
+
+
+

(fi.)fb_comb

+

Feed-Back Comb Filter (integer delay).

+

Usage

+
_ : fb_comb(maxdel,del,b0,aN) : _
+
+

Where:

+
    +
  • maxdel: maximum delay (a power of 2)
  • +
  • del: current (float) comb-filter delay between 0 and maxdel
  • +
  • b0: gain applied to delay-line input and forwarded to output
  • +
  • aN: minus the gain applied to delay-line output before summing with the input + and feeding to the delay line
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+fb_comb_test = src : fi.fb_comb(2048, 64, 0.7, 0.6);
+
+

References

+ +
+

(fi.)fb_fcomb

+

Feed-Back Comb Filter (floating point delay).

+

Usage

+
_ : fb_fcomb(maxdel,del,b0,aN) : _
+
+

Where:

+
    +
  • maxdel: maximum delay (a power of 2)
  • +
  • del: current (float) comb-filter delay between 0 and maxdel
  • +
  • b0: gain applied to delay-line input and forwarded to output
  • +
  • aN: minus the gain applied to delay-line output before summing with the input + and feeding to the delay line
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+fb_fcomb_test = src : fi.fb_fcomb(2048, 64.5, 0.7, 0.6);
+
+

References

+ +
+

(fi.)rev1

+

Special case of fb_comb (rev1(maxdel,N,g)). +The "rev1 section" dates back to the 1960s in computer-music reverberation. +See the jcrev and brassrev in reverbs.lib for usage examples.

+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+rev1_test = src : fi.rev1(2048, 64, 0.6);
+
+
+

(fi.)fbcombfilter and (fi.)ffbcombfilter

+

Other special cases of Feed-Back Comb Filter.

+

Usage

+
_ : fbcombfilter(maxdel,intdel,g) : _
+_ : ffbcombfilter(maxdel,del,g) : _
+
+

Where:

+
    +
  • maxdel: maximum delay (a power of 2)
  • +
  • intdel: current (integer) comb-filter delay between 0 and maxdel
  • +
  • del: current (float) comb-filter delay between 0 and maxdel
  • +
  • g: feedback gain
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+fbcombfilter_test = src : fi.fbcombfilter(2048, 64, 0.6);
+
+

References

+ +
+

(fi.)allpass_comb

+

Schroeder Allpass Comb Filter. Note that:

+
allpass_comb(maxlen,len,aN) = ff_comb(maxlen,len,aN,1) : fb_comb(maxlen,len-1,1,aN);
+
+

which is a direct-form-1 implementation, requiring two delay lines. +The implementation here is direct-form-2 requiring only one delay line.

+

Usage

+
_ : allpass_comb(maxdel,intdel,aN) : _
+
+

Where:

+
    +
  • maxdel: maximum delay (a power of 2)
  • +
  • intdel: current (integer) comb-filter delay between 0 and maxdel
  • +
  • del: current (float) comb-filter delay between 0 and maxdel
  • +
  • aN: minus the feedback gain
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+allpass_comb_test = src : fi.allpass_comb(2048, 64, 0.6);
+
+

References

+ +
+

(fi.)allpass_fcomb

+

Schroeder Allpass Comb Filter. Note that:

+
allpass_comb(maxlen,len,aN) = ff_comb(maxlen,len,aN,1) : fb_comb(maxlen,len-1,1,aN);
+
+

which is a direct-form-1 implementation, requiring two delay lines. +The implementation here is direct-form-2 requiring only one delay line.

+

allpass_fcomb is a standard Faust library.

+

Usage

+
_ : allpass_comb(maxdel,intdel,aN) : _
+_ : allpass_fcomb(maxdel,del,aN) : _
+
+

Where:

+
    +
  • maxdel: maximum delay (a power of 2)
  • +
  • intdel: current (float) comb-filter delay between 0 and maxdel
  • +
  • del: current (float) comb-filter delay between 0 and maxdel
  • +
  • aN: minus the feedback gain
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+allpass_fcomb_test = src : fi.allpass_fcomb(2048, 64.5, 0.6);
+
+

References

+ +
+

(fi.)rev2

+

Special case of allpass_comb (rev2(maxlen,len,g)). +The "rev2 section" dates back to the 1960s in computer-music reverberation. +See the jcrev and brassrev in reverbs.lib for usage examples.

+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+rev2_test = src : fi.rev2(2048, 64, 0.6);
+
+
+

(fi.)allpass_fcomb5 and (fi.)allpass_fcomb1a

+

Same as allpass_fcomb but use fdelay5 and fdelay1a internally +(Interpolation helps - look at an fft of faust2octave on: +1-1' <: allpass_fcomb(1024,10.5,0.95), allpass_fcomb5(1024,10.5,0.95);)

+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+allpass_fcomb5_test = src : fi.allpass_fcomb5(2048, 64.5, 0.6);
+
+

Direct-Form Digital Filter Sections

+
+

(fi.)iir

+

Nth-order Infinite-Impulse-Response (IIR) digital filter, +implemented in terms of the Transfer-Function (TF) coefficients. +Such filter structures are termed "direct form".

+

iir is a standard Faust function.

+

Usage

+
_ : iir(bcoeffs,acoeffs) : _
+
+

Where:

+
    +
  • bcoeffs: (b0,b1,...,b_order) = TF numerator coefficients
  • +
  • acoeffs: (a1,...,a_order) = TF denominator coeffs (a0=1)
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+iir_test = src : fi.iir((0.5, 0.5), (0.3));
+
+

References

+ +
+

(fi.)fir

+

FIR filter (convolution of FIR filter coefficients with a signal). fir is standard Faust function.

+

Usage

+
_ : fir(bv) : _
+
+

Where:

+
    +
  • bv: b0,b1,...,bn, a parallel bank of coefficient signals
  • +
+

Note

+

bv is processed using pattern-matching at compile time, + so it must have this normal form (parallel signals).

+

Example test program

+

Smoothing white noise with a five-point moving average:

+
bv = .2,.2,.2,.2,.2;
+process = noise : fir(bv);
+
+

Equivalent (note double parens):

+
process = noise : fir((.2,.2,.2,.2,.2));
+
+
+

(fi.)conv and (fi.)convN

+

Convolution of input signal with given coefficients.

+

Usage

+
_ : conv((k1,k2,k3,...,kN)) : _ // Argument = one signal bank
+_ : convN(N,(k1,k2,k3,...)) : _ // Useful when N < count((k1,...))
+
+
+

(fi.)tf1, (fi.)tf2 and (fi.)tf3

+

tfN = N'th-order direct-form digital filter.

+

Usage

+
_ : tf1(b0,b1,a1) : _
+_ : tf2(b0,b1,b2,a1,a2) : _
+_ : tf3(b0,b1,b2,b3,a1,a2,a3) : _
+
+

Where:

+
    +
  • b: transfer-function numerator
  • +
  • a: transfer-function denominator (monic)
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+tf1_test = src : fi.tf1(0.5, 0.25, -0.4);
+
+

References

+ +
+

(fi.)notchw

+

Simple notch filter based on a biquad (tf2). +notchw is a standard Faust function.

+

Usage:

+
_ : notchw(width,freq) : _
+
+

Where:

+
    +
  • width: "notch width" in Hz (approximate)
  • +
  • freq: "notch frequency" in Hz
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+notchw_test = src : fi.notchw(200, 1000);
+
+

References

+ +

Direct-Form Second-Order Biquad Sections

+

Direct-Form Second-Order Biquad Sections

+

References

+ +
+

(fi.)tf21, (fi.)tf22, (fi.)tf22t and (fi.)tf21t

+

tfN = N'th-order direct-form digital filter where:

+
    +
  • tf21 is tf2, direct-form 1
  • +
  • tf22 is tf2, direct-form 2
  • +
  • tf22t is tf2, direct-form 2 transposed
  • +
  • tf21t is tf2, direct-form 1 transposed
  • +
+

Usage

+
_ : tf21(b0,b1,b2,a1,a2) : _
+_ : tf22(b0,b1,b2,a1,a2) : _
+_ : tf22t(b0,b1,b2,a1,a2) : _
+_ : tf21t(b0,b1,b2,a1,a2) : _
+
+

Where:

+
    +
  • b: transfer-function numerator
  • +
  • a: transfer-function denominator (monic)
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+tf21_test = src : fi.tf21(0.1, 0.2, 0.1, -0.5, 0.06);
+
+

References

+ +

Ladder/Lattice Digital Filters

+

Ladder and lattice digital filters generally have superior numerical +properties relative to direct-form digital filters. They can be derived +from digital waveguide filters, which gives them a physical interpretation.

+

References

+ +
+

(fi.)av2sv

+

Compute reflection coefficients sv from transfer-function denominator av.

+

Usage

+
sv = av2sv(av)
+
+

Where:

+
    +
  • av: parallel signal bank a1,...,aN
  • +
  • sv: parallel signal bank s1,...,sN
  • +
+

where ro = ith reflection coefficient, and + ai = coefficient of z^(-i) in the filter + transfer-function denominator A(z).

+

Test

+
fi = library("filters.lib");
+si = library("signals.lib");
+av2sv_test = fi.av2sv((-0.4, 0.1)) : si.bus(2);
+
+

References

+ +
+

(fi.)bvav2nuv

+

Compute lattice tap coefficients from transfer-function coefficients.

+

Usage

+
nuv = bvav2nuv(bv,av)
+
+

Where:

+
    +
  • av: parallel signal bank a1,...,aN
  • +
  • bv: parallel signal bank b0,b1,...,aN
  • +
  • nuv: parallel signal bank nu1,...,nuN
  • +
+

where nui is the i'th tap coefficient, + bi is the coefficient of z^(-i) in the filter numerator, + ai is the coefficient of z^(-i) in the filter denominator

+

Test

+
fi = library("filters.lib");
+si = library("signals.lib");
+bvav2nuv_test = fi.bvav2nuv((0.1, 0.2, 0.3), (-0.4, 0.1)) : si.bus(3);
+
+
+

(fi.)iir_lat2

+

Two-multiply lattice IIR filter of arbitrary order.

+

Usage

+
_ : iir_lat2(bv,av) : _
+
+

Where:

+
    +
  • bv: transfer-function numerator
  • +
  • av: transfer-function denominator (monic)
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+iir_lat2_test = src : fi.iir_lat2((0.1, 0.2, 0.3), (-0.4, 0.1));
+
+
+

(fi.)allpassnt

+

Two-multiply lattice allpass (nested order-1 direct-form-ii allpasses), with taps.

+

Usage

+
_ : allpassnt(n,sv) : si.bus(n+1)
+
+

Where:

+
    +
  • n: the order of the filter
  • +
  • sv: the reflection coefficients (-1 1)
  • +
+

The first output is the n-th order allpass output, +while the remaining outputs are taps taken from the +input of each delay element from the input to the output. +See (fi.)allpassn for the single-output case.

+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+si = library("signals.lib");
+src = os.osc(440);
+allpassnt_test = src : fi.allpassnt(2, (0.3, -0.2)) : si.bus(3);
+
+
+

(fi.)iir_kl

+

Kelly-Lochbaum ladder IIR filter of arbitrary order.

+

Usage

+
_ : iir_kl(bv,av) : _
+
+

Where:

+
    +
  • bv: transfer-function numerator
  • +
  • av: transfer-function denominator (monic)
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+iir_kl_test = src : fi.iir_kl((0.1, 0.2, 0.3), (-0.4, 0.1));
+
+
+

(fi.)allpassnklt

+

Kelly-Lochbaum ladder allpass.

+

Usage:

+
_ : allpassnklt(n,sv) : _
+
+

Where:

+
    +
  • n: the order of the filter
  • +
  • sv: the reflection coefficients (-1 1)
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+si = library("signals.lib");
+src = os.osc(440);
+allpassnklt_test = src : fi.allpassnklt(2, (0.3, -0.2)) : si.bus(3);
+
+
+

(fi.)iir_lat1

+

One-multiply lattice IIR filter of arbitrary order.

+

Usage

+
_ : iir_lat1(bv,av) : _
+
+

Where:

+
    +
  • bv: transfer-function numerator as a bank of parallel signals
  • +
  • av: transfer-function denominator as a bank of parallel signals
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+iir_lat1_test = src : fi.iir_lat1((0.1, 0.2, 0.3), (-0.4, 0.1));
+
+
+

(fi.)allpassn1mt

+

One-multiply lattice allpass with tap lines.

+

Usage

+
_ : allpassn1mt(N,sv) : _
+
+

Where:

+
    +
  • N: the order of the filter (fixed at compile time)
  • +
  • sv: the reflection coefficients (-1 1)
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+si = library("signals.lib");
+src = os.osc(440);
+allpassn1mt_test = src : fi.allpassn1mt(2, (0.3, -0.2)) : si.bus(3);
+
+
+

(fi.)iir_nl

+

Normalized ladder filter of arbitrary order.

+

Usage

+
_ : iir_nl(bv,av) : _
+
+

Where:

+
    +
  • bv: transfer-function numerator
  • +
  • av: transfer-function denominator (monic)
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+iir_nl_test = src : fi.iir_nl((0.1, 0.2, 0.3), (-0.4, 0.1));
+
+

References

+ +
+

(fi.)allpassnnlt

+

Normalized ladder allpass filter of arbitrary order.

+

Usage:

+
_ : allpassnnlt(N,sv) : _
+
+

Where:

+
    +
  • N: the order of the filter (fixed at compile time)
  • +
  • sv: the reflection coefficients (-1 1)
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+si = library("signals.lib");
+src = os.osc(440);
+allpassnnlt_test = src : fi.allpassnnlt(2, (0.3, -0.2)) : si.bus(3);
+
+

References

+ +

Useful Special Cases

+
+

(fi.)tf2np

+

Biquad based on a stable second-order Normalized Ladder Filter +(more robust to modulation than tf2 and protected against instability).

+

Usage

+
_ : tf2np(b0,b1,b2,a1,a2) : _
+
+

Where:

+
    +
  • b: transfer-function numerator
  • +
  • a: transfer-function denominator (monic)
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+tf2np_test = src : fi.tf2np(0.6, 0.3, 0.2, -0.5, 0.2);
+
+
+

(fi.)wgr

+

Second-order transformer-normalized digital waveguide resonator.

+

Usage

+
_ : wgr(f,r) : _
+
+

Where:

+
    +
  • f: resonance frequency (Hz)
  • +
  • r: loss factor for exponential decay (set to 1 to make a numerically stable oscillator)
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+wgr_test = fi.wgr(440, 0.995, src);
+
+

References

+ +
+

(fi.)nlf2

+

Second order normalized digital waveguide resonator.

+

Usage

+
_ : nlf2(f,r) : _
+
+

Where:

+
    +
  • f: resonance frequency (Hz)
  • +
  • r: loss factor for exponential decay (set to 1 to make a sinusoidal oscillator)
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+nlf2_test = fi.nlf2(440, 0.995, src);
+
+

References

+ +
+

(fi.)apnl

+

Passive Nonlinear Allpass based on Pierce switching springs idea. +Switch between allpass coefficient a1 and a2 at signal zero crossings.

+

Usage

+
_ : apnl(a1,a2) : _
+
+

Where:

+
    +
  • a1: first allpass coefficient
  • +
  • a2: second allpass coefficient
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+apnl_test = fi.apnl(0.5, -0.5, src);
+
+

References

+
    +
  • "A Passive Nonlinear Digital Filter Design ..." by John R. Pierce and Scott +A. Van Duyne, JASA, vol. 101, no. 2, pp. 1120-1126, 1997
  • +
+

Ladder/Lattice Allpass Filters

+

An allpass filter has gain 1 at every frequency, but variable phase. +Ladder/lattice allpass filters are specified by reflection coefficients. +They are defined here as nested allpass filters, hence the names allpassn*.

+

References

+ +
+

(fi.)scatN

+

N-port scattering junction.

+

Usage

+
si.bus(N) : scatN(N,av,filter) : si.bus(N)
+
+

Where:

+ +

With no filter:

+
    +
  • The junction is lossless when the alpha parameters sum to 2 ("allpass").
  • +
  • The junction is passive but lossy when the alpha parameters sum to less than 2 ("resistive loss").
  • +
  • Dynamic and reactive junctions are obtained using the filter argument. + For guaranteed stability, the filter should be positive real. (See 2nd ref. below).
  • +
+

For (two-port scattering), the reflection coefficient corresponds +to alpha parameters .

+

Example: Whacky echo chamber made of 16 lossless "acoustic tubes":

+
process = _ : *(1.0/sqrt(N)) <: daisyRev(16,2,0.9999) :> _,_ with { 
+  daisyRev(N,Dp2,G) = si.bus(N) : (si.bus(2*N) :> si.bus(N)
+    : fi.scatN(N, par(i,N,2*G/float(N)), fi.lowpass(1,5000.0))
+    : par(i,N,de.delay(DS(i),DS(i)-1))) ~ si.bus(N) with { DS(i) = 2^(Dp2+i); };
+};
+
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+dual_src = os.osc(440), os.osc(660);
+scatN_test = dual_src : fi.scatN(2, (1, 1), _);
+
+

References

+ +
+

(fi.)scat

+

Scatter off of reflectance r with reflection coefficient s.

+

Usage:

+
_ : scat(s,r) : _
+
+

Where:

+
    +
  • s: reflection coefficient between -1 and 1 for stability
  • +
  • r: single-input, single-output block diagram, + having gain less than 1 at all frequencies for stability.
  • +
+

Example: the following program should produce all zeros:

+
process = fi.allpassn(3,(.3,.2,.1)), fi.scat(.1, fi.scat(.2, fi.scat(.3, _)))
+          :> - : ^(2) : +~_;
+
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+scat_test = src : fi.scat(0.5, _);
+
+

References

+ +
+

(fi.)allpassn

+

Two-multiply lattice filter.

+

Usage:

+
_ : allpassn(n,sv) : _
+
+

Where:

+
    +
  • n: the order of the filter
  • +
  • sv: the reflection coefficients (s1,s2,...,sN), each between -1 and 1
  • +
+

Equivalent to fi.allpassnt(n,sv) : _, par(i,n,!);

+

Equivalent to fi.scat( s(n), fi.scat( s(n-1), ..., fi.scat( s(1), _ ))) + with { s(k) = ba.take(k,sv); } ;

+

Identical to allpassn in old/filter.lib.

+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+allpassn_test = src : fi.allpassn(3, (0.3, 0.2, 0.1));
+
+

References

+ +
+

(fi.)allpassnn

+

Normalized form - four multiplies and two adds per section, +but coefficients can be time varying and nonlinear without +"parametric amplification" (modulation of signal energy).

+

Usage:

+
_ : allpassnn(n,tv) : _
+
+

Where:

+
    +
  • n: the order of the filter
  • +
  • tv: the reflection coefficients (-PI PI)
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+allpassnn_test = src : fi.allpassnn(3, (0.3, 0.2, 0.1));
+
+
+

(fi.)allpassnkl

+

Kelly-Lochbaum form - four multiplies and two adds per +section, but all signals have an immediate physical +interpretation as traveling pressure waves, etc.

+

Usage:

+
_ : allpassnkl(n,sv) : _
+
+

Where:

+
    +
  • n: the order of the filter
  • +
  • sv: the reflection coefficients (-1 1)
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+allpassnkl_test = src : fi.allpassnkl(3, (0.3, 0.2, 0.1));
+
+
+

(fi.)allpass1m

+

One-multiply form - one multiply and three adds per section. +Normally the most efficient in special-purpose hardware.

+

Usage:

+
_ : allpassn1m(n,sv) : _
+
+

Where:

+
    +
  • n: the order of the filter
  • +
  • sv: the reflection coefficients (-1 1)
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+allpassn1m_test = src : fi.allpassn1m(3, (0.3, 0.2, 0.1));
+
+

Digital Filter Sections Specified as Analog Filter Sections

+
+

(fi.)tf2s and (fi.)tf2snp

+

Second-order direct-form digital filter, +specified by ANALOG transfer-function polynomials B(s)/A(s), +and a frequency-scaling parameter. Digitization via the +bilinear transform is built in.

+

Usage

+
_ : tf2s(b2,b1,b0,a1,a0,w1) : _
+
+

Where:

+
        b2 s^2 + b1 s + b0
+H(s) = --------------------
+           s^2 + a1 s + a0
+
+

and w1 is the desired digital frequency (in radians/second) +corresponding to analog frequency 1 rad/sec (i.e., s = j).

+

Example test program

+

A second-order ANALOG Butterworth lowpass filter, +normalized to have cutoff frequency at 1 rad/sec, +has transfer function:

+
             1
+H(s) = -----------------
+        s^2 + a1 s + 1
+
+

where a1 = sqrt(2). Therefore, a DIGITAL Butterworth lowpass +cutting off at SR/4 is specified as tf2s(0,0,1,sqrt(2),1,PI*SR/2);

+

Method

+

Bilinear transform scaled for exact mapping of w1.

+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+ma = library("maths.lib");
+src = os.osc(440);
+tf2s_test = src : fi.tf2s(0, 0, 1, sqrt(2), 1, ma.PI*ma.SR/2);
+
+

References

+ +
+

(fi.)tf1snp

+

First-order special case of tf2snp above.

+

Usage

+
_ : tf1snp(b1,b0,a0,w1) : _
+
+

Where:

+
    +
  • b1: analog numerator coefficient for s
  • +
  • b0: analog numerator constant coefficient
  • +
  • a0: analog denominator constant coefficient
  • +
  • w1: desired digital frequency (radians/second) corresponding to analog frequency 1 rad/sec
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+ma = library("maths.lib");
+src = os.osc(440);
+tf1snp_test = src : fi.tf1snp(0, 1, 1, ma.PI*ma.SR/2);
+
+
+

(fi.)tf3slf

+

Analogous to tf2s above, but third order, and using the typical +low-frequency-matching bilinear-transform constant 2/T ("lf" series) +instead of the specific-frequency-matching value used in tf2s and tf1s. +Note the lack of a "w1" argument.

+

Usage

+
_ : tf3slf(b3,b2,b1,b0,a3,a2,a1,a0) : _
+
+

Where:

+
    +
  • b3: analog numerator coefficient of s^3
  • +
  • b2: analog numerator coefficient of s^2
  • +
  • b1: analog numerator coefficient of s
  • +
  • b0: analog numerator constant term
  • +
  • a3: analog denominator coefficient of s^3
  • +
  • a2: analog denominator coefficient of s^2
  • +
  • a1: analog denominator coefficient of s
  • +
  • a0: analog denominator constant term
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+tf3slf_test = src : fi.tf3slf(0, 0, 0, 1, 1, 2, 2, 1);
+
+
+

(fi.)tf1s

+

First-order direct-form digital filter, +specified by ANALOG transfer-function polynomials B(s)/A(s), +and a frequency-scaling parameter.

+

Usage

+
_ : tf1s(b1,b0,a0,w1) : _
+
+

Where:

+
    +
  • b1: analog numerator coefficient of s
  • +
  • b0: analog numerator constant term
  • +
  • a0: analog denominator constant term in s + a0
  • +
  • w1: desired digital frequency in radians per second corresponding to analog frequency 1 rad/s
  • +
+

Where:

+
   b1 s + b0
+
+

H(s) = ---------- + s + a0

+

and w1 is the desired digital frequency (in radians/second) +corresponding to analog frequency 1 rad/sec (i.e., s = j).

+

Example test program

+

A first-order ANALOG Butterworth lowpass filter, +normalized to have cutoff frequency at 1 rad/sec, +has transfer function:

+
      1
+
+

H(s) = ------- + s + 1

+

so b0 = a0 = 1 and b1 = 0. Therefore, a DIGITAL first-order +Butterworth lowpass with gain -3dB at SR/4 is specified as

+
tf1s(0,1,1,PI*SR/2); // digital half-band order 1 Butterworth
+
+

Method

+

Bilinear transform scaled for exact mapping of w1.

+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+ma = library("maths.lib");
+src = os.osc(440);
+tf1s_test = src : fi.tf1s(0, 1, 1, ma.PI*ma.SR/2);
+
+

References

+ +
+

(fi.)tf2sb

+

Bandpass mapping of tf2s: In addition to a frequency-scaling parameter +w1 (set to HALF the desired passband width in rad/sec), +there is a desired center-frequency parameter wc (also in rad/s). +Thus, tf2sb implements a fourth-order digital bandpass filter section +specified by the coefficients of a second-order analog lowpass prototype +section. Such sections can be combined in series for higher orders. +The order of mappings is (1) frequency scaling (to set lowpass cutoff w1), +(2) bandpass mapping to wc, then (3) the bilinear transform, with the +usual scale parameter 2*SR. Algebra carried out in maxima and pasted here.

+

Usage

+
_ : tf2sb(b2,b1,b0,a1,a0,w1,wc) : _
+
+

Where:

+
    +
  • b2, b1, b0: analog lowpass numerator coefficients
  • +
  • a1, a0: analog lowpass denominator coefficients
  • +
  • w1: half the desired passband width in radians/second
  • +
  • wc: desired center frequency in radians/second
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+ma = library("maths.lib");
+src = os.osc(440);
+tf2sb_test = src : fi.tf2sb(0, 0, 1, sqrt(2), 1, 2*ma.PI*200, 2*ma.PI*1000);
+
+
+

(fi.)tf1sb

+

First-to-second-order lowpass-to-bandpass section mapping, +analogous to tf2sb above.

+

Usage

+
_ : tf1sb(b1,b0,a0,w1,wc) : _
+
+

Where:

+
    +
  • b1, b0: analog numerator coefficients
  • +
  • a0: analog denominator constant coefficient
  • +
  • w1: half the desired passband width in radians/second
  • +
  • wc: desired center frequency in radians/second
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+ma = library("maths.lib");
+src = os.osc(440);
+tf1sb_test = src : fi.tf1sb(0, 1, 1, 2*ma.PI*200, 2*ma.PI*1000);
+
+

Simple Resonator Filters

+
+

(fi.)resonlp

+

Simple resonant lowpass filter based on tf2s (virtual analog). +resonlp is a standard Faust function.

+

Usage

+
_ : resonlp(fc,Q,gain) : _
+_ : resonhp(fc,Q,gain) : _
+_ : resonbp(fc,Q,gain) : _
+
+
+

Where:

+
    +
  • fc: center frequency (Hz)
  • +
  • Q: q
  • +
  • gain: gain (0-1)
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+resonlp_test = src : fi.resonlp(1000, 2, 0.8);
+
+
+

(fi.)resonhp

+

Simple resonant highpass filters based on tf2s (virtual analog). +resonhp is a standard Faust function.

+

Usage

+
_ : resonlp(fc,Q,gain) : _
+_ : resonhp(fc,Q,gain) : _
+_ : resonbp(fc,Q,gain) : _
+
+
+

Where:

+
    +
  • fc: center frequency (Hz)
  • +
  • Q: q
  • +
  • gain: gain (0-1)
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+resonhp_test = fi.resonhp(1000, 2, 0.8, src);
+
+
+

(fi.)resonbp

+

Simple resonant bandpass filters based on tf2s (virtual analog). +resonbp is a standard Faust function.

+

Usage

+
_ : resonlp(fc,Q,gain) : _
+_ : resonhp(fc,Q,gain) : _
+_ : resonbp(fc,Q,gain) : _
+
+
+

Where:

+
    +
  • fc: center frequency (Hz)
  • +
  • Q: q
  • +
  • gain: gain (0-1)
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+resonbp_test = src : fi.resonbp(1000, 2, 0.8);
+
+

Butterworth Lowpass/Highpass Filters

+
+

(fi.)lowpass

+

Nth-order Butterworth lowpass filter. +lowpass is a standard Faust function.

+

Usage

+
_ : lowpass(N,fc) : _
+
+

Where:

+
    +
  • N: filter order (number of poles), nonnegative constant numerical expression
  • +
  • fc: desired cut-off frequency (-3dB frequency) in Hz
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+lowpass_test = src : fi.lowpass(4, 2000);
+
+

References

+ +
+

(fi.)highpass

+

Nth-order Butterworth highpass filter. +highpass is a standard Faust function.

+

Usage

+
_ : highpass(N,fc) : _
+
+

Where:

+
    +
  • N: filter order (number of poles), nonnegative constant numerical expression
  • +
  • fc: desired cut-off frequency (-3dB frequency) in Hz
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+highpass_test = src : fi.highpass(4, 500);
+
+

References

+ +
+

(fi.)lowpass0_highpass1

+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+lowpass0_highpass1_test = src : fi.lowpass0_highpass1(0, 2, 1000);
+
+

Special Filter-Bank Delay-Equalizing Allpass Filters

+

These special allpass filters are needed by filterbank et al. below. +They are equivalent to (lowpass(N,fc) +|- highpass(N,fc))/2, but with +canceling pole-zero pairs removed (which occurs for odd N).

+
+

(fi.)highpass_plus_lowpass

+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+highpass_plus_lowpass_test = os.osc(440) : fi.highpass_plus_lowpass(3, 1000);
+
+
+

(fi.)highpass_minus_lowpass

+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+highpass_minus_lowpass_test = os.osc(440) : fi.highpass_minus_lowpass(3, 1000);
+
+
+

(fi.)highpass_minus_lowpass_even

+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+highpass_plus_lowpass_even_test = os.osc(440), os.osc(440) : fi.highpass_plus_lowpass_even(4, 1000);
+
+
+

(fi.)highpass_plus_lowpass_even

+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+highpass_minus_lowpass_even_test = os.osc(440), os.osc(440) : fi.highpass_minus_lowpass_even(4, 1000);
+
+
+

(fi.)highpass_plus_lowpass_odd

+

Sum of the odd-order highpass and lowpass responses.

+

Usage

+
_ : highpass_plus_lowpass_odd(N,fc) : _
+
+

Where:

+
    +
  • N: odd Butterworth order
  • +
  • fc: cutoff frequency in Hz
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+highpass_plus_lowpass_odd_test = os.osc(440), os.osc(440) : fi.highpass_plus_lowpass_odd(3, 1000);
+
+

FIXME: Rewrite the following, as for orders 3 and 5 above, + to eliminate pole-zero cancellations:

+
+

(fi.)highpass_minus_lowpass_odd

+

Difference between the odd-order highpass and lowpass responses.

+

Usage

+
_ : highpass_minus_lowpass_odd(N,fc) : _
+
+

Where:

+
    +
  • N: odd Butterworth order
  • +
  • fc: cutoff frequency in Hz
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+highpass_minus_lowpass_odd_test = os.osc(440), os.osc(440) : fi.highpass_minus_lowpass_odd(3, 1000);
+
+

FIXME: Rewrite the following, as for orders 3 and 5 above, + to eliminate pole-zero cancellations/

+

Elliptic (Cauer) Lowpass Filters

+

Elliptic (Cauer) Lowpass Filters

+

References

+ +
+

(fi.)lowpass3e

+

Third-order Elliptic (Cauer) lowpass filter.

+

Usage

+
_ : lowpass3e(fc) : _
+
+

Where:

+
    +
  • fc: -3dB frequency in Hz
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+lowpass3e_test = src : fi.lowpass3e(1000);
+
+

Design

+

For spectral band-slice level display (see octave_analyzer3e):

+
[z,p,g] = ncauer(Rp,Rs,3);  % analog zeros, poles, and gain, where
+Rp = 60  % dB ripple in stopband
+Rs = 0.2 % dB ripple in passband
+
+
+

(fi.)lowpass6e

+

Sixth-order Elliptic/Cauer lowpass filter.

+

Usage

+
_ : lowpass6e(fc) : _
+
+

Where:

+
    +
  • fc: -3dB frequency in Hz
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+lowpass6e_test = src : fi.lowpass6e(1000);
+
+

Design

+

For spectral band-slice level display (see octave_analyzer6e):

+
[z,p,g] = ncauer(Rp,Rs,6);  % analog zeros, poles, and gain, where
+ Rp = 80  % dB ripple in stopband
+ Rs = 0.2 % dB ripple in passband
+
+

Elliptic Highpass Filters

+
+

(fi.)highpass3e

+

Third-order Elliptic (Cauer) highpass filter. Inversion of lowpass3e wrt unit +circle in s plane (s <- 1/s).

+

Usage

+
_ : highpass3e(fc) : _
+
+

Where:

+
    +
  • fc: -3dB frequency in Hz
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+highpass3e_test = src : fi.highpass3e(1000);
+
+
+

(fi.)highpass6e

+

Sixth-order Elliptic/Cauer highpass filter. Inversion of lowpass3e wrt unit +circle in s plane (s <- 1/s).

+

Usage

+
_ : highpass6e(fc) : _
+
+

Where:

+
    +
  • fc: -3dB frequency in Hz
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+highpass6e_test = src : fi.highpass6e(1000);
+
+

Butterworth Bandpass/Bandstop Filters

+
+

(fi.)bandpass

+

Order 2*Nh Butterworth bandpass filter made using the transformation +s <- s + wc^2/s on lowpass(Nh), where wc is the desired bandpass center +frequency. The lowpass(Nh) cutoff w1 is half the desired bandpass width. +bandpass is a standard Faust function.

+

Usage

+
_ : bandpass(Nh,fl,fu) : _
+
+

Where:

+
    +
  • Nh: HALF the desired bandpass order (which is therefore even)
  • +
  • fl: lower -3dB frequency in Hz
  • +
  • fu: upper -3dB frequency in Hz +Thus, the passband width is fu-fl, + and its center frequency is (fl+fu)/2.
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+bandpass_test = src : fi.bandpass(2, 500, 1500);
+
+
+

(fi.)bandpass0_bandstop1

+

Order 2*Nh Butterworth bandstop filter made using the transformation +s <- s + wc^2/s on highpass(Nh), where wc is the desired bandpass center +frequency. The highpass(Nh) cutoff w1 is half the desired bandpass width. +bandstop is a standard Faust function.

+

Usage

+
_ : bandstop(Nh,fl,fu) : _
+
+

Where:

+
    +
  • Nh: HALF the desired bandstop order (which is therefore even)
  • +
  • fl: lower -3dB frequency in Hz
  • +
  • fu: upper -3dB frequency in Hz +Thus, the passband (stopband) width is fu-fl, + and its center frequency is (fl+fu)/2.
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+bandstop_test = src : fi.bandstop(2, 500, 1500);
+
+
+

(fi.)bandstop

+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+bandpass0_bandstop1_test = src : fi.bandpass0_bandstop1(0, 2, 500, 1500);
+
+

Elliptic Bandpass Filters

+
+

(fi.)bandpass6e

+

Order 12 elliptic bandpass filter analogous to bandpass(6).

+
+

(fi.)bandpass12e

+

Order 24 elliptic bandpass filter analogous to bandpass(6).

+
+

(fi.)pospass

+

Positive-Pass Filter (single-side-band filter).

+

Usage

+
_ : pospass(N,fc) : _,_
+
+

where

+
    +
  • N: filter order (Butterworth bandpass for positive frequencies).
  • +
  • fc: lower bandpass cutoff frequency in Hz.
  • +
  • Highpass cutoff frequency at ma.SR/2 - fc Hz.
  • +
+

Example test program

+
    +
  • See dm.pospass_demo
  • +
  • Look at frequency response
  • +
+

Method

+

A filter passing only positive frequencies can be made from a +half-band lowpass by modulating it up to the positive-frequency range. +Equivalently, down-modulate the input signal using a complex sinusoid at -SR/4 Hz, +lowpass it with a half-band filter, and modulate back up by SR/4 Hz. +In Faust/math notation: + +

+

An approximation to the Hilbert transform is given by the +imaginary output signal:

+
hilbert(N) = pospass(N) : !,*(2);
+
+

References

+ +

Parametric Equalizers (Shelf, Peaking)

+

Parametric Equalizers (Shelf, Peaking).

+

References

+ +
+

(fi.)lowshelf

+

First-order "low shelf" filter (gain boost|cut between dc and some frequency) +low_shelf is a standard Faust function.

+

Usage

+
_ : lowshelf(N,L0,fx) : _
+_ : low_shelf(L0,fx) : _ // default case (order 3)
+_ : lowshelf_other_freq(N,L0,fx) : _
+
+

Where:

+
    +
  • N: filter order 1, 3, 5, ... (odd only, default should be 3, a constant numerical expression)
  • +
  • L0: desired level (dB) between dc and fx (boost L0>0 or cut L0<0)
  • +
  • fx: -3dB frequency of lowpass band (L0>0) or upper band (L0<0) + (see "SHELF SHAPE" below).
  • +
+

The gain at SR/2 is constrained to be 1. +The generalization to arbitrary odd orders is based on the well known +fact that odd-order Butterworth band-splits are allpass-complementary +(see filterbank documentation below for references).

+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+lowshelf_test = src : fi.lowshelf(3, 6, 500);
+
+

Shelf Shape

+

The magnitude frequency response is approximately piecewise-linear +on a log-log plot ("BODE PLOT"). The Bode "stick diagram" approximation +L(lf) is easy to state in dB versus dB-frequency lf = dB(f):

+
    +
  • L0 > 0:
  • +
  • L(lf) = L0, f between 0 and fx = 1st corner frequency;
  • +
  • L(lf) = L0 - N * (lf - lfx), f between fx and f2 = 2nd corner frequency;
  • +
  • L(lf) = 0, lf > lf2.
  • +
  • lf2 = lfx + L0/N = dB-frequency at which level gets back to 0 dB.
  • +
  • L0 < 0:
  • +
  • L(lf) = L0, f between 0 and f1 = 1st corner frequency;
  • +
  • L(lf) = - N * (lfx - lf), f between f1 and lfx = 2nd corner frequency;
  • +
  • L(lf) = 0, lf > lfx.
  • +
  • lf1 = lfx + L0/N = dB-frequency at which level goes up from L0.
  • +
+

See lowshelf_other_freq.

+

References

+
    +
  • See "Parametric Equalizers" above for references regarding low_shelf, high_shelf, and peak_eq.
  • +
+
+

(fi.)low_shelf

+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+low_shelf_test = src : fi.low_shelf(6, 500);
+
+
+

(fi.)low_shelf1

+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+low_shelf1_l_test = fi.low_shelf1_l(2, 500, src);
+
+
+

(fi.)low_shelf1_l

+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+low_shelf1_l_test = fi.low_shelf1_l(2, 500, src);
+
+
+

(fi.)lowshelf_other_freq

+

Test

+
fi = library("filters.lib");
+lowshelf_other_freq_test = fi.lowshelf_other_freq(3, 6, 500);
+
+
+

(fi.)highshelf

+

First-order "high shelf" filter (gain boost|cut above some frequency). +high_shelf is a standard Faust function.

+

Usage

+
_ : highshelf(N,Lpi,fx) : _
+_ : high_shelf(L0,fx) : _ // default case (order 3)
+_ : highshelf_other_freq(N,Lpi,fx) : _
+
+

Where:

+
    +
  • N: filter order 1, 3, 5, ... (odd only, a constant numerical expression).
  • +
  • Lpi: desired level (dB) between fx and SR/2 (boost Lpi>0 or cut Lpi<0)
  • +
  • fx: -3dB frequency of highpass band (L0>0) or lower band (L0<0) + (Use highshelf_other_freq() below to find the other one.)
  • +
+

The gain at dc is constrained to be 1. +See lowshelf documentation above for more details on shelf shape.

+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+highshelf_test = src : fi.highshelf(3, 6, 2000);
+
+

References

+
    +
  • See "Parametric Equalizers" above for references regarding low_shelf, high_shelf, and peak_eq.
  • +
+
+

(fi.)high_shelf

+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+high_shelf_test = src : fi.high_shelf(6, 2000);
+
+
+

(fi.)high_shelf1

+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+high_shelf1_test = fi.high_shelf1(6, 2000, src);
+
+
+

(fi.)high_shelf1_l

+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+high_shelf1_l_test = fi.high_shelf1_l(2, 2000, src);
+
+
+

(fi.)highshelf_other_freq

+

Test

+
fi = library("filters.lib");
+highshelf_other_freq_test = fi.highshelf_other_freq(3, 6, 2000);
+
+
+

(fi.)peak_eq

+

Second order "peaking equalizer" section (gain boost or cut near some frequency) +Also called a "parametric equalizer" section. +peak_eq is a standard Faust function.

+

Usage

+
_ : peak_eq(Lfx,fx,B) : _
+
+

Where:

+
    +
  • Lfx: level (dB) at fx (boost Lfx>0 or cut Lfx<0)
  • +
  • fx: peak frequency (Hz)
  • +
  • B: bandwidth (B) of peak in Hz
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+peak_eq_test = src : fi.peak_eq(6, 1000, 200);
+
+

References

+
    +
  • See "Parametric Equalizers" above for references regarding low_shelf, high_shelf, and peak_eq.
  • +
+
+

(fi.)peak_eq_cq

+

Constant-Q second order peaking equalizer section.

+

Usage

+
_ : peak_eq_cq(Lfx,fx,Q) : _
+
+

Where:

+
    +
  • Lfx: level (dB) at fx
  • +
  • fx: boost or cut frequency (Hz)
  • +
  • Q: "Quality factor" = fx/B where B = bandwidth of peak in Hz
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+peak_eq_cq_test = src : fi.peak_eq_cq(6, 1000, 4);
+
+

References

+
    +
  • See "Parametric Equalizers" above for references regarding low_shelf, high_shelf, and peak_eq.
  • +
+
+

(fi.)peak_eq_rm

+

Regalia-Mitra second order peaking equalizer section.

+

Usage

+
_ : peak_eq_rm(Lfx,fx,tanPiBT) : _
+
+

Where:

+
    +
  • Lfx: level (dB) at fx
  • +
  • fx: boost or cut frequency (Hz)
  • +
  • tanPiBT: tan(PI*B/SR), where B = -3dB bandwidth (Hz) when 10^(Lfx/20) = 0 + ~ PI*B/SR for narrow bandwidths B
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+ma = library("maths.lib");
+src = os.osc(440);
+peak_eq_rm_test = src : fi.peak_eq_rm(6, 1000, tan(ma.PI*200/ma.SR));
+
+

References

+

P.A. Regalia, S.K. Mitra, and P.P. Vaidyanathan, +"The Digital All-Pass Filter: A Versatile Signal Processing Building Block" +Proceedings of the IEEE, 76(1):19-37, Jan. 1988. (See pp. 29-30.) +See also "Parametric Equalizers" above for references on shelf +and peaking equalizers in general.

+
+

(fi.)spectral_tilt

+

Spectral tilt filter, providing an arbitrary spectral rolloff factor +alpha in (-1,1), where + -1 corresponds to one pole (-6 dB per octave), and + +1 corresponds to one zero (+6 dB per octave). +In other words, alpha is the slope of the ln magnitude versus ln frequency. +For a "pinking filter" (e.g., to generate 1/f noise from white noise), +set alpha to -1/2.

+

Usage

+
_ : spectral_tilt(N,f0,bw,alpha) : _
+
+

Where:

+
    +
  • N: desired integer filter order (fixed at compile time)
  • +
  • f0: lower frequency limit for desired roll-off band > 0
  • +
  • bw: bandwidth of desired roll-off band
  • +
  • alpha: slope of roll-off desired in nepers per neper, + between -1 and 1 (ln mag / ln radian freq)
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+spectral_tilt_test = src : fi.spectral_tilt(4, 200, 2000, -0.5);
+
+

Example test program

+

See dm.spectral_tilt_demo and the documentation for no.pink_noise.

+

References

+

J.O. Smith and H.F. Smith, +"Closed Form Fractional Integration and Differentiation via Real Exponentially Spaced Pole-Zero Pairs", +* arXiv.org publication arXiv:1606.06154 [cs.CE], June 7, 2016, http://arxiv.org/abs/1606.06154

+
+

(fi.)levelfilter

+

Dynamic level lowpass filter. +levelfilter is a standard Faust function.

+

Usage

+
_ : levelfilter(L,freq) : _
+
+

Where:

+
    +
  • L: desired level (in dB) at Nyquist limit (SR/2), e.g., -60
  • +
  • freq: corner frequency (-3dB point) usually set to fundamental freq
  • +
  • N: Number of filters in series where L = L/N
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+levelfilter_test = fi.levelfilter(0.1, 200, src);
+
+

References

+ +
+

(fi.)levelfilterN

+

Dynamic level lowpass filter.

+

Usage

+
_ : levelfilterN(N,freq,L) : _
+
+

Where:

+
    +
  • N: Number of filters in series where L = L/N, a constant numerical expression
  • +
  • freq: corner frequency (-3dB point) usually set to fundamental freq
  • +
  • L: desired level (in dB) at Nyquist limit (SR/2), e.g., -60
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+levelfilterN_test = src : fi.levelfilterN(3, 200, 0.1);
+
+

References

+ +

Mth-Octave Filter-Banks

+

Mth-octave filter-banks split the input signal into a bank of parallel signals, one +for each spectral band. They are related to the Mth-Octave Spectrum-Analyzers in +analysis.lib. +The documentation of this library contains more details about the implementation. +The parameters are:

+
    +
  • M: number of band-slices per octave (>1), a constant numerical expression
  • +
  • N: total number of bands (>2), a constant numerical expression
  • +
  • ftop: upper bandlimit of the Mth-octave bands (<SR/2)
  • +
+

In addition to the Mth-octave output signals, there is a highpass signal +containing frequencies from ftop to SR/2, and a "dc band" lowpass signal +containing frequencies from 0 (dc) up to the start of the Mth-octave bands. +Thus, the N output signals are

+
highpass(ftop), MthOctaveBands(M,N-2,ftop), dcBand(ftop*2^(-M*(N-1)))
+
+

A Filter-Bank is defined here as a signal bandsplitter having the +property that summing its output signals gives an allpass-filtered +version of the filter-bank input signal. A more conventional term for +this is an "allpass-complementary filter bank". If the allpass filter +is a pure delay (and possible scaling), the filter bank is said to be +a "perfect-reconstruction filter bank" (see Vaidyanathan-1993 cited +below for details). A "graphic equalizer", in which band signals +are scaled by gains and summed, should be based on a filter bank.

+

The filter-banks below are implemented as Butterworth or Elliptic +spectrum-analyzers followed by delay equalizers that make them +allpass-complementary.

+

Increasing Channel Isolation

+

Go to higher filter orders - see Regalia et al. or Vaidyanathan (cited +below) regarding the construction of more aggressive recursive +filter-banks using elliptic or Chebyshev prototype filters.

+

References

+
    +
  • "Tree-structured complementary filter banks using all-pass sections", Regalia et al., IEEE Trans. Circuits & Systems, CAS-34:1470-1484, Dec. 1987
  • +
  • "Multirate Systems and Filter Banks", P. Vaidyanathan, Prentice-Hall, 1993
  • +
  • Elementary filter theory: https://ccrma.stanford.edu/~jos/filters/
  • +
+
+

(fi.)mth_octave_filterbank[n]

+

Allpass-complementary filter banks based on Butterworth band-splitting. +For Butterworth band-splits, the needed delay equalizer is easily found.

+

Usage

+
_ : mth_octave_filterbank(O,M,ftop,N) : par(i,N,_)     // Oth-order
+_ : mth_octave_filterbank_alt(O,M,ftop,N) : par(i,N,_) // dc-inverted version
+
+

Also for convenience:

+
_ : mth_octave_filterbank3(M,ftop,N) : par(i,N,_) // 3rd-order Butterworth
+_ : mth_octave_filterbank5(M,ftop,N) : par(i,N,_) // 5th-order Butterworth
+mth_octave_filterbank_default = mth_octave_filterbank5;
+
+

Where:

+
    +
  • O: order of filter used to split each frequency band into two, a constant numerical expression
  • +
  • M: number of band-slices per octave, a constant numerical expression
  • +
  • ftop: highest band-split crossover frequency (e.g., 20 kHz)
  • +
  • N: total number of bands (including dc and Nyquist), a constant numerical expression
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+sig = os.osc(440);
+mth_octave_filterbank_test = sig : fi.mth_octave_filterbank(3, 2, 8000, 2);
+
+
+

(fi.)mth_octave_filterbank_alt

+

Usage

+
_ : mth_octave_filterbank_alt(O,M,ftop,N) : par(i,N,_)
+
+

Where:

+
    +
  • O: filter order used to split each band
  • +
  • M: number of band-slices per octave
  • +
  • ftop: highest band-split crossover frequency
  • +
  • N: total number of bands
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+sig = os.osc(440);
+mth_octave_filterbank_alt_test = sig : fi.mth_octave_filterbank_alt(3, 2, 8000, 2);
+
+
+

(fi.)mth_octave_filterbank3

+

Usage

+
_ : mth_octave_filterbank3(M,ftop,N) : par(i,N,_)
+
+

Where:

+
    +
  • M: number of band-slices per octave
  • +
  • ftop: highest band-split crossover frequency
  • +
  • N: total number of bands
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+sig = os.osc(440);
+mth_octave_filterbank3_test = sig : fi.mth_octave_filterbank3(2, 8000, 2);
+
+
+

(fi.)mth_octave_filterbank5

+

Usage

+
_ : mth_octave_filterbank5(M,ftop,N) : par(i,N,_)
+
+

Where:

+
    +
  • M: number of band-slices per octave
  • +
  • ftop: highest band-split crossover frequency
  • +
  • N: total number of bands
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+sig = os.osc(440);
+mth_octave_filterbank5_test = sig : fi.mth_octave_filterbank5(2, 8000, 2);
+
+
+

(fi.)mth_octave_filterbank_default

+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+sig = os.osc(440);
+mth_octave_filterbank_default_test = sig : fi.mth_octave_filterbank_default(2, 8000, 2);
+
+

Arbitrary-Crossover Filter-Banks and Spectrum Analyzers

+

These are similar to the Mth-octave analyzers above, except that the +band-split frequencies are passed explicitly as arguments.

+
+

(fi.)filterbank

+

Filter bank. +filterbank is a standard Faust function.

+

Usage

+
_ : filterbank (O,freqs) : par(i,N,_) // Butterworth band-splits
+
+

Where:

+
    +
  • O: band-split filter order (odd integer required for filterbank[i], a constant numerical expression)
  • +
  • freqs: (fc1,fc2,...,fcNs) [in numerically ascending order], where + Ns=N-1 is the number of octave band-splits + (total number of bands N=Ns+1).
  • +
+

If frequencies are listed explicitly as arguments, enclose them in parens:

+
_ : filterbank(3,(fc1,fc2)) : _,_,_
+
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+filterbank_test = src : fi.filterbank(3, (500, 2000));
+
+
+

(fi.)filterbanki

+

Inverted-dc filter bank.

+

Usage

+
_ : filterbanki(O,freqs) : par(i,N,_) // Inverted-dc version
+
+

Where:

+
    +
  • O: band-split filter order (odd integer required for filterbank[i], a constant numerical expression)
  • +
  • freqs: (fc1,fc2,...,fcNs) [in numerically ascending order], where + Ns=N-1 is the number of octave band-splits + (total number of bands N=Ns+1).
  • +
+

If frequencies are listed explicitly as arguments, enclose them in parens:

+
_ : filterbanki(3,(fc1,fc2)) : _,_,_
+
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+filterbanki_test = src : fi.filterbanki(3, (500, 2000));
+
+

State Variable Filters

+

References

+ +
+

(fi.)svf

+

An environment with lp, bp, hp, notch, peak, ap, bell, ls, hs SVF based filters. +All filters have freq and Q parameters, the bell, ls, hs ones also have a gain third parameter.

+

Usage

+
_ : svf.xx(freq, Q, [gain]) : _
+
+

Where:

+
    +
  • freq: cut frequency
  • +
  • Q: quality factor
  • +
  • [gain]: gain in dB
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+sig = os.osc(440);
+svf_lp_test = fi.svf.lp(1000, 0.707, sig);
+
+
+

(fi.)svf_morph

+

An SVF-based filter that can smoothly morph between +being lowpass, bandpass, and highpass.

+

Usage

+
_ : svf_morph(freq, Q, blend) : _
+
+

Where:

+
    +
  • freq: cutoff frequency
  • +
  • Q: quality factor
  • +
  • blend: [0..2] continuous, where 0 is lowpass, 1 is bandpass, and 2 is highpass. For performance, the value is not clamped to [0..2].
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+sig = os.osc(440);
+svf_morph_test = fi.svf_morph(1000, 0.707, 1, sig);
+
+

Example test program

+
process = no.noise : svf_morph(freq, q, blend)
+with {
+  blend = hslider("Blend", 0, 0, 2, .01) : si.smoo;
+  q = hslider("Q", 1, 0.1, 10, .01) : si.smoo;
+  freq = hslider("freq", 5000, 100, 18000, 1) : si.smoo;
+};
+
+

References

+ +
+

(fi.)svf_notch_morph

+

An SVF-based notch-filter that can smoothly morph between +being lowpass, notch, and highpass.

+

Usage

+
_ : svf_notch_morph(freq, Q, blend) : _
+
+

Where:

+
    +
  • freq: cutoff frequency
  • +
  • Q: quality factor
  • +
  • blend: [0..2] continuous, where 0 is lowpass, 1 is notch, and 2 is highpass. For performance, the value is not clamped to [0..2].
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+sig = os.osc(440);
+svf_notch_morph_test = fi.svf_notch_morph(1000, 0.707, 1, sig);
+
+

Example test program

+
process = no.noise : svf_notch_morph(freq, q, blend)
+with {
+  blend = hslider("Blend", 0, 0, 2, .01) : si.smoo;
+  q = hslider("Q", 1, 0.1, 10, .01) : si.smoo;
+  freq = hslider("freq", 5000, 100, 18000, 1) : si.smoo;
+};
+
+

References

+ +
+

(fi.)SVFTPT

+

Topology-preserving transform implementation following Zavalishin's method.

+

Outputs: lowpass, highpass, bandpass, normalised bandpass, notch, allpass, +peaking.

+

Each individual output can be recalled with its name in the environment as in: + SVFTPT.LP2(1000.0, .707).

+

The 7 outputs can be recalled by using SVF name as in: + SVFTPT.SVF(1000.0, .707).

+

Even though the implementation is different, the characteristics of this +filter are comparable to those of the svf environment in this library.

+

Usage:

+
_ : SVFTPT.xxx(CF, Q) : _
+
+

Where:

+
    +
  • xxx can be one of the following: LP2, HP2, BP2, BP2Norm, Notch2, AP2, Peaking2
  • +
  • CF: cutoff in Hz
  • +
  • Q: resonance
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+sig = os.osc(440);
+SVFTPT_SVF_test = fi.SVFTPT.SVF(1000, 0.707, sig);
+
+
+

(fi.)dynamicSmoothing

+

Adaptive smoother based on Andy Simper's paper.

+

This filter uses both the lowpass and bandpass outputs of a +state-variable filter. The lowpass is used to smooth out the input signal, +the bandpass, which is a smoothed out version of the highpass, provides +information on the rate of change of the input. Hence, the bandpass signal +can be used to adjust the cutoff of the filter to quickly follow the input's +fast and large variations while effectively filtering out local +perturbations.

+

This implementation does not use an approximation for the CF computation, +and it deploys guards to prevent overshooting with extreme sensitivity +values.

+

Usage:

+
_ : dynamicSmoothing(sensitivity, baseCF) : _
+
+

Where:

+
    +
  • sensitivity: sensitivity to changes in the input signal. + The range is, theoretically, from 0 to INF, though anything between + 0.0 and 1.0 should be reasonable
  • +
  • baseCF: cutoff frequency, in Hz, when there is no variation in the + input signal
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+sig = os.osc(440);
+dynamicSmoothing_test = fi.dynamicSmoothing(0.5, 500, sig);
+
+

References

+ +
+

(fi.)oneEuro

+

The One Euro Filter (1€ Filter) is an adaptive lowpass filter. +This kind of filter is commonly used in object-tracking, +not necessarily audio processing.

+

Usage

+
_ : oneEuro(derivativeCutoff, beta, minCutoff) : _
+
+

Where:

+
    +
  • derivativeCutoff: Used to filter the first derivative of the input. 1 Hz is a good default.
  • +
  • beta: "Speed" parameter where higher values reduce latency.
  • +
  • minCutoff: Minimum cutoff frequency in Hz. Lower values remove more jitter.
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+sig = os.osc(440);
+oneEuro_test = sig : fi.oneEuro(1, 0.5, 5);
+
+

References

+ +

Linkwitz-Riley 4th-order 2-way, 3-way, and 4-way crossovers

+

The Linkwitz-Riley (LR) crossovers are designed to produce a fully-flat +magnitude response when their outputs are combined. The 4th-order +LR filters (LR4) have a 24dB/octave slope and they are rather popular audio +crossovers used in multi-band processing.

+

The LR4 can be constructed by cascading two second-order Butterworth +filters. For the second-order Butterworth filters, we will use the SVF +filter implemented above by setting the Q-factor to 1.0 / sqrt(2.0). +These will be cascaded in pairs to build the LR4 highpass and lowpass. +For the phase correction, we will use the 2nd-order Butterworth allpass.

+

References

+

Zavalishin, Vadim. "The art of VA filter design." Native Instruments, Berlin, Germany (2012).

+
+

(fi.)lowpassLR4

+

4th-order Linkwitz-Riley lowpass.

+

Usage

+
_ : lowpassLR4(cf) : _
+
+

Where:

+
    +
  • cf: lowpass cutoff in Hz
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+lowpassLR4_test = src : fi.lowpassLR4(1000);
+
+
+

(fi.)highpassLR4

+

4th-order Linkwitz-Riley highpass.

+

Usage

+
_ : highpassLR4(cf) : _
+
+

Where:

+
    +
  • cf: highpass cutoff in Hz
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+highpassLR4_test = src : fi.highpassLR4(1000);
+
+
+

(fi.)crossover2LR4

+

Two-way 4th-order Linkwitz-Riley crossover.

+

Usage

+
_ : crossover2LR4(cf) : si.bus(2)
+
+

Where:

+
    +
  • cf: crossover split cutoff in Hz
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+crossover2LR4_test = src : fi.crossover2LR4(1000);
+
+
+

(fi.)crossover3LR4

+

Three-way 4th-order Linkwitz-Riley crossover.

+

Usage

+
_ : crossover3LR4(cf1, cf2) : si.bus(3)
+
+

Where:

+
    +
  • cf1: crossover lower split cutoff in Hz
  • +
  • cf2: crossover upper split cutoff in Hz
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+crossover3LR4_test = src : fi.crossover3LR4(500, 2000);
+
+
+

(fi.)crossover4LR4

+

Four-way 4th-order Linkwitz-Riley crossover.

+

Usage

+
_ : crossover4LR4(cf1, cf2, cf3) : si.bus(4)
+
+

Where:

+
    +
  • cf1: crossover lower split cutoff in Hz
  • +
  • cf2: crossover mid split cutoff in Hz
  • +
  • cf3: crossover upper split cutoff in Hz
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+crossover4LR4_test = src : fi.crossover4LR4(300, 1000, 3000);
+
+
+

(fi.)crossover8LR4

+

Eight-way 4th-order Linkwitz-Riley crossover.

+

Usage

+
_ : crossover8LR4(cf1, cf2, cf3, cf4, cf5, cf6, cf7) : si.bus(8)
+
+

Where:

+
    +
  • cf1: lowest crossover cutoff frequency in Hz
  • +
  • cf2: second crossover cutoff frequency in Hz
  • +
  • cf3: third crossover cutoff frequency in Hz
  • +
  • cf4: fourth crossover cutoff frequency in Hz
  • +
  • cf5: fifth crossover cutoff frequency in Hz
  • +
  • cf6: sixth crossover cutoff frequency in Hz
  • +
  • cf7: highest crossover cutoff frequency in Hz
  • +
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+crossover8LR4_test = src : fi.crossover8LR4(100, 200, 400, 800, 1600, 3200, 6400);
+
+

Standardized Filters

+
+

(fi.)itu_r_bs_1770_4_kfilter

+

The prefilter from Recommendation ITU-R BS.1770-4 for loudness +measurement. Also known as "K-filter". The recommendation defines +biquad filter coefficients for a fixed sample rate of 48kHz (page +4-5). Here, we construct biquads for arbitrary samplerates. The +resulting filter is normalized, such that the magnitude at 997Hz is +unity gain 1.0.

+

Please note, the ITU-recommendation handles the normalization in +equation (2) by subtracting 0.691dB, which is not needed with +itu_r_bs_1770_4_kfilter.

+

One option for future improvement might be, to round those filter +coefficients, that are almost equal to one. Second, the maximum +magnitude difference at 48kHz between the ITU-defined filter and +itu_r_bs_1770_4_kfilter is 0.001dB, which obviously could be +less.

+

Usage

+
_ : itu_r_bs_1770_4_kfilter : _
+
+

Test

+
fi = library("filters.lib");
+os = library("oscillators.lib");
+src = os.osc(440);
+itu_r_bs_1770_4_kfilter_test = src : fi.itu_r_bs_1770_4_kfilter;
+
+

References

+ +

Averaging Functions

+
+

(fi.)avg_rect

+

Moving average.

+

Usage

+
_ : avg_rect(period) : _
+
+

Where:

+
    +
  • period: averaging frame duration in seconds
  • +
+
+

(fi.)avg_tau

+

Averaging function based on a one-pole filter and the tau response time. +Tau represents the effective length of the one-pole impulse response, +that is, tau is the integral of the filter's impulse response. This +response is slower to reach the final value but has less ripples in +non-steady signals.

+

Usage

+
_ : avg_tau(period) : _
+
+

Where:

+
    +
  • period: time, in seconds, for the system to decay by 1/e, +or to reach 1-1/e of its final value.
  • +
+

References

+ +
+

(fi.)avg_t60

+

Averaging function based on a one-pole filter and the t60 response time. +This response is particularly useful when the system is required to +reach the final value after about period seconds.

+

Usage

+
_ : avg_t60(period) : _
+
+

Where:

+
    +
  • period: time, in seconds, for the system to decay by 1/1000, +or to reach 1-1/1000 of its final value.
  • +
+

References

+ +
+

(fi.)avg_t19

+

Averaging function based on a one-pole filter and the t19 response time. +This response is close to the moving-average algorithm as it roughly reaches +the final value after period seconds and shows about the same +oscillations for non-steady signals.

+

Usage

+
_ : avg_t19(period) : _
+
+

Where:

+
    +
  • period: time, in seconds, for the system to decay by 1/e^2.2, +or to reach 1-1/e^2.2 of its final value.
  • +
+

References

+

Zölzer, U. (2008). Digital audio signal processing (Vol. 9). New York: Wiley.

+

Kalman Filters

+
+

(fi.)kalman

+

The Kalman filter. It returns the state (a bus of size N). +Note that the only compile-time constant arguments are N and M. +Other arguments are capitalized because they're matrices, and it makes +reading them much easier.

+

Usage

+
kalman(N, M, B, R, H, Q, F, reset, u, z) : si.bus(N)
+
+

Where:

+
    +
  • N: State size (constant int)
  • +
  • M: Measurement size (constant int)
  • +
  • B: Control input matrix (NxM)
  • +
  • R: Measurement noise covariance matrix (MxM)
  • +
  • H: Observation matrix (MxN)
  • +
  • Q: Process noise covariance matrix (NxN)
  • +
  • F: State transition matrix (NxN)
  • +
  • reset: Reset trigger. Whenever reset>0, the internal state x and covariance matrix P are reset.
  • +
  • u: Control input (Mx1)
  • +
  • z: Measurement signal (Mx1)
  • +
+

Example test programs

+

Demo 1 (N=1, M=1) (don't listen, just use oscilloscope):

+
process = fi.kalman(N, M, B, R, H, Q, F, reset, u, z) : it.interpolate_linear(filteredAmt, z)
+with {
+   B = 1.;
+   R = 0.1;
+   H = 1;
+   Q = .01; 
+   F = la.identity(N);
+   reset = button("reset");
+
+   // Dimensions
+   N = 1; // State size
+   M = 1; // Measurement size
+
+   freq = hslider("Freq", 1, 0.01, 10, .01);
+   u = 0.; // constant input
+   trueState = os.osc(freq)*.5 + u;
+   noiseGain = hslider("Noise Gain", .1, 0, 1, .01);
+
+   filteredAmt = hslider("Filter Amount", 1, 0, 1, .01) : si.smoo;
+
+   measurementNoise = no.noise*noiseGain;
+   z = trueState + measurementNoise; // Observed state
+};
+
+

Demo 2 (N=2, M=1) (don't listen, just use oscilloscope)

+
process = fi.kalman(N, M, B, R, H, Q, F, reset, u, z)
+with {
+    B = par(i, N, 0);
+    R = (0.1);
+    H = (1, 0);
+    Q = la.diag(2, par(i, N, .1));
+    F = la.identity(N);
+    reset = 0;
+    u = si.bus(M);
+    z = si.bus(M);
+
+    // Dimensions
+    N = 2; // State size
+    M = 1; // Measurement size
+};
+
+

References

+
+
+
+ + + + + + + + + + + diff --git a/research/vocal-source-grounding/sources/faust-noises-doc.html b/research/vocal-source-grounding/sources/faust-noises-doc.html new file mode 100644 index 0000000..e154e55 --- /dev/null +++ b/research/vocal-source-grounding/sources/faust-noises-doc.html @@ -0,0 +1,751 @@ + + + + + + + + + + + noises - Faust Libraries + + + + + + + + + + + + + + + + + +
+
+
+ +

noises.lib

+

Noises library. Its official prefix is no.

+

This library provides various noise generators and stochastic signal sources +for audio synthesis and testing. It includes white, pink, brown, and blue noise, +as well as pseudo-random number generators and utilities for decorrelated signals +and random modulation in Faust DSP programs.

+

The Noises library is organized into 1 section:

+ +

References

+ +

Functions Reference

+
+

(no.)noise

+

White noise generator (outputs random number between -1 and 1). +noise is a standard Faust function.

+

Usage

+
noise : _
+
+

Where:

+
    +
  • output: white noise signal in [-1, 1].
  • +
+

Test

+
no = library("noises.lib");
+noise_test = no.noise;
+
+
+

(no.)multirandom

+

Generates multiple decorrelated random numbers in parallel.

+

Usage

+
multirandom(N) : si.bus(N)
+
+

Where:

+
    +
  • N: the number of decorrelated random numbers in parallel, a constant numerical expression
  • +
+

Test

+
no = library("noises.lib");
+multirandom_test = no.multirandom(3);
+
+
+

(no.)multinoise

+

Generates multiple decorrelated noises in parallel.

+

Usage

+
multinoise(N) : si.bus(N)
+
+

Where:

+
    +
  • N: the number of decorrelated random numbers in parallel, a constant numerical expression
  • +
+

Test

+
no = library("noises.lib");
+multinoise_test = no.multinoise(3);
+
+
+

(no.)noises

+

A convenient wrapper around multinoise.

+

Usage

+
noises(N,i) : _
+
+

Where:

+
    +
  • N: the number of decorrelated random numbers in parallel, a constant numerical expression
  • +
  • i: the selected random number (i in [0..N[)
  • +
+

Test

+
no = library("noises.lib");
+noises_test = no.noises(4, 2);
+
+
+

(no.)dnoise

+

A deterministic noise burst with a dynamically adjustable seed, enabling consistent recall. +Useful for noise variation sensitive applications like replicable/recallable percussion sounds and waveguide excitation.

+

Usage

+
dnoise(t,sx) : _
+
+

Where:

+
    +
  • t: is a noise burst trigger
  • +
  • sx: defines the range of integer seed multipliers.
  • +
+

Test

+
no = library("noises.lib");
+ba = library("basics.lib");
+dnoise_test = (trigger, seedRange) : no.dnoise
+with {
+  trigger = 1 : ba.impulsify;
+  seedRange = 10.0;
+};
+
+

Example

+

This expression sx = hslider("seed multiplier",1,1,1000,1) allows 1000 distinct seed variations. +To generate a burst with a fixed length, use ba.spulse(bLength, t) (as trigger for the t parameter), where bLength is the burst duration in samples and t is a trigger.

+
+

(no.)randomseed

+

A random seed based on the foreign function arc4random +(see man arc4random). Used in rnoise, rmultirandom, etc. to +avoid having the same pseudo random sequence at each run.

+

WARNING: using the foreign function arc4random, so only available in C/C++ and LLVM backends.

+

Usage

+
randomseed : _
+
+

Where:

+
    +
  • output: platform-specific random seed value.
  • +
+

Test

+
no = library("noises.lib");
+randomseed_test = no.randomseed;
+
+
+

(no.)rnoise

+

A randomized white noise generator (outputs random number between -1 and 1).

+

WARNING: using the foreign function arc4random, so only available in C/C++ and LLVM backends.

+

Usage

+
rnoise : _
+
+

Test

+
no = library("noises.lib");
+rnoise_test = no.rnoise;
+
+
+

(no.)rmultirandom

+

Generates multiple decorrelated random numbers in parallel.

+

WARNING: using the foreign function arc4random, so only available in C/C++ and LLVM backends.

+

Usage

+
rmultirandom(N) : _
+
+

Where:

+
    +
  • N: the number of decorrelated random numbers in parallel, a constant numerical expression
  • +
+

Test

+
no = library("noises.lib");
+rmultirandom_test = no.rmultirandom(3);
+
+
+

(no.)rmultinoise

+

Generates multiple decorrelated noises in parallel.

+

WARNING: using the foreign function arc4random, so only available in C/C++ and LLVM backends.

+

Usage

+
rmultinoise(N) : _
+
+

Where:

+
    +
  • N: the number of decorrelated random numbers in parallel, a constant numerical expression
  • +
+

Test

+
no = library("noises.lib");
+rmultinoise_test = no.rmultinoise(3);
+
+
+

(no.)rnoises

+

A convenient wrapper around rmultinoise.

+

WARNING: using the foreign function arc4random, so only available in C/C++ and LLVM backends.

+

Usage

+
rnoises(N,i) : _
+
+

Where:

+
    +
  • N: the number of decorrelated random numbers in parallel
  • +
  • i: the selected random number (i in [0..N[)
  • +
+

Test

+
no = library("noises.lib");
+rnoises_test = no.rnoises(4, 1);
+
+
+

(no.)pink_noise

+

Pink noise (1/f noise) generator (third-order approximation covering the audio band well). +pink_noise is a standard Faust function.

+

Usage

+
pink_noise : _
+
+

Where:

+
    +
  • output: pink (1/f) noise signal.
  • +
+

Test

+
no = library("noises.lib");
+pink_noise_test = no.pink_noise;
+
+

Alternatives

+

Higher-order approximations covering any frequency band can be obtained using

+
no.noise : fi.spectral_tilt(order,lowerBandLimit,Bandwidth,p)
+
+

where p=-0.5 means filter rolloff f^(-1/2) which gives 1/f rolloff in the +power spectral density, and can be changed to other real values.

+

Example

+

pink_noise_compare.dsp - compare three pinking filters

+
process = pink_noises with {
+    f0 = 35; // Lower bandlimit in Hz
+    bw3 = 0.7 * ma.SR/2.0 - f0; // Bandwidth in Hz, 3rd order case
+    bw9 = 0.8 * ma.SR/2.0 - f0; // Bandwidth in Hz, 9th order case
+    pink_tilt_3 = fi.spectral_tilt(3,f0,bw3,-0.5);
+    pink_tilt_9 = fi.spectral_tilt(9,f0,bw9,-0.5);
+    pink_noises = 1-1' <:
+      no.pink_filter, // original designed by invfreqz in Octave
+      pink_tilt_3,    // newer method using the same filter order
+      pink_tilt_9;    // newer method using a higher filter order
+};
+
+

Output of Example

+
faust2octave pink_noise_compare.dsp
+Octave:1> semilogx(20*log10(abs(fft(faustout,8192))(1:4096,:)));
+...
+
+

pink_noise_demo figure

+

References

+ +
+

(no.)pink_noise_vm

+

Multi pink noise generator.

+

Usage

+
pink_noise_vm(N) : _
+
+

Where:

+
    +
  • N: number of latched white-noise processes to sum, +not to exceed sizeof(int) in C++ (typically 32).
  • +
+

Test

+
no = library("noises.lib");
+pink_noise_vm_test = no.pink_noise_vm(4);
+
+

References

+ +
+

(no.)lfnoise, (no.)lfnoise0 and (no.)lfnoiseN

+

Low-frequency noise generators (Butterworth-filtered downsampled white noise).

+

Usage

+
lfnoise0(rate) : _   // new random number every int(ma.SR/rate) samples or so
+lfnoiseN(N,rate) : _ // same as "lfnoise0(rate) : fi.lowpass(N,rate)" [see filters.lib]
+lfnoise(rate) : _    // same as "lfnoise0(rate) : seq(i,5,fi.lowpass(N,rate))" (no overshoot)
+
+

Example

+

(view waveforms in faust2octave):

+
rate = ma.SR/100.0; // new random value every 100 samples (ma.SR from maths.lib)
+process = lfnoise0(rate),   // sampled/held noise (piecewise constant)
+          lfnoiseN(3,rate), // lfnoise0 smoothed by 3rd order Butterworth LPF
+          lfnoise(rate);    // lfnoise0 smoothed with no overshoot
+
+

Test

+
no = library("noises.lib");
+lfnoise0_test = no.lfnoise0(10.0);
+
+
+

(no.)sparse_noise

+

Sparse noise generator.

+

Usage

+
sparse_noise(f0) : _
+
+

Where:

+
    +
  • f0: average frequency of noise impulses per second
  • +
+

Random impulses in the amplitude range -1 to 1 are generated +at an average rate of f0 impulses per second.

+

Test

+
no = library("noises.lib");
+sparse_noise_test = no.sparse_noise(5.0);
+
+

References

+
    +
  • See velvet_noise
  • +
+
+

(no.)velvet_noise_vm

+

Velvet noise generator.

+

Usage

+
velvet_noise(amp, f0) : _
+
+

Where:

+
    +
  • amp: amplitude of noise impulses (positive and negative)
  • +
  • f0: average frequency of noise impulses per second
  • +
+

Test

+
no = library("noises.lib");
+velvet_noise_test = no.velvet_noise(0.5, 5.0);
+
+

References

+
    +
  • Matti Karjalainen and Hanna Jarvelainen, + "Reverberation Modeling Using Velvet Noise", + in Proc. 30th Int. Conf. Intelligent Audio Environments (AES07), + March 2007.
  • +
+
+

(no.)gnoise

+

Approximate zero-mean, unit-variance Gaussian white noise generator.

+

Usage

+
gnoise(N) : _
+
+

Where:

+
    +
  • N: number of uniform random numbers added to approximate Gaussian white noise
  • +
+

Test

+
no = library("noises.lib");
+gnoise_test = no.gnoise(8);
+
+

References

+
    +
  • See Central Limit Theorem
  • +
+
+

(no.)colored_noise

+

Generates a colored noise signal with an arbitrary spectral +roll-off factor (alpha) over the entire audible frequency range +(20-20000 Hz). The output is normalized so that an equal RMS +level is maintained for different values of alpha.

+

Usage

+
colored_noise(N,alpha) : _
+
+

Where:

+
    +
  • N: desired integer filter order (constant numerical expression)
  • +
  • alpha: slope of roll-off, between -1 and 1. -1 corresponds to +brown/red noise, -1/2 pink noise, 0 white noise, 1/2 blue noise, +and 1 violet/azure noise.
  • +
+

Test

+
no = library("noises.lib");
+colored_noise_test = no.colored_noise(4, 0.0);
+
+

Examples

+

See dm.colored_noise_demo.

+
+
+ + + + + + + + + + + diff --git a/research/vocal-source-grounding/sources/faust-physmodels-doc.html b/research/vocal-source-grounding/sources/faust-physmodels-doc.html new file mode 100644 index 0000000..b6565cb --- /dev/null +++ b/research/vocal-source-grounding/sources/faust-physmodels-doc.html @@ -0,0 +1,3742 @@ + + + + + + + + + + + physmodels - Faust Libraries + + + + + + + + + + + + + + + + + +
+
+
+ +

physmodels.lib

+

Faust physical modeling library. Its official prefix is pm.

+

This library provides an environment to facilitate physical modeling of musical +instruments. It includes waveguide, mass-spring, and digital wave +models for strings, membranes, bars, and resonant systems used in physical modeling +synthesis and acoustic simulation research. It contains dozens of functions implementing +low and high level elements going from a simple waveguide to fully operational models with +built-in UI, etc.

+

It is organized as follows:

+
    +
  • Global Variables: useful pre-defined variables for +physical modeling (e.g., speed of sound, etc.).
  • +
  • Conversion Tools: conversion functions specific +to physical modeling (e.g., length to frequency, etc.).
  • +
  • Bidirectional Utilities: functions to create +bidirectional block diagrams for physical modeling.
  • +
  • Basic Elements: waveguides, specific types of filters, etc.
  • +
  • String Instruments: various types of strings +(e.g., steel, nylon, etc.), bridges, guitars, etc.
  • +
  • Bowed String Instruments: parts and models +specific to bowed string instruments (e.g., bows, bridges, violins, etc.).
  • +
  • Wind Instrument: parts and models specific to wind +instruments (e.g., reeds, mouthpieces, flutes, clarinets, etc.).
  • +
  • Exciters: pluck generators, "blowers", etc.
  • +
  • Modal Percussions: percussion instruments based on +modal models.
  • +
  • Vocal Synthesis: functions for various vocal synthesis +techniques (e.g., fof, source/filter, etc.) and vocal synthesizers.
  • +
  • Misc Functions: any other functions that don't fit in +the previous category (e.g., nonlinear filters, etc.).
  • +
+

This library is part of the Faust Physical Modeling ToolKit. +More information on how to use this library can be found on this page or this video. Tutorials on how to make +physical models of musical instruments using Faust can be found +here as well.

+

References

+ +

Global Variables

+

Useful pre-defined variables for physical modeling.

+
+

(pm.)speedOfSound

+

Speed of sound in meters per second (340m/s).

+
+

(pm.)maxLength

+

The default maximum length (3) in meters of strings and tubes used in this +library. This variable should be overriden to allow longer strings or tubes.

+

Conversion Tools

+

Useful conversion tools for physical modeling.

+
+

(pm.)f2l

+

Frequency to length in meters.

+

Usage

+
f2l(freq) : distanceInMeters
+
+

Where:

+
    +
  • freq: the frequency
  • +
+

Test

+
pm = library("physmodels.lib");
+f2l_test = pm.f2l(440);
+
+
+

(pm.)l2f

+

Length in meters to frequency.

+

Usage

+
l2f(length) : freq
+
+

Where:

+
    +
  • length: length/distance in meters
  • +
+

Test

+
pm = library("physmodels.lib");
+l2f_test = pm.l2f(0.75);
+
+
+

(pm.)l2s

+

Length in meters to number of samples.

+

Usage

+
l2s(l) : numberOfSamples
+
+

Where:

+
    +
  • l: length in meters
  • +
+

Test

+
pm = library("physmodels.lib");
+l2s_test = pm.l2s(1.2);
+
+

Bidirectional Utilities

+

Set of fundamental functions to create bi-directional block diagrams in Faust. +These elements are used as the basis of this library to connect high level +elements (e.g., mouthpieces, strings, bridge, instrument body, etc.). Each +block has 3 inputs and 3 outputs. The first input/output carry left going +waves, the second input/output carry right going waves, and the third +input/output is used to carry any potential output signal to the end of the +algorithm.

+
+

(pm.)basicBlock

+

Empty bidirectional block to be used with chain: 3 signals ins +and 3 signals out.

+

Usage

+
chain(basicBlock : basicBlock : etc.)
+
+

Where:

+
    +
  • basicBlock: any bidirectional block with 3 inputs and 3 outputs
  • +
+

Test

+
pm = library("physmodels.lib");
+basicBlock_test = 0.25, -0.15, 0.05 : pm.basicBlock;
+
+
+

(pm.)chain

+

Creates a chain of bidirectional blocks. +Blocks must have 3 inputs and outputs. The first input/output carry left +going waves, the second input/output carry right going waves, and the third +input/output is used to carry any potential output signal to the end of the +algorithm. The implied one sample delay created by the ~ operator is +generalized to the left and right going waves. Thus, n blocks in chain() +will add an n samples delay to both left and right going waves.

+

Usage

+
leftGoingWaves,rightGoingWaves,mixedOutput : chain( A : B ) : leftGoingWaves,rightGoingWaves,mixedOutput
+with {
+   A = _,_,_;
+   B = _,_,_;
+};
+
+

Where:

+
    +
  • A: first bidirectional block in the chain
  • +
  • B: next bidirectional block in the chain
  • +
+

Test

+
pm = library("physmodels.lib");
+chain_test = 0.25, -0.15, 0.05 : pm.chain(pm.basicBlock);
+
+
+

(pm.)inLeftWave

+

Adds a signal to left going waves anywhere in a chain of blocks.

+

Usage

+
model(x) = chain(A : inLeftWave(x) : B)
+
+

Where:

+
    +
  • A: preceding bidirectional block
  • +
  • x: signal added to the left-going wave
  • +
  • B: following bidirectional block
  • +
+

Test

+
pm = library("physmodels.lib");
+inLeftWave_test = 0, 0, 0 : pm.inLeftWave(0.25);
+
+
+

(pm.)inRightWave

+

Adds a signal to right going waves anywhere in a chain of blocks.

+

Usage

+
model(x) = chain(A : inRightWave(x) : B)
+
+

Where:

+
    +
  • A: preceding bidirectional block
  • +
  • x: signal added to the right-going wave
  • +
  • B: following bidirectional block
  • +
+

Test

+
pm = library("physmodels.lib");
+inRightWave_test = 0, 0, 0 : pm.inRightWave(0.25);
+
+
+

(pm.)in

+

Adds a signal to left and right going waves anywhere in a chain +of blocks.

+

Usage

+
model(x) = chain(A : in(x) : B)
+
+

Where:

+
    +
  • A: preceding bidirectional block
  • +
  • x: signal added to both left- and right-going waves
  • +
  • B: following bidirectional block
  • +
+

Test

+
pm = library("physmodels.lib");
+in_test = 0, 0, 0 : pm.in(0.25);
+
+
+

(pm.)outLeftWave

+

Sends the signal of left going waves to the output channel of the chain.

+

Usage

+
chain(A : outLeftWave : B)
+
+

Where:

+
    +
  • A: preceding bidirectional block
  • +
  • B: following bidirectional block
  • +
+

Test

+
pm = library("physmodels.lib");
+outLeftWave_test = pm.outLeftWave(0.1, 0.2, 0.3);
+
+
+

(pm.)outRightWave

+

Sends the signal of right going waves to the output channel of the chain.

+

Usage

+
chain(A : outRightWave : B)
+
+

Where:

+
    +
  • A: preceding bidirectional block
  • +
  • B: following bidirectional block
  • +
+

Test

+
pm = library("physmodels.lib");
+outRightWave_test = pm.outRightWave(0.1, 0.2, 0.3);
+
+
+

(pm.)out

+

Sends the signal of right and left going waves to the output channel of the +chain.

+

Usage

+
chain(A : out : B)
+
+

Where:

+
    +
  • A: preceding bidirectional block
  • +
  • B: following bidirectional block
  • +
+

Test

+
pm = library("physmodels.lib");
+out_test = pm.out(0.1, 0.2, 0.3);
+
+
+

(pm.)terminations

+

Creates terminations on both sides of a chain without closing +the inputs and outputs of the bidirectional signals chain. As for +chain, this function adds a 1 sample delay to the bidirectional +signal, both ways. Of course, this function can be nested within a +chain.

+

Usage

+
terminations(a,b,c)
+with {
+   a = *(-1); // left termination
+   b = chain(D : E : F); // bidirectional chain of blocks (D, E, F, etc.)
+   c = *(-1); // right termination
+};
+
+

Where:

+
    +
  • a: left termination filter
  • +
  • b: bidirectional chain to terminate
  • +
  • c: right termination filter
  • +
+

Test

+
pm = library("physmodels.lib");
+terminations_test = 0.25, -0.15, 0.05 : pm.terminations(*(-1), pm.basicBlock, *(-1));
+
+
+

(pm.)lTermination

+

Creates a termination on the left side of a chain without +closing the inputs and outputs of the bidirectional signals chain. This +function adds a 1 sample delay near the termination and can be nested +within another chain.

+

Usage

+
lTermination(a,b)
+with {
+   a = *(-1); // left termination
+   b = chain(D : E : F); // bidirectional chain of blocks (D, E, F, etc.)
+};
+
+

Where:

+
    +
  • a: left termination filter
  • +
  • b: bidirectional chain to terminate
  • +
+

Test

+
pm = library("physmodels.lib");
+lTermination_test = 0.25, -0.15, 0.05 : pm.lTermination(*(-1), pm.basicBlock);
+
+
+

(pm.)rTermination

+

Creates a termination on the right side of a chain without +closing the inputs and outputs of the bidirectional signals chain. This +function adds a 1 sample delay near the termination and can be nested +within another chain.

+

Usage

+
rTermination(b,c)
+with {
+   b = chain(D : E : F); // bidirectional chain of blocks (D, E, F, etc.)
+   c = *(-1); // right termination
+};
+
+

Where:

+
    +
  • b: bidirectional chain to terminate
  • +
  • c: right termination filter
  • +
+

Test

+
pm = library("physmodels.lib");
+rTermination_test = 0.25, -0.15, 0.05 : pm.rTermination(pm.basicBlock, *(-1));
+
+
+

(pm.)closeIns

+

Closes the inputs of a bidirectional chain in all directions.

+

Usage

+
closeIns : _,_,_
+
+

Typical use: closeIns : chain(...) : _,_,_

+

Test

+
pm = library("physmodels.lib");
+closeIns_test = pm.closeIns, 0.25;
+
+
+

(pm.)closeOuts

+

Closes the outputs of a bidirectional chain in all directions except for the +main signal output (3d output).

+

Usage

+
_,_,_ : chain(...) : _
+
+

Test

+
pm = library("physmodels.lib");
+closeOuts_test = ((0.25, -0.15, 0.05) : pm.closeOuts), 0.25;
+
+
+

(pm.)endChain

+

Closes the inputs and outputs of a bidirectional chain in all directions +except for the main signal output (3d output).

+

Usage

+
endChain(chain(...)) : _
+
+

Where:

+
    +
  • b: bidirectional chain to close on all non-audio ports
  • +
+

Test

+
pm = library("physmodels.lib");
+endChain_test = pm.endChain((_, _, _ + 0.25));
+
+

Basic Elements

+

Basic elements for physical modeling (e.g., waveguides, specific filters, +etc.).

+
+

(pm.)waveguideN

+

A series of waveguide functions based on various types of delays (see +fdelay[n]).

+

List of functions

+
    +
  • waveguideUd: unit delay waveguide
  • +
  • waveguideFd: fractional delay waveguide
  • +
  • waveguideFd2: second order fractional delay waveguide
  • +
  • waveguideFd4: fourth order fractional delay waveguide
  • +
+

Usage

+
chain(A : waveguideUd(nMax,n) : B)
+
+

Where:

+
    +
  • nMax: the maximum length of the delays in the waveguide
  • +
  • n: the length of the delay lines in samples.
  • +
+

Test

+
pm = library("physmodels.lib");
+waveguideUd_test = 0.25, -0.15, 0.05 : pm.waveguideUd(512, 32);
+
+
+

(pm.)waveguide

+

Standard pm.lib waveguide (based on waveguideFd4).

+

Usage

+
chain(A : waveguide(nMax,n) : B)
+
+

Where:

+
    +
  • nMax: the maximum length of the delays in the waveguide
  • +
  • n: the length of the delay lines in samples.
  • +
+

Test

+
pm = library("physmodels.lib");
+waveguide_test = 0.25, -0.15, 0.05 : pm.waveguide(512, 32);
+
+
+

(pm.)bridgeFilter

+

Generic two zeros bridge FIR filter (as implemented in the +STK) that can be used to +implement the reflectance violin, guitar, etc. bridges.

+

Usage

+
_ : bridgeFilter(brightness,absorption) : _
+
+

Where:

+
    +
  • brightness: controls the damping of high frequencies (0-1)
  • +
  • absorption: controls the absorption of the brige and thus the t60 of +the string connected to it (0-1) (1 = 20 seconds)
  • +
+

Test

+
pm = library("physmodels.lib");
+os = library("oscillators.lib");
+bridgeFilter_test = os.osc(110) : pm.bridgeFilter(0.6, 0.4);
+
+
+

(pm.)modeFilter

+

Resonant bandpass filter that can be used to implement a single resonance +(mode).

+

Usage

+
_ : modeFilter(freq,t60,gain) : _
+
+

Where:

+
    +
  • freq: mode frequency
  • +
  • t60: mode resonance duration (in seconds)
  • +
  • gain: mode gain (0-1)
  • +
+

Test

+
pm = library("physmodels.lib");
+os = library("oscillators.lib");
+modeFilter_test = os.osc(110) : pm.modeFilter(440, 1.5, 0.8);
+
+

String Instruments

+

Low and high level string instruments parts. Most of the elements in +this section can be used in a bidirectional chain.

+
+

(pm.)stringSegment

+

A string segment without terminations (just a simple waveguide).

+

Usage

+
chain(A : stringSegment(maxLength,length) : B)
+
+

Where:

+
    +
  • maxLength: the maximum length of the string in meters (should be static)
  • +
  • length: the length of the string in meters
  • +
+

Test

+
pm = library("physmodels.lib");
+stringSegment_test = 0.25, -0.15, 0.05 : pm.stringSegment(1.0, 0.5);
+
+
+

(pm.)openString

+

A bidirectional block implementing a basic "generic" string with a +selectable excitation position. Lowpass filters are built-in and +allow to simulate the effect of dispersion on the sound and thus +to change the "stiffness" of the string.

+

Usage

+
chain(... : openString(length,stiffness,pluckPosition,excitation) : ...)
+
+

Where:

+
    +
  • length: the length of the string in meters
  • +
  • stiffness: the stiffness of the string (0-1) (1 for max stiffness)
  • +
  • pluckPosition: excitation position (0-1) (1 is bottom)
  • +
  • excitation: the excitation signal
  • +
+

Test

+
pm = library("physmodels.lib");
+ba = library("basics.lib");
+openString_test = 0.25, -0.15, 0.05 : pm.openString(0.8, 0.5, 0.2, pm.impulseExcitation(ba.pulse(64)));
+
+
+

(pm.)nylonString

+

A bidirectional block implementing a basic nylon string with selectable +excitation position. This element is based on openString +and has a fix stiffness corresponding to that of a nylon string.

+

Usage

+
chain(... : nylonString(length,pluckPosition,excitation) : ...)
+
+

Where:

+
    +
  • length: the length of the string in meters
  • +
  • pluckPosition: excitation position (0-1) (1 is bottom)
  • +
  • excitation: the excitation signal
  • +
+

Test

+
pm = library("physmodels.lib");
+ba = library("basics.lib");
+nylonString_test = 0.25, -0.15, 0.05 : pm.nylonString(0.8, 0.3, pm.impulseExcitation(ba.pulse(64)));
+
+
+

(pm.)steelString

+

A bidirectional block implementing a basic steel string with selectable +excitation position. This element is based on openString +and has a fix stiffness corresponding to that of a steel string.

+

Usage

+
chain(... : steelString(length,pluckPosition,excitation) : ...)
+
+

Where:

+
    +
  • length: the length of the string in meters
  • +
  • pluckPosition: excitation position (0-1) (1 is bottom)
  • +
  • excitation: the excitation signal
  • +
+

Test

+
pm = library("physmodels.lib");
+ba = library("basics.lib");
+steelString_test = 0.25, -0.15, 0.05 : pm.steelString(0.8, 0.3, pm.impulseExcitation(ba.pulse(64)));
+
+
+

(pm.)openStringPick

+

A bidirectional block implementing a "generic" string with selectable +excitation position. It also has a built-in pickup whose position is the +same as the excitation position. Thus, moving the excitation position +will also move the pickup.

+

Usage

+
chain(... : openStringPick(length,stiffness,pluckPosition,excitation) : ...)
+
+

Where:

+
    +
  • length: the length of the string in meters
  • +
  • stiffness: the stiffness of the string (0-1) (1 for max stiffness)
  • +
  • pluckPosition: excitation position (0-1) (1 is bottom)
  • +
  • excitation: the excitation signal
  • +
+

Test

+
pm = library("physmodels.lib");
+openStringPick_test = pm.endChain(pm.openStringPick(0.8, 0.4, 0.3, pm.impulseExcitation(button("pm.openStringPick/gate"))));
+
+
+

(pm.)openStringPickUp

+

A bidirectional block implementing a "generic" string with selectable +excitation position and stiffness. It also has a built-in pickup whose +position can be independenly selected. The only constraint is that the +pickup has to be placed after the excitation position.

+

Usage

+
chain(... : openStringPickUp(length,stiffness,pluckPosition,pickupPosition,excitation) : ...)
+
+

Where:

+
    +
  • length: the length of the string in meters
  • +
  • stiffness: the stiffness of the string (0-1) (1 for max stiffness)
  • +
  • pluckPosition: pluck position between the top of the string and the +pickup (0-1) (1 for same as pickup position)
  • +
  • pickupPosition: position of the pickup on the string (0-1) (1 is bottom)
  • +
  • excitation: the excitation signal
  • +
+

Test

+
pm = library("physmodels.lib");
+openStringPickUp_test = pm.endChain(pm.openStringPickUp(0.8, 0.4, 0.6, 0.7, pm.impulseExcitation(button("pm.openStringPickUp/gate"))));
+
+
+

(pm.)openStringPickDown

+

A bidirectional block implementing a "generic" string with selectable +excitation position and stiffness. It also has a built-in pickup whose +position can be independenly selected. The only constraint is that the +pickup has to be placed before the excitation position.

+

Usage

+
chain(... : openStringPickDown(length,stiffness,pluckPosition,pickupPosition,excitation) : ...)
+
+

Where:

+
    +
  • length: the length of the string in meters
  • +
  • stiffness: the stiffness of the string (0-1) (1 for max stiffness)
  • +
  • pluckPosition: pluck position on the string (0-1) (1 is bottom)
  • +
  • pickupPosition: position of the pickup between the top of the string +and the excitation position (0-1) (1 is excitation position)
  • +
  • excitation: the excitation signal
  • +
+

Test

+
pm = library("physmodels.lib");
+openStringPickDown_test = pm.endChain(pm.openStringPickDown(0.8, 0.4, 0.6, 0.5, pm.impulseExcitation(button("pm.openStringPickDown/gate"))));
+
+
+

(pm.)ksReflexionFilter

+

The "typical" one-zero Karplus-strong feedforward reflexion filter. This +filter will be typically used in a termination (see below).

+

Usage

+
_ : ksReflexionFilter : _
+
+

Typical use: terminations(_,chain(...),ksReflexionFilter)

+

Test

+
pm = library("physmodels.lib");
+os = library("oscillators.lib");
+ksReflexionFilter_test = os.osc(220) : pm.ksReflexionFilter;
+
+
+

(pm.)rStringRigidTermination

+

Bidirectional block implementing a right rigid string termination (no damping, +just phase inversion).

+

Usage

+
_,_,_ : rStringRigidTermination
+
+

Typical use: chain(rStringRigidTermination : stringSegment : ...)

+

Test

+
pm = library("physmodels.lib");
+rStringRigidTermination_test = 0.25, -0.15, 0.05 : pm.rStringRigidTermination;
+
+
+

(pm.)lStringRigidTermination

+

Bidirectional block implementing a left rigid string termination (no damping, +just phase inversion).

+

Usage

+
_,_,_ : lStringRigidTermination
+
+

Typical use: chain(... : stringSegment : lStringRigidTermination)

+

Test

+
pm = library("physmodels.lib");
+lStringRigidTermination_test = 0.25, -0.15, 0.05 : pm.lStringRigidTermination;
+
+
+

(pm.)elecGuitarBridge

+

Bidirectional block implementing a simple electric guitar bridge. This +block is based on bridgeFilter. The bridge doesn't +implement transmittance since it is not meant to be connected to a +body (unlike acoustic guitar). It also partially sets the resonance +duration of the string with the nuts used on the other side.

+

Usage

+
_,_,_ : elecGuitarBridge
+
+

Typical use: chain(... : stringSegment : elecGuitarBridge)

+

Test

+
pm = library("physmodels.lib");
+elecGuitarBridge_test = 0.25, -0.15, 0.05 : pm.elecGuitarBridge;
+
+
+

(pm.)elecGuitarNuts

+

Bidirectional block implementing a simple electric guitar nuts. This +block is based on bridgeFilter and does essentially +the same thing as elecGuitarBridge, but on the +other side of the chain. It also partially sets the resonance duration of +the string with the bridge used on the other side.

+

Usage

+
_,_,_ : elecGuitarNuts
+
+

Typical use: chain(elecGuitarNuts : stringSegment : ...)

+

Test

+
pm = library("physmodels.lib");
+elecGuitarNuts_test = 0.25, -0.15, 0.05 : pm.elecGuitarNuts;
+
+
+

(pm.)guitarBridge

+

Bidirectional block implementing a simple acoustic guitar bridge. This +bridge damps more hight frequencies than +elecGuitarBridge and implements a transmittance +filter. It also partially sets the resonance duration of the string with +the nuts used on the other side.

+

Usage

+
_,_,_ : guitarBridge
+
+

Typical use: chain(... : stringSegment : guitarBridge)

+

Test

+
pm = library("physmodels.lib");
+guitarBridge_test = 0.25, -0.15, 0.05 : pm.guitarBridge;
+
+
+

(pm.)guitarNuts

+

Bidirectional block implementing a simple acoustic guitar nuts. This +nuts damps more hight frequencies than +elecGuitarNuts and implements a transmittance +filter. It also partially sets the resonance duration of the string with +the bridge used on the other side.

+

Usage

+
chain(guitarNuts : stringSegment : ...)
+
+

Test

+
pm = library("physmodels.lib");
+guitarNuts_test = 0.25, -0.15, 0.05 : pm.guitarNuts;
+
+
+

(pm.)idealString

+

An "ideal" string with rigid terminations and where the plucking position +and the pick-up position are the same. Since terminations are rigid, this +string will ring forever.

+

Usage

+
_ : idealString(length,pluckPosition,excitation) : _
+
+

Where:

+
    +
  • length: the length of the string in meters
  • +
  • pluckPosition: the plucking position (0.001-0.999)
  • +
  • excitation: the excitation signal
  • +
+

Test

+
pm = library("physmodels.lib");
+idealString_test = pm.closeIns : pm.idealString(0.9, 0.2, pm.impulseExcitation(button("pm.idealString/gate")));
+
+
+

(pm.)ks

+

A Karplus-Strong string (in that case, the string is implemented as a +one dimension waveguide).

+

Usage

+
ks(length,damping,excitation) : _
+
+

Where:

+
    +
  • length: the length of the string in meters
  • +
  • damping: string damping (0-1)
  • +
  • excitation: excitation signal
  • +
+

Test

+
pm = library("physmodels.lib");
+ks_test = pm.ks(0.9, 0.3, pm.impulseExcitation(button("pm.ks/gate")));
+
+
+

(pm.)ks_ui_MIDI

+

Ready-to-use, MIDI-enabled Karplus-Strong string with buil-in UI.

+

Usage

+
ks_ui_MIDI : _
+
+

Test

+
pm = library("physmodels.lib");
+ks_ui_MIDI_test = pm.ks_ui_MIDI;
+
+
+

(pm.)elecGuitarModel

+

A simple electric guitar model (without audio effects, of course) with +selectable pluck position. +This model implements a single string. Additional strings should be created +by making a polyphonic application out of this function. Pitch is changed by +changing the length of the string and not through a finger model.

+

Usage

+
elecGuitarModel(length,pluckPosition,mute,excitation) : _
+
+

Where:

+
    +
  • length: the length of the string in meters
  • +
  • pluckPosition: pluck position (0-1) (1 is on the bridge)
  • +
  • mute: mute coefficient (1 for no mute and 0 for instant mute)
  • +
  • excitation: excitation signal
  • +
+

Test

+
pm = library("physmodels.lib");
+elecGuitarModel_test = pm.elecGuitarModel(0.9, 0.3, 0.8, pm.impulseExcitation(button("pm.elecGuitarModel/gate")));
+
+
+

(pm.)elecGuitar

+

A simple electric guitar model with steel strings (based on +elecGuitarModel) implementing an excitation +model. +This model implements a single string. Additional strings should be created +by making a polyphonic application out of this function.

+

Usage

+
elecGuitar(length,pluckPosition,mute,gain,trigger) : _
+
+

Where:

+
    +
  • length: the length of the string in meters
  • +
  • pluckPosition: pluck position (0-1) (1 is on the bridge)
  • +
  • mute: mute coefficient (1 for no mute and 0 for instant mute)
  • +
  • gain: gain of the pluck (0-1)
  • +
  • trigger: trigger signal (1 for on, 0 for off)
  • +
+

Test

+
pm = library("physmodels.lib");
+elecGuitar_test = pm.elecGuitar(0.9, 0.3, 0.8, 0.6, button("pm.elecGuitar/gate"));
+
+
+

(pm.)elecGuitar_ui_MIDI

+

Ready-to-use MIDI-enabled electric guitar physical model with built-in UI.

+

Usage

+
elecGuitar_ui_MIDI : _
+
+

Test

+
pm = library("physmodels.lib");
+elecGuitar_ui_MIDI_test = pm.elecGuitar_ui_MIDI;
+
+
+

(pm.)guitarBody

+

WARNING: not implemented yet! +Bidirectional block implementing a simple acoustic guitar body.

+

Usage

+
chain(... : guitarBody)
+
+

Test

+
pm = library("physmodels.lib");
+guitarBody_test = 0.25, -0.15, 0.05 : pm.guitarBody;
+
+
+

(pm.)guitarModel

+

A simple acoustic guitar model with steel strings and selectable excitation +position. This model implements a single string. Additional strings should be created +by making a polyphonic application out of this function. Pitch is changed by +changing the length of the string and not through a finger model. +WARNING: this function doesn't currently implement a body (just strings and +bridge).

+

Usage

+
guitarModel(length,pluckPosition,excitation) : _
+
+

Where:

+
    +
  • length: the length of the string in meters
  • +
  • pluckPosition: pluck position (0-1) (1 is on the bridge)
  • +
  • excitation: excitation signal
  • +
+

Test

+
pm = library("physmodels.lib");
+guitarModel_test = pm.guitarModel(0.9, 0.25, pm.impulseExcitation(button("pm.guitarModel/gate")));
+
+
+

(pm.)guitar

+

A simple acoustic guitar model with steel strings (based on +guitarModel) implementing an excitation model. +This model implements a single string. Additional strings should be created +by making a polyphonic application out of this function.

+

Usage

+
guitar(length,pluckPosition,gain,trigger) : _
+
+

Where:

+
    +
  • length: the length of the string in meters
  • +
  • pluckPosition: pluck position (0-1) (1 is on the bridge)
  • +
  • gain: gain of the excitation
  • +
  • trigger: trigger signal (1 for on, 0 for off)
  • +
+

Test

+
pm = library("physmodels.lib");
+guitar_test = pm.guitar(0.9, 0.25, 0.8, button("pm.guitar/gate"));
+
+
+

(pm.)guitar_ui_MIDI

+

Ready-to-use MIDI-enabled steel strings acoustic guitar physical model with +built-in UI.

+

Usage

+
guitar_ui_MIDI : _
+
+

Test

+
pm = library("physmodels.lib");
+guitar_ui_MIDI_test = pm.guitar_ui_MIDI;
+
+
+

(pm.)nylonGuitarModel

+

A simple acoustic guitar model with nylon strings and selectable excitation +position. This model implements a single string. Additional strings should be created +by making a polyphonic application out of this function. Pitch is changed by +changing the length of the string and not through a finger model. +WARNING: this function doesn't currently implement a body (just strings and +bridge).

+

Usage

+
nylonGuitarModel(length,pluckPosition,excitation) : _
+
+

Where:

+
    +
  • length: the length of the string in meters
  • +
  • pluckPosition: pluck position (0-1) (1 is on the bridge)
  • +
  • excitation: excitation signal
  • +
+

Test

+
pm = library("physmodels.lib");
+nylonGuitarModel_test = pm.nylonGuitarModel(0.9, 0.25, pm.impulseExcitation(button("pm.nylonGuitarModel/gate")));
+
+
+

(pm.)nylonGuitar

+

A simple acoustic guitar model with nylon strings (based on +nylonGuitarModel) implementing an excitation model. +This model implements a single string. Additional strings should be created +by making a polyphonic application out of this function.

+

Usage

+
nylonGuitar(length,pluckPosition,gain,trigger) : _
+
+

Where:

+
    +
  • length: the length of the string in meters
  • +
  • pluckPosition: pluck position (0-1) (1 is on the bridge)
  • +
  • gain: gain of the excitation (0-1)
  • +
  • trigger: trigger signal (1 for on, 0 for off)
  • +
+

Test

+
pm = library("physmodels.lib");
+nylonGuitar_test = pm.nylonGuitar(0.9, 0.25, 0.8, button("pm.nylonGuitar/gate"));
+
+
+

(pm.)nylonGuitar_ui_MIDI

+

Ready-to-use MIDI-enabled nylon strings acoustic guitar physical model with +built-in UI.

+

Usage

+
nylonGuitar_ui_MIDI : _
+
+

Test

+
pm = library("physmodels.lib");
+nylonGuitar_ui_MIDI_test = pm.nylonGuitar_ui_MIDI;
+
+
+

(pm.)modeInterpRes

+

Modular string instrument resonator based on IR measurements made on 3D +printed models. The 2D space allowing for the control of the shape and the +scale of the model is enabled by interpolating between modes parameters. +More information about this technique/project can be found here: +* https://ccrma.stanford.edu/~rmichon/3dPrintingModeling/.

+

Usage

+
_ : modeInterpRes(nModes,x,y) : _
+
+

Where:

+
    +
  • nModes: number of modeled modes (40 max)
  • +
  • x: shape of the resonator (0: square, 1: square with rounded corners, 2: round)
  • +
  • y: scale of the resonator (0: small, 1: medium, 2: large)
  • +
+

Test

+
pm = library("physmodels.lib");
+os = library("oscillators.lib");
+modeInterpRes_test = os.osc(110) : pm.modeInterpRes(20, 1.0, 1.5);
+
+
+

(pm.)modularInterpBody

+

Bidirectional block implementing a modular string instrument resonator +(see modeInterpRes).

+

Usage

+
chain(... : modularInterpBody(nModes,shape,scale) : ...)
+
+

Where:

+
    +
  • nModes: number of modeled modes (40 max)
  • +
  • shape: shape of the resonator (0: square, 1: square with rounded corners, 2: round)
  • +
  • scale: scale of the resonator (0: small, 1: medium, 2: large)
  • +
+

Test

+
pm = library("physmodels.lib");
+modularInterpBody_test = 0.25, -0.15, 0.05 : pm.modularInterpBody(20, 1.0, 1.5);
+
+
+

(pm.)modularInterpStringModel

+

String instrument model with a modular body (see +modeInterpRes and +* https://ccrma.stanford.edu/~rmichon/3dPrintingModeling/).

+

Usage

+
modularInterpStringModel(length,pluckPosition,shape,scale,bodyExcitation,stringExcitation) : _
+
+

Where:

+
    +
  • stringLength: the length of the string in meters
  • +
  • pluckPosition: pluck position (0-1) (1 is on the bridge)
  • +
  • shape: shape of the resonator (0: square, 1: square with rounded corners, 2: round)
  • +
  • scale: scale of the resonator (0: small, 1: medium, 2: large)
  • +
  • bodyExcitation: excitation signal for the body
  • +
  • stringExcitation: excitation signal for the string
  • +
+

Test

+
pm = library("physmodels.lib");
+modularInterpStringModel_test = pm.modularInterpStringModel(0.9, 0.3, 1.0, 1.5, pm.impulseExcitation(button("pm.modularInterpStringModel/body")), pm.impulseExcitation(button("pm.modularInterpStringModel/string")));
+
+
+

(pm.)modularInterpInstr

+

String instrument with a modular body (see +modeInterpRes and +* https://ccrma.stanford.edu/~rmichon/3dPrintingModeling/).

+

Usage

+
modularInterpInstr(stringLength,pluckPosition,shape,scale,gain,tapBody,triggerString) : _
+
+

Where:

+
    +
  • stringLength: the length of the string in meters
  • +
  • pluckPosition: pluck position (0-1) (1 is on the bridge)
  • +
  • shape: shape of the resonator (0: square, 1: square with rounded corners, 2: round)
  • +
  • scale: scale of the resonator (0: small, 1: medium, 2: large)
  • +
  • gain: of the string excitation
  • +
  • tapBody: send an impulse in the body of the instrument where the string is connected (1 for on, 0 for off)
  • +
  • triggerString: trigger signal for the string (1 for on, 0 for off)
  • +
+

Test

+
pm = library("physmodels.lib");
+modularInterpInstr_test = pm.modularInterpInstr(0.9, 0.3, 1.0, 1.5, 0.8, button("pm.modularInterpInstr/body"), button("pm.modularInterpInstr/string"));
+
+
+

(pm.)modularInterpInstr_ui_MIDI

+

Ready-to-use MIDI-enabled string instrument with a modular body (see +modeInterpRes and +* https://ccrma.stanford.edu/~rmichon/3dPrintingModeling/) +with built-in UI.

+

Usage

+
modularInterpInstr_ui_MIDI : _
+
+

Test

+
pm = library("physmodels.lib");
+modularInterpInstr_ui_MIDI_test = pm.modularInterpInstr_ui_MIDI;
+
+

Bowed String Instruments

+

Low and high level basic string instruments parts. Most of the elements in +this section can be used in a bidirectional chain.

+
+

(pm.)bowTable

+

Extremely basic bow table that can be used to implement a wide range of +bow types for many different bowed string instruments (violin, cello, etc.).

+

Usage

+
excitation : bowTable(offset,slope) : _
+
+

Where:

+
    +
  • excitation: an excitation signal
  • +
  • offset: table offset
  • +
  • slope: table slope
  • +
+

Test

+
pm = library("physmodels.lib");
+bowTable_test = pm.bowTable(0.4, 0.1);
+
+
+

(pm.)violinBowTable

+

Violin bow table based on bowTable.

+

Usage

+
bowVelocity : violinBowTable(bowPressure) : _
+
+

Where:

+
    +
  • bowVelocity: velocity of the bow/excitation signal (0-1)
  • +
  • bowPressure: bow pressure on the string (0-1)
  • +
+

Test

+
pm = library("physmodels.lib");
+violinBowTable_test = pm.violinBowTable(0.4, 0.1);
+
+
+

(pm.)bowInteraction

+

Bidirectional block implementing the interaction of a bow in a +chain.

+

Usage

+
chain(... : stringSegment : bowInteraction(bowTable) : stringSegment : ...)
+
+

Where:

+
    +
  • bowTable: the bow table
  • +
+

Test

+
pm = library("physmodels.lib");
+bowInteraction_test = pm.bowInteraction((0.4, 0.05));
+
+
+

(pm.)violinBow

+

Bidirectional block implementing a violin bow and its interaction with +a string.

+

Usage

+
chain(... : stringSegment : violinBow(bowPressure,bowVelocity) : stringSegment : ...)
+
+

Where:

+
    +
  • bowVelocity: velocity of the bow / excitation signal (0-1)
  • +
  • bowPressure: bow pressure on the string (0-1)
  • +
+

Test

+
pm = library("physmodels.lib");
+violinBow_test = pm.violinBow(0.4, 0.05);
+
+
+

(pm.)violinBowedString

+

Violin bowed string bidirectional block with controllable bow position. +Terminations are not implemented in this model.

+

Usage

+
chain(nuts : violinBowedString(stringLength,bowPressure,bowVelocity,bowPosition) : bridge)
+
+

Where:

+
    +
  • stringLength: the length of the string in meters
  • +
  • bowVelocity: velocity of the bow / excitation signal (0-1)
  • +
  • bowPressure: bow pressure on the string (0-1)
  • +
  • bowPosition: the position of the bow on the string (0-1)
  • +
+

Test

+
pm = library("physmodels.lib");
+violinBowedString_test = 0.25, -0.15, 0.05 : pm.violinBowedString(0.82, 0.35, 0.2, 0.15);
+
+
+

(pm.)violinNuts

+

Bidirectional block implementing simple violin nuts. This function is +based on bridgeFilter.

+

Usage

+
_,_,_ : violinNuts
+
+

Typical use: chain(violinNuts : stringSegment : ...)

+

Test

+
pm = library("physmodels.lib");
+violinNuts_test = 0.25, -0.15, 0.05 : pm.violinNuts;
+
+
+

(pm.)violinBridge

+

Bidirectional block implementing a simple violin bridge. This function is +based on bridgeFilter.

+

Usage

+
chain(... : stringSegment : violinBridge
+
+

Test

+
pm = library("physmodels.lib");
+violinBridge_test = 0.25, -0.15, 0.05 : pm.violinBridge;
+
+
+

(pm.)violinBody

+

Bidirectional block implementing a simple violin body (just a simple +resonant lowpass filter).

+

Usage

+
chain(... : stringSegment : violinBridge : violinBody)
+
+

Test

+
pm = library("physmodels.lib");
+violinBody_test = 0.25, -0.15, 0.05 : pm.violinBody;
+
+
+

(pm.)violinModel

+

Ready-to-use simple violin physical model. This model implements a single +string. Additional strings should be created +by making a polyphonic application out of this function. Pitch is changed +by changing the length of the string (and not through a finger model).

+

Usage

+
violinModel(stringLength,bowPressure,bowVelocity,bowPosition) : _
+
+

Where:

+
    +
  • stringLength: the length of the string in meters
  • +
  • bowPressure: bow pressure on the string (0-1)
  • +
  • bowVelocity: velocity of the bow / excitation signal (0-1)
  • +
  • bowPosition: the position of the bow on the string (0-1)
  • +
+

Test

+
pm = library("physmodels.lib");
+violinModel_test = pm.violinModel(0.82, 0.4, 0.05, 0.15);
+
+
+

(pm.)violin_ui

+

Ready-to-use violin physical model with built-in UI.

+

Usage

+
violinModel_ui : _
+
+

Test

+
pm = library("physmodels.lib");
+violin_ui_test = pm.violinModel(0.82, 0.4, 0.05, 0.15);
+
+
+

(pm.)violin_ui_MIDI

+

Ready-to-use MIDI-enabled violin physical model with built-in UI.

+

Usage

+
violin_ui_MIDI : _
+
+

Test

+
pm = library("physmodels.lib");
+violin_ui_MIDI_test = pm.violin_ui_MIDI;
+
+

Wind Instruments

+

Low and high level basic wind instruments parts. Most of the elements in +this section can be used in a bidirectional chain.

+
+

(pm.)openTube

+

A tube segment without terminations (same as stringSegment).

+

Usage

+
chain(A : openTube(maxLength,length) : B)
+
+

Where:

+
    +
  • maxLength: the maximum length of the tube in meters (should be static)
  • +
  • length: the length of the tube in meters
  • +
+

Test

+
pm = library("physmodels.lib");
+openTube_test = 0.25, -0.15, 0.05 : pm.openTube(pm.maxLength, 0.9);
+
+
+

(pm.)reedTable

+

Extremely basic reed table that can be used to implement a wide range of +single reed types for many different instruments (saxophone, clarinet, etc.).

+

Usage

+
excitation : reedTable(offset,slope) : _
+
+

Where:

+
    +
  • excitation: an excitation signal
  • +
  • offset: table offset
  • +
  • slope: table slope
  • +
+

Test

+
pm = library("physmodels.lib");
+os = library("oscillators.lib");
+reedTable_test = os.osc(220) : pm.reedTable(0.4, 0.2);
+
+
+

(pm.)fluteJetTable

+

Extremely basic flute jet table.

+

Usage

+
excitation : fluteJetTable : _
+
+

Where:

+
    +
  • excitation: an excitation signal
  • +
+

Test

+
pm = library("physmodels.lib");
+os = library("oscillators.lib");
+fluteJetTable_test = os.osc(220) : pm.fluteJetTable;
+
+
+

(pm.)brassLipsTable

+

Simple brass lips/mouthpiece table. Since this implementation is very basic +and that the lips and tube of the instrument are coupled to each other, the +length of that tube must be provided here.

+

Usage

+
excitation : brassLipsTable(tubeLength,lipsTension) : _
+
+

Where:

+
    +
  • excitation: an excitation signal (can be DC)
  • +
  • tubeLength: length in meters of the tube connected to the mouthpiece
  • +
  • lipsTension: tension of the lips (0-1) (default: 0.5)
  • +
+

Test

+
pm = library("physmodels.lib");
+os = library("oscillators.lib");
+brassLipsTable_test = os.osc(220) : pm.brassLipsTable(0.3, 0.2);
+
+
+

(pm.)clarinetReed

+

Clarinet reed based on reedTable with controllable +stiffness.

+

Usage

+
excitation : clarinetReed(stiffness) : _
+
+

Where:

+
    +
  • excitation: an excitation signal
  • +
  • stiffness: reed stiffness (0-1)
  • +
+

Test

+
pm = library("physmodels.lib");
+os = library("oscillators.lib");
+clarinetReed_test = os.osc(440) : pm.clarinetReed(0.6);
+
+
+

(pm.)clarinetMouthPiece

+

Bidirectional block implementing a clarinet mouthpiece as well as the various +interactions happening with traveling waves. This element is ready to be +plugged to a tube...

+

Usage

+
chain(clarinetMouthPiece(reedStiffness,pressure) : tube : etc.)
+
+

Where:

+
    +
  • pressure: the pressure of the air flow (DC) created by the virtual performer (0-1). +This can also be any kind of signal that will directly injected in the mouthpiece +(e.g., breath noise, etc.).
  • +
  • reedStiffness: reed stiffness (0-1)
  • +
+

Test

+
pm = library("physmodels.lib");
+clarinetMouthPiece_test = 0.25, -0.15, 0.05 : pm.clarinetMouthPiece(0.6, 0.4);
+
+
+

(pm.)brassLips

+

Bidirectional block implementing a brass mouthpiece as well as the various +interactions happening with traveling waves. This element is ready to be +plugged to a tube...

+

Usage

+
chain(brassLips(tubeLength,lipsTension,pressure) : tube : etc.)
+
+

Where:

+
    +
  • tubeLength: length in meters of the tube connected to the mouthpiece
  • +
  • lipsTension: tension of the lips (0-1) (default: 0.5)
  • +
  • pressure: the pressure of the air flow (DC) created by the virtual performer (0-1). +This can also be any kind of signal that will directly injected in the mouthpiece +(e.g., breath noise, etc.).
  • +
+

Test

+
pm = library("physmodels.lib");
+brassLips_test = 0.25, -0.15, 0.05 : pm.brassLips(0.3, 0.2, 0.1);
+
+
+

(pm.)fluteEmbouchure

+

Bidirectional block implementing a flute embouchure as well as the various +interactions happening with traveling waves. This element is ready to be +plugged between tubes segments...

+

Usage

+
chain(... : tube : fluteEmbouchure(pressure) : tube : etc.)
+
+

Where:

+
    +
  • pressure: the pressure of the air flow (DC) created by the virtual +performer (0-1). +This can also be any kind of signal that will directly injected in the +mouthpiece (e.g., breath noise, etc.).
  • +
+

Test

+
pm = library("physmodels.lib");
+fluteEmbouchure_test = 0.25, -0.15, 0.05 : pm.fluteEmbouchure(0.5);
+
+
+

(pm.)wBell

+

Generic wind instrument bell bidirectional block that should be placed at +the end of a chain.

+

Usage

+
chain(... : wBell(opening))
+
+

Where:

+
    +
  • opening: the "opening" of bell (0-1)
  • +
+

Test

+
pm = library("physmodels.lib");
+wBell_test = 0.25, -0.15, 0.05 : pm.wBell(0.4);
+
+
+

(pm.)fluteHead

+

Simple flute head implementing waves reflexion.

+

Usage

+
_,_,_ : fluteHead
+
+

Typical use: chain(fluteHead : tube : ...)

+

Test

+
pm = library("physmodels.lib");
+fluteHead_test = 0.25, -0.15, 0.05 : pm.fluteHead;
+
+
+

(pm.)fluteFoot

+

Simple flute foot implementing waves reflexion and dispersion.

+

Usage

+
chain(... : tube : fluteFoot)
+
+

Test

+
pm = library("physmodels.lib");
+fluteFoot_test = 0.25, -0.15, 0.05 : pm.fluteFoot;
+
+
+

(pm.)clarinetModel

+

A simple clarinet physical model without tone holes (pitch is changed by +changing the length of the tube of the instrument).

+

Usage

+
clarinetModel(tubeLength,pressure,reedStiffness,bellOpening) : _
+
+

Where:

+
    +
  • tubeLength: the length of the tube in meters
  • +
  • pressure: the pressure of the air flow created by the virtual performer (0-1). +This can also be any kind of signal that will directly injected in the mouthpiece +(e.g., breath noise, etc.).
  • +
  • reedStiffness: reed stiffness (0-1)
  • +
  • bellOpening: the opening of bell (0-1)
  • +
+

Test

+
pm = library("physmodels.lib");
+clarinetModel_test = pm.clarinetModel(0.9, 0.4, 0.3, 0.2);
+
+
+

(pm.)clarinetModel_ui

+

Same as clarinetModel but with a built-in UI. This function +doesn't implement a virtual "blower", thus pressure remains an argument here.

+

Usage

+
clarinetModel_ui(pressure) : _
+
+

Where:

+
    +
  • pressure: the pressure of the air flow created by the virtual performer (0-1). +This can also be any kind of signal that will be directly injected in the mouthpiece +(e.g., breath noise, etc.).
  • +
+

Test

+
pm = library("physmodels.lib");
+clarinetModel_ui_test = pm.clarinetModel_ui(0.4);
+
+
+

(pm.)clarinet_ui

+

Ready-to-use clarinet physical model with built-in UI based on +clarinetModel.

+

Usage

+
clarinet_ui : _
+
+

Test

+
pm = library("physmodels.lib");
+clarinet_ui_test = pm.clarinet_ui;
+
+
+

(pm.)clarinet_ui_MIDI

+

Ready-to-use MIDI compliant clarinet physical model with built-in UI.

+

Usage

+
clarinet_ui_MIDI : _
+
+

Test

+
pm = library("physmodels.lib");
+clarinet_ui_MIDI_test = pm.clarinet_ui_MIDI;
+
+
+

(pm.)brassModel

+

A simple generic brass instrument physical model without pistons +(pitch is changed by changing the length of the tube of the instrument). +This model is kind of hard to control and might not sound very good if +bad parameters are given to it...

+

Usage

+
brassModel(tubeLength,lipsTension,mute,pressure) : _
+
+

Where:

+
    +
  • tubeLength: the length of the tube in meters
  • +
  • lipsTension: tension of the lips (0-1) (default: 0.5)
  • +
  • mute: mute opening at the end of the instrument (0-1) (default: 0.5)
  • +
  • pressure: the pressure of the air flow created by the virtual performer (0-1). +This can also be any kind of signal that will directly injected in the mouthpiece +(e.g., breath noise, etc.).
  • +
+

Test

+
pm = library("physmodels.lib");
+brassModel_test = pm.brassModel(0.9, 0.4, 0.2, 0.6);
+
+
+

(pm.)brassModel_ui

+

Same as brassModel but with a built-in UI. This function +doesn't implement a virtual "blower", thus pressure remains an argument here.

+

Usage

+
brassModel_ui(pressure) : _
+
+

Where:

+
    +
  • pressure: the pressure of the air flow created by the virtual performer (0-1). +This can also be any kind of signal that will be directly injected in the mouthpiece +(e.g., breath noise, etc.).
  • +
+

Test

+
pm = library("physmodels.lib");
+brassModel_ui_test = pm.brassModel_ui(0.4);
+
+
+

(pm.)brass_ui

+

Ready-to-use brass instrument physical model with built-in UI based on +brassModel.

+

Usage

+
brass_ui : _
+
+

Test

+
pm = library("physmodels.lib");
+brass_ui_test = pm.brass_ui;
+
+
+

(pm.)brass_ui_MIDI

+

Ready-to-use MIDI-controllable brass instrument physical model with built-in UI.

+

Usage

+
brass_ui_MIDI : _
+
+

Test

+
pm = library("physmodels.lib");
+brass_ui_MIDI_test = pm.brass_ui_MIDI;
+
+
+

(pm.)fluteModel

+

A simple generic flute instrument physical model without tone holes +(pitch is changed by changing the length of the tube of the instrument).

+

Usage

+
fluteModel(tubeLength,mouthPosition,pressure) : _
+
+

Where:

+
    +
  • tubeLength: the length of the tube in meters
  • +
  • mouthPosition: position of the mouth on the embouchure (0-1) (default: 0.5)
  • +
  • pressure: the pressure of the air flow created by the virtual performer (0-1). +This can also be any kind of signal that will directly injected in the mouthpiece +(e.g., breath noise, etc.).
  • +
+

Test

+
pm = library("physmodels.lib");
+fluteModel_test = pm.fluteModel(0.9, 0.4, 0.6);
+
+
+

(pm.)fluteModel_ui

+

Same as fluteModel but with a built-in UI. This function +doesn't implement a virtual "blower", thus pressure remains an argument here.

+

Usage

+
fluteModel_ui(pressure) : _
+
+

Where:

+
    +
  • pressure: the pressure of the air flow created by the virtual performer (0-1). +This can also be any kind of signal that will be directly injected in the mouthpiece +(e.g., breath noise, etc.).
  • +
+

Test

+
pm = library("physmodels.lib");
+fluteModel_ui_test = pm.fluteModel_ui(0.4);
+
+
+

(pm.)flute_ui

+

Ready-to-use flute physical model with built-in UI based on +fluteModel.

+

Usage

+
flute_ui : _
+
+

Test

+
pm = library("physmodels.lib");
+flute_ui_test = pm.flute_ui;
+
+
+

(pm.)flute_ui_MIDI

+

Ready-to-use MIDI-controllable flute physical model with built-in UI.

+

Usage

+
flute_ui_MIDI : _
+
+

Test

+
pm = library("physmodels.lib");
+flute_ui_MIDI_test = pm.flute_ui_MIDI;
+
+

Exciters

+

Various kind of excitation signal generators.

+
+

(pm.)impulseExcitation

+

Creates an impulse excitation of one sample.

+

Usage

+
gate = button('gate');
+impulseExcitation(gate) : chain;
+
+

Where:

+
    +
  • gate: a gate button
  • +
+

Test

+
pm = library("physmodels.lib");
+impulseExcitation_test = pm.impulseExcitation(button("pm.impulseExcitation/gate"));
+
+
+

(pm.)strikeModel

+

Creates a filtered noise excitation.

+

Usage

+
gate = button('gate');
+strikeModel(LPcutoff,HPcutoff,sharpness,gain,gate) : chain;
+
+

Where:

+
    +
  • HPcutoff: highpass cutoff frequency
  • +
  • LPcutoff: lowpass cutoff frequency
  • +
  • sharpness: sharpness of the attack and release (0-1)
  • +
  • gain: gain of the excitation
  • +
  • gate: a gate button/trigger signal (0/1)
  • +
+

Test

+
pm = library("physmodels.lib");
+strikeModel_test = pm.strikeModel(200, 4000, 0.5, 0.8, button("pm.strikeModel/gate"));
+
+
+

(pm.)strike

+

Strikes generator with controllable excitation position.

+

Usage

+
gate = button('gate');
+strike(exPos,sharpness,gain,gate) : chain;
+
+

Where:

+
    +
  • exPos: excitation position wiht 0: for max low freqs and 1: for max high +freqs. So, on membrane for example, 0 would be the middle and 1 the edge
  • +
  • sharpness: sharpness of the attack and release (0-1)
  • +
  • gain: gain of the excitation
  • +
  • gate: a gate button/trigger signal (0/1)
  • +
+

Test

+
pm = library("physmodels.lib");
+strike_test = pm.strike(0.4, 0.5, 0.8, button("pm.strike/gate"));
+
+
+

(pm.)pluckString

+

Creates a plucking excitation signal.

+

Usage

+
trigger = button('gate');
+pluckString(stringLength,cutoff,maxFreq,sharpness,gain,trigger)
+
+

Where:

+
    +
  • stringLength: length of the string to pluck
  • +
  • cutoff: cutoff ratio (1 for default)
  • +
  • maxFreq: max frequency ratio (1 for default)
  • +
  • sharpness: sharpness of the attack and release (1 for default)
  • +
  • gain: gain of the excitation (0-1)
  • +
  • trigger: trigger signal (1 for on, 0 for off)
  • +
+

Test

+
pm = library("physmodels.lib");
+pluckString_test = pm.pluckString(0.9, 1, 1, 1, 0.6, button("pm.pluckString/gate"));
+
+
+

(pm.)blower

+

A virtual blower creating a DC signal with some breath noise in it.

+

Usage

+
blower(pressure,breathGain,breathCutoff,vibratoFreq,vibratoGain) : _
+
+

Where:

+
    +
  • pressure: pressure (0-1)
  • +
  • breathGain: breath noise gain (0-1) (recommended: 0.005)
  • +
  • breathCutoff: breath cutoff frequency (Hz) (recommended: 2000)
  • +
  • vibratoFreq: vibrato frequency in Hz (recommended: 5)
  • +
  • vibratoGain: vibrato depth (0-1) (recommended: 0.2)
  • +
+

Test

+
pm = library("physmodels.lib");
+blower_test = pm.blower(0.5, 0.05, 2000, 5, 0.2);
+
+
+

(pm.)blower_ui

+

Same as blower but with a built-in UI.

+

Usage

+
blower : somethingToBeBlown
+
+

Test

+
pm = library("physmodels.lib");
+blower_ui_test = pm.blower_ui;
+
+ +

High and low level functions for modal synthesis of percussion instruments.

+
+

(pm.)djembeModel

+

Dirt-simple djembe modal physical model. Mode parameters are empirically +calculated and don't correspond to any measurements or 3D model. They +kind of sound good though :).

+

Usage

+
excitation : djembeModel(freq)
+
+

Where:

+
    +
  • excitation: excitation signal
  • +
  • freq: fundamental frequency of the bar
  • +
+

Test

+
pm = library("physmodels.lib");
+os = library("oscillators.lib");
+djembeModel_test = os.impulse : pm.djembeModel(110);
+
+
+

(pm.)djembe

+

Dirt-simple djembe modal physical model. Mode parameters are empirically +calculated and don't correspond to any measurements or 3D model. They +kind of sound good though :).

+

This model also implements a virtual "exciter".

+

Usage

+
djembe(freq,strikePosition,strikeSharpness,gain,trigger)
+
+

Where:

+
    +
  • freq: fundamental frequency of the model
  • +
  • strikePosition: strike position (0 for the middle of the membrane and + 1 for the edge)
  • +
  • strikeSharpness: sharpness of the strike (0-1, default: 0.5)
  • +
  • gain: gain of the strike
  • +
  • trigger: trigger signal (0: off, 1: on)
  • +
+

Test

+
pm = library("physmodels.lib");
+djembe_test = pm.djembe(110, 0.3, 0.5, 0.8, button("pm.djembe/gate"));
+
+
+

(pm.)djembe_ui_MIDI

+

Simple MIDI controllable djembe physical model with built-in UI.

+

Usage

+
djembe_ui_MIDI : _
+
+

Test

+
pm = library("physmodels.lib");
+djembe_ui_MIDI_test = pm.djembe_ui_MIDI;
+
+
+

(pm.)marimbaBarModel

+

Generic marimba tone bar modal model.

+

This model was generated using +mesh2faust from a 3D CAD model of a marimba tone bar +(libraries/modalmodels/marimbaBar). The corresponding CAD model is that +of a C2 tone bar (original fundamental frequency: ~65Hz). While +marimbaBarModel allows to translate the harmonic content of the generated +sound by providing a frequency (freq), mode transposition has limits and +the model will sound less and less like a marimba tone bar as it +diverges from C2. To make an accurate model of a marimba, we'd want to have +an independent model for each bar...

+

This model contains 5 excitation positions going linearly from the center +bottom to the center top of the bar. Obviously, a model with more excitation +position could be regenerated using mesh2faust.

+

Usage

+
excitation : marimbaBarModel(freq,exPos,t60,t60DecayRatio,t60DecaySlope)
+
+

Where:

+
    +
  • excitation: excitation signal
  • +
  • freq: fundamental frequency of the bar
  • +
  • exPos: excitation position (0-4)
  • +
  • t60: T60 in seconds (recommended value: 0.1)
  • +
  • t60DecayRatio: T60 decay ratio (recommended value: 1)
  • +
  • t60DecaySlope: T60 decay slope (recommended value: 5)
  • +
+

Test

+
pm = library("physmodels.lib");
+os = library("oscillators.lib");
+marimbaBarModel_test = os.impulse : pm.marimbaBarModel(220, 2, 0.1, 1, 5);
+
+
+

(pm.)marimbaResTube

+

Simple marimba resonance tube.

+

Usage

+
marimbaResTube(tubeLength,excitation)
+
+

Where:

+
    +
  • tubeLength: the length of the tube in meters
  • +
  • excitation: the excitation signal (audio in)
  • +
+

Test

+
pm = library("physmodels.lib");
+os = library("oscillators.lib");
+marimbaResTube_test = os.impulse : pm.marimbaResTube(0.5);
+
+
+

(pm.)marimbaModel

+

Simple marimba physical model implementing a single tone bar connected to +tube. This model is scalable and can be adapted to any size of bar/tube +(see marimbaBarModel to know more about the +limitations of this type of system).

+

Usage

+
excitation : marimbaModel(freq,exPos) : _
+
+

Where:

+
    +
  • excitation: the excitation signal
  • +
  • freq: the frequency of the bar/tube couple
  • +
  • exPos: excitation position (0-4)
  • +
+

Test

+
pm = library("physmodels.lib");
+os = library("oscillators.lib");
+marimbaModel_test = os.impulse : pm.marimbaModel(220, 2);
+
+
+

(pm.)marimba

+

Simple marimba physical model implementing a single tone bar connected to +tube. This model is scalable and can be adapted to any size of bar/tube +(see marimbaBarModel to know more about the +limitations of this type of system).

+

This function also implements a virtual exciter to drive the model.

+

Usage

+
marimba(freq,strikePosition,strikeCutoff,strikeSharpness,gain,trigger) : _
+
+

Where:

+
    +
  • freq: the frequency of the bar/tube couple
  • +
  • strikePosition: strike position (0-4)
  • +
  • strikeCutoff: cutoff frequency of the strike generator (recommended: ~7000 Hz)
  • +
  • strikeSharpness: sharpness of the strike (recommended: ~0.25)
  • +
  • gain: gain of the strike (0-1)
  • +
  • trigger: signal (0: off, 1: on)
  • +
+

Test

+
pm = library("physmodels.lib");
+marimba_test = pm.marimba(220, 0.4, 1, 0.5, 0.8, button("pm.marimba/gate"));
+
+
+

(pm.)marimba_ui_MIDI

+

Simple MIDI controllable marimba physical model with built-in UI +implementing a single tone bar connected to +tube. This model is scalable and can be adapted to any size of bar/tube +(see marimbaBarModel to know more about the +limitations of this type of system).

+

Usage

+
marimba_ui_MIDI : _
+
+

Test

+
pm = library("physmodels.lib");
+marimba_ui_MIDI_test = pm.marimba_ui_MIDI;
+
+
+

(pm.)churchBellModel

+

Generic church bell modal model generated by mesh2faust from +libraries/modalmodels/churchBell.

+

Modeled after T. Rossing and R. Perrin, Vibrations of Bells, Applied +Acoustics 2, 1987.

+

Model height is 301 mm.

+

This model contains 7 excitation positions going linearly from the +bottom to the top of the bell. Obviously, a model with more excitation +position could be regenerated using mesh2faust.

+

Usage

+
excitation : churchBellModel(nModes,exPos,t60,t60DecayRatio,t60DecaySlope)
+
+

Where:

+
    +
  • excitation: the excitation signal
  • +
  • nModes: number of synthesized modes (max: 50)
  • +
  • exPos: excitation position (0-6)
  • +
  • t60: T60 in seconds (recommended value: 0.1)
  • +
  • t60DecayRatio: T60 decay ratio (recommended value: 1)
  • +
  • t60DecaySlope: T60 decay slope (recommended value: 5)
  • +
+

Test

+
pm = library("physmodels.lib");
+os = library("oscillators.lib");
+churchBellModel_test = os.impulse : pm.churchBellModel(50, 0, 30, 1, 2.5);
+
+
+

(pm.)churchBell

+

Generic church bell modal model.

+

Modeled after T. Rossing and R. Perrin, Vibrations of Bells, Applied +Acoustics 2, 1987.

+

Model height is 301 mm.

+

This model contains 7 excitation positions going linearly from the +bottom to the top of the bell. Obviously, a model with more excitation +position could be regenerated using mesh2faust.

+

This function also implements a virtual exciter to drive the model.

+

Usage

+
churchBell(strikePosition,strikeCutoff,strikeSharpness,gain,trigger) : _
+
+

Where:

+
    +
  • strikePosition: strike position (0-6)
  • +
  • strikeCutoff: cutoff frequency of the strike generator (recommended: ~7000 Hz)
  • +
  • strikeSharpness: sharpness of the strike (recommended: ~0.25)
  • +
  • gain: gain of the strike (0-1)
  • +
  • trigger: signal (0: off, 1: on)
  • +
+

Test

+
pm = library("physmodels.lib");
+churchBell_test = pm.churchBell(0.4, 2000, 0.5, 0.8, button("pm.churchBell/gate"));
+
+
+

(pm.)churchBell_ui

+

Church bell physical model based on churchBell with +built-in UI.

+

Usage

+
churchBell_ui : _
+
+

Test

+
pm = library("physmodels.lib");
+churchBell_ui_test = pm.churchBell_ui;
+
+
+

(pm.)englishBellModel

+

English church bell modal model generated by mesh2faust from +libraries/modalmodels/englishBell.

+

Modeled after D.Bartocha and Baron, Influence of Tin Bronze Melting and +Pouring Parameters on Its Properties and Bell' Tone, Archives of Foundry +Engineering, 2016.

+

Model height is 1 m.

+

This model contains 7 excitation positions going linearly from the +bottom to the top of the bell. Obviously, a model with more excitation +position could be regenerated using mesh2faust.

+

Usage

+
excitation : englishBellModel(nModes,exPos,t60,t60DecayRatio,t60DecaySlope)
+
+

Where:

+
    +
  • excitation: the excitation signal
  • +
  • nModes: number of synthesized modes (max: 50)
  • +
  • exPos: excitation position (0-6)
  • +
  • t60: T60 in seconds (recommended value: 0.1)
  • +
  • t60DecayRatio: T60 decay ratio (recommended value: 1)
  • +
  • t60DecaySlope: T60 decay slope (recommended value: 5)
  • +
+

Test

+
pm = library("physmodels.lib");
+os = library("oscillators.lib");
+englishBellModel_test = os.impulse : pm.englishBellModel(50, 0, 30, 1, 3);
+
+
+

(pm.)englishBell

+

English church bell modal model.

+

Modeled after D.Bartocha and Baron, Influence of Tin Bronze Melting and +Pouring Parameters on Its Properties and Bell' Tone, Archives of Foundry +Engineering, 2016.

+

Model height is 1 m.

+

This model contains 7 excitation positions going linearly from the +bottom to the top of the bell. Obviously, a model with more excitation +position could be regenerated using mesh2faust.

+

This function also implements a virtual exciter to drive the model.

+

Usage

+
englishBell(strikePosition,strikeCutoff,strikeSharpness,gain,trigger) : _
+
+

Where:

+
    +
  • strikePosition: strike position (0-6)
  • +
  • strikeCutoff: cutoff frequency of the strike generator (recommended: ~7000 Hz)
  • +
  • strikeSharpness: sharpness of the strike (recommended: ~0.25)
  • +
  • gain: gain of the strike (0-1)
  • +
  • trigger: signal (0: off, 1: on)
  • +
+

Test

+
pm = library("physmodels.lib");
+englishBell_test = pm.englishBell(0.4, 2000, 0.5, 0.8, button("pm.englishBell/gate"));
+
+
+

(pm.)englishBell_ui

+

English church bell physical model based on englishBell with +built-in UI.

+

Usage

+
englishBell_ui : _
+
+

Test

+
pm = library("physmodels.lib");
+englishBell_ui_test = pm.englishBell_ui;
+
+
+

(pm.)frenchBellModel

+

French church bell modal model generated by mesh2faust from +libraries/modalmodels/frenchBell.

+

Modeled after D.Bartocha and Baron, Influence of Tin Bronze Melting and +Pouring Parameters on Its Properties and Bell' Tone, Archives of Foundry +Engineering, 2016.

+

Model height is 1 m.

+

This model contains 7 excitation positions going linearly from the +bottom to the top of the bell. Obviously, a model with more excitation +position could be regenerated using mesh2faust.

+

Usage

+
excitation : frenchBellModel(nModes,exPos,t60,t60DecayRatio,t60DecaySlope)
+
+

Where:

+
    +
  • excitation: the excitation signal
  • +
  • nModes: number of synthesized modes (max: 50)
  • +
  • exPos: excitation position (0-6)
  • +
  • t60: T60 in seconds (recommended value: 0.1)
  • +
  • t60DecayRatio: T60 decay ratio (recommended value: 1)
  • +
  • t60DecaySlope: T60 decay slope (recommended value: 5)
  • +
+

Test

+
pm = library("physmodels.lib");
+os = library("oscillators.lib");
+frenchBellModel_test = os.impulse : pm.frenchBellModel(50, 0, 30, 1, 3);
+
+
+

(pm.)frenchBell

+

French church bell modal model.

+

Modeled after D.Bartocha and Baron, Influence of Tin Bronze Melting and +Pouring Parameters on Its Properties and Bell' Tone, Archives of Foundry +Engineering, 2016.

+

Model height is 1 m.

+

This model contains 7 excitation positions going linearly from the +bottom to the top of the bell. Obviously, a model with more excitation +position could be regenerated using mesh2faust.

+

This function also implements a virtual exciter to drive the model.

+

Usage

+
+

Where:

+
    +
  • strikePosition: strike position (0-6)
  • +
  • strikeCutoff: cutoff frequency of the strike generator (recommended: ~7000 Hz)
  • +
  • strikeSharpness: sharpness of the strike (recommended: ~0.25)
  • +
  • gain: gain of the strike (0-1)
  • +
  • trigger: signal (0: off, 1: on)
  • +
+

Test

+
pm = library("physmodels.lib");
+frenchBell_test = pm.frenchBell(0.4, 2000, 0.5, 0.8, button("pm.frenchBell/gate"));
+
+
+

(pm.)frenchBell_ui

+

French church bell physical model based on frenchBell with +built-in UI.

+

Usage

+
frenchBell_ui : _
+
+

Test

+
pm = library("physmodels.lib");
+frenchBell_ui_test = pm.frenchBell_ui;
+
+
+

(pm.)germanBellModel

+

German church bell modal model generated by mesh2faust from +libraries/modalmodels/germanBell.

+

Modeled after D.Bartocha and Baron, Influence of Tin Bronze Melting and +Pouring Parameters on Its Properties and Bell' Tone, Archives of Foundry +Engineering, 2016.

+

Model height is 1 m.

+

This model contains 7 excitation positions going linearly from the +bottom to the top of the bell. Obviously, a model with more excitation +position could be regenerated using mesh2faust.

+

Usage

+
excitation : germanBellModel(nModes,exPos,t60,t60DecayRatio,t60DecaySlope)
+
+

Where:

+
    +
  • excitation: the excitation signal
  • +
  • nModes: number of synthesized modes (max: 50)
  • +
  • exPos: excitation position (0-6)
  • +
  • t60: T60 in seconds (recommended value: 0.1)
  • +
  • t60DecayRatio: T60 decay ratio (recommended value: 1)
  • +
  • t60DecaySlope: T60 decay slope (recommended value: 5)
  • +
+

Test

+
pm = library("physmodels.lib");
+os = library("oscillators.lib");
+germanBellModel_test = os.impulse : pm.germanBellModel(50, 0, 30, 1, 2.5);
+
+
+

(pm.)germanBell

+

German church bell modal model.

+

Modeled after D.Bartocha and Baron, Influence of Tin Bronze Melting and +Pouring Parameters on Its Properties and Bell' Tone, Archives of Foundry +Engineering, 2016.

+

Model height is 1 m.

+

This model contains 7 excitation positions going linearly from the +bottom to the top of the bell. Obviously, a model with more excitation +position could be regenerated using mesh2faust.

+

This function also implements a virtual exciter to drive the model.

+

Usage

+
germanBell(strikePosition,strikeCutoff,strikeSharpness,gain,trigger) : _
+
+

Where:

+
    +
  • strikePosition: strike position (0-6)
  • +
  • strikeCutoff: cutoff frequency of the strike generator (recommended: ~7000 Hz)
  • +
  • strikeSharpness: sharpness of the strike (recommended: ~0.25)
  • +
  • gain: gain of the strike (0-1)
  • +
  • trigger: signal (0: off, 1: on)
  • +
+

Test

+
pm = library("physmodels.lib");
+germanBell_test = pm.germanBell(0.4, 2000, 0.5, 0.8, button("pm.germanBell/gate"));
+
+
+

(pm.)germanBell_ui

+

German church bell physical model based on germanBell with +built-in UI.

+

Usage

+
germanBell_ui : _
+
+

Test

+
pm = library("physmodels.lib");
+germanBell_ui_test = pm.germanBell_ui;
+
+
+

(pm.)russianBellModel

+

Russian church bell modal model generated by mesh2faust from +libraries/modalmodels/russianBell.

+

Modeled after D.Bartocha and Baron, Influence of Tin Bronze Melting and +Pouring Parameters on Its Properties and Bell' Tone, Archives of Foundry +Engineering, 2016.

+

Model height is 2 m.

+

This model contains 7 excitation positions going linearly from the +bottom to the top of the bell. Obviously, a model with more excitation +position could be regenerated using mesh2faust.

+

Usage

+
excitation : russianBellModel(nModes,exPos,t60,t60DecayRatio,t60DecaySlope)
+
+

Where:

+
    +
  • excitation: the excitation signal
  • +
  • nModes: number of synthesized modes (max: 50)
  • +
  • exPos: excitation position (0-6)
  • +
  • t60: T60 in seconds (recommended value: 0.1)
  • +
  • t60DecayRatio: T60 decay ratio (recommended value: 1)
  • +
  • t60DecaySlope: T60 decay slope (recommended value: 5)
  • +
+

Test

+
pm = library("physmodels.lib");
+os = library("oscillators.lib");
+russianBellModel_test = os.impulse : pm.russianBellModel(50, 0, 30, 1, 3);
+
+
+

(pm.)russianBell

+

Russian church bell modal model.

+

Modeled after D.Bartocha and Baron, Influence of Tin Bronze Melting and +Pouring Parameters on Its Properties and Bell' Tone, Archives of Foundry +Engineering, 2016.

+

Model height is 2 m.

+

This model contains 7 excitation positions going linearly from the +bottom to the top of the bell. Obviously, a model with more excitation +position could be regenerated using mesh2faust.

+

This function also implements a virtual exciter to drive the model.

+

Usage

+
russianBell(strikePosition,strikeCutoff,strikeSharpness,gain,trigger) : _
+
+

Where:

+
    +
  • strikePosition: strike position (0-6)
  • +
  • strikeCutoff: cutoff frequency of the strike generator (recommended: ~7000 Hz)
  • +
  • strikeSharpness: sharpness of the strike (recommended: ~0.25)
  • +
  • gain: gain of the strike (0-1)
  • +
  • trigger: signal (0: off, 1: on)
  • +
+

Test

+
pm = library("physmodels.lib");
+russianBell_test = pm.russianBell(0.4, 2000, 0.5, 0.8, button("pm.russianBell/gate"));
+
+
+

(pm.)russianBell_ui

+

Russian church bell physical model based on russianBell with +built-in UI.

+

Usage

+
russianBell_ui : _
+
+

Test

+
pm = library("physmodels.lib");
+russianBell_ui_test = pm.russianBell_ui;
+
+
+

(pm.)standardBellModel

+

Standard church bell modal model generated by mesh2faust from +libraries/modalmodels/standardBell.

+

Modeled after T. Rossing and R. Perrin, Vibrations of Bells, Applied +Acoustics 2, 1987.

+

Model height is 1.8 m.

+

This model contains 7 excitation positions going linearly from the +bottom to the top of the bell. Obviously, a model with more excitation +position could be regenerated using mesh2faust.

+

Usage

+
excitation : standardBellModel(nModes,exPos,t60,t60DecayRatio,t60DecaySlope)
+
+

Where:

+
    +
  • excitation: the excitation signal
  • +
  • nModes: number of synthesized modes (max: 50)
  • +
  • exPos: excitation position (0-6)
  • +
  • t60: T60 in seconds (recommended value: 0.1)
  • +
  • t60DecayRatio: T60 decay ratio (recommended value: 1)
  • +
  • t60DecaySlope: T60 decay slope (recommended value: 5)
  • +
+

Test

+
pm = library("physmodels.lib");
+os = library("oscillators.lib");
+standardBellModel_test = os.impulse : pm.standardBellModel(50, 0, 30, 1, 2.5);
+
+
+

(pm.)standardBell

+

Standard church bell modal model.

+

Modeled after T. Rossing and R. Perrin, Vibrations of Bells, Applied +Acoustics 2, 1987.

+

Model height is 1.8 m.

+

This model contains 7 excitation positions going linearly from the +bottom to the top of the bell. Obviously, a model with more excitation +position could be regenerated using mesh2faust.

+

This function also implements a virtual exciter to drive the model.

+

Usage

+
standardBell(strikePosition,strikeCutoff,strikeSharpness,gain,trigger) : _
+
+

Where:

+
    +
  • strikePosition: strike position (0-6)
  • +
  • strikeCutoff: cutoff frequency of the strike generator (recommended: ~7000 Hz)
  • +
  • strikeSharpness: sharpness of the strike (recommended: ~0.25)
  • +
  • gain: gain of the strike (0-1)
  • +
  • trigger signal (0: off, 1: on)
  • +
+

Test

+
pm = library("physmodels.lib");
+standardBell_test = pm.standardBell(0.4, 2000, 0.5, 0.8, button("pm.standardBell/gate"));
+
+
+

(pm.)standardBell_ui

+

Standard church bell physical model based on standardBell with +built-in UI.

+

Usage

+
standardBell_ui : _
+
+

Test

+
pm = library("physmodels.lib");
+standardBell_ui_test = pm.standardBell_ui;
+
+

Vocal Synthesis

+

Vocal synthesizer functions (source/filter, fof, etc.).

+
+

(pm.)formantValues

+

Formant data values in an environment.

+

The formant data used here come from the CSOUND manual +* http://www.csounds.com/manual/html/.

+

Usage

+
ba.take(j+1,formantValues.f(i)) : _
+ba.take(j+1,formantValues.g(i)) : _
+ba.take(j+1,formantValues.bw(i)) : _
+
+

Where:

+
    +
  • i: formant number
  • +
  • j: (voiceType*nFormants)+vowel
  • +
  • voiceType: the voice type (0: alto, 1: bass, 2: countertenor, 3: +soprano, 4: tenor)
  • +
  • vowel: the vowel (0: a, 1: e, 2: i, 3: o, 4: u)
  • +
+

Test

+
pm = library("physmodels.lib");
+formantValues_test = pm.formantValues.f(0);
+
+
+

(pm.)voiceGender

+

Calculate the gender for the provided voiceType value. (0: male, 1: female)

+

Usage

+
voiceGender(voiceType) : _
+
+

Where:

+
    +
  • voiceType: the voice type (0: alto, 1: bass, 2: countertenor, 3: soprano, 4: tenor)
  • +
+

Test

+
pm = library("physmodels.lib");
+voiceGender_test = pm.voiceGender(0);
+
+
+

(pm.)skirtWidthMultiplier

+

Calculates value to multiply bandwidth to obtain skirtwidth +for a FOF filter.

+

Usage

+
skirtWidthMultiplier(vowel,freq,gender) : _
+
+

Where:

+
    +
  • vowel: the vowel (0: a, 1: e, 2: i, 3: o, 4: u)
  • +
  • freq: the fundamental frequency of the excitation signal
  • +
  • gender: gender of the voice used in the fof filter (0: male, 1: female)
  • +
+

Test

+
pm = library("physmodels.lib");
+skirtWidthMultiplier_test = pm.skirtWidthMultiplier(0, 220, 0);
+
+
+

(pm.)autobendFreq

+

Autobends the center frequencies of formants 1 and 2 based on +the fundamental frequency of the excitation signal and leaves +all other formant frequencies unchanged. Ported from chant-lib.

+

Usage

+
_ : autobendFreq(n,freq,voiceType) : _
+
+

Where:

+
    +
  • n: formant index
  • +
  • freq: the fundamental frequency of the excitation signal
  • +
  • voiceType: the voice type (0: alto, 1: bass, 2: countertenor, 3: soprano, 4: tenor)
  • +
  • input is the center frequency of the corresponding formant
  • +
+

Test

+
pm = library("physmodels.lib");
+autobendFreq_test = 440 : pm.autobendFreq(0, 220, 0);
+
+

References

+ +
+

(pm.)vocalEffort

+

Changes the gains of the formants based on the fundamental +frequency of the excitation signal. Higher formants are +reinforced for higher fundamental frequencies. +Ported from chant-lib.

+

Usage

+
_ : vocalEffort(freq,gender) : _
+
+

Where:

+
    +
  • freq: the fundamental frequency of the excitation signal
  • +
  • gender: the gender of the voice type (0: male, 1: female)
  • +
  • input is the linear amplitude of the formant
  • +
+

Test

+
pm = library("physmodels.lib");
+vocalEffort_test = 1 : pm.vocalEffort(440, 0);
+
+

References

+ +
+

(pm.)fof

+

Function to generate a single Formant-Wave-Function.

+

Usage

+
_ : fof(fc,bw,sw,g) : _
+
+

Where:

+
    +
  • fc: formant center frequency,
  • +
  • bw: formant bandwidth (Hz),
  • +
  • sw: formant skirtwidth (Hz)
  • +
  • g: linear scale factor (g=1 gives 0dB amplitude response at fc)
  • +
  • input is an impulse signal to excite filter
  • +
+

Test

+
pm = library("physmodels.lib");
+os = library("oscillators.lib");
+fof_test = pm.fof(0.3, 440, 880, 0.5) + os.osc(110) * 0.001;
+
+

References

+ +
+

(pm.)fofSH

+

FOF with sample and hold used on bw and a parameter +used in the filter-cycling FOF function fofCycle.

+

Usage

+
_ : fofSH(fc,bw,a,g) : _
+
+

Where:

+
    +
  • fc: formant center frequency
  • +
  • bw: formant bandwidth (Hz)
  • +
  • a: formant skirtwidth (Hz)
  • +
  • g: linear scale factor
  • +
+

Test

+
pm = library("physmodels.lib");
+os = library("oscillators.lib");
+fofSH_test = pm.fofSH(0.3, 440, 880, 0.5) + os.osc(110) * 0.001;
+
+

References

+ +
+

(pm.)fofCycle

+

FOF implementation where time-varying filter parameter noise is +mitigated by using a cycle of n sample and hold FOF filters.

+

Usage

+
_ : fofCycle(fc,bw,a,g,n) : _
+
+

Where:

+
    +
  • fc: center frequency of the filter in Hz
  • +
  • bw: bandwidth of the filter in Hz
  • +
  • a: attack bandwidth / skirt width in Hz
  • +
  • g: linear gain multiplier
  • +
  • n: the number of FOF filters to cycle through
  • +
+

Test

+
pm = library("physmodels.lib");
+os = library("oscillators.lib");
+fofCycle_test = pm.fofCycle(0.3, 440, 880, 0.5, 3) + os.osc(110) * 0.001;
+
+

References

+ +
+

(pm.)fofSmooth

+

FOF implementation where time-varying filter parameter +noise is mitigated by lowpass filtering the filter +parameters bw and a with smooth.

+

Usage

+
_ : fofSmooth(fc,bw,sw,g,tau) : _
+
+

Where:

+
    +
  • fc: center frequency of the filter in Hz
  • +
  • bw: bandwidth of the filter in Hz
  • +
  • sw: skirt width in Hz
  • +
  • g: linear gain multiplier
  • +
  • tau: the desired smoothing time constant in seconds
  • +
+

Test

+
pm = library("physmodels.lib");
+os = library("oscillators.lib");
+fofSmooth_test = pm.fofSmooth(0.3, 440, 880, 0.5, 0.2) + os.osc(110) * 0.001;
+
+
+

(pm.)formantFilterFofCycle

+

Formant filter based on a single FOF filter. +Formant parameters are linearly interpolated allowing to go smoothly from +one vowel to another. A cycle of n fof filters with sample-and-hold is +used so that the fof filter parameters can be varied in realtime. +This technique is more robust but more computationally expensive than +formantFilterFofSmooth. Voice type can be +selected but must correspond to +the frequency range of the provided source to be realistic.

+

Usage

+
_ : formantFilterFofCycle(voiceType,vowel,nFormants,i,freq) : _
+
+

Where:

+
    +
  • voiceType: the voice type (0: alto, 1: bass, 2: countertenor, + 3: soprano, 4: tenor)
  • +
  • vowel: the vowel (0: a, 1: e, 2: i, 3: o, 4: u)
  • +
  • nFormants: number of formant regions in frequency domain, typically 5
  • +
  • i: formant number (i.e. 0 - 4) used to index formant data value arrays
  • +
  • freq: fundamental frequency of excitation signal. Used to calculate + rise time of envelope
  • +
+

Test

+
pm = library("physmodels.lib");
+os = library("oscillators.lib");
+formantFilterFofCycle_test = (os.osc(110) : pm.formantFilterFofCycle(1, 1, 5, 1, 200)) + os.osc(55) * 0.001;
+
+
+

(pm.)formantFilterFofSmooth

+

Formant filter based on a single FOF filter. +Formant parameters are linearly interpolated allowing to go smoothly from +one vowel to another. FOF filter parameters are lowpass filtered +to mitigate possible noise from varying them in realtime. +Voice type can be selected but must correspond to +the frequency range of the provided source to be realistic.

+

Usage

+
_ : formantFilterFofSmooth(voiceType,vowel,nFormants,i,freq) : _
+
+

Where:

+
    +
  • voiceType: the voice type (0: alto, 1: bass, 2: countertenor, + 3: soprano, 4: tenor)
  • +
  • vowel: the vowel (0: a, 1: e, 2: i, 3: o, 4: u)
  • +
  • nFormants: number of formant regions in frequency domain, typically 5
  • +
  • i: formant number (i.e. 1 - 5) used to index formant data value arrays
  • +
  • freq: fundamental frequency of excitation signal. Used to calculate +rise time of envelope
  • +
+

Test

+
pm = library("physmodels.lib");
+os = library("oscillators.lib");
+formantFilterFofSmooth_test = os.osc(110) : pm.formantFilterFofSmooth(0, 0, 5, 0, 200);
+
+
+

(pm.)formantFilterBP

+

Formant filter based on a single resonant bandpass filter. +Formant parameters are linearly interpolated allowing to go smoothly from +one vowel to another. Voice type can be selected but must correspond to +the frequency range of the provided source to be realistic.

+

Usage

+
_ : formantFilterBP(voiceType,vowel,nFormants,i,freq) : _
+
+

Where:

+
    +
  • voiceType: the voice type (0: alto, 1: bass, 2: countertenor, 3: soprano, 4: tenor)
  • +
  • vowel: the vowel (0: a, 1: e, 2: i, 3: o, 4: u)
  • +
  • nFormants: number of formant regions in frequency domain, typically 5
  • +
  • i: formant index used to index formant data value arrays
  • +
  • freq: fundamental frequency of excitation signal.
  • +
+

Test

+
pm = library("physmodels.lib");
+os = library("oscillators.lib");
+formantFilterBP_test = os.osc(110) : pm.formantFilterBP(0, 0, 5, 0, 200);
+
+
+

(pm.)formantFilterbank

+

Formant filterbank which can use different types of filterbank +functions and different excitation signals. Formant parameters are +linearly interpolated allowing to go smoothly from one vowel to another. +Voice type can be selected but must correspond to the frequency range +of the provided source to be realistic.

+

Usage

+
_ : formantFilterbank(voiceType,vowel,formantGen,freq) : _
+
+

Where:

+
    +
  • voiceType: the voice type (0: alto, 1: bass, 2: countertenor, 3: soprano, 4: tenor)
  • +
  • vowel: the vowel (0: a, 1: e, 2: i, 3: o, 4: u)
  • +
  • formantGen: the specific formant filterbank function + (i.e. FormantFilterbankBP, FormantFilterbankFof,...)
  • +
  • freq: fundamental frequency of excitation signal. Needed for FOF + version to calculate rise time of envelope
  • +
+

Test

+
pm = library("physmodels.lib");
+os = library("oscillators.lib");
+formantFilterbank_test = os.osc(110) : pm.formantFilterbank(0, 0, pm.formantFilterBP, 200);
+
+
+

(pm.)formantFilterbankFofCycle

+

Formant filterbank based on a bank of fof filters. +Formant parameters are linearly interpolated allowing to go smoothly from +one vowel to another. Voice type can be selected but must correspond to +the frequency range of the provided source to be realistic.

+

Usage

+
_ : formantFilterbankFofCycle(voiceType,vowel,freq) : _
+
+

Where:

+
    +
  • voiceType: the voice type (0: alto, 1: bass, 2: countertenor, 3: soprano, 4: tenor)
  • +
  • vowel: the vowel (0: a, 1: e, 2: i, 3: o, 4: u)
  • +
  • freq: the fundamental frequency of the excitation signal. Needed to calculate the skirtwidth +of the FOF envelopes and for the autobendFreq and vocalEffort functions
  • +
+

Test

+
pm = library("physmodels.lib");
+os = library("oscillators.lib");
+formantFilterbankFofCycle_test = (os.osc(110) : pm.formantFilterbankFofCycle(1, 1, 200)) + os.osc(55) * 0.001;
+
+
+

(pm.)formantFilterbankFofSmooth

+

Formant filterbank based on a bank of fof filters. +Formant parameters are linearly interpolated allowing to go smoothly from +one vowel to another. Voice type can be selected but must correspond to +the frequency range of the provided source to be realistic.

+

Usage

+
_ : formantFilterbankFofSmooth(voiceType,vowel,freq) : _
+
+

Where:

+
    +
  • voiceType: the voice type (0: alto, 1: bass, 2: countertenor, 3: soprano, 4: tenor)
  • +
  • vowel: the vowel (0: a, 1: e, 2: i, 3: o, 4: u)
  • +
  • freq: the fundamental frequency of the excitation signal. Needed to +calculate the skirtwidth of the FOF envelopes and for the +autobendFreq and vocalEffort functions
  • +
+

Test

+
pm = library("physmodels.lib");
+os = library("oscillators.lib");
+formantFilterbankFofSmooth_test = os.osc(110) : pm.formantFilterbankFofSmooth(0, 0, 200);
+
+
+

(pm.)formantFilterbankBP

+

Formant filterbank based on a bank of resonant bandpass filters. +Formant parameters are linearly interpolated allowing to go smoothly from +one vowel to another. Voice type can be selected but must correspond to +the frequency range of the provided source to be realistic.

+

Usage

+
_ : formantFilterbankBP(voiceType,vowel,freq) : _
+
+

Where:

+
    +
  • voiceType: the voice type (0: alto, 1: bass, 2: countertenor, 3: soprano, 4: tenor)
  • +
  • vowel: the vowel (0: a, 1: e, 2: i, 3: o, 4: u)
  • +
  • freq: the fundamental frequency of the excitation signal. Needed for the autobendFreq and vocalEffort functions.
  • +
+

Test

+
pm = library("physmodels.lib");
+os = library("oscillators.lib");
+formantFilterbankBP_test = os.osc(110) : pm.formantFilterbankBP(0, 0, 200);
+
+
+

(pm.)SFFormantModel

+

Simple formant/vocal synthesizer based on a source/filter model. The source +and filterbank must be specified by the user. filterbank must take the same +input parameters as formantFilterbank (BP/FofCycle +/FofSmooth). +Formant parameters are linearly interpolated allowing to go smoothly from +one vowel to another. Voice type can be selected but must correspond to +the frequency range of the synthesized voice to be realistic.

+

Usage

+
SFFormantModel(voiceType,vowel,exType,freq,gain,source,filterbank,isFof) : _
+
+

Where:

+
    +
  • voiceType: the voice type (0: alto, 1: bass, 2: countertenor, 3: soprano, 4: tenor)
  • +
  • vowel: the vowel (0: a, 1: e, 2: i, 3: o, 4: u)
  • +
  • exType: voice vs. fricative sound ratio (0-1 where 1 is 100% fricative)
  • +
  • freq: the fundamental frequency of the source signal
  • +
  • gain: linear gain multiplier to multiply the source by
  • +
  • source: excitation signal generator used by the model
  • +
  • filterbank: formant filterbank function, typically one of + formantFilterbankBP, formantFilterbankFofCycle, or formantFilterbankFofSmooth
  • +
  • isFof: whether model is FOF based (0: no, 1: yes)
  • +
+

Test

+
pm = library("physmodels.lib");
+os = library("oscillators.lib");
+SFFormantModel_test = pm.SFFormantModel(0, 0, 0.2, 220, 0.7, os.lf_imptrain(220), pm.formantFilterbankFofCycle, 1);
+
+
+

(pm.)SFFormantModelFofCycle

+

Simple formant/vocal synthesizer based on a source/filter model. The source +is just a periodic impulse and the "filter" is a bank of FOF filters. +Formant parameters are linearly interpolated allowing to go smoothly from +one vowel to another. Voice type can be selected but must correspond to +the frequency range of the synthesized voice to be realistic. This model +does not work with noise in the source signal, so exType has been removed +and the model does not depend on SFFormantModel.

+

Usage

+
SFFormantModelFofCycle(voiceType,vowel,freq,gain) : _
+
+

Where:

+
    +
  • voiceType: the voice type (0: alto, 1: bass, 2: countertenor, 3: soprano, 4: tenor)
  • +
  • vowel: the vowel (0: a, 1: e, 2: i, 3: o, 4: u)
  • +
  • freq: the fundamental frequency of the source signal
  • +
  • gain: linear gain multiplier to multiply the source by
  • +
+

Test

+
pm = library("physmodels.lib");
+SFFormantModelFofCycle_test = pm.SFFormantModelFofCycle(0, 0, 220, 0.7);
+
+
+

(pm.)SFFormantModelFofSmooth

+

Simple formant/vocal synthesizer based on a source/filter model. The source +is just a periodic impulse and the "filter" is a bank of FOF filters. +Formant parameters are linearly interpolated allowing to go smoothly from +one vowel to another. Voice type can be selected but must correspond to +the frequency range of the synthesized voice to be realistic.

+

Usage

+
SFFormantModelFofSmooth(voiceType,vowel,freq,gain) : _
+
+

Where:

+
    +
  • voiceType: the voice type (0: alto, 1: bass, 2: countertenor, 3: soprano, 4: tenor)
  • +
  • vowel: the vowel (0: a, 1: e, 2: i, 3: o, 4: u)
  • +
  • freq: the fundamental frequency of the source signal
  • +
  • gain: linear gain multiplier to multiply the source by
  • +
+

Test

+
pm = library("physmodels.lib");
+SFFormantModelFofSmooth_test = pm.SFFormantModelFofSmooth(0, 0, 220, 0.7);
+
+
+

(pm.)SFFormantModelBP

+

Simple formant/vocal synthesizer based on a source/filter model. The source +is just a sawtooth wave and the "filter" is a bank of resonant bandpass filters. +Formant parameters are linearly interpolated allowing to go smoothly from +one vowel to another. Voice type can be selected but must correspond to +the frequency range of the synthesized voice to be realistic.

+

The formant data used here come from the CSOUND manual +* http://www.csounds.com/manual/html/.

+

Usage

+
SFFormantModelBP(voiceType,vowel,exType,freq,gain) : _
+
+

Where:

+
    +
  • voiceType: the voice type (0: alto, 1: bass, 2: countertenor, 3: soprano, 4: tenor)
  • +
  • vowel: the vowel (0: a, 1: e, 2: i, 3: o, 4: u)
  • +
  • exType: voice vs. fricative sound ratio (0-1 where 1 is 100% fricative)
  • +
  • freq: the fundamental frequency of the source signal
  • +
  • gain: linear gain multiplier to multiply the source by
  • +
+

Test

+
pm = library("physmodels.lib");
+SFFormantModelBP_test = pm.SFFormantModelBP(0, 0, 0.2, 220, 0.7);
+
+
+

(pm.)SFFormantModelFofCycle_ui

+

Ready-to-use source-filter vocal synthesizer with built-in user interface.

+

Usage

+
SFFormantModelFofCycle_ui : _
+
+

Test

+
pm = library("physmodels.lib");
+SFFormantModelFofCycle_ui_test = pm.SFFormantModelFofCycle_ui;
+
+
+

(pm.)SFFormantModelFofSmooth_ui

+

Ready-to-use source-filter vocal synthesizer with built-in user interface.

+

Usage

+
SFFormantModelFofSmooth_ui : _
+
+

Test

+
pm = library("physmodels.lib");
+SFFormantModelFofSmooth_ui_test = pm.SFFormantModelFofSmooth_ui;
+
+
+

(pm.)SFFormantModelBP_ui

+

Ready-to-use source-filter vocal synthesizer with built-in user interface.

+

Usage

+
SFFormantModelBP_ui : _
+
+

Test

+
pm = library("physmodels.lib");
+SFFormantModelBP_ui_test = pm.SFFormantModelBP_ui;
+
+
+

(pm.)SFFormantModelFofCycle_ui_MIDI

+

Ready-to-use MIDI-controllable source-filter vocal synthesizer.

+

Usage

+
SFFormantModelFofCycle_ui_MIDI : _
+
+

Test

+
pm = library("physmodels.lib");
+SFFormantModelFofCycle_ui_MIDI_test = pm.SFFormantModelFofCycle_ui_MIDI;
+
+
+

(pm.)SFFormantModelFofSmooth_ui_MIDI

+

Ready-to-use MIDI-controllable source-filter vocal synthesizer.

+

Usage

+
SFFormantModelFofSmooth_ui_MIDI : _
+
+

Test

+
pm = library("physmodels.lib");
+SFFormantModelFofSmooth_ui_MIDI_test = pm.SFFormantModelFofSmooth_ui_MIDI;
+
+
+

(pm.)SFFormantModelBP_ui_MIDI

+

Ready-to-use MIDI-controllable source-filter vocal synthesizer.

+

Usage

+
SFFormantModelBP_ui_MIDI : _
+
+

Test

+
pm = library("physmodels.lib");
+SFFormantModelBP_ui_MIDI_test = pm.SFFormantModelBP_ui_MIDI;
+
+

Misc Functions

+

Various miscellaneous functions.

+
+

(pm.)allpassNL

+

Bidirectional block adding nonlinearities in both directions in a chain. +Nonlinearities are created by modulating the coefficients of a passive +allpass filter by the signal it is processing.

+

Usage

+
chain(... : allpassNL(nonlinearity) : ...)
+
+

Where:

+
    +
  • nonlinearity: amount of nonlinearity to be added (0-1)
  • +
+

Test

+
pm = library("physmodels.lib");
+allpassNL_test = 0.25, -0.15, 0.05 : pm.allpassNL(0.4);
+
+
+

(pm.)modalModel

+

Implement multiple resonance modes using resonant bandpass filters.

+

Usage

+
_ : modalModel(n, freqs, t60s, gains) : _
+
+

Where:

+
    +
  • n: number of given modes
  • +
  • freqs : list of filter center frequencies
  • +
  • t60s : list of mode resonance durations (in seconds)
  • +
  • gains : list of mode gains (0-1)
  • +
+

For example, to generate a model with 2 modes (440 Hz and 660 Hz, a +fifth) where the higher one decays faster and is attenuated:

+
os.impulse : modalModel(2, (440, 660),
+                        (0.5, 0.25),
+                        (ba.db2linear(-1), ba.db2linear(-6)));
+
+

Test

+
pm = library("physmodels.lib");
+os = library("oscillators.lib");
+modalModel_test = os.impulse : pm.modalModel(3, (440,660,880), (0.5,0.4,0.3), (0.8,0.6,0.4));
+
+

Further reading: Grumiaux et. al., 2017: +Impulse-Response and CAD-Model-Based Physical Modeling in +Faust

+
+

(pm.)rk_solve

+

Solves the system of ordinary differential equations of any order using +the explicit Runge-Kutta methods.

+

Usage

+
rk_solve(ts,ks, ni,h, eq,iv) : si.bus(outputs(eq))
+
+

Where:

+
    +
  • ts,ks : the Butcher tableau (see below)
  • +
  • ni : number of iterations at each tick, compile time constant + ni > 1 can improve accuracy but will degrade performance
  • +
  • h : time step, run time constant, e.g. 1/ma.SR
  • +
  • eq : list of derivative functions
  • +
  • iv : list of initial values
  • +
+

rk_solve() with the "standard" 1-4 tableaux and ni = 1:

+
rk_solve_1 = rk_solve((0), (1), 1);
+rk_solve_2 = rk_solve((0,1/2), (1/2, 0,1), 1);
+rk_solve_3 = rk_solve((0,1/2,1), (1/2,-1,2, 1/6,2/3,1/6), 1);
+rk_solve_4 = rk_solve((0,1/2,1/2,1), (1/2,0,1/2,0,0,1, 1/6,1/3,1/3,1/6), 1);
+
+

Test

+
pm = library("physmodels.lib");
+ma = library("maths.lib");
+rk_solve_test = pm.rk_solve((0), (1), 1, 1.0/ma.SR, eq, (1)) with { eq(t,x) = -x; };
+
+

Example test program

+

Suppose we have a system of differential equations:

+
dx/dt = dx_dt(t,x,y,z)
+dy/dt = dy_dt(t,x,y,z)
+dz/dt = dz_dt(t,x,y,z)
+
+

with initial conditions:

+
   x(0) = x0
+   y(0) = y0
+   z(0) = z0
+
+

and we want to solve it using this Butcher tableau:

+
 0 |
+c2 | a21
+c3 | a31 a32
+c4 | a41 a42 a43
+-------------------
+   | b1  b1  b3  b4
+
+
EQ(t,x,y,z) = dx_dt(t,x,y,z),
+              dy_dt(t,x,y,z),
+              dz_dt(t,x,y,z);
+
+IV = x0, y0, z0;
+
+TS = 0, c2, c3, c4;
+KS = a21,
+     a31, a32,
+     a41, a42, a43,
+     b1,  b2,  b3,  b4;
+
+process = rk_solve(TS,KS, 1,1/ma.SR, EQ,IV);
+
+

Less abstract example which can actually be compiled/tested:

+
// Lotka-Volterra equations parameterized by a,b,c,d:
+LV(a,b,c,d, t,x,y) =
+    a*x - b*x*y,
+    c*x*y - d*y;
+
+// Solved using the "standard" fourth-order method:
+process = rk_solve_4(
+    0.01,                  // time step
+    LV(0.1,0.02,0.03,0.4), // LV() with random parameters
+    (3,4)                  // initial values
+);
+
+

References

+
+
+
+ + + + + + + + + + + diff --git a/research/vocal-source-grounding/sources/nokia-ishizaka-flanagan-two-mass.html b/research/vocal-source-grounding/sources/nokia-ishizaka-flanagan-two-mass.html new file mode 100644 index 0000000..5b2e9bf --- /dev/null +++ b/research/vocal-source-grounding/sources/nokia-ishizaka-flanagan-two-mass.html @@ -0,0 +1,1768 @@ + + + + + + Synthesis of Voiced Sounds From a Two-Mass Model of the Vocal Chords | Nokia.com + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ + + + + +
+
+ + + + + + +
+
+
+
+

Synthesis of Voiced Sounds From a Two-Mass Model of the Vocal Chords

+

01 July 1972

+
+ New Image +
+
+
+
+
+

Vol. 51, No. 6, July-August, 1972 Printed in U.S.A. Synthesis of Voiced Sounds From a Two-Mass Model of the Vocal Cords By K. ISHIZAKA and J. L. FLANAGAN ( M a n u s c r i p t received J a n u a r y 13, 1972) A model of voiced-sound generation is derived in which the detailed acoustic behavior of the human vocal cords and the vocal tract is computed. The vocal cords are approximated by a self-oscillating source composed of two stiffness-coupled masses. The vocal tract is represented as a bilateral transmission line. One-dimensional Bernoulli flow through the vocal cords and plane-wave propagation in the tract are used to establish acoustic factors dominant in the generation of voiced speech. A difference-equation description of the continuous system is derived, and the cord-tract system is programmed for interactive study on a DDP-516 computer. Sampled waveforms are calculated for: acoustic volume velocity through the cord opening (glottis)] glottal area; and mouth-output sound pressure. Functional relations between fundamental voice frequency, subglottal (lung) pressure, cord tension, glottal area, and duty ratio of cord vibration are also determined. Results show that the two-mass model duplicates principal features of cord behavior in the human. The variation of fundamental frequency with subglottal pressure is found to be 2 to 3 Hz/cm H20, and is essentially independent of vowel configuration in the programmed tract. Acoustic interaction between tract eigenfrequencies and glottal volume flow is strong.

+ + +
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+ + + diff --git a/research/vocal-source-grounding/sources/pmc-elemans-2015-universal-mechanisms.html b/research/vocal-source-grounding/sources/pmc-elemans-2015-universal-mechanisms.html new file mode 100644 index 0000000..9ce0a5e --- /dev/null +++ b/research/vocal-source-grounding/sources/pmc-elemans-2015-universal-mechanisms.html @@ -0,0 +1,2854 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + Universal mechanisms of sound production and control in birds and mammals - PMC + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + Skip to main content + + + + + + +
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Nature Portfolio logoLink to Nature Portfolio
+
. 2015 Nov 27;6:8978. doi: 10.1038/ncomms9978 +
+
+

Universal mechanisms of sound production and control in birds and mammals

+CPH Elemans +1,2,3,a, JH Rasmussen +1,*, CT Herbst +4,*, DN Düring +1,*, SA Zollinger +5, H Brumm +5, K Srivastava +6,7, N Svane +1, M Ding +8, ON Larsen +1, SJ Sober +6, JG Švec +4 +
+
    +
  • +
  • +
  • +
+
+ + + +
+
PMCID: PMC4674827  PMID: 26612008 +
+

Abstract

+

As animals vocalize, their vocal organ transforms motor commands into vocalizations for social communication. In birds, the physical mechanisms by which vocalizations are produced and controlled remain unresolved because of the extreme difficulty in obtaining in vivo measurements. Here, we introduce an ex vivo preparation of the avian vocal organ that allows simultaneous high-speed imaging, muscle stimulation and kinematic and acoustic analyses to reveal the mechanisms of vocal production in birds across a wide range of taxa. Remarkably, we show that all species tested employ the myoelastic-aerodynamic (MEAD) mechanism, the same mechanism used to produce human speech. Furthermore, we show substantial redundancy in the control of key vocal parameters ex vivo, suggesting that in vivo vocalizations may also not be specified by unique motor commands. We propose that such motor redundancy can aid vocal learning and is common to MEAD sound production across birds and mammals, including humans.


+

+Inline graphicIn contrast to the larynx of mammals, birds produce sound using a unique vocal organ called the syrinx. Using ex vivo preparations, Elemans et al. show that, despite large anatomical differences, sound production across a range of avian taxa is via the myoelastic-aerodynamic mechanism, the same mechanism involved in human speech.


+

In contrast to laryngeally vocalizing mammals, ∼10,000 species of extant birds vocalize with a uniquely avian vocal organ, the syrinx, located at the tracheobronchial junction and suspended in an air sac of the respiratory system1. The syrinx is structurally highly diverse across species1, but how morphological diversity reflects functional diversity remains unexplored. In addition, while songbirds are a widely used experimental animal model for neural mechanisms underlying vocal imitation learning2,3, we lack the empirical evidence to precisely map motor function onto neural circuitry4. Addressing these questions requires empirical quantification of syringeal dynamics as a function of control parameters in different species under physiologically realistic, controlled conditions. However, imaging the syrinx in vivo remains a challenge5,6, and we thus still lack this quantification of syringeal dynamics and control parameters.

+

Earlier endoscopic imaging identified syringeal vibratory tissues in songbirds and non-songbirds5,6, arguing against purely aerodynamical whistle mechanisms in which sound is produced without periodic movement of the vocal apparatus. Many mathematical models for birdsong7,8,9,10,11 assume that syringeal sound production is based on a myoelastic-aerodynamic (MEAD) system12,13,14,15. However, conclusive empirical evidence for MEAD is lacking4,16. The MEAD framework explains the physical mechanism underlying laryngeal sound production in mammals12,13,14,15,17. In brief, self-sustaining laryngeal vocal fold oscillations are maintained through fluid-tissue interactions and (myo)elastic restoring forces generated within the tissues12,13,14,15, preventing the need for muscle contractions at the rate of tissue vibration or other periodic input18. Expiratory airflow is mechanically converted by vocal folds into pulse-like airflow, which causes air pressure disturbances constituting the acoustic excitation of the system13. The mechanical properties and recruitment of different layers of vibrating tissues affect their resonance properties, which in combination with aerodynamic driving forces determine the frequency and mode of oscillation19,20,21,22.

+

According to MEAD theory, the medio-lateral vibration of the inner vocal fold surface (vibrational component 1 (VC1)) that gates airflow23 can only be self-sustaining if moving around a stable equilibrium position and if no net energy loss occurs per oscillation cycle13,24. The latter requires the presence of an aerodynamic force that changes magnitude with direction of vocal fold motion and thus is asymmetric over the oscillation cycle13. One possibility is that during self-sustained vocal fold vibration the required asymmetric aerodynamic force is produced by time-varying supraglottal pressure due to inertia of air in the vocal tract23. Such a mechanism would result in uniform medio-lateral vibration of the vocal folds24. However, models suggest that this mechanism limits the range of fundamental frequencies (F0) produced14. Another, more robust possibility is that the asymmetric aerodynamic force during self-sustained vocal fold vibration is produced by out-of-phase motion of the superior and inferior edge of the vibrating tissue (vibrational component 2 (VC2))13,25. VC1 and VC2 are the respective medio-lateral and caudo-cranial components of a tissue surface wave, or mucosal wave, that travels on the inner vocal fold surface along the expiratory air stream and facilitates aerodynamic energy transfer into tissue24. The wave phase changes cause the vocal folds to change shape from convergent during opening to divergent during closing parts of the cycle24. Because the intraglottal pressure is higher for the convergent shape than for the divergent shape26,27, the vocal folds are pushed apart during opening and pulled together during closing14,24,25. VC2 presence thus indicates that intraglottal pressure forms the asymmetric forcing function over opening and closing phases of vibration25 essential to self-sustained oscillation. Sound excitation events in mammals occur mainly at glottal closure and/or opening, when airflow abruptly stops or starts28,29,30.

+

Although isolated aspects of syringeal dynamics have been studied in birds5,6,31,32,33,34,35, the asymmetric forcing function essential to maintain self-sustained oscillation has not yet been identified, and the caudo-cranial tissue-wave component VC2—a crucial underlying assumption in modelling studies7,9,36—has not been demonstrated experimentally in the intact syrinx under appropriate physiological conditions16. Furthermore, it is unknown how syringeal dynamics relate to sound generating events within a single oscillatory cycle. These essential features of syringeal dynamics required to confirm MEAD have yet to be established16.

+

The translation of vocal motor commands into acoustic output depends on neural activity, musculature, morphology and physical mechanism of sound production4,16,37. These variables define a multi-dimensional parameter space that the brain needs to explore and navigate to control vocal output. In birds, these control variables have been studied in vivo by correlating acoustical parameters, for example, F0, with physiological parameters, for example, lung pressure or muscle activity, taking advantage of the highly stereotyped vocal patterns employed by adult birds38. This approach can inform us about a particular solution an individual uses to control its vocal output. However, if the control space is redundant (that is, there is more than one possible solution to achieve a specific vocal target, for example, F0), as commonly observed in motor control systems39, studying stereotyped in vivo behaviour provides limited insight in the behaviour of the entire system as we only observe the final solution the individual uses that may not be unique. Furthermore if vocal control parameters covary it may be difficult to establish causal relationships. To understand how the brain controls vocal behaviour therefore requires systematic quantification of the system's behaviour across its multi-dimensional parameter space. However, we currently lack an experimental paradigm to systematically study physiological control of the vocal system in birds.

+

Here, we present a novel ex vivo paradigm of the syrinx, which allows unprecedented experimental control and high-resolution imaging during sound production. First, to investigate if the MEAD physical mechanism of self-sustained oscillations as observed in mammals is applicable to birds, we test the hypotheses that a caudo-cranial travelling tissue surface wave is present and that this tissue wave is associated with sound production events. Second, to determine whether vocalizations are encoded by unique motor commands we test the hypothesis that the physiological control space of the syrinx ex vivo is redundant for key acoustic parameters. We show that birds employ the MEAD mechanism for sound production and that key vocal parameters exhibit redundant control ex vivo. We propose that motor redundancy may accelerate vocal learning and is common to MEAD sound production across birds and mammals.

+

Results

+

Physical mechanism of sound production

+

We developed an experimental paradigm that allows imaging of syringeal dynamics under controlled conditions ex vivo (Methods section; Supplementary Fig. 1). To test our first hypothesis, if the MEAD physical mechanism of self-sustained oscillations is applicable to birds (Fig. 1a), we took advantage of the diversity in syringeal morphology across species and first studied the domestic pigeon syrinx (Fig. 1b) because of its relatively simple morphology. We found self-sustained syringeal oscillations when both bronchial and air sac pressures were >0.5 kPa (N=12). The lateral vibratory masses (LVMs)7 were visualized using transillumination of the syrinx (Fig. 1c). Within an oscillation cycle the LVM inner wall changed shape from divergent during closing, rectangular during full collision and to convergent during opening (Fig. 1c, Supplementary Movie 1). A consistent phase shift in LVM position, confirmed by simultaneous micro-electroglottography (μEGG) recordings (Methods section), was present along the caudo-cranial axis (Fig. 1d). Spatiotemporal analysis of the LVM inner wall displacement and syringeal opening identified both components VC1 and VC2 of a tissue travelling wave along the caudo-cranial axis (Fig. 1e). Furthermore, we observed medio-lateral, that is, laterally travelling, tissue waves on the cranial surface of the LVMs (Fig. 1f), which are continuations of the caudo-cranial waves accompanying the LVM opening, and commonly observed on mammalian vocal folds (Supplementary Fig. 2). Sound pressure excitation occurred both during opening and closing events (Fig. 1g). The presence of both VC1 and VC2 components confirms our hypotheses that a caudo-cranial travelling tissue surface wave is present and that this wave is associated with sound producing events in pigeons.

+

Figure 1. The MEAD theory explains sound production in the domestic pigeon (Columba livia) syrinx.

+

Figure 1

+ +

(a) Schematic illustration of vocal organs in mammals (larynx) and birds (syrinx) showing the two vibrational components essential to MEAD theory: medio-lateral oscillation (VC1), and caudo-cranial phase differences (VC2). The latter are related to a tissue surface wave moving cranially and cause the inner wall of the vibratory tissue to be divergent during closing (solid line, black arrows) and convergent during opening motion (dashed line, white arrows). The syrinx is suspended in the ICAS. Three pressures act on the syrinx: subsyringeal (psub), suprasyringeal (psupra) and ICAS pressure (pICAS). (b) Annotated micro-CT scan of the pigeon syrinx showing LVM (yellow) and their inner edges (right, green; left, red), muscle (pink) and tracheal rings (T1–4). (c) Transilluminated syrinx filmed at 4 kHz with traced outlines of right (green) and left (red) LVM during closing, collision and opening phases of oscillation. The region shown is indicated by the dotted box in b. White arrows indicate movement. Circles indicate μEGG electrode pairs channel A (cyan fill) and B (black fill). (d) Two DKG (compiled at dotted lines in c) and simultaneous μEGG recordings show consistent caudo-cranial time delay of syringeal closure between the caudal line DKG2 and cranial line DKG1 (ΔtDKG) as well as between the caudal and cranial μEGG signals (ΔtμEGG). (e) Spatiotemporal displacement analysis of the left LVM (top) shows a caudo-cranial travelling tissue wave (dashed line), which is also present in the glottovibrogram of syringeal opening (bottom). (f) Simultaneous tracheal endoscopic VKG confirms opening and closing event timing of the cranial LVM edge, and reveals tissue waves (arrowheads) travelling mediolaterally over the epithelia. (g) Abrupt positive and negative excitation of the acoustic waveform aligns with opening and closing of the LVM cranial edge.

To test whether the presence of a tissue surface wave is a shared trait across birds, we studied syringeal oscillatory behaviour in six additional bird species from five orders. We selected species ranging in size (∼15 g–200 kg) and vocal complexity, each with highly divergent syrinx morphologies, containing one or two paired oscillators and controlled by zero to seven pairs of intrinsic syringeal muscles (Figs 2 and 3). We reconstructed three-dimensional geometries including bone, soft tissue and muscle based on micro-computed tomography (CT) scans (Figs 2a and 3a). Our study species included the largest extant bird (ostrich), a phylogenetically basal paleognathid bird (elegant-crested tinamou) and several neognathids: a parrot (cockatiel), dove (Barbary dove) and two songbirds (zebra finch and Bengalese finch). Medio-lateral vibration components (VC1) were observed in each species using tracheal endoscopy (Figs 2c and 3c). These VC1 vibrations resulted in complete syringeal closure within an oscillatory cycle in each species except for the ostrich, where full closure was never observed, more closely resembling human breathy phonation40.

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Figure 2. MEAD theory explains syringeal sound production in paleognaths.

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Figure 2

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(a) Three-dimensional syrinx geometry of the ostrich (Struthio camelus) and elegant-crested tinamou (Eudromia elegans) showing bone (grey), LVM (yellow) and muscles (pink). Both views are ventral. Muscle is rendered transparent in tinamou syrinx to show vibratory tissue. (b) High-speed imaging stills of endoscopic tracheal (ostrich) and transilluminated frontal views (tinamou) of the syrinx at two different phases during the oscillatory cycle. The region and location of these stills is indicated with a dotted box in a. For the ostrich the position of VKG analysis (dotted horizontal line) and DKG analysis (solid white line from point 1–2) presented in panel c is indicated. Transillumination provides sufficient detail to identify inner edges of right (green) and left (red) LVM in tinamou. (c) Evidence for medio-lateral vibrations (VC1) using tracheal endoscopic VKG. In the ostrich predominantly the right side vibrated. Full opening and closure of the cranial edge can be observed in tinamou. (d) Evidence for the caudo-cranial component (VC2) of the tissue wave as demonstrated by DKG for ostrich, and glottovibrogram for tinamou. (e) Synchronised acoustic waveforms.

Figure 3. MEAD theory explains syringeal sound production in neognaths.

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Figure 3

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(a) Three-dimensional syrinx geometry of the cockatiel (Nymphicus hollandicus, ventral view) and zebra finch (Taeniopygia guttata, dorsal view) showing bone (grey), LVM (yellow) and muscles (pink). Muscle is rendered transparent in zebra finch right hemisyrinx to show vibratory tissue. (b) High-speed imaging stills of frontal transilluminated frontal views of the syrinx at two different phases during the oscillatory cycle at view and location indicated with a dotted box in a. While transillumination does not provide detail on motion in the cockatiel syrinx, it provides sufficient detail to identify inner edges of vibratory tissue in female zebra finches (green). Circles indicate location of μEGG electrodes (cyan, channel A; black, channel B). (c) Tracheal endoscopic VKG shows opening and closing events and thus evidence for medio-lateral vibrations (VC1). In the zebra finch sound production was induced in the right hemisyrinx. (d) Evidence for caudo-cranial component (VC2) of the tissue wave as demonstrated by μEGG phase delays for cockatiel and zebra finch and glottovibrogram analysis for zebra finch. (e) Synchronised acoustic waveforms.

In each species, regardless of syringeal morphology, we confirmed the presence of the caudo-cranial component (VC2) of a travelling tissue wave using spatiotemporal analysis of syringeal inner wall displacement, syringeal opening and/or μEGG (Figs 2d and 3d, Supplementary Movies 1–6). To further test if the tissue wave was present over a range of fundamental frequencies, we subjected the syrinx to bronchial pressure ramps and measured the direction and speed of the tissue wave when present (Methods section). During self-sustained oscillations over a range of F0 values, the tissue wave was always present (Fig. 4) and running from caudal to cranial (indicated by all velocities being positive in Fig. 4). The wave speed did either not vary (pigeon and tinamou; linear regression, P=0.56 (n=10) and P=0.26 (n=10), respectively) or increased significantly with F0 (zebra finch and cockatiel; linear regression, P<0.001 (n=11) and P<<0.001 (n=118) respectively) within a range of 0.5–4.0 m s−1.

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Figure 4. The caudo-cranial tissue wave is present across a range of fundamental frequencies.

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Figure 4

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Magnitude of the caudo-cranial component (vVC2) of the travelling tissue-wave's velocity in (a) pigeon and (b) tinamou, (c) zebra finch and (d) cockatiel. The positive velocity values indicate that the wave travelled from caudal to cranial. Wave speed remained constant with F0 in pigeon and tinamou (Linear regression, P=0.56 (n=10) and P=0.26 (n=10), respectively), but increased significantly with F0 in zebra finch and cockatiel (linear regression, P<0.001 (n=11) and P<<0.001 (n=118), respectively).

Furthermore, to investigate the relationship between tissue motion dynamics and sound generation events within a single oscillatory cycle, we quantified the delay between sound excitation events and first opening and closing events of the syringeal passage over a range of F0 values (Fig. 5). In the pigeon, both opening and closing events were precisely accompanied by an acoustic excitation at very short delays of 170 and 90 μs, respectively (Fig. 5a), which are both below the 250 μs temporal accuracy of the opening and closing event timing (that is, one frame duration of high-speed video). The tinamou showed a strong acoustic excitation on syringeal opening, with a delay of 100 μs, also below the 250 μs temporal accuracy of the opening and closing event timing (Fig. 5b). A second, often weaker, excitation occurred 1.63 ms after closing. The zebra finch showed a very precisely timed strong acoustic excitation on syringeal closing at a delay of 40 μs (at a temporal accuracy of 33 μs; Fig. 5c).

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Figure 5. Sound excitation is associated with syringeal opening and closing events.

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Figure 5

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The relative duration of the syrinx in open (white bar starting at phase ϕ=0°) and closed (grey bar) state within a single oscillatory cycle (full oscillation equals 360°) over a range of fundamental frequencies in (a) pigeon, (b) tinamou and (c) zebra finch (left) based on transillumination data (Methods section). Sound excitation events are associated with opening (red circles: mean±s.d.) and/or closing (blue circles: mean±s.d.) of the syrinx. The thick vertical black line at the base of each column indicates the duration of a single movie frame relative to the cycle duration and thus the timing accuracy for determining a syringeal closing or opening event. Note that in zebra finch the lines are short due to high frame-rates used (25 kHz). The histograms (right) show that timing of sound excitation is closely associated with syringeal opening (red) and closing (blue) events.

In conclusion, these data confirm our first hypothesis that a caudo-cranial travelling tissue surface wave is present across a range of syringeal morphologies and sizes. Furthermore, our data confirm a close association between opening/closing event timing and sound generation events within single oscillatory cycles across a range of species. Collectively, our data thus provide the essential lacking demonstrations of syringeal dynamics and sound generation events required to conclusively show that MEAD theory is applicable to sound production in birds.

Vocal control redundancy ex vivo +

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To test our second hypothesis that the physiological control space of the vocal organ is redundant for key acoustic parameters, we systematically investigated the relationship between syringeal control parameters and acoustic output ex vivo. In mammals, the brain can control bronchial pressure and laryngeal muscle activity to modulate aerodynamic forces and vocal fold tissue properties (for example, geometry and elasticity) and attain a target fundamental frequency (F0)12,13,14,15. In birds, in addition to bronchial pressure, pressure in the interclavicular air sac (ICAS) enclosing the syrinx also affects F0, as suggested by models7,9,10 and experimental manipulations10. We first quantified syringeal oscillatory behaviour in different species as a function of bronchial and air sac pressure (Figs 6 and 7a–c). For each species the F0 ranges produced ex vivo corresponded well to the lower-end distribution of spontaneous vocalizations (Figs 6 and 7b,c). We further found that in each investigated species, multiple different combinations of bronchial and ICAS pressures could achieve the same target frequency (iso-F0 contours in Figs 6 and 7c), indicating that F0 control is redundant within the pressure control space. To investigate how much two other important vocal parameters, that is, sound pressure level (SPL) and sound quality, changed with F0, we quantified the SPL and Wiener entropy (WE) along evenly spaced iso-F0 contours. A point on the iso-F0 contour was considered to be redundant in all three acoustic parameters if neither SPL nor WE changed along the iso-F0 contour (Methods section). The percentage of the explored control space that demonstrated redundancy for the three vocal parameters measured 79.8±21.4% (mean±s.d.) for pigeon (N=7), 83.0±7.7% for Barbary dove (N=3), 67.8±4.7% for tinamou (N=3), 71.4±18.9% for cockatiel (N=2), 44.3% for zebra finch right hemisyrinx, 62.4±13.3% for Bengalese finch left hemisyrinx (N=6) and 71.6±18.6% for Bengalese finch left hemisyrinx (N=6). These results demonstrate that F0 control by pressure ex vivo is redundant in subspaces within the pressure control space, and that this redundancy is conserved across species exhibiting a wide range of syringeal morphologies. Therefore, in the ex vivo preparation redundant acoustic output can be achieved by modulating air pressure, without any active control of syringeal muscles.

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Figure 6. Pressure control of F0 in sound production is redundant across avian taxa.

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Figure 6

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Spectrograms and oscillograms of spontaneous vocalisation (left) and representative pressure control spaces ex vivo (right) of (a) pigeon (Columba livia), (b) Barbary dove (Streptopelia risoria), (c) cockatiel and (d) Bengalese finch (Lonchura striata domestica). The F0 ranges of sounds produced ex vivo (grey vertical bar right of spectrogram) correspond well to the lower range of spontaneous vocalizations. Pressure control may allow higher F0 values, as indicated by the grey bar fading out. Iso-F0 contours (values in Hz) are overlaid on the pressure control spaces and shown in white when redundant for all three acoustics parameters (F0, SPL and WE), or black when not. In the Bengalese finch, the left hemisyrinx produces higher F0 than the right hemisyrinx, corroborating earlier in vivo studies70. (e) Spectrogram and oscillogram (left) of ostrich mating call, and ex vivo sound production including bronchial pressure (pb) patterns underlying phonation (right). A complete pressure control space was not obtained for this species.

Figure 7. Motor control of F0 in sound production is redundant.

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Figure 7

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(a) Three-dimensional geometry of the tinamou and zebra finch syrinx with pressure control parameters; bronchial or subsyringeal (psub), and ICAS pressure (pICAS). Stimulated muscles are indicated. (b) Sound spectrogram (top) and oscillogram (bottom) of a tinamou honksqueal call and zebra finch song motif. (c) Representative pressure control spaces ex vivo of one individual. Iso-F0 contour as in previous figure (values in Hz). (d) Sound spectrogram (top) and muscle stimulus (bottom) during syringeal muscle stimulation. Black dots indicate measurements points. (e) Fundamental frequency (F0) is affected by muscle stimulation (blue dots, no stimulation; red dots, maximal stimulation) and pressure. The grey bar indicates the individuals' frequency range achieved by varying only pressure. Pressure control may allow higher F0 values, as indicated by the grey bar fading out. Multiple different combinations result in the same frequency, for example, 500 and 650 Hz in tinamou and zebra finch, respectively, (green horizontal line).

We furthermore examined whether muscular control introduced an additional source of redundancy and quantified the effect of syringeal muscle recruitment on F0 using local micro-stimulation (Fig. 7d). Muscle stimulation caused an F0 increase of 300–750 Hz and 75–200 Hz for tinamou and zebra finch, respectively (Fig. 7e). The F0 range achieved by pressure and muscle recruitment overlapped within each species (tinamou (N=1) and zebra finch (N=5)) and multiple different combinations of muscle recruitment and bronchial pressure resulted in the same F0. These results thus demonstrate that muscular control of F0 is redundant in the ex vivo preparation.

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Taken together, the above data confirm our second hypothesis that the physiological control space of the vocal organ ex vivo is redundant for key acoustic parameters across a range of syringeal morphologies and sizes.

Discussion

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Our data establish that birds use MEAD as the primary physical mechanism for sound production with strong similarities to mammalian MEAD systems: First, we demonstrate the presence of a tissue wave that travels from the caudal to cranial end of the syringeal vibratory tissue (Figs 1, 2, 3, 4). This tissue wave thus causes the syringeal vibratory tissue shape to be convergent when opening, and divergent when closing during expiratory sound production, and can be considered analogous to the caudo-cranial mucosal wave observed in mammalian vocal folds. Our data therefore strongly suggest that in birds, just as in mammals, the dominant asymmetric forcing function over the opening and closing phases of vibration essential to maintain self-sustained oscillation is not formed by the mass inertance of the air column in the vocal tract23,24, but by the tissue-wave-induced intraglottal pressure changes. This mechanism reduces the dependency of the self-sustained syringeal oscillations on acoustic resonances of the vocal tract and allows for an expanded F0 range of vocalization14, which in addition to labial morphology41 could aid birds in extending their F0 range. Second, the magnitude range of the tissue-wave speed measured (0.5–3.0 m s−1) is in excellent agreement with values reported for the mammalian larynx30,41,42,43,44,45,46 (human41,43,44,45, 0.5–2.0 m s−1; dog42,46,47, 0.5–2 m s−1; calf45, 0.4 m s−1; and an African elephant30, 1.2 m s−1) suggesting that no scaling effects occur. Third, our data show that in some species (zebra finch, cockatiel) the tissue-wave speed increased with F0, similar to what has been observed in humans47, whereas in other species (pigeon, tinamou) the tissue-wave remained constant with respect to F0 (Fig. 4). The different relationships are possibly related to biomechanical properties of the tissue layers involved in the vibrations or varying aerodynamic forces acting on the vibrating structures. Future work will be required to establish the respective causality. Last, our findings demonstrate that acoustic excitation occurs at opening and/or closing of the syringeal passage (Fig. 5), which strongly suggests a causal relation between tissue vibration and generation of acoustic energy by modulating the glottal airflow as found in the mammalian larynx28,29,30. While in humans the maximum acoustic excitation has been shown to occur mainly at the instant of glottal closure28,29, a recent study reported that in an excised elephant larynx the maximum acoustic excitation occurred at the instant of glottal opening30. The mammalian larynx thus exhibits more diversity than previously thought in what movements cause the predominant acoustic excitation. Our work demonstrates that this diversity is also present in birds and that more comparative studies are needed to explain the causal link between airflow, tissue vibration and acoustic excitation.

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In conclusion, we find that despite the large diversity present in syringeal morphology of the bird species included in this study, all use MEAD as the primary physical mechanism of sound production, supporting MEAD-based approaches to modelling avian sound production7,8,9,10,11. Moreover, our findings suggest that despite their different evolutionary origins1, laryngeally vocalizing mammals and syringeally vocalizing birds have converged on the same physical mechanism for vocalization.

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Furthermore, our data show that key acoustic parameters, such as particular F0 values, can be achieved by multiple distinct combinations of respiratory pressure and syringeal muscle recruitment ex vivo (Figs 6 and 7). This finding thus supports the hypothesis that subspaces within the entire physiological control space of the vocal organ ex vivo are redundant for acoustic parameters.

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Our work represents the first systematic exploration of syringeal behaviour in a controlled environment using pressure differentials up to 2 kPa. Although it remains unresolved to what degree birds can independently control bronchial pressure and ICAS air sac pressure in vivo, ventilation flow across the lungs requires the existence of pressure differences between different parts of the respiratory system48,49,50. Especially in dynamic situations such as vocal behaviour, the passive geometry of the air sac system can lead to substantial pressure differences between air sacs51,52 and indeed transient pressure differences up to 1.0 kPa occur during vocalizations in Barbary doves7,53. These pressure fluctuations can result in local transmural pressure differentials over the syringeal walls and thus in transmural forces on the vibrating tissues7,37. The individual bird can either avoid or exploit such regimes during vocalization. However, regardless of pressure differentials, only bronchial pressure in combination with different levels of recruitment in a single vocal muscle leads to redundancy in F0 (Fig. 7e).

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How acoustic redundancy of the vocal organ ex vivo reflects the functional motor redundancy in vivo remains to be explored. The speed at which consecutive motor commands can be executed in vivo (either on the same side of the syrinx or when vocal production switches rapidly from one side to the other within a complex syllable) may cause a significant reduction of the available functional redundancy, especially because at least some songbirds possess superfast syringeal muscles that produce peak force in <5 ms (refs 54, 55). Here, we did not investigate the rapid time-varying pressure and muscle recruitment patterns that occur in vivo, and indeed for most species more detailed experimental in vivo data are required to meaningfully explore the high-dimensional control space ex vivo. On the other hand, we show that redundancy emerges when only varying the activity level of a single vocal muscle. Redundancy can thus be expected to increase when the brain can produce a given acoustic output by choosing from a large set of redundant motor commands when coordinating the ∼16 syringeal muscles56 with several thousand motor units57.

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A recent study used zebra finch song acoustics to infer low-dimensional motor commands11, which were then used to generate synthetic songs that closely resembled the acoustic output of natural vocal behaviour, and evoked auditory responses that closely resembled the pattern of premotor activity. These results led the authors to suggest that premotor area HVC encodes a low-dimensional forward model of gesture dynamics11. In contrast, our data indicate that particular acoustic outputs can be specified by multiple motor states, suggesting that motor commands cannot be uniquely inferred from acoustics. It will therefore be important for future studies to investigate whether the method used in ref. 11 to infer motor commands from acoustic data yields the actual combination of control parameters employed by the bird to generate the sound, rather than a different set of control parameters that redundantly produces the same acoustic output. Similarly, future ex vivo studies employing time-varying stimulus patterns across multiple muscles will allow us to explore the limits of vocal redundancy during sophisticated motor trajectories similar to those in behaving animals. Despite the apparent conflict between our findings and elements of ref. 11, it is important to note that the instantiation of a low-dimensional forward model within HVC—which is multiple synapses upstream from the vocal and respiratory muscles—is not incompatible with a redundant vocal organ. Indeed, one strength of low-dimensional encoding in HVC is that it would allow HVC to represent control parameters (for example, vocal fold tension) without regard to the details of the redundant combinations of muscle contraction states required to achieve that tension.

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In many fine motor control systems such as arm reaching, the brain must negotiate the so-called motor redundancy problem39, in which a particular behavioural target can be achieved by vast numbers of motor commands. However, one potential advantage to a redundant control space is that it allows the brain to find subspaces of possible motor commands (for example, along the iso-F0 contours in Figs 6 and 7c in our ex vivo paradigm) rather than searching for unique motor commands to achieve the target. Crucially, redundant control spaces allow variability in task-irrelevant directions58,59. In vocal production, the brain may select from within this motor command space to meet other demands, such as acoustic targets in future and/or past syllables. Consequently, we speculate that vocal motor redundancy may simplify trial-and-error learning during song acquisition by allowing the brain to rapidly discover one of many motor solutions60 before learning how to further improve performance by exploiting motor redundancy39. Vocal redundancy may therefore have aided, or even been necessary for, the evolutionary development of vocal learning. Future studies might evaluate this speculation by quantifying whether learned vocalizations exploit vocal redundancy. Furthermore, because many species do not learn their vocalizations and many vocal learners produce innate vocalizations in addition to learned ones, future work might also determine whether innate vocal motor programs similarly exploit redundancy to improve performance.

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Our ex vivo results suggest that the redundant control of key vocal parameters represents a significant aspect of avian vocal control, and one that merits further investigation. Because redundancy in F0 control by pressure and muscle recruitment is also observed in various simplified computational models of the human larynx13, and songbird syrinx9 as well as in ex vivo dog larynx preparations61,62, we propose that vocal control redundancy is a typical feature of MEAD sound production systems and hence a common feature of vocal production and control in mammals and birds.

Methods

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Subjects

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To study sound production mechanisms and the effect of muscle stimulation on sound production, we used 12 adult domestic pigeons (Columba livia; order Columbiformes; nine males, three females), four domestic Barbary doves (Streptopelia risoria; order Columbiformes; three males, one female), three elegant-crested tinamous (Eudromia elegans; order Tinamiformes; two males, one female), two ostriches (Struthio camelus; order Struthioniformes; sex unknown), three cockatiels (Nymphicus hollandicus; order Psittaciformes; two males, one female), six Bengalese finches (Lonchura striata domestica; order Passeriformes; six males) and 19 zebra finches (Taenopygia guttata, order Passeriformes; five adult males; two juvenile males (∼40 dph); 12 females). Ostrich syrinxes were obtained from a local breeding farm. They were transferred to ice immediately after extraction, flash frozen in liquid nitrogen and stored at −80 °C. Bengalese finches were kept in indoor aviaries on a 14-h light:10-h dark light cycle with food and water ad libitum (Emory University, Atlanta, GA, USA). Zebra finches were kept in indoor aviaries on a 12-h light:dark photoperiod with food and water ad libitum (University of Southern Denmark (SDU), Odense, Denmark). All other animals were kept in 3 × 6 × 2 m outdoor aviary with food and water ad libitum (SDU, Odense, Denmark). Pigeons, doves, cockatiels and tinamous were obtained from local breeders. Bengalese finch experiments were carried out at Emory University, and all other experiments at SDU, Denmark. All experiments were conducted in accordance with the Institutional Animal Care and Use Committee of Emory University and of SDU.

Surgical and mounting procedures

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Animals were euthanized with isoflurane and cooled on ice or icepacks. The syrinx and associated blood vessels were dissected out using a stereoscope (M165-FC, Leica Microsystems) through a ventral incision to the sternum while regularly flushing with oxygenated Ringers solution (5 °C, recipe cf. refs 54, 55, 56), and transferred to a Sylgard-covered petri dish on ice containing oxygenated Ringer solution. The syrinx was cleaned of fat and connected to species–specific tubing assemblies of non-reactive polyethylene tubing (Instech Salomon, PA, USA) in the experimental chamber with 10/0 nylon suture (S&T, Neuhausen, Switzerland). Special care was taken to mount the syrinx of each species in its natural position by leaving structural elements, such as bronchidesmus and collagen tissue strands, intact. Two pairs of μEGG electrodes (see below) were inserted in tissue and fixed with 10/0 suture at locations indicated in Figs 1 and 2. For muscle stimulation experiments ex vivo, perfusion pathways were established in the zebra finch that allowed perfusion through the original syringeal vasculature. All arteriole capillaries were localized and closed using 10/0 suture immediately after exposure of the syrinx by a ventral incision to the sternum. The syrinx was then transferred to a Sylgard-covered petri dish on ice and connected to micro-perfusion lines, gravity fed with oxygenated Ringers. Perfusion pressure was kept at 2–4 kPa until patent perfusion was observed and immediately reduced to 1–2 kPa. The syrinx was typically mounted ventral side up in the experimental chamber to two bronchial and one tracheal connector (Supplementary Fig. 1).

Experimental chamber design

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To study syringeal sound production, we developed an experimental chamber that allowed for study of the syrinx ex vivo (that is, intact perfused organ) under controlled conditions. This experimental chamber was milled out of aluminium (temperature controlled) or PVC and covered by an airtight glass lid that allowed pressurization and a clear view (Supplementary Fig. 1). The glass was either coated with nano-particles (Percenta AG, Germany) or heated to 10 °C above chamber temperature by a 18-μm diameter Formvar coated Nichrome wire assembly (A-M Systems, Sequim, WA, USA), to prevent droplet forming fogging up the glass. In the floor centre of the chamber, a 1-mm raised edge with glass bottom covered in Sylgard allowed transillumination of the syrinx. We separately controlled pressure in the bronchial connectors (pb) and chamber (pICAS) with dual valve differential pressure PID controllers (model PCD, 0–10 kPa, Alicat Scientific, AZ, USA), referenced to atmospheric pressure, and a response time of 1 ms. Bronchial mass flow was measured with micro-electro-mechanical system (MEMS) flow sensors of various ranges (PMF series, Posifa Microsystems, San Jose, USA) and a response time of 1 ms. The supply of pressurized air to the controllers was heated and humidified with deionised water in a pressure cooker. Excess vapour condensed in a downstream second pressure cooker. The pressure controllers were temperature controlled at 37 °C (HD4034 with PT100 sensor, Hotek Technologies, WA, USA) ensuring pre-heated, fully humidified air to the syrinx. The temperature of the aluminium experimental chamber was controlled with a recirculating water bath (Julebo F12-ED, Seelbach, Germany) and logged at 1 s intervals with a 1-mm diameter J-type miniature temperature probe (USBTC01, National Instruments, TX, USA) 1–2 mm away from the syrinx. Perfusion fluids attained the same temperature as the chamber due to physical contact with a platform in the chamber (labelled ‘Perfusate platform' in Supplementary Fig. 1). During the mounting process the temperature of the chamber was kept at 7 °C.

Image acquisition and analysis

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The syrinx was imaged through the chamber lid with a high-speed camera (MotionPro-X4, 12 bit CMOS sensor, Integrated Design Tools, Inc.; 4,000–25,000 frames s–1) mounted on a stereomicroscope (M165-FC, Leica Microsystems). For the zebra finch, we also used a more light-sensitive 16 bit high-speed camera (Fastcam SA1, Photron, San Diego, CA, USA; 20,000–35,000 frames s−1). We used a 1.2-mm (Schölly Fiberoptics, Denzlingen, Germany) and 300-μm (Advanced Inspection Technologies, Melbourne, FL, USA) diameter flexible fiberscope for endoscopic imaging. The low-light images obtained with the endoscopes were captured with a videokymographic (VKG) system (model 2156, Cymo B.V., Groningen, The Netherlands), which combines a high-speed linescan camera (7,200 line images s−1) with a full frame CMOS camera (25 frames s−1). The analogue video output from the VKG was captured together with the microphone and a synchronization signal using a capturing device (Intensity Extreme, Black Magic Design, Australia). Light for transillumination was provided by a 1,700 lumen LED (Luxeon S, Philips, The Netherlands) powered by a stable power source (PS23023, HQ Power, Belgium) or plasma light source (HPLS200, Thorlabs, Germany) through liquid light guides and reflected of a 45° angled silver coated prism (MRA series, Thorlabs) to absorb heat.

Kymography

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A kymogram displays pixel intensity over time along a set line in an image. The VKG system used here generates a kymogram at the fixed position of the linescan camera63. Digital kymograms (DKG) are kymograms along any arbitrary line in a digital image64 and were extracted from high-speed image recordings using Matlab (The Mathworks). Two kymograms in Supplementary Fig. 2 were previously published: human from ref. 40, and elephant from ref. 30.

Micro-electroglottography

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As an independent proxy for kinematics of the syringeal vibratory tissues, we used EGG. This non-invasive technique measures electrical impedance between electrodes and is commonly used to quantify vocal fold contact area in the larynx65. μEGG electrodes consisting of single stranded 25 μm diameter Formvar coated Nichrome wires (A-M Systems) were inserted as described above and connected to a modified two-channel electroglottograph (model EG2, Glottal Enterprises Inc. NY, USA).

Data acquisition and synchronisation

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Sound was recorded with a ½ inch pressure microphone-pre-amplifier assembly (model 46AD with preamplifier type 26AH, G.R.A.S., Denmark), amplified and high-pass filtered (10 Hz, 3-pole Butterworth filter, model 12AQ, G.R.A.S.). The microphone sensitivity was measured before each experiment (sound calibrator model 42AB, G.R.A.S.). The microphone was placed at 2–3 cm from the tracheal connector outlet in the acoustic near field, and on a 45° angle to avoid the air jet from the tracheal outlet. The sound signal was time shifted for the travelling distance from vibratory membranes to microphone. Microphone, μEGG, pressure and flow signals were low-pass filtered at 10 kHz (custom-built filter). These signals together with synchronization signals from camera systems and muscle stimulators were digitized at 50 kHz (USB 6259, 16 bit, National Instruments, Austin, TX, USA). These signals were synchronized with all imaging systems with an accuracy of <21 μs before each experiment. All control and analysis software was written in Labview (National Instruments) or Matlab.

Tissue-wave imaging protocol and analysis

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Transillumination successfully visualized the inside outlines of vibratory tissues in the domestic pigeon, Barbary dove, elegant-crested tinamou and zebra finch. High optical density of the ostrich and cockatiel syrinx did not allow transillumination. In the tinamou, we dissected apart M. syringealis to allow LVMs imaging using transillumination. In zebra finch transillumination was successful in adult females and juvenile males, but attempts in adult males were unsuccessful due to the high optical density of M. syringealis ventralis (VS) muscles. In the zebra finch sound production was induced in the right hemisyrinx. Substantially different requirements in lighting conditions did not allow for simultaneous transillumination and tracheal endoscopy in zebra finches.

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To image syringeal oscillatory behaviour we subjected the syrinx to a single bronchial pressure ramps at constant air sac pressure, while filming from 5,000 to 35,000 frames s−1. Our system could acquire and save a maximum of 2–10 s of data depending on frame rates, which comprised (tens of) thousands of frames. Due to the image complexity of the data, analysis could not be automatized, and required frame-by-frame manual analysis. On selected sequences of high-speed images, the left and right LVM or labia were traced manually in Amira (Visage Imaging GmbH, Berlin, Germany) and processed in Matlab. We calculated displacement (for example, Fig. 1e top panel) as current position minus the most lateral position during oscillation (indicated by the green line ‘min' on the top left in Fig. 1e). With both left and right LVM shapes quantified we could then compute the syringeal opening as a function of position and time, a graph also known as the glottovibrogram30 as can be seen in Figs 1e, 2d and 3d.

+

To quantify syringeal dynamics over a range of F0 values, full glottovibrogram reconstructions over several cycles were not suitable due to the labour intensive manual tracing required. Therefore we used an alternative approach to determine the presence of the VC2 component and speed of the tissue wave across a range of F0 values. For pigeon, tinamou and zebra finch we used transilluminated frontal views of the syrinx and calculated one DKG at the caudal edge and one DKG at the cranial edge of the LVM or labia (top two panels in Fig. 1d) at distance Δy (indicated in middle panel Fig. 1c). DKG's contain many periodic traces as many structures move with each oscillation. By tracing selected LVM and labial inner edges in video stills over five oscillation cycles, we could identify the wave representing the motion of the LVM or labial inner edge in the DKG's and as such measure the time difference between maximal lateral position of LVM or labium on the two DKG's (ΔtDKG in Fig. 1d). The wave speed equalled vVC2=Δy/ΔtDKG and was averaged over five consecutive cycles. Because in the cockatiel syrinx transillumination was not successful, we used cross-correlation between two μEGG electrode pairs located at distance Δy to calculate time delay (ΔtμEGG) and wave speed vVC2. The ostrich was not included in this analysis because both transillumination was not successful and μEGG did not resolve vibrations due to lack of syringeal closure. We did not estimate wave speed from the tracheal endoscopic view because the VC2 velocity component was almost normal to the imaging plane, leading to large inaccuracies.

+

In these five consecutive oscillations, we quantified the timing of syringeal opening and closing from the transilluminated frontal views as the first frame in which the entire syringeal passage was open or closed, respectively. The minimal precision for these measurements equals the duration of one frame as indicated by the black vertical line at the base of each column in Fig. 5. In addition, we quantified the timing of acoustic excitations in the sound pressure signal. The timing of the sound signals was corrected for the time needed for the sound to propagate from the oscillators through trachea and tubing to the microphone, assuming a sound speed of 340 m s−1. With these parameters we quantified the timing of acoustic excitation with respect to syringeal opening and closing events within single oscillatory cycles.

Pressure control space protocol

+

To explore syringeal oscillatory behaviour in the pressure control space we subjected the syrinx to a set of bronchial pressure ramps at randomized and variable air sac pressure, and one additional ramp where pb equalled pICAS. Ramp speed was 1 kPa s−1. Depending on species, we used pressures <2.0–4.0 kPa and |pb−pICAS|<2.0 kPa to avoid regimes of high flow (that is, combinations of high pb and low pICAS) and/or mechanical failure of syringeal oscillatory structures. These sets were performed without transillumination imaging. SPL and WE were calculated on 100 ms segments by applying a sliding window with 50 ms steps. If the SPL of these segments were above the 60 dB re. 20 μPa threshold, segments were zero-padded to the next power of two, and a 4,096 point power spectral density estimate was computed (periodogram method in Matlab). Additional filtering was used to extract the fundamental frequency (F0) reliably from the spectral density estimate. WE was calculated as the geometric mean of the power spectrum over the arithmetic mean of the power spectrum.

+

We extracted iso-F0 contours in pb, pICAS control space. SPL and WE were evaluated along the iso-F0 contours at a resolution of 10 Pa (Supplementary Fig. 3). To evaluate whether points on these iso-F0 contour lines were redundant for all three quantified acoustic parameters (F0, SPL and WE) we computed acoustic parameters at a fixed distance of 100 Pa both before and after each point along the iso-F0 contour line locations in pb, pICAS control space (Supplementary Fig. 3). For the 100 Pa start and end sections of the contour, only forward and backward values could be computed. A point along the iso-F0 contour was considered redundant for all the three parameters if the WE and SPL variation within the 100 Pa interval was below 0.2 units of WE and 1 dB SPL (ref. 66). This resulted in a logical (1/0) redundancy array for each iso-F0 contour. The iso-F0 contour is plotted white when redundant and black when not in the pb, pICAS control spaces in Figs 6a–d and 7c.

+

We computed iso-F0 contours at fixed intervals (Columba, 10 Hz; Streptopelia, 50 Hz Eudromia, 50 Hz; Nymphicus, 100 Hz; Lonchura, 100 Hz; Taenopygia, 50 Hz) within the F0 range observed in the preparation. The percentage redundancy of a pressure control space was expressed as the ratio of redundant points to the total amount of points on all iso-F0 contours computed in the pb, pICAS control space.

Muscle stimulation protocol

+

Muscles were stimulated with 50 μm diameter Teflon-coated twisted silver wire electrodes (A-M Systems) that were fixed with 10/0 suture. We used a stimulus isolator (model A395, WPI, Sarasota, FL, USA) to apply variable currents (0–10 mA) when limited compliance voltage was sufficient to contract muscles (tinamou). For zebra finches and Bengalese finches, we used two stimulators (model 14E11, DISA, Herlev, Denmark and model 2100, A-M Systems, respectively). To ensure muscle specificity, we placed carbon microspheres (20–40 μm diameter) at regular intervals on the muscles and surrounding tissues and filmed contractions at 1 kHz. We stimulated the single syringeal muscle present in tinamous, M. syringealis. In songbirds, activity of the M. syringealis ventralis correlates to F0 (ref. 67). Therefore we focussed on this muscle to study F0 control in zebra finches (N=5 adult males). F0 of the sound was determined 30 ms prior (control) and 30 ms after stimulation. We computed 512-point fast Fourier transforms and used parabolic interpolation around the peak power to determine F0.

Statistics

+

Linear regressions were calculated to test the significance of wave speed as a function of F0 in Matlab. All values are presented as mean±1 s.d.

Morphome reconstruction

+

We constructed three-dimensional annotated syrinx morphologies, that is, morphomes, based on IKI contrasted CT scans56. All specimens were scanned at Odense University Hospital with a μCT scanner (VivaCT 40, Scanco Medical AG, Switzerland) with 10 μm resolution, except the ostrich syrinx which was scanned with 80 μm resolution on a XtremeCT (Scanco Medical AG). These scans were annotated manually in Amira for bone, soft tissue and muscle using protocols cf. ref. 56.

Natural vocalizations

+

Sound recordings of natural vocalizations were obtained in previous studies for domestic Barbary dove7, elegant-crested tinamou68 and zebra finch69. A domestic pigeon call recording was obtained from www.xeno-canto.com (catalogue nr: XC92264). We recorded the mating calls of two male ostriches at an open-range ostrich-breeding farm (Langeskov, Denmark) from April to May 2013 using a shotgun microphone (model KMR82i, Neumann, Berlin, Germany) and a 24-bit digital recorder (Olympus LS-100). Cockatiel recordings were made with the same shotgun microphone and solid-state recorder (model PMD-670, Marantz, Mahwah, NJ, USA).

Additional information

+

How to cite this article: Elemans, C. P. H. et al. Universal mechanisms of sound production and control in birds and mammals. Nat. Commun. 6:8978 doi: 10.1038/ncomms9978 (2015).

Supplementary Material

+
+Supplementary Information

Supplementary Figures 1-3

+
+
+ncomms9978-s1.pdf (460.5KB, pdf) +
+Supplementary Movie 1

High-speed video of syringeal kinematics during sound production in the domestic pigeon. The first part of the video is imaged under incident lighting, followed by trans-illumination, which clearly reveals the inner contours of lateral vibratory mass (LVM) motion. The visible wires are 18 μm diameter nichrome μEEG wires. Recorded at 4000 frames s-1 and slowed 133 times. The extracted LVM inner contours were superimposed upon the individual images (right, green; left, red)

+
+
+Download video file (7.8MB, mov) +
+Supplementary Movie 2

High-speed video of syringeal kinematics during sound production in the elegant crested tinamou. Trans-illumination clearly reveals the inner contours of LVM motion. The visible wires are 18 μm diameter nichrome μEEG wires. Recorded at 4000 frames s-1 and slowed 133 times.

+
+
+Download video file (8MB, mov) +
+Supplementary Movie 3

High-speed video of syringeal kinematics during sound production in the Barbary dove. Trans-illumination clearly reveals the inner contours of LVM motion. The visible wires are 18 μm diameter nichrome μEEG wires. Recorded at 5000 frames s-1 and slowed 167 times.

+
+
+Download video file (13.1MB, mov) +
+Supplementary Movie 4

High-speed video of syringeal kinematics during sound production in the ostrich. Tracheal endoscopic view shows presence of both caudocranial as well as ventrodorsal waves. Recorded at 1000 frames s-1 and slowed 67 times.

+
+
+Download video file (11.7MB, mov) +
+Supplementary Movie 5

High-speed video of syringeal kinematics during sound production in the cockatiel. Recorded at 5000 frames/s and slowed 167 times. The morphology of this syrinx does not allow transillumination, but the tracheal endoscopic view clearly shows LVM kinematics during opening and closing of the. Recorded at 5000 frames s-1 and slowed 670 times.

+
+
+Download video file (15MB, mov) +
+Supplementary Movie 6

High-speed video of syringeal kinematics during sound production in the zebra finch. Trans-illumination reveals the inner contours of the left medial labium (ML) motion. The visible wires are 18 μm diameter nichrome μEEG wires. Recorded at 2000 frames s-1 and slowed 335 times. The extracted ML contours (green) were superimposed upon the individual images.

+
+
+Download video file (4.8MB, mov) +

Acknowledgments

+

We thank T. Christensen, P. Martensen, F. Mortensen, F. Andreasen, A. Chandler, V. Shanbogue and N. Ditzel for technical assistance, J. Brewer for optics advice, L. Jakobsen for use of equipment, S. Pedersen for ostrich access, A. Qiu for videokymography advice and M. Rothenberg for EGG advice. H. Mehaffey, J.M. Ratcliffe and A. Surlykke commented on the manuscript. This study was funded by grants from the Danish Research Council (FNU), Carlsberg Foundation, visiting professorship (Université de Saint-Etienne) and QuanTM fellowship (Emory University) to C.P.H.E., a Heisenberg Fellowship of the German Research Foundation (Br 2309/8-1) to H.B., US National Institutes of Health grants F31DC013753 to K.S., P30NS069250 and R01NS084844 to S.J.S., European Social Fund and the state budget of the Czech Republic, project numbers OPVK CZ.1.07/2.3.00/30.0004 ‘POST-UP' to C.T.H. and J.G.Š., the institutional fund of Palacký University Olomouc to C.T.H. and OPVK CZ.1.07/2.3.00/20.0057 to J.G.Š.

Footnotes

+

Author contributions C.P.H.E. conceived the study and built the set-up. All authors contributed to data acquisition: pigeon (C.P.H.E., J.H.R., C.T.H., D.N.D., J.G.Š.), Barbary dove (C.P.H.E.), ostrich (N.S., C.P.H.E.), tinamou (S.A.Z., H.B., C.P.H.E.), cockatiel (O.N.L., C.P.H.E.), Bengalese finch (K.S., S.J.S., C.P.H.E.) and zebra finch (D.N.D., C.P.H.E.). CT scans were performed by D.N.D. and M.D., data annotation by D.N.D. All authors contributed to data analysis and the manuscript. All authors read and approved the final manuscript.

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Associated Data

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This section collects any data citations, data availability statements, or supplementary materials included in this article.

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Supplementary Materials

+
+Supplementary Information

Supplementary Figures 1-3

+
+
+ncomms9978-s1.pdf (460.5KB, pdf) +
+Supplementary Movie 1

High-speed video of syringeal kinematics during sound production in the domestic pigeon. The first part of the video is imaged under incident lighting, followed by trans-illumination, which clearly reveals the inner contours of lateral vibratory mass (LVM) motion. The visible wires are 18 μm diameter nichrome μEEG wires. Recorded at 4000 frames s-1 and slowed 133 times. The extracted LVM inner contours were superimposed upon the individual images (right, green; left, red)

+
+
+Download video file (7.8MB, mov) +
+Supplementary Movie 2

High-speed video of syringeal kinematics during sound production in the elegant crested tinamou. Trans-illumination clearly reveals the inner contours of LVM motion. The visible wires are 18 μm diameter nichrome μEEG wires. Recorded at 4000 frames s-1 and slowed 133 times.

+
+
+Download video file (8MB, mov) +
+Supplementary Movie 3

High-speed video of syringeal kinematics during sound production in the Barbary dove. Trans-illumination clearly reveals the inner contours of LVM motion. The visible wires are 18 μm diameter nichrome μEEG wires. Recorded at 5000 frames s-1 and slowed 167 times.

+
+
+Download video file (13.1MB, mov) +
+Supplementary Movie 4

High-speed video of syringeal kinematics during sound production in the ostrich. Tracheal endoscopic view shows presence of both caudocranial as well as ventrodorsal waves. Recorded at 1000 frames s-1 and slowed 67 times.

+
+
+Download video file (11.7MB, mov) +
+Supplementary Movie 5

High-speed video of syringeal kinematics during sound production in the cockatiel. Recorded at 5000 frames/s and slowed 167 times. The morphology of this syrinx does not allow transillumination, but the tracheal endoscopic view clearly shows LVM kinematics during opening and closing of the. Recorded at 5000 frames s-1 and slowed 670 times.

+
+
+Download video file (15MB, mov) +
+Supplementary Movie 6

High-speed video of syringeal kinematics during sound production in the zebra finch. Trans-illumination reveals the inner contours of the left medial labium (ML) motion. The visible wires are 18 μm diameter nichrome μEEG wires. Recorded at 2000 frames s-1 and slowed 335 times. The extracted ML contours (green) were superimposed upon the individual images.

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+
+Download video file (4.8MB, mov) +

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Philosophical transactions. Series A, Mathematical, physical, and engineering sciences logoLink to Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
+
. 2009 Aug 28;367(1901):3239–3254. doi: 10.1098/rsta.2009.0076 +
+
+

New perspectives on the physics of birdsong

+M A Trevisan +1,*, G B Mindlin +1 +
+
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  • +
  • +
+
+ + +
+
PMCID: PMC3263773  PMID: 19620121 +
+

Abstract

+

In this work, we revisit the path that has been travelled during the last few years towards the modelling of the avian vocal organ, the syrinx, using numerical and theoretical techniques from bifurcation theory as analysing tools and present experimental support for the models. This fruitful perspective allowed the retracing of many acoustic features of syllables to intrinsic properties of the syrinx, thereby relocating the bird phonatory organ from the role of a mere vocal instrument of the nervous system to a central source of complex acoustical behaviour.

+

Keywords: birdsong, syrinx, dynamical models

1. Introduction

+

Vocal learning ability, accurate mimicry, song repertoires of extraordinary richness and acoustic versatility are some of the most seductive and intriguing aspects of the field of birdsong.

+

When confronted with the analysis of these phenomena, one might be tempted to think that such complex behaviours are to be associated with extremely complex, sophisticated neural control. This is a reasonable yet delicate hypothesis to make, the main objection being that the role of the peripheric anatomy could be considered mostly as a passive one. In the particular case of songbirds, articulation between the neural code and the actual song is exerted by the avian vocal organ. This organ, the syrinx, is a versatile organ that can display extremely rich dynamics when driven at different regimes. It is located at the junction of the primary bronchi and the trachea, where free moveable connective tissue membranes, the labia, are set in oscillatory motion through an energy exchange from the airstream propelled from the air sacs. Finally, the pressure perturbation attained at the level of the syrinx travels through the trachea and beak before leaving the bird as we hear it.

+

Birdsongs are constituted by sequences of stereotyped acoustic elements called syllables. These song units can be characterized by the shape of their fundamental frequency and their spectral content; in this work, we explore the acoustical effects that can be directly retraced to anatomical and physiological properties of the syrinx. In order to do so, we travel the path from descriptive to operational models of sound production in songbirds, translating sound features to physiological-related parameters of the model.

+

This work is organized as follows. In §2, we present a brief glossary of birdsong, describing the basic anatomical elements involved in sound production, along with an acoustical description of the songs. These elements will be dealt with in §3, where we present a dynamical model for the syrinx and the physically relevant parameters driving it. In this section, we also present experimental support for the model and electronic applications. In §4, we go from descriptive to operational models of the syrinx, relating the physical parameters to physiological ones, and accounting for the acoustical features of song that are inherent to the nature of the vocal organ. In §5, we introduce other sources of acoustical complexity: the interaction between vocal tract and syrinx, and the coupling of the two sound sources in the oscine syrinx. The conclusions and future directions of this research line are discussed in the last section.

2. Elements of birdsong

+

Songbirds can be divided in two classes; roughly one half of the known species are vocal learners, i.e. they need tutors to incorporate their songs. For these birds, learning through imitation is essential for normal communication. Of special interest in this group is the suborder Oscines, equipped with a neural vocal architecture in which two neural pathways can be distinguished: a motor pathway and a pathway involved in song learning (Amador et al. 2008).

+

The suborder Suboscines presents many neural and anatomical differences with respect to the oscines. For instance, they are believed to be vocal non-learners and this difference is manifested in a central motor control of song that appears to be quite different in these two groups of birds. In fact, in some suboscine species, the forebrain set of vocal nuclei is entirely absent (Farries 2004).

+

Since oscines are capable of vocal learning, they have been largely studied, not only at the level of their neural organization but also at the physiological level. The oscine tracheobronchial syrinx is a double, bilateral structure located at the junction of the bronchi and the trachea as schematized in figure 1.

+

Figure 1.

+

Figure 1.

+ +

(a) Sketch of a ventral section of the tracheobronchial syrinx (adapted from Laje et al. 2002) and (b) the main muscles governing it (adapted from Gardner et al. 2001) along with (c) the constituents of the physical model of the syrinx.

Located into the syrinx, the labia are analogous to the vocal folds that are anchored to the larynx in the human phonatory system: they act as valves that are set in motion by the airflow passing through them. These oscillatory valves are composed of connective tissue and are surrounded by a family of muscles. There are evidences that the tracheobronchialis ventralis (vTB) and tracheolateralis muscles actively control the separation of the labia, while the siringealis dorsalis (dS) and the dorsal tracheobronchial (dTB) close the air passage through the labia. This group is therefore correlated with the adjusting of oscillatory conditions of the labia (Goller & Suthers 1996). On the other hand, the siringealis ventralis (vS) muscle is correlated with the frequency of the vocalizations and is believed to control the stiffness of the labia by adjusting the distance between the supporting cartilaginous rings. Two other types of syrinx have been reported: the tracheal syrinx, with a single sound source, and the bronchial syrinx, in which the two sound sources are asymmetrically located in each bronchus. Throughout this work, we deal mainly with tracheobronchial syringes, which have been extensively studied in oscines, it remaining largely unknown whether vocal muscles contribute to frequency control in suboscines. Despite the differences among these groups, the physical mechanisms that lead to sound production are general for all birds. Once the oscillations at the syrinx are reached, the air perturbation travels upwards through the tract formed by the trachea and the beak. This passage through a confined region affects the final acoustic signal. Most importantly, a filtering effect takes place. From a physical point of view, the problem is that of a tube excited by a sound source at one end and opened at the other. The processing of the acoustic signal can be described as follows: the sound waves travel back and forth in the tube, bouncing at the ends and interfering with themselves. The interference enhances the so-called resonant frequencies fn (for an open-end tube of length L, fn=(2n−1)c/4L) and depresses others. The global result is a modulation of the original sound spectrum. All these physiological processes are therefore articulated to produce the sounds that ultimately configure the songs. We next analyse the elements of the song structure.

+

From an acoustical point of view, birdsongs are complex, organized acoustic compositions. The conventional song unit is the syllable, the smallest repetitive sound gesture. Syllables are easily recognized in the standard representation of birdsong, the sonogram, in which the time evolution of the sound frequency is displayed in a colour code associated with the power intensity. In this work (figures 2–5), darker shades of grey correspond to higher spectral intensities.

+

Figure 2.

+

Figure 2.

+ +

(a,b) Two sonograms of a recorded song of a chingolo sparrow and the numerical simulation using syrinx equation (3.4) together with equation (3.5) for the tract. (c) The ellipses correspond to the excursions in parameter space (p0,k) leading to each syllable. The phonation is prevented whenever f0>0 (dotted line) and to allow phonation when the muscle is inactive (f0=0). The numbering corresponds to the successive syllables, the last one (number 4) repeated seven times. This figure is adapted from Laje et al. (2002), where parameter values are specified.

Figure 3.

+

Figure 3.

+ +

Experimental support for the sound production model (equations (3.4) and (3.5)) fed with physiological instructions (a) of air sac pressure, vS and dTB muscle activities. The smoothed time traces of the solid curve with squares, solid curve and dotted curve are associated with parameters p0, k and f0, respectively. (b,c) Sonograms of the recorded and resulting synthetic syllables. Adapted from Mindlin et al. (2003).

Figure 4.

+

Figure 4.

+ +

(a) Sonogram from a song of zebra finch Taeniopygia guttata and (b) syllable classification scheme (faff, SCI). Adapted from Sitt et al. (2008).

Figure 5.

+

Figure 5.

+ +

Typical great kiskadee (Pitangus sulfuratus) three-syllable song. (a) Simultaneous measurements of air sac pressure and song spectrogram and (b) the simulated song using (i) a linear restitution function, (ii) a first order nonlinear restitution function when the syrinx model is fed with (iii) the pressure time trace. Adapted from Amador et al. (2008).

In figures 2–4, we show sonograms from oscine birds: a chingolo sparrow (Zonotrichia capensis), a cardinal (Cardinalis cardinalis) and a zebra finch (Taeniopygia guttata), respectively. In figure 5, a very stereotyped song from the suboscine great kiskadee (Pitangus sulfuratus) is displayed.

+

As readily seen from the figures, the different song programmes can be the result of quite complicated combinations of syllabic repertoires (for some species such as brown thrashers, repertoires can have thousands of syllables), sometimes organized out of nearly fixed blocks of syllables called motifs. From pressure studies, it is known that songs are not completed with a single breath at the beginning but instead very short falls of pressure below atmospheric pressure occur between syllables that enable the bird to execute very long song sequences (Hartley 1990). These minibreaths are observable in the pressure time traces of figures 3 and 5.

+

A spectroscopic analysis of the syllables reveals many possible fundamental frequency traces: constant, up-sweeps, down-sweeps, ‘n’-shaped and more complex curves. Frequency and duration ranges vary across the different bird species; for instance, the chingolo sparrow presents syllabic fundamental frequencies typically ranging from 2 to 7 kHz and durations from 10 to 300 ms (figure 3).

+

A first question then arises: what are the basic physical ingredients to construct a model for the generation of sounds in the syllabic ranges? We address this issue in the next section.

3. A descriptive model of the syrinx

+

One of the simplest models that captures the physical principle of energy transfer from the airflow to the tissue membranes was originally introduced by Titze (1988) for the vocal folds. This mechanism was recently observed using videography in the syrinx Larsen & Goller (1999), and is based upon the observation of surface waves travelling upwards through the folds during the oscillatory cycle, presenting a syrinx of convergent profile when the labia move away from each other and a syrinx of divergent profile in the closing semicycle (figure 1).

+

While presenting a convergent profile during the opening cycle, the interlabial pressure is closer to the bronchial pressure, while it approaches atmospheric pressure when presenting a divergent profile, in the closing cycle. This asymmetry of the syringeal pressure values in the complete cycle ensures an overall force in the direction of the velocity of the labia, transferring energy from the airstream to the moving tissue, eventually compensating its dissipative effects and allowing sustained oscillations.

+

The simplest way to describe the principle of self-oscillating dynamics of the labia is to consider the dynamics (per unit area) for the midpoint of the folds +

+ + + +
3.3.1
+

+where M is the mass of the labium, K its stiffness and B a constant characterizing the dissipation of the tissue. Ps is the syrinx interlabial pressure and F0 a constant force term that controls the stationary position of the labia. Dividing by the mass and rearranging the equation into an explicit two-dimensional form gives +

+ + + +
3.3.2
+

+where we use lower cases for the redimensioned parameters, and a first-order approximation for the average interlabial pressure ps=p0y (Titze 1988), making it proportional to the air sac pressure p0 and ‘in phase’ with the velocity of the oscillating membrane. Even at first order, this system captures the basis of labial dynamics: when the energy transfer from the airstream p0 compensates the dissipation β1, we have β1−p0=0 and the system reduces to the harmonic oscillator, with solutions reproducing the appropriate syllable frequencies for realistic parameter values (Laje et al. 2002). On the other hand, whenever the dissipation takes over pressure (β1>p0), the oscillations are damped, and the system returns eventually to rest.

+

A first correction to the system would be to avoid the divergence of solutions in the case β1<p0. For this, we consider a nonlinear dissipation function, +

+ + + +
3.3.3
+ + + +
3.3.4
+

+which accounts for the effect of collision of the labia for large-amplitude oscillations. This is a first-order nonlinear function that preserves the symmetry of the dissipation funtion, i.e. an odd function of the velocity and even function of the space.

+

From a dynamical point of view, this system is a slight variation of the van der Pol oscillator: at the point of instability, relaxation oscillations are born in a Hopf bifurcation with no spectral content and they become spectrally richer as they grow in amplitude.

+

In order to generate song, it is assumed then that the bird produces a set of basic gestures that are identified with the parameters of the model: the elasticity term k is associated with the activity of syringeal muscles controlling the stiffness of the labia (vS activity is shown to be correlated with the frequency of the vocalization and not with airflow gating; Goller & Suthers 1995), the parameter p0 with the air sac pressure and f0 with the active airflow gating controlled by muscles dS and vTB (Laje et al. 2002).

+

Right after being created at the syrinx, the sound wave of speed v travels through the bird’s trachea and beak.

+

Approximating this vocal tract by a tube of length L characterized by an impedance with respect to atmospheric pressure, i.e. a reflection coefficient α, the sound wave at the tube entrance a(t) can be calculated as the result of the reflections in the tube: +

+ + + +
3.3.5
+

+where pin stands for the pressure fluctuations injected into the tract owing to the airflow modulations.

+

With the complete model for the vocal anatomy (equation (3.4) for the syrinx and equation (3.5) for the tract), a natural question arises: what kind of excursions in the parameter space should the bird have to coordinate in order to reproduce the different syllable types?

+

In order to answer this question, we first make the following remarks. +

+
    +
  1. We note that the bifurcation diagram in parameter space (p0,k) shows a critical value of pressure p0 above which the self-oscillations are induced through a Hopf bifurcation (figure 2, shaded region). In this region, the fundamental frequency of the oscillations increases with tension k as indicated by the curves of iso-fundamental frequency (Gardner et al. 2001).

  2. +
  3. The time scales associated with the duration and the fundamental frequency of the syllables are well separated, and therefore the time course of k will essentially trace the time course of the fundamental frequency.

  4. +
  5. Since many birdsongs are consituted by repetitions of roughly similar elements followed by minibreaths, we assume that the paths in parameter space (p0,k) should be cyclic across songs (Laje et al. 2002).

  6. +
+

In this way, each syllable type can be expressed as follows: +

+ + + +
3.3.6
+ + + +
3.3.7
+

+i.e. as elliptic paths in parameter space (p0,k) that depend on simple linear ϕ(t) functions. The onset and termination of phonation is controlled by f0, as phonation is prevented when a threshold is exceeded (Inline graphic).

+

Examples of the synthesized syllables are displayed in figure 2 for a chingolo sparrow song (Laje et al. 2002). Minibreaths between syllables are easily explained from this description: they correspond to the little portion of the excursion in parameter space occurring outside the oscillation region for negative pressure values.

+

This is a remarkable property of the proposed model: a two-dimensional dynamical system driven through elliptic trajectories in parameter space span all the repertoire of syllabic types (Mindlin & Laje 2005).

+

Beyond this appealing property, such a small number of variables and parameters needed to synthetize song from physiologically related instructions allow us to conceive applications for the proposed model. There is evidence that during the period of vocal learning, juvenile songbirds reconfigure their brains. Moreover, adult birds are subjected to active auditory feedback to maintain the quality and stability of their crystallized songs: in particular, recent experiments showed that deafening adult birds causes normal song degradation (Nordeen & Nordeen 1992; Leonardo & Konishi 1999). Therefore, it is of particular interest to design experiments to manipulate auditory feedback in real time, without interfering with either the motor or the auditory pathways.

+

In Zysman et al. (2005), a biomimetic device emulating the action of the avian vocal organ was constructed. This electronic circuit analogically integrates equation (3.4) for the dynamics of a syringeal labium which is equivalent to the acoustic pressure pattern executed by tonal birds, constituting a robust, low time-processing device suitable for carrying out online alterations of auditory feedback. Yet, these experiments require measuring physiological variables for long periods of time, keeping cannulae inserted in the air sacs or muscles wired for days after surgery, which is unlikely to be feasible.

+

A solution was explored by extracting the controlling parameters of the syrinx out of birdsongs in real time. For that, two transducers were built: one that reconstructs the air sac pressure from the sound signal in real time and the other for the tension of the vS muscle.

+

Tests were performed in which recorded vocalizations of cardinals were reconstructed in two steps: first, air sac pressure and tension of the labia were driving reconstructed using the transducers and, second, the reconstructed functions were fed to the electronic syrinx. Sonograms of both the real song and the reconstructd one present qualitatively the same features.

+

In this way, these devices open new perspectives for the experimental work in the field, making it possible to perform specific changes in biologically relevant parameters that can be made within very short response times (of approx. 10% of the syllabic duration).

+

So far, we successfully compared the synthetic sounds coming from the numerical integration of the descriptive model for the syrinx equation (3.4) and vocal tract equation (3.5) with experimental song recordings. Moreover, features like low-dimensionality and few driving parameters allowed the construction of biomimetic applications. Beyond all these suggestive features, the model can also be tested and validated when driven with experimental instructions from singing birds.

+

In Mindlin et al. (2003), simultaneous recordings of dTB and vS muscle activities along with air sac pressure were made from 13 samples of spontaneous songs from two cardinals (Cardinalis cardinalis). With this specific choice, i.e. one gating and one labium stiffness-related muscles, experimental signals were associated to the parameters of the model f0 and k. The muscle activity was recorded through electromyographs (EMGs), measured by electrodes implanted into the syringeal muscles. EMG records consist of spiky signals that need to be smoothed and rectified (Mindlin et al. 2003) in order to obtain envelope curves that can be used as inputs for the model equation (3.4).

+

On the other hand, pressure–time traces were captured by a cannula inserted into the anterior thoracic air sac and connected to a piezoresistive pressure transducer. The details of the procedure can be found elsewhere (Goller & Suthers 1996). These time traces were associated with the parameter p0.

+

Linear relationships were assumed between smoothed vS and dS muscle activity and air sac pressure and the corresponding parameters of the model. After the scaling, the syrinx model was fed with the parameters in order to synthesize song.

+

Beyond the remarkable agreement between synthetic and experimental songs (as shown in figure 3), the model predicts that for upsweeps, the lower value of f0 that prevents phonation at the beginning of the syllable is smaller than the value of f0 at its end. This prediction of the model was observed for all the experimental data analysed.

4. Acoustic complexity and syrinx dynamics

+

So far, we analysed the implications of a descriptive model of the syrinx. Within this model, modulations of fundamental frequency could be mapped to simple trajectories in phase space for the driving parameters. For many bird species that produce nearly tonal syllables, like sparrows (figure 2) and cardinals (figure 3), this model holds. On the other hand, zebra finches produce a wide variety of syllables with variable spectral load (figure 4).

+

In order to investigate the nature of this variability, two quantities were defined from the spectral characterization of the syllables: the average fundamental frequency (faff) and the mean spectral frequency (fmsf; Sitt et al. 2008). The faff is determined as the mean pulse rate for low-frequency sound segments and as the first peak in the fast Fourier transform for high-frequency sound segments and the fmsf as the ponderate sum of the frequency peaks fi using the relative spectral energies as weights +

+ + + +
4.4.1
+

The spectral content index SCI=fmsf/faff allows us to compare the spectral content of different syllables.

+

Then, for a large variety of songs of different birds, a graph was constructed with each syllable corresponding to a point in the (faff,fsci) space (figure 4). Surprisingly, all the points cluster in a small region, strongly suggesting a funtional relationship between fundamental frequency and spectral richness of the bird sounds.

+

In order to analyse the data, we consider the model described in equation (3.4) taking explicitely into account the surface profile of the syrinx observed during videoscopy. Taking straight lines to simplify the geometry of the membranes (figure 1), it is possible to relate the positions of the upper edge a and lower edge b of the labium in terms of a phenomenological constant τ as follows (Gardner et al. 2001): +

+ + + +
4.4.2
+

Substituting these equations into an expression proposed by Titze (1988) for the average syringeal pressure p0=ps(1−a/b) in terms of the air sac pressure ps, the dynamics of the labium results +

+ + + +
4.4.3
+ + + +
4.4.4
+

+where Δ=a0−b0 is the syrinx profile difference at rest (figure 1).

+

Compatible with the symmetry of the restitution (odd spatial function) and the dissipation (odd velocity and even space funtions), the first terms of their nonlinear expansions are: k(x)=k1+k2x2 and β(x,y)=β1+β2x2+β3y2.

+

The coefficients k2, β2 and β3 become relevant as the departure of the rest position and the velocity of the labia reach large values, i.e. for fast and large oscillations, and their actual values (used to synthesize song) are several orders of magnitude smaller than the coefficients of the linear terms k1 and β1 (Sitt et al. 2008).

+

From a dynamical point of view, a possible candidate bifurcation for the described spectral richness is a saddle node in a limit cycle (SNILC): oscillations start as a stable stationary point is annihilated by an unstable one. Right after the bifurcation takes place, the system spends much of its time in the region near the bifurcation (its period T is proportional to (ac−c)1/2, where a is the control parameter and ac its value at the bifurcation). As the oscillations are born with finite amplitude and zero period (Sitt et al. 2008), they display a rich spectral content. In Sitt et al. (2008), it is shown that this bifurcation can be identified in system (4.4).

+

Remarkably, placing the parameters in the vicinity of the bifurcation and classifing the simulated sounds in the SCI=fmsf/faff space as a function of the pressure p0, we obtained a curve that closely fits the experimental points (dotted line in figure 4) for low-frequency syllables. This prediction of the model is consistent with experimental observations of no ventral syringeal muscle activity for low-frequency sounds (Vicario 1991).

+

Moreover, the model gives an insight for a possible biological mechanism responsible for the relationship between fundamental frequency and spectral load in high-frequency sounds (above 1.5 kHz): assuming a linear coupling between the ventral syringeal muscle activity f0 and the pressure p0, the obtained theoretical curve fits closely the experimental data points (figure 4, solid line).

+

In this way, the dynamical signature revealed by the spectral content versus fundamental frequency in the zebra finch allows a simple biological explanation in terms of the model: a vocal organ ‘tuned’ in the vicinity of an SNILC bifurcation can produce a variety of spectrally rich sounds by the driving action of the air sac pressure or a simple combination of air sac pressure and dorsal muscles.

+

Another very illustrative example supporting the key role of nonlinearities in the syrinx comes from the order Suboscines, a group of birds that does not belong to the songbirds and whose general differences from oscines were presented in §2.

+

The particular case of the great kiskadee (Pitangus sulfuratus) presents a tracheosyringeal syrinx with two independently controlled sound generators, each of which consists of a pair of oscillating labia. Three pairs of muscles take control of the syrinx: the extrinsic muscles m. sternotrachealis and m. tracheolateralis and the intrinsic muscle m. obliquus lateralis.

+

The song of the great kiskadee consists of a nearly fixed sequence of three syllables that presents an interesting property: simultaneous recordings of air sac pressure and fundamental frequency look very alike (both time traces are shown in figure 5b).

+

This resemblance was quantified in Amador et al. (2008) and the analysis confirmed a highly significant linear correlation between fundamental frequency of the syllables and air sac pressure for this bird, suggesting a weak (if any) dependence of the song on the activity of the syringeal muscles.

+

To confirm the independency of the sound generation from the activity of syringeal muscles, experiments were performed comparing songs of normal birds and birds with both tracheosyringeal muscles transected. While equivalent experiments performed in songbirds reveal striking changes in song production and even complete loss of phonation (Daley & Goller 2004; Suthers & Zollinger 2004), the air sac pressure patterns and songs of the kiskadee remained remarkably unaffected by denervation (Amador et al. 2008).

+

How does the syrinx behave when controlled by the single variable representing air sac pressure p0? In Amador et al. (2008), numerical integration of a set of equations for a flapping model was performed. Interestingly, a striking quantitative agreement between synthetic and natural songs was achieved when the restitution constant k was expanded to first-order nonlinear terms (consistent with its odd symmetry), k=k1+k2x3, while the linear case performed poorly (figure 5b).

+

In this way, a very simple mechanism of transducing air sac pressure into frequency modulations is revealed: when the hypothesis of a linear restitution approximation is replaced by a first-order nonlinear one, the air sac pressure does not only account for the onset of oscillations but it also shifts the midpoint of the folds, transducing higher pressure into higher oscillation frequencies.

5. Other sources of acoustic complexity

+

In the previous section, we showed that much of the acoustic richness of birdsong emerges from the nonlinear nature of the syrinx. Nevertheless, the isolated sound source is not the only possible origin of rich acoustic behaviour in birds. In this section, we will briefly describe the acoustical effects that may take place when considering the feedback between the syrinx and the vocal tract, i.e. the source–filter interaction, and the source–source interaction, in the case of bilateral syringes.

+

Throughout this work, we treated the problem of sound generation in birds under the assumption of the source–filter hypothesis. According to this hypothesis, the source of sound and the filtering of the tract are acoustically uncoupled. This is the case for the voice during normal speech (Titze 1988).

+

In Laje & Mindlin (2005), a two-dimensional model for the syrinx (as the one of equation (4.4)) is used to explore the coupling effects with the vocal tract. The reason behind this choice is a compromise between realism and mathematical simplicity: a higher dimensional model of the syrinx would be capable of generating complex labial dynamics by itself, so we restrict ourselves to the simplest case to specifically study the coupling effects.

+

The coupling is taken into account by considering an expression for the interlabial pressure p0 that explicitly depends on both the sublabial pressure ps and input pressure at the vocal tract pi. In Laje & Mindlin (2005), it is shown that pi is a combination of both the pressure perturbations injected locally into the vocal tract by the sound source and the pressure resulting from the reflections at the end of the tract, pi(t)=s(t)−γpi(t−T), where Inline graphic. Here, T is the time for the sound wave to propagate back and forth through the tract and γ is the reflection coefficient for the tract–atmosphere interface.

+

From the simulations of the complete model of interacting sources and tract, it is observed that complex periodic and aperiodic solutions appear, as well as period-doubling bifurcations. In the particular case of supressing the tract coupling and considering only the two sources active, sound simulations display subharmonic content that is not present in the individual source spectra. The analysis developed in Laje & Mindlin (2005) allows us to make predictions that could be tested through specific experiments. The core idea is that coupling parameters Inline graphic and Inline graphic can be modified through the atmospheric pressure ρ if, for instance, atmospheric nitrogen were replaced with the lighter helium.

+

Experiments of this type were performed in the past to test other hypotheses (Nowicki 1987). Results were either changes in the fundamental frequency of the oscillations or changes in the resonant frequencies of the vocal tract with little or no effect on the fundamental frequency. However, other effects could be expected from strong enough coupling effects: in particular, simulations of a single source with feedback show that as the pressure parameter ps is decreased, subharmonic frequencies disappear in a period-halving bifurcation in normal air, while they are not present at all in a helium-like atmosphere. Interestingly, this effect would disappear if the dynamical origin was different: simulations of more complex syrinx models such as the asymmetric two-mass model without vocal tract coupling are less sensitive to density changes in the athmosphere and consequently the subharmonic spectral content is present in either the normal or the heliox atmosphere.

6. Conclusions and future perspectives

+

In this work, we reviewed the main results in the mathematical modelling of the syrinx. The starting point was a sound production model capturing the physics of the oscillatory dynamics of the labia, driven by parameters that can be easily associated with physiological instructions. This model is capable of producing synthetic songs in the correct acoustical ranges, showing good qualitative agreement with experimental sound records for all the studied species. Moreover, driving the syrinx model with real physiological instructions recorded from the activity of muscles and air sac pressure during spontaneous singing allowed one to test specific predictions of the model and producing very similar real and synthetic songs.

+

An interesting feature of the model is its mathematical austerity: a condition that allows conceiving robust, self-standing biomimetic applications. As a particular case, in this work, we reviewed an analogic circuit that successfully mimics an electronic syrinx, adaptable to generate sound in real time upon physiological instructions, making it specially suitable for feedback auditory experiments.

+

Next we showed how the addition of first-order nonlinear terms to the basic model leads to the dynamical conditions accounting for the spectral richness displayed by non-tonal birds. Of special interest is the study of a bird belonging to the Suboscine suborder, a class of birds whose vocal mechanisms remain in other respects largely unknown.

+

Finally, alternative sources of acoustical complexity in birdsong were presented when the coupling effects of two sound sources and the acoustic coupling of the sound sources with the vocal tract were taken into account.

+

Merging mathematical modelling with complex biological behaviour accounts for just a few successful examples in the literature (Golubitsky et al. 1999). The analytic programme reviewed in this work demonstrates it to be a good vehicle to identify the different sources of complexity in birdsong and, interestingly, it also suggests what types of syringeal control could be expected from a vocal neural programme: one that exploits the nonlinear nature of its peripheric organs, in which slight changes in the neural instructions could promote rich and complex acoustic responses.

+

This programme opens a spectrum of future research lines, starting with the exploration of the dynamical regimes of a fully developed syrinx model, which is already an ongoing work (Amador & Mindlin 2008).

+

Another branch is the development of biomimetic technology devoted to artificially replace not only anatomical parts but also neural portions of biological systems and helping elucidate the neural song programme through acoustic feedback experiments. We arrive in this way at the theoretical motivation of this research, which is to unveil the path that goes from the syrinx to the brain (Abarbanel et al. 2004; Amador et al. 2005; Trevisan et al. 2006) and to build a model of the vocal production and song generation and coding, a virtual brain and periphery revealing the very nature of the interactions between nervous system and anatomy.

Acknowledgements

+

This work was partially funded by the University of Buenos Aires, CONICET, ANPCyT and NIH (through grants R01 DC-06876 and R01 DC-04390).

Footnotes

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The Journal of the Acoustical Society of America logoLink to The Journal of the Acoustical Society of America
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. 2024 Aug 22;156(2):1283–1308. doi: 10.1121/10.0028267 +
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+

Synthetic, self-oscillating vocal fold models for voice production researcha) +

+Scott L Thomson +1,b),✉ +
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PMCID: PMC11348498  PMID: 39172710 +
+

Abstract

+

Sound for the human voice is produced by vocal fold flow-induced vibration and involves a complex coupling between flow dynamics, tissue motion, and acoustics. Over the past three decades, synthetic, self-oscillating vocal fold models have played an increasingly important role in the study of these complex physical interactions. In particular, two types of models have been established: “membranous” vocal fold models, such as a water-filled latex tube, and “elastic solid” models, such as ultrasoft silicone formed into a vocal fold-like shape and in some cases with multiple layers of differing stiffness to mimic the human vocal fold tissue structure. In this review, the designs, capabilities, and limitations of these two types of models are presented. Considerations unique to the implementation of elastic solid models, including fabrication processes and materials, are discussed. Applications in which these models have been used to study the underlying mechanical principles that govern phonation are surveyed, and experimental techniques and configurations are reviewed. Finally, recommendations for continued development of these models for even more lifelike response and clinical relevance are summarized.

I. BACKGROUND AND OVERVIEW

+

Human voice production arises from a complex set of interactions between neurological, physiological, and mechanical processes (Gray, 2000; Titze, 2000; Zhang, 2016). During voicing, air flow from the lungs provides the energy for vocal fold (VF) self-oscillation, which in turn causes a temporal pressure fluctuation within the supraglottal airway that is the source of voiced sounds. In this process of phonation, aerodynamics, tissue dynamics, and acoustics are tightly coupled. To understand these mechanical processes, researchers have employed a range of theoretical analyses, computational simulations, and physical experiments.

+

Early experiment-based explorations of the larynx and voice production include Leonardo da Vinci's 17th century annotated anatomical sketches (da Vinci, c. 1510-11; Clayton and Philo, 2014). Excised larynx studies were conducted as early as the 18th century, including Ferrein (1741), who is credited as having been the first to use the term “vocal cords” (Berke et al., 1987; Markatos et al., 2019). Müller (1839) reported experiments using excised avian and primate larynges. As summarized by Flanagan (1972) and Fagyal (2001), this time period also saw the development of mechanical devices to synthesize voiced sounds via flow-induced vibration of reeds (e.g., von Kempelen, 1791). Development of vocal fold-like structures to provide sound for talking robots has continued in modern times (e.g., Fukui et al., 2005; Fukui et al., 2007; Fukui et al., 2008; Endo et al., 2014). For additional historical discussion, see Berke et al. (1987) and Markatos et al. (2019).

+

Synthetic VF models have also long been used to study the physics of phonation, including static models (e.g., Scherer et al., 2001), models with prescribed motion (e.g., Mongeau et al., 1997), and self-oscillating models. Self-oscillating VF models mimic the fundamental flow-induced vibration characteristic of human VFs to study coupled fluid, structure, and acoustic interactions and have been designed with varying degrees of fidelity. In addition to his excised larynx studies mentioned previously, Müller (1839) described synthetic larynx and vocal fold models (see Fig. 1). Other early descriptions of synthetic, self-oscillating VF models include Ewald (1913), Wethlo (1918), and Smith (1961, 1966). Since the 1990s, there has been a significant increase in the number of studies using self-oscillating VF models. Scientific advances that have facilitated these increased modeling efforts include the availability of commercial materials with stiffness characteristics suitable for VF modeling; the emergence of modern experimental tools, such as high-speed imaging, particle image velocimetry (PIV), and data acquisition devices; and continued research into laryngeal morphology and function that has driven the need for experimental validation as well as in-depth, systematic exploration.

+

FIG. 1.

+

FIG. 1.

+ +

Self-oscillating synthetic vocal fold model. Adapted from Fig. 39 of Müller, J. P. (1839). Über die Compensation der physischen Kräfte am menschlichen Stimmorgan: Mit Bemerkungen über die Stimme der Säugethiere, Vögel und Amphibien (On the compensation of the physical forces in the human vocal organ: With remarks on the voice of mammals, birds and amphibians) (A. Hirschwald, Berlin); from the Digital Collections of Weimar University Library.

A review of static, driven, and self-oscillating VF models was published by Kniesburges et al. (2011). Since that time, self-oscillating VF modeling has experienced accelerated growth in terms of design, functionality, and application. The purpose of this review is to provide an up-to-date, comprehensive review of synthetic, self-oscillating VF models. This paper is organized as follows. A brief overview of human VF morphology and function is provided, the use of VF models in voice research is introduced, and the two most common types of synthetic, self-oscillating VF models are described in detail. Applications in which these models have been used are surveyed, and experimentation techniques are summarized. Finally, areas for future development are recommended.

II. VOCAL FOLD MORPHOLOGY AND FUNCTION

+

The structure and function of the human VFs are well-documented (e.g., Hirano and Sato, 1993; Gray, 2000; Titze, 2000; Sato, 2018). A brief overview of aspects most pertinent to VF modeling is here provided; for a more complete review, see Zhang (2016). As illustrated in Fig. 2, two opposing VFs are located at the top of the trachea in the respiratory airway within the larynx. The glottis is the space between the VFs, and the spaces above and below are the supraglottic and subglottic regions, respectively. Each VF is comprised of multiple layers of tissue of differing composition and stiffness, including muscle, lamina propria, and epithelium, with the lamina propria consisting of three layers as shown in Fig. 2. The intermediate and deep layers of the lamina propria are commonly collectively termed the vocal ligament (Hirano et al., 1982).

+

FIG. 2.

+

FIG. 2.

+ +

Frontal cross-sections of the larynx (left; Gray, 1918) and VF (right; Titze, 2000). The intermediate and deep layers of the lamina propria are commonly collectively referred to as the vocal ligament, and the muscular region as the vocal fold body. Credits: (Left) Adapted from Gray, H. (1918). Anatomy of the Human Body, 20th ed., edited by W. H. Lewis (Lea and Febiger, Philadelphia). (Right) Adapted with permission from Titze, I. R. (2000). Principles of Voice Production, Second Printing. (National Center for Voice and Speech, Iowa City). Copyright 2000 National Center for Voice and Speech.

During respiration, the VFs are abducted to allow air exchange between the lungs and mouth. During voicing, the VFs are adducted and air flowing from the lungs initiates and sustains VF flow-induced vibration. This causes periodic interruption of the glottal jet, with the associated pressure fluctuations being the source of sound for voice production. This process is termed phonation.

+

The relative composition of collagen and elastin fibers causes a variation in stiffness between VF layers (Gray, 2000; Madruga de Melo et al. (2003); Tateya et al., 2006; Chan et al., 2007). For modeling purposes, key characteristics of the spatial stiffness variation include the following. The muscle, which is also referred to as the VF body, is relatively stiff when active. The ligament consists of the intermediate and deep layers of the lamina propria and is transversely isotropic, with the plane of isotropy being aligned with the frontal anatomical plane and the anterior-posterior (out-of-plane) stiffness exceeding that of the in-plane stiffness. The superficial lamina propria is exceedingly flexible, and the epithelium is thin yet strong enough to withstand vibration. During voicing, the superficial lamina propria and epithelium layers experience the bulk of vibration, although the ligament and body also experience motion.

III. VOCAL FOLD MODELING

+

Phonation involves coupled, complex biological and mechanical phenomena including neurological feedback and control mechanisms, cellular mechanobiological responses, muscle activity, air flow, blood flow, vibrating tissue dynamics, acoustical source-filter interactions, and ultimately sound production. A variety of models have been employed to investigate the underlying mechanical components of phonation, i.e., primarily air flow, tissue dynamics, and acoustics. Such approaches have included in vivo and excised larynx models (Döllinger et al., 2011), theoretical and computational models (Alipour et al., 2011; Döllinger et al., 2023), and synthetic models (Kniesburges et al., 2011).

+

In vivo, excised, computational, and synthetic models constitute a set of approaches with complementary limitations and capabilities. The relative merits of these types of models include the following (portions of which have been adapted from Hilton and Thomson, 2022). In vivo and excised larynx models are morphologically authentic but limited in terms of repeatability, parameterizability, and longevity. Excised larynges are subject to tissue degradation. The material properties and geometries of computational models can be precisely defined and used to directly generate desired data (e.g., pressure, velocity, flow rate, and vibratory motion) with spatiotemporal resolution commensurate with model fidelity. However, computational models are based on mathematical approximations of highly nonlinear physical phenomena, and high-fidelity simulations require substantial resources of time and hardware to set up, validate, simulate, and post-process. In contrast, the physical phenomena that are only approximated in computational simulations are inherently present within in vivo, excised, and synthetic model experiments; physical experiments are thus necessary to validate computational simulations. Synthetic models typically exhibit greater longevity and are generally more materially and geometrically parameterizable than in vivo and excised larynges but less so than computational models.

+

Experiments using synthetic VF models possess several key advantages. First, experimental data are directly measured, as opposed to being modeled in simulations. This is critical owing to complex, nonlinear, and coupled phenomena such as turbulence, flow separation, large deformation and strain, collision, acoustic coupling, and radiated acoustics that are, in many cases, difficult to accurately model theoretically or simulate computationally. This first advantage is shared with in vivo/excised larynx-based experiments. Second, data can be gathered in a benchtop setup that would be more difficult to acquire (if not impossible) than in vivo. This is facilitated by synthetic model longevity as well as greater instrument access than in vivo and that is, in some cases, more convenient than in excised larynx experiments. Third, control over synthetic model stiffness and geometry enables parametric exploration of isolated variables. With in vivo and excised larynges, abduction and adduction can be controlled, but there is only limited control over other parameters such as viscoelasticity and underlying geometry. Further, duplicate synthetic models of the same nominal configuration can be fabricated and tested. Fourth, synthetic VF models can vibrate without interruption for a very long time. For example, the study of Drechsel and Thomson (2008) required approximately 4.5 h of continuous vibration of a synthetic, self-oscillating VF model, in addition to several additional hours of vibration during experiment preparation. Finally, while synthetic model experimentation requires model fabrication and setup, they can be conducted without excised larynx procurement and preparation, and they do not require heating and humidification of air or periodic specimen hydration.

+

The previously noted synthetic VF modeling advantages are common to rigid, driven, and self-oscillating models. The need for self-oscillating models stems from human phonation being, fundamentally, a flow-induced vibratory process in which flow, solid, and acoustic dynamics are tightly coupled. Thus, self-oscillating models offer the advantages of synthetic models with the benefit of providing a phonomimetic platform to facilitate the study of phonatory flow-structure-acoustic interactions.

+

Synthetic VF models, and particularly self-oscillating VF models, possess limitations and present unique challenges. First, physiological and neuromuscular processes are not represented. Second, owing to the complex tissue composition of the VFs, developing models that accurately mimic human VF form and function is difficult. For example, VF tissue is materially nonlinear (Alipour‐Haghighi and Titze, 1991; Alipour et al., 2013), anisotropic (Alipour et al., 2000; Cook and Mongeau, 2007; Cook et al., 2008; Cook et al., 2009), and exhibits variations between tissue types (Gray, 2000) with concomitant spatial variations in stiffness. On the other hand, synthetic models typically have distinct layer transitions and are comprised of linear, isotropic materials (with a few exceptions, as discussed in the following). Further, the geometries and material properties of the human VFs have yet to be fully defined and are highly variable between individuals, across the lifespan, and according to physiological state (e.g., health, hydration, and vocal conditioning). Fabrication challenges arise due to some human VF tissue layers being exceptionally soft and thin (e.g., Hirano et al., 1982, reported cover layer thicknesses of around 0.3 mm and combined intermediate and deep lamina propria layer thicknesses of around 1 mm). Third, achieving synthetic VF model self-oscillation with lifelike characteristics (e.g., mucosal wave and collision) is nontrivial. Finally, whereas the motion of driven synthetic models is known and highly repeatable, the motion of self-oscillating models is unknown and must be measured, is less repeatable, and is subject to temporal and vibration-induced material property changes, such as creep and stress relaxation. In many respects, therefore, self-oscillating models occupy a space between rigid/driven models and excised/in vivo larynges in terms of complexity.

IV. SYNTHETIC, SELF-OSCILLATING VOCAL FOLD MODELS

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The advantages and limitations of synthetic, self-oscillating VF models have led to numerous development and application research pursuits. A key underlying premise is that if a model is defined with a spatial distribution of stiffness (i.e., a combination of geometry and material properties) that matches the human VFs, and if the airway configuration is similarly representative of the human airway, then the model will vibrate with frequency, onset pressure, and motion characteristics that are typical of human phonation. However, phenomenological modeling approaches have also proved to be beneficial. While efforts to develop truly phonomimetic models are still ongoing, models with favorable flow-induced responses have been developed and successfully used in a range of applications. In this section, the models are presented in detail, and in Sec. V, applications are surveyed.

+

While the different synthetic, self-oscillating VF models described in the literature share varying degrees of structural and functional commonality, most can be classified as being one of two types: those comprised of a thin membrane that encapsulates a liquid or viscoelastic substance (e.g., a water-filled latex tube), and those that are predominantly comprised of soft elastic solid(s) (e.g., ultrasoft silicone formed into a VF-like shape). For convenience, these are here referred to as “membranous” and “elastic solid” types, respectively. Other types of self-oscillating models have been studied, such as collapsible tubes for human phonation (Conrad, 1980, 1985; Berke et al., 1991), avian phonation (Elemans et al., 2009), and tracheoesophageal speech (Tourinho and da Silva, 2023); a spring-supported VF model (Sidlof et al., 2011); and a vibrating reed (Yoshinaga et al., 2021). The membranous and elastic solid models are the focus of this review owing to their prevalence in recent literature and are discussed in Secs. IV A and IV B, respectively.

+

A. Membranous vocal fold models

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Membranous VF models are comprised of a vibrating, flexible membrane encapsulating a liquid or viscoelastic substance that occupies the space between the membrane and a rigid body. Several examples are shown in Fig. 3. Most commonly, this encapsulated region has been filled with a liquid—most commonly water—although other materials have been used. The undeformed shape of the vibrating portion is primarily dictated by the initial membrane and rigid body geometries as well as the hydrostatic pressure within the encapsulated region.

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FIG. 3.

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FIG. 3.

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(Color online) (a) Silicone membrane covering a rigid body with fluid filling the space between the membrane and body. (b) Schematic of pressurized latex tube (PLT) model to represent a brass player's lips, along with top view illustration with flow out of the page (inset region with dashed border). (c) Picture of PLT model of human VFs. (d) PLT model. (e,f) Membranous VF model with latex fitted to wedge-shaped body. Credits: (a) Adapted from Titze, I. R., Schmidt, S. S., and Titze, M. R. (1995). “Phonation threshold pressure in a physical model of the vocal fold mucosa,” J. Acoust. Soc. Am. 97, 3080-3084, with permission of Acoustical Society of America. Copyright 1995 Acoustical Society of America. (b) Adapted from Vilain, C. E., Pelorson, X., Hirschberg, A., Le Marrec, L., Op't Root, W., and Willems, J. (2003). “Contribution to the physical modeling of the lips. Influence of the mechanical boundary conditions,” Acta Acust. United Ac. 89, 882-887, with permission of European Acoustics Association. Copyright 2003 European Acoustics Association. (c) Reproduced from Ruty, N., Van Hirtum, A., Pelorson, X., Lopez, I., and Hirschberg, A. (2005). “A mechanical experimental setup to simulate vocal folds vibrations: preliminary results,” ZAS Papers in Linguistics 40, 161-175; licensed under a Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0) license (https://creativecommons.org/licenses/by-sa/4.0/). (d) Used with permission from van Hirtum, A., Ahmad, M., Chottin, R., Pelorson, X. (2023a). “A Composite Analogy to study the Linear Elasticity of a Pressurised Latex Tube with application to a mechanical vocal fold replica,” Int. J. Appl. Mech. 15, 2350068. Copyright 2023 World Scientific Publishing Co., Inc. (e,f) Adapted from Krebs, F., Silva, F., Sciamarella, D., and Artana, G. (2012). “A three-dimensional study of the glottal jet,” Exp. Fluids 52, 1133-1147, with permission from SNCSC. Copyright 2011 Springer-Verlag.

Titze et al. (1995) developed and tested a membranous, self-oscillating VF model to explore a previous theoretical expression for phonation threshold pressure (Titze, 1988). The model, shown in Fig. 3(a), consisted of a stainless-steel VF “body,” a silicone membrane attached to the body to represent the epithelium, and a liquid or other substance filling the gap between the membrane and body to represent the cover. The application of this model is discussed in Sec. V. This synthetic model concept was subsequently used by Chan et al. (1997) and Chan and Titze (2006).

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Around the same time, another type of membranous model was developed, initially to simulate the flow-induced vibration of a brass musical instrument player's lips. The model concept consisted of two parallel water-filled latex tubes [Figs. 3(b) and 3(c)], wherein air flow between the tubes excited oscillation of the tube walls, enabling study of vibrating lip aerodynamics, vibrations, and acoustics (Gilbert and Petiot, 1997a,b; Cullen et al., 1998; Gilbert et al., 1998; Cullen et al., 2000; Campbell, 2004; Newton et al., 2008; Vilain et al., 2003; Lopez et al., 2006). The lip model of Vilain et al. (2003) included a metal cylinder with a section of the cylinder removed, latex stretched over the cylinder [Fig. 3(c)], and water within the space between the latex tube and the cylinder. The water was connected to a reservoir with an adjustable elevation to control the water pressure within the models and hence the stiffness of the latex tubes. This approach was adopted by Ruty et al. (2005) to model human VF vibration, and subsequent modifications of this design incorporated features such as asymmetric stiffness (e.g., Ruty et al., 2006; Haas et al., 2016; Lucero et al., 2020) and separate control over glottal gap and stiffness (e.g., Haas et al., 2016). Such models have been used in conjunction with reduced-order numerical models (e.g., Ruty et al., 2007; Van Hirtum et al., 2007; Lucero et al., 2009; Bailly et al., 2010; Cisonni et al., 2011; Lucero et al., 2011) and to explore source-tract acoustic coupling (Lucero et al., 2012), the influence of vocal tract constriction on phonation onset (Van Hirtum and Pelorson, 2015), left-right asymmetry (Haas et al., 2016; Lucero et al., 2020), nodule-like surface growths (Luizard and Pelorson, 2017), varying initial condition configurations (Van Hirtum and Pelorson, 2017), external photoglottography (Bouvet et al., 2019), and liquid being sprayed on the model surface (Van Hirtum et al., 2019; Bouvet et al., 2020a,b). Van Hirtum et al. (2023a) discussed material stress-strain considerations of the PLT model [Fig. 3(d)].

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Variations of the PLT model have been reported. Water-filled, latex membranes attached to a wedge-shaped (rather than cylindrical) body have been developed and used to study asymmetric VF vibration (Ruty et al., 2006), constrictions near the VFs (Bailly et al., 2008), and three-dimensional (3D) detailed characteristics of the glottal jet (Krebs et al., 2012; Sciamarella et al., 2012) [see Figs. 3(e) and 3(f)]. Finally, it is worth noting the limited use of vibrating membranes without adjacent liquid regions as surrogates for VF vibration (Isogai et al., 1988; Kakita, 1988; Misun, 2005; Misun et al., 2011) (see Baken and Švec, 2012; Misun, 2012) as well as for modeling voice-producing element prostheses (Tack et al., 2006), the avian syrinx (Elemans et al., 2009), and the tracheoesophageal segment (Tourinho and da Silva, 2023). For modeling the vibration of the human VFs, however, the liquid-filled membranous model concept is superior to the “liquid-less” membrane concept since the former more closely resembles the human VF structure.

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Membranous liquid-filled tube models possess several favorable characteristics for studying VF flow-induced vibration. Their fabrication process is generally simpler and less prone to failure than the elastic solid models discussed in Sec. IV B. As observed by Van Hirtum and Pelorson (2017), different degrees of stiffness can be tested using the same model by varying internal liquid pressure, whereas to explore stiffness variation in elastic solid models, multiple models are needed. Liquid-filled tube models appear to be more readily able to achieve onset pressures typical of human phonation; Ruty et al. (2007) reported onset pressures as low as approximately 250 Pa, and onset pressures in this range are not uncommon for these models. A range of frequencies has been reported; for example, Ruty et al. (2007) reported a frequency range of 110 to 170 Hz, Luizard and Pelorson (2017) reported a range from around 70 to 120 Hz, and the model used by Krebs et al. (2012) and Sciamarella et al. (2012) vibrated at approximately 55 Hz. The response with different encapsulated substances can be studied. Finally, these models are robust to sustained, large-amplitude vibration. To the best of this author's knowledge, the longevities of membranous and elastic solid models have not been directly compared. However, based on the compositions of these two types of models, it is postulated that relative to elastic models, liquid-filled latex tube models have longer shelf lives than elastic solid models and can be vibrated for longer periods of time without exhibiting material-related changes in model performance. This hypothesis is based on the tube models typically utilizing commercially available rubber materials, whereas elastic solid models are most commonly fabricated using silicone compounds diluted with significantly larger than recommended quantities of silicone thinner and are thus subject to temporal drifts in material properties (discussed further in Sec. IV B 2). Direct comparisons between these two model types are needed to confirm this hypothesis, however.

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A few present limitations of membranous models are here noted. While the shape of membranous models can be influenced by the shape of the mounting surface (e.g., cylindrical; Ruty et al., 2007, vs wedge-shaped Krebs et al., 2012) and by the interior liquid pressure, control over their shapes is somewhat more limited than for elastic solid models. Further, membranous models with nonlinear and/or anisotropic material properties have not yet appeared in the literature. Finally, the vibratory motion of a membranous model was shown by Krebs et al. (2012), but in general, the motion of membranous models has not been extensively compared with that of the human VFs.

B. Elastic solid vocal fold models

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1. Overview

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Elastic solid models are the second primary type of synthetic, self-oscillating VF models discussed in this review. These models are comprised of ultrasoft polymers formed into a VF-like shape. Casting of silicone has been the most common material and fabrication approach, although cast polyurethanes (e.g., Thomson et al., 2005; Drechsel and Thomson, 2008), cast hydrogels (Choo et al., 2010), and 3D-printed silicones (discussed in Sec. IV B 2) have also been reported.

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Elastic solid models were developed to enable the testing of self-oscillating VF models with prescribed geometries mimicking those of the human VFs. Thomson et al. (2003, 2005) and Thomson et al. (2004) reported a single-material, homogeneous model of the human VFs with a shape based on the so-called “M5” profile of Scherer et al. (2001) which had been defined based on laminagraphic tracings of the VFs. The model of Thomson et al. (2005) was fabricated by casting a mixture of the liquid polyurethane rubber compound Evergreen and flexibilizer Everflex (both from Smooth-On, Inc., but no longer commercially available) into a VF-shaped mold as shown in Fig. 4(a). The flexibilizer lowered the cured modulus to where it was comparable to that of human VF tissue. The cured model was demolded and mounted to a clear acrylic plate as shown in Fig. 4(b). Thomson et al. (2005) reported a model vibration frequency of approximately 120 Hz and an onset pressure of 1.15 kPa. This model thus vibrated at a desirable frequency, subglottal pressure, and amplitude, and the fabrication process was relatively straightforward.

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FIG. 4.
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FIG. 4.

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(Color online) One-layer VF model mold (a), attachment to mounting plate (b), and vibratory motion (c). (d) Two-layer VF model fabrication process and cross section. (e) “EPI” model design and close-up image. (f) Geometry of multi-layer model with adipose tissue layer and superior surface undercut (dimensions in mm). (g) Superior views and cross-sections of multi-layer models of differing geometries. Credits: (a–c) Adapted from Thomson, S. L., Mongeau, L., and Frankel, S. H. (2005). “Aerodynamic transfer of energy to the vocal folds,” J. Acoust. Soc. Am. 118, 1689-1700, with permission of Acoustical Society of America. Copyright 2005 Acoustical Society of America. (d) Adapted from Riede, T., Tokuda, I. T., Munger, J. B., and Thomson, S. L. (2008). “Mammalian laryngeal air sacs add variability to the vocal tract impedance: Physical and computational modeling,” J. Acoust. Soc. Am. 124, 634-647, with permission of Acoustical Society of America. Copyright 2008 Acoustical Society of America. (e) Adapted from Murray, P. R., and Thomson, S. L. (2012). “Vibratory responses of synthetic, self-oscillating vocal fold models,” J. Acoust. Soc. Am. 132, 3428-3438, with permission of Acoustical Society of America. Copyright 2012 Acoustical Society of America. (f) Adapted from Motie-Shirazi, M., Zañartu, M., Peterson, S. D., Mehta, D. D., Kobler, J. B., Hillman, R. E., and Erath, B. D. (2019). “Toward development of a vocal fold contact pressure probe: sensor characterization and validation using synthetic vocal fold models,” Appl. Sci. 9, 3002; licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) license (https://creativecommons.org/licenses/by/4.0/). (g) Used with permission of Elsevier Science & Technology Journals, from Bouvet, A., Pelorson, X., and Van Hirtum, A. (2020b). “Influence of water spraying on an oscillating channel,” J. Fluid. Struct. 93, 102840. Copyright 2019 Elsevier Science & Technology Journals.

Development of this model introduced the concept of fabricating self-oscillating VF models with geometries that could be controlled by creating molds of the desired shapes and with stiffnesses that could be controlled by adjusting the composition of the cast material. This model was termed a “one-layer” model because of its homogeneous composition. Other one-layer models were subsequently developed and used to study aspects of VF flow-induced vibration, such as mechanisms of irregular vibration (Berry et al., 2006), acoustic loading and acoustic vs aerodynamic modes of vibration (Zhang et al., 2006a,b, 2009), glottal jet aerodynamic structures (Neubauer et al., 2007), glottal contact pressure (Spencer et al., 2008; Chen and Mongeau, 2011), and fluid-structure and fluid-structure-acoustic interactions (Becker et al., 2009; Kniesburges et al., 2013).

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The one-layer model typically exhibited “swinging door”-type motion and lacked a mucosal wave, as is evident in Fig. 4(c) and video Mm. 1. +Zhang et al. (2006a,b, 2009) reported that the “swinging door”-type motion was due to model vibration being acoustically coupled with the upstream flow supply tube resonance. Further, while one-layer model onset pressures were within the pressure-producing capability of the human lung, they were higher than typical human onset pressures. Low onset pressures in one-layer models were facilitated by strong subglottic tube resonance coupling, which is not expected to occur in this manner during conversational speech owing to the lowest subglottic resonance frequency typically being significantly higher than the VF vibration frequency (e.g., Sundberg et al., 2013, reported a subglottal resonance frequency of 496 Hz during a vowel sequence produced at 122 Hz).

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Studies were conducted to create models that retained the advantages of the one-layer model but with more favorable characteristics in terms of onset pressure and/or mucosal wave-like motion. Models comprised of two layers of different stiffness, such as shown in Fig. 4(d), were fabricated to mimic the body-cover concept of Hirano and Kakita (1985) (Riede et al., 2008; Drechsel and Thomson, 2008; Mendelsohn and Zhang, 2011), although these models did not produce the desired wave-like motion. Zhang (2011) found that imposing vertical restraints suppressed the inferior-superior model motion that was typical of one-layer models. Shaw et al. (2012) and Xuan and Zhang (2014) added fibers to mimic the material nonlinearity of human VF tissue, the latter also including an epithelial layer. Tur et al. (2023) added fibers of varying characteristics to the ligament layer. While adding fibers resulted in greater sensitivity of frequency to subglottal pressure (Shaw et al., 2012), significant frequency range (Tur et al., 2023), and improved glottal closure characteristics (Xuan and Zhang, 2014), the process for adding fibers has not been refined and fibers are generally not presently incorporated in VF models. Adding fibers may yet yield improved mucosal wave-like motion, however, noting that Wang et al. (2023) found in computational simulations that superior-inferior fiber orientation in the conus elasticus improved mucosal wave characteristics.

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A model with four silicone layers—epithelium, superficial lamina propria, ligament, and body (muscle)—was developed by Murray and Thomson (2011, 2012) [see Fig. 4(e)]. Additionally, a fiber through the ligament layer modeled the inferior-superior restraining effect of the vocal ligament. This so-called “EPI” model also included more significant rounding of the inferior margin than the M5 model. The model vibrated between approximately 85 and 100 Hz, at an onset pressure of between 0.27 and 0.37 kPa, and with favorable mucosal wave-like motion (Murray, 2011; Murray and Thomson, 2012) as shown in Mm. 2. While these characteristics are favorable and the model continues to be used (e.g., Shimamura and Tokuda, 2017; Häsner et al., 2021; Yoshinaga et al., 2023), the multiple layers—particularly the soft superficial lamina propria layer—render this model significantly more difficult to fabricate than one- and two-layer models.

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DOI: 10.1121/10.0028267.1
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Stroboscopic video of vibrating one-layer synthetic model of Thomson et al. (2005).

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DOI: 10.1121/10.0028267.2
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High-speed video of vibrating EPI model of Murray (2011) in a hemilarynx configuration. Video courtesy of Preston R. Murray.

Other notable adjustments to elastic solid VF models include using magnetic resonance imaging (MRI) to define geometry (Pickup and Thomson, 2010; Bouvet et al., 2020b) [Fig. 4(g)], “undercutting” of the superior surface for improved mucosal wave-like motion and glottal contact characteristics (Motie-Shirazi et al., 2019), modeling the paraglottic space (adipose tissue) to lower modal frequency (Motie-Shirazi et al., 2019) [Fig. 4(f)], using an optimization approach to define geometry (Taylor and Thomson, 2022; Hilton and Thomson, 2022), creating a poroelastic cover layer for quantifying the effects of vibration on perfusion pressure-flow relationships (Thacker, 2023), and creation of a graphite-filled epithelial layer to create electrically-conductive VF models for measuring glottal closure (Syndergaard et al., 2017). This latter approach was utilized by Motie-Shirazi et al. (2019) and Motie-Shirazi et al. (2022) to identify VF model impact location and Conte et al. (2021b) and Conte et al. (2021a) to study EGG-like signals in VFs simulating normal and pathologic conditions. Variation in anterior-posterior cross-sectional geometry has been incorporated in MRI-based models (Bouvet et al., 2021; Häsner et al., 2021; Matsumoto et al., 2021; Matsumoto et al., 2024; Van Hirtum et al., 2022; Hasegawa et al., 2022; Tur et al., 2023). VF models with control over adduction and/or elongation have been developed (Shaw et al., 2012; Manti et al., 2015; Girault et al., 2021; Tur et al., 2023) (see Fig. 5). Hilton (2019) introduced an MRI-compatible posturing device capable of abduction and adduction, and Burks et al. (2021) described an electromagnetic-based concept for adducting VF models.

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FIG. 5.
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FIG. 5.

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(Color online) Schematic of VF posturing device of Tur et al. (2023). Adapted from Tur, B., Gühring, L., Wendler, O., Schlicht, S., Drummer, D., and Kniesburges, S. (2023). “Effect of ligament fibers on dynamics of synthetic, self-oscillating vocal folds in a biomimetic larynx model,” Bioengineering 10, 1130; licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) license (https://creativecommons.org/licenses/by/4.0/).

Due to the importance of matching Reynolds, Strouhal, and Mach numbers for flow, vibration, and acoustic similarity, nearly all elastic solid VF models have been life-sized, although some scaled studies have been performed. Sidlof et al. (2011) developed a 4× scaled-up model consisting of a relatively stiff silicone mounted on lateral springs; the springs facilitated flow-induced vibration frequencies between 10 and 14 Hz. A one-layer, fully elastic 4× model was reported by Taylor et al. (2019) that exhibited flow-induced vibration at a frequency of 13 to 15 Hz with an onset pressure of 150 Pa when connected to a 7.88-m long tube. Embedded markers were distributed throughout the frontal midplane during fabrication and MRI was used to image the internal deformation of the vibrating model (Fig. 6). This model vibrated with primarily “swinging-door”-type motion since it was coupled to upstream tube subglottal acoustic resonance.

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FIG. 6.
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FIG. 6.

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(Color online) (a) Fabrication process of 4× model with MRI fiducial markers placed halfway during model casting. (b) Illustration of model mounted in shroud. (c) Motion of model profile and internal markers obtained via MRI. Adapted from Taylor, C. J., Tarbox, G. J., Bolster, B. D., Bangerter, N. K., and Thomson, S. L. (2019). “Magnetic resonance imaging-based measurement of internal deformation of vibrating vocal fold models,” J. Acoust. Soc. Am. 145, 989-997, with permission of Acoustical Society of America. Copyright 2019 Acoustical Society of America.

2. Fabrication and materials

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Most elastic VF models have been fabricated using a sequential casting process such as that which is illustrated in Figs. 4(e) and 7. Because this process includes steps and materials that have been customized for VF modeling and that pose unique challenges, an overview and discussion of the processes and materials for fabricating elastic solid VF models is here provided.

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FIG. 7.
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FIG. 7.

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(Color online) Sequential casting process for fabricating the multi-layer EPI model. Adapted from Murray, P. R., and Thomson, S. L. (2012). “Vibratory responses of synthetic, self-oscillating vocal fold models,” J. Acoust. Soc. Am. 132, 3428-3438, with permission of Acoustical Society of America. Copyright 2012 Acoustical Society of America.

The EPI model was fabricated as follows and as illustrated in Fig. 7. Individual negative molds for the body, ligament, and cover layers were created by pouring liquid rubber (Smooth-Sil 950, Smooth-On, Inc., Macungie, PA) around respective 3D-printed positives. The body layer was then created by pouring Ecoflex (EF) 00–30 at a ratio of 1:1:1 into the body mold (i.e., one part EF 00–30 A, one part EF 00–30 B, and one part Silicone Thinner, by weight; all Smooth-On, Inc. products). After the body layer was cured, an acrylic thread was inserted into the ligament mold, EF 00–30 1:1:4 was poured into the ligament mold, and the cured body layer was inserted into the ligament mold for ligament layer formation. Provided that the body layer exterior surface was free from contaminants such as dust, oil, or release agent, the ligament layer naturally bonded to the body layer. After ligament layer curing, EF 00–30 1:1:9 was poured into the superficial lamina propria (SLP) layer mold, and the cured, combined ligament-body structure was inserted into the SLP mold, with the SLP layer then naturally adhering to the ligament and body layers. The cured part was then removed and Dragon Skin (Smooth-On, Inc.) at a ratio of 1:1:1 was poured over the SLP layer to form the epithelial layer, and once cured, the model was trimmed to remove molding guide sections. Powder was applied to the model surface prior to testing to minimize surface tackiness that would cause the model to tear with vibratory collision. Note that the influence of powder applied to candidate silicones for VF modeling was documented by Gabriel et al. (2019).

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Commercial materials used to fabricate elastic solid VF models include Evergreen (Smooth-On, Inc.), a now-discontinued two-component polyurethane product; Ecoflex and Solaris, addition-cure families of silicones (Smooth-On, Inc.); Silopren UV Electro 225-1 (Momentive Performance Materials, Inc.), an ultraviolet-cure silicone; and the urethane rubber Vytaflex (Smooth-On, Inc.) Of these, Ecoflex has been the most widely used and is discussed in more detail in the following. The use of Solaris has recently been explored (Motie-Shirazi, 2022) because it is optically transparent, whereas Ecoflex is only translucent. Silopren UV Electro is also transparent but differs from the other materials in that it cures upon exposure to ultraviolet light. This feature has led to its use in 3D-printed VF models (discussed in the following), but it can also be cast. However, Silopren UV Electro is only distributed in expensive large quantities, thus availability is, at present, a major limitation. Vytaflex has been reported in only one study (Horacek et al., 2011), and its potential for VF modeling has not been thoroughly investigated. The addition-cure silicone Dragon Skin (Smooth-On, Inc.) is compatible with the aforementioned silicones and has been used for some VF layers but is generally too stiff for the superficial lamina propria layer. Ecoflex and Dragon Skin are two-component liquid silicone rubber materials available in different formulations with varying pre-cured viscosities and stiffnesses. Ecoflex 00–30 is the most commonly used product in the elastic solid VF models surveyed in this paper. In addition to its use in VF modeling, Ecoflex has been used in numerous other applications, such as wearable devices (e.g., Wang et al., 2019), organ phantoms (e.g., Adams et al., 2017), and soft robotics (e.g., Wang et al., 2021).

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The pre-cured viscosity and post-cured modulus of Ecoflex, as well as the other silicone materials, can be lowered by adding Silicone Thinner or other silicone oils (Shivapooja et al., 2016). Silicone Thinner has been used almost exclusively in VF modeling for this purpose. This ability to tune stiffness by varying the amount of Silicone Thinner enables the fabrication of VF models with layers of differing stiffness. As discussed in the following, researchers have reported that EF 00–30 with a mixing ratio of 1:1:0 (part A:part B:thinner, by weight) has a modulus on the order of 60 kPa. The manufacturer recommends a maximum added Silicone Thinner quantity of 10% of the combined weight of parts A and B, or a mixing ratio of 1:1:0.2; however, significantly greater quantities of Silicone Thinner are commonly used in VF modeling. For example, Spencer et al. (2008) reported a modulus of 6 kPa for a mixing ratio of 1:1:4 (i.e., 200% of the combined weight of parts A and B), and Murray and Thomson (2012) reported a modulus of 0.2 kPa for a mixing ratio of 1:1:9 (450% of the combined weight of parts A and B). Models with these higher-than-recommended ratios have been successfully fabricated and used, but drawbacks include difficulties with demolding, leeching, and curing. Other difficulties arising from oversaturation have been recently studied and documented (Häsner and Birkholz, 2023). Curing can be improved by eliminating or limiting the amount of release agent used when preparing molds (discussed further in the following), curing and/or post-curing in an oven (Murray and Thomson, 2012), and curing in a microwave (Greenwood and Thomson, 2021). The latter results in much faster curing than oven curing, although care must be taken to avoid overheating. Further, reproducibility is a challenge in VF modeling because curability and cured stiffness vary with factors such as silicone liquid component age, gradual separation and settling of silicone liquid material while sitting for extended periods of time, and other environmental factors (e.g., humidity and temperature). Because of such variations, geometric and material properties of fabricated models should be measured, ideally as close as possible to when experiments (e.g., flow-induced vibration tests) are conducted. For in-depth study of some of these effects, see Häsner and Birkholz (2023).

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Elastic properties of Ecoflex and other similar materials have been reported elsewhere (e.g., Case et al., 2015; Park et al., 2018; Marechal et al., 2021; Darby et al., 2022). The stress-strain response of Ecoflex and Dragon Skin is generally linear at moderately low strains (e.g., Shaw et al., 2012; Burks et al., 2021; Ahmad et al., 2023), but nonlinearity at higher strains has been reported (Ahmad et al., 2023). Ecoflex 00–30 modulus of elasticity values from a selection of VF- related publications are listed in Table I; these are included here given the larger range of Silicone Thinner ratios used in VF modeling compared to what is typical in other applications such as those listed previously. These values are representative of those found in the human VFs (e.g., Tran et al., 1993; Chan et al., 2007; Alipour and Vigmostad, 2012; Chan, 2018; Cochereau et al., 2020). The Ecoflex 00–30 data are also plotted in Fig. 8 with a curve fit. Significant variations between reported values at given ratios are evident and may be attributable to material properties actually varying due to fabrication environmental and process considerations (e.g., temperature, humidity, time between curing and testing, and pre-mixing settling of material), variations in material testing protocols (e.g., sample geometry, strain rate, applied force in rheometry, engineering vs true stress/strain), and/or different values of Poisson's ratio used when converting shear modulus to tensile modulus. Consequently, it is recommended that standardized testing procedures be followed, specifically ASTM-D412-16 (2016) for stress vs strain measurement (as was used by Marechal et al., 2021). It is also recommended that, in the case of rheological testing, the Poisson's ratio also be measured for transparent conversion from shear to tensile modulus values. Finally, as many synthetic VF models possess multiple layers of differing stiffness, the effective properties of combined layers vs individual layers constitute an important characteristic that should be studied, such as has been reported by Ahmad et al. (2021), Ahmad et al. (2022), and Ahmad et al. (2023), as well as Van Hirtum et al. (2023b).

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TABLE I.
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Tensile modulus of Ecoflex 00-30 with various mixing ratios and testing methods reported in a selection of VF modeling-related literature. “0” denotes a mixing ration of 1:1:0 (part A:part B:thinner, by weight), “1” denotes 1:1:1, and so on.

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+Motie-Shirazi et al. (2019) +17.36.80.95
+Taylor et al. (2019) +2
+Bouvet et al. (2020c) +21.910.44.90.2
+Burks et al. (2021) +42.927.920.6
+Motie-Shirazi et al. (2021a) +7.134.041.10
+Stewart and Erath (2021) +9.385.782.22
+Taylor and Thomson (2022) +0.960.63
+Motie-Shirazi et al. (2023) +13.25.81.0
+ +
+
+ +a +

Range provided since multiple values were reported from different specimens.

+
+
+ +b +

Values converted from published shear modulus data at 1.26 Hz using the relationship +E=2G(1+ν), with +ν=0.49, where +E and +G denote tensile and shear modulus, respectively, and +ν denotes Poisson's ratio.

+
+
+ +c +

Values obtained by digitizing the published plot of modulus vs thinner ratio.

+
+
FIG. 8.
+

FIG. 8.

+ +

Ecoflex 00-30 modulus of elasticity, +E, vs thinner ratio, +r. Note the use of a log scale for the +y-axis. Gray open markers are individual values reported in Table I. Black solid markers are values averaged for each integer ratio from r = 0 to r = 8. The solid line is the rational polynomial +E=(0.5354r2−9.017r+42.71)/(r+0.5398) with an R-square value of 0.84. The polynomial provides a reasonable fit to the data for r = 1 through r = 8, but poorly for r = 0 and r = 9.

Poisson's ratio data for Ecoflex 00–30 from two VF modeling studies are listed in Table II. Methods for analyzing silicone material properties for VF modeling, including those of composite layers, can be found in Ahmad et al. (2021), Ahmad et al. (2022), and Ahmad et al. (2023), as well as Van Hirtum et al. (2023b). Additionally, two surface characteristics, tackiness and waviness, of various silicones that could be used for VF modeling, including Ecoflex 00–30, were explored by Gabriel et al. (2019).

+
TABLE II.
+

Poisson's ratio for different mixing ratios of Ecoflex 00-30 and thinner.

+
++++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + +
1:1:01:1:0.51:1:11:1:21:1:4
+Weiss et al. (2016) +0.4750.4570.460
+Burks et al. (2021) +0.460.450.44
+

Common difficulties encountered when casting elastic solid VF models include inconsistency over time of uncured material composition due to long-term sedimentation while not being used, inadequate mixing of material parts, entrainment of air bubbles during mixing and pouring, incomplete curing after mixing, and material tearing during demolding. Effects of sedimentation can be mitigated by thoroughly mixing each individual material—including scraping the container bottom—prior to weighing out amounts for mixing. Complete mixing can be most effectively and efficiently achieved using dual axis centrifugal mixers, also termed planetary centrifugal mixers (e.g., FlackTek, Inc., Landrum, SC, USA; THINKY U.S.A., Inc., Laguna Hills, CA, USA; Torrey Hills Technology, San Diego, SC, USA). Air bubbles formed during mixing can be removed by vacuum degassing, and air entrainment during pouring can be avoided by employing proper pouring techniques.

+

Incomplete curing and material tearing during the demolding of ultrasoft silicones are largely due to the use of large quantities of thinner. Consequently, some models are prone to low yield when fabricating ultrasoft layers (such as the superficial lamina propria layer of the EPI model). Post-cure oven treatment improves, but does not always guarantee, curing. Release agent is typically applied to molds to facilitate demolding. However, insufficient release agent leads to cured material sticking to the mold, and too much release agent inhibits curing. Alternative fabrication processes have therefore been explored. One such approach has been the use of soluble molds or mold negatives. In Ward (2014), VF models were cast into molds comprised of compacted powdered sugar blocks that had been milled into the desired shape. After the silicone had been poured and cured in the molds, the molds were dissolved with water. This process required the creation of a new set of molds for each model but did not require a release agent and was immune to the primary demolding difficulties associated with casting silicone in traditional molds. Häsner et al. (2021) demonstrated the use of water-soluble 3D-printed negatives using polyvinyl alcohol (PVA) [see Fig. 9(a)]. This method holds significant promise for VF modeling owing to the speed and flexibility of various 3D printing techniques for mold and mold negative fabrication. Additionally, methods for 3D printing VF models have been reported, including homogeneous models with a poured epithelial layer (Romero et al., 2021) as well as multi-layer models with discrete layers of different stiffness (Greenwood and Thomson, 2021) and with material stiffness gradients (Young et al., 2024) [see Figs. 9(b)–9(d)]. In these methods, liquid silicone (Ecoflex or UV Electro) is extruded into a gel-like support matrix as is illustrated in Figs. 9(c) and 9(d) and as can be seen in Mm. 3. Advantages of 3D printing VF models include omission of the demolding step, ability to efficiently print new geometries without making new molds, possible control over anisotropy by varying print orientation, alternative methods of creating spatial stiffness variations, and potential ability to 3D print geometries that could not be cast. Disadvantages include coarser spatial resolution than casting, the need for specialized hardware and software tools, and the fact that 3D printing ultrasoft silicone is a relatively immature technology.

+
FIG. 9.
+

FIG. 9.

+ +

(Color online) Water-soluble (a) and additive manufacturing (b-d) techniques for fabricating elastic solid VF models. (a) Combination of non-water-soluble and water-soluble 3D-printed molds and mold negatives. (b) One-layer model pictured at three instances during printing. (c) Multi-layer model fabricated using embedded 3D printing. (d) Multi-layer model with stiffness gradient fabricated using functionally graded 3D printing. Credits: (a) Adapted with permission from Häsner, P., Prescher, A. and Birkholz, P. (2021). “Effect of wavy trachea walls on the oscillation onset pressure of silicone vocal folds,” J. Acoust. Soc. Am. 149, 466-475. Copyright 2021 Acoustical Society of America. (b) Adapted from Romero, R. G. T., Colton, M. B., and Thomson, S. L. (2020). “3D-printed synthetic vocal fold models,” J. Voice 35, 685-694, Copyright 2020 The Voice Foundation. (c) Adapted with permission from Greenwood, T. E. and Thomson, S. L. (2021). “Embedded 3D printing of multi-layer, self-oscillating vocal fold models,” J. Biomech. 121, 110388. Copyright 2021, Elsevier. (d) Adapted from Young, C. A., O'Bannon, M., Thomson, S. L. (2024). “Three-dimensional printing of ultrasoft silicone with a functional stiffness gradient,” 3D Print. Addit. Manuf. 11, 435-445; licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) license (https://creativecommons.org/licenses/by/4.0/).

Mm. 3.
+
+
+
+Download video file (58.8MB, mp4) +
+
DOI: 10.1121/10.0028267.3
+
+ +

Time-lapse video showing 3D printing of silicone VF model reported by Romero et al. (2021). Video courtesy of Taylor E. Greenwood and Ryan G. T. Romero.

Currently, issues with consistency, repeatability, and fabrication yield are the greatest limitations of elastic solid VF modeling, and membranous models are superior in these regards. However, their ability to be fabricated into specific geometries with spatial control over stiffness is a notable strength. Future development in materials and fabrication processes will likely result in elastic solid modeling improvements. Ultimately, given their respective advantages and limitations, it is anticipated that both membranous and elastic solid models will continue to be used in phonation research in the foreseeable future.

V. APPLICATIONS

+

Synthetic VF models have been used for a wide variety of purposes, ranging from theoretical model validation to experimental exploration of complex fluid, solid, and acoustic phenomena. In this section, examples of such applications are discussed. Additionally, values for measures of primary relevance to phonation are summarized in Table III for membranous and elastic solid VF models along with corresponding human in vivo values.

+

TABLE III.

+

Values for primary phonatory measures from selected membranous and elastic solid VF model studies, along with typical values for human speech. Some values are approximate owing to their having been obtained from figures in the original sources.

+
++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Onset pressure (kPa)Frequency (Hz)Maximum glottal width (mm)
+Human VFs (in vivo) +0.29–0.49 a +100–136 (male) a +2 b +
189–224 (female) a +
Membranous models
 Ruty et al. (2007) +0.27–0.97107-168
 Bailly et al. (2008) +0.47–1.7153-1801.9
 Luizard and Pelorson (2017) +0.37–1.0c +75–226c +
Elastic solid models
 Murray and Thomson (2012) +0.27–1.6886–1361.2-4.2
 Zhang et al. (2009) +0.7–2.7105–162
 Motie-Shirazi et al. (2019) +1.61681.48 d +
 Tokuda and Shimamura (2017) +0.4–0.7770–126e +
 Tur et al. (2023) +1.6–4.8227–454e +
+ +
+ + +
+ +c +

Study included VF models with and without nodule-like masses; values reported here are without.

+
+
+ +d +

Study used a single VF model in a hemilarynx position. The maximum glottal width value listed here is double their reported value of 0.74 mm.

+
+
+ +e +

Values reported here are at onset.

+
+

Titze (1988) developed a theoretical expression for phonation onset pressure, +Pth, +

+ + + +
Pth=ktTBcξ0(1)
+

where +kt is the transglottal pressure coefficient, +T is the vocal fold thickness, +B is a viscous damping coefficient, +c is the mucosal wave velocity, and +ξ0 is the pre-phonatory glottal half-width. Titze et al. (1995) used the membranous VF model shown in Fig. 3(a) to test the predicted linear relationships between +Pth and +ξ0 and between +Pth and +B. Onset and offset pressures were measured for varying degrees of pre-phonatory glottal half-width and different fluids, with the lowest onset pressures being on the order of 0.4 kPa for water and from around 0.45 to 0.5 kPa for higher-viscosity fluids. The expected linear relationship between +Pth and +B was confirmed. However, while a portion of the +Pth vs +ξ0 data were linear, the data also suggested the presence of an optimal non-zero pre-phonatory glottal gap for minimum +Pth and showed consistent hysteresis between onset and offset threshold pressures (Fig. 10). These trends and other associated phenomena were subsequently explored by Lucero (1995, 1996, 1998, 1999, 2009), Fulcher et al. (2019), and Lucero et al. (2020). Additional studies using synthetic models based on that of Titze et al. (1995) were conducted by Chan et al. (1997) and Chan and Titze (2006) to explore relationships between threshold pressure and prephonatory angle, membrane thickness, vocal tract inertance, and other cover materials, including fat, hyaluronic acid, and fibronectin.

+

FIG. 10.

+

FIG. 10.

+ +

Measured threshold pressure vs pre-phonatory glottal half-width at onset (open circles) and offset (closed circles). Reproduced with permission from Titze, I. R., Schmidt, S. S., and Titze, M. R. (1995). “Phonation threshold pressure in a physical model of the vocal fold mucosa,” J. Acoust. Soc. Am. 97, 3080–3084. Copyright 1995 Acoustical Society of America.

Physical models have also been used for the development, validation, and exploration of theoretical and low-order models of VF flow-induced vibration (e.g., Ruty et al., 2007; Van Hirtum et al., 2007; Van Hirtum and Pelorson, 2015; Tokuda and Shimamura, 2017; Lucero et al., 2020; Yokota et al., 2021) as well as for high-fidelity computational model development, validation, and comparison (Farahani and Zhang, 2016; Sadeghi et al., 2019; Schoder et al., 2020; Falk et al., 2021). Regarding the latter, however, synthetic VF models remain relatively underutilized as a tool for providing data for development and validation of high-fidelity computational models.

+

Because repeated collision of opposing vocal folds is thought to be an important contributor to the etiology of voice disorders (Titze, 1994; Gunter, 2003; Gunter et al., 2005; Motie-Shirazi et al., 2023), methods to predict and measure contact stress have been of considerable interest. Synthetic VF models have been used to develop such methods. Spencer et al. (2008) used digital image correlation to measure stress and strain on the superior surface of a VF model, and then used a Hertzian impact model to estimate the collision stress. Diaz-Cadiz et al. (2019) proposed a first-order approximation for estimating collision stress from high-speed videoendoscopy, and using a synthetic VF model, compared the approximation to the actual collision pressure measured using a pressure sensor. Direct measurements of synthetic VF model impact stress have been obtained using a probe microphone mounted in a hemilarynx wall (Chen and Mongeau, 2011), a contact sensor placed between opposing VF models (Horacek et al., 2016), a pressure sensor array using an electromechanical film transducer (Weiss et al., 2016), and a contact pressure transducer mounted in a hemilarynx wall with inferior-superior sliding capability (Diaz-Cadiz et al., 2019; Motie-Shirazi et al., 2019; Motie-Shirazi et al., 2021a,b; Motie-Shirazi et al., 2022, Motie-Shirazi et al., 2023).

+

Synthetic VF models have been used as initial test beds for development activities related to excised larynx or in vivo quantitative phonation instruments. For example, the synthetic model contact pressure study of Motie-Shirazi et al. (2019) was a precursor to the excised larynx intraglottal pressure study of Mehta et al. (2019). Other examples include the development of an endoscopic two-point laser projection device for measuring glottal width (Popolo and Titze, 2008), a laser grid projection system for acquiring 3D measurements of the vibrating superior surface of the VFs (Luegmair et al., 2010), and validation of stereo-endoscopic high-speed imaging (Stevens et al., 2016).

+

Fluid-structure-acoustic interactions are at the core of the mechanics of phonation. Consequently, characterization and study of the glottal jet and other flow-structure-acoustic effects and interactions have led to greater understanding of the fundamental physics of phonation. Owing to their longevity, ability to be parameterized, and similar dependence on flow-structure-acoustic interactions, self-oscillating synthetic VF models have been used for this purpose. Neubauer et al. (2007) used flow visualization of the glottal jet in a synthetic VF model to describe aspects of an unconfined supraglottal jet and identify flow structures that could be of relevance during phonation (see Fig. 11). Studies on the confined supraglottal jet using PIV have been conducted with (e.g., Drechsel and Thomson, 2008; Bailly et al., 2008; Kniesburges et al., 2017) and without (e.g., Becker et al., 2009; Sidlof et al., 2011; Sciamarella et al., 2012; Kniesburges et al., 2013; Lodermeyer et al., 2015; Näger et al., 2023) ventricular folds. In the case of Sciamarella et al. (2012), the phenomenon of axis switching was evident in the confined tube downstream of the VFs. However, the presence of axis switching and other flow structures and phenomena identified by these authors has yet to be experimentally verified using realistic vocal tract models. Other studies involving interactions between fluid flow, structural motion, and/or acoustics include the role of supraglottal flow structures on acoustic production (Zhang and Neubauer, 2010); source-tract interactions using straight (Migimatsu and Tokuda, 2019) and MRI-based vocal tract models (Probst et al., 2019), as well as using vocal tract models with varying degrees of constriction (May and Scherer, 2023) and of varying lengths (Kraxberger et al., 2023); the role of model closure on sound generation (Kniesburges et al., 2020); and the use of PIV to identify aeroacoustic sound sources during phonation (Lodermeyer et al., 2018; McPhail et al., 2019; Lodermeyer et al., 2021).

+

FIG. 11.

+

FIG. 11.

+ +

(Color online) Visualization of supraglottal jet exiting a self-oscillating, synthetic VF model, with distinguishable flow features labeled. Reproduced with permission from Neubauer, J., Zhang, Z., Miraghaie, R. and Berry, D.A. (2007). “Coherent structures of the near field flow in a self-oscillating physical model of the vocal folds,” J. Acoust. Soc. Am. 121, 1102-1118. Copyright 2007 Acoustical Society of America.

While a degree of asymmetry in VF motion is not uncommon in normal phonation (e.g., Shaw and Deliyski, 2008; Bonilha and Deliyski, 2008; Kendall, 2009; Chen et al., 2014), significant asymmetries concomitant with some voice disorders (e.g., paralysis, paresis, or asymmetric lesions) may result in impaired voicing. Since synthetic VF models can be fabricated and tested with pre-determined asymmetries in geometry, material properties, and/or tension, they may be used to understand the effects of asymmetry on phonation, the degree to which various asymmetric conditions cause asymmetric motion, and the potential effects of phonosurgical interventions to repair asymmetry. For example, left-right stiffness asymmetry has been studied in membranous models by varying internal liquid pressure (Ruty et al., 2006; Haas et al., 2016; Lucero et al., 2020) and in cast synthetic VF models by varying material stiffness (Pickup and Thomson, 2009; Zhang, 2010; Zhang and Hieu Luu, 2012; Zhang et al., 2013; Signorello et al., 2016). Geometric asymmetries that have been explored using synthetic VF models include (see Fig. 12) simulated unilateral cordectomy (Mendelsohn et al., 2014), left-right vertical asymmetry (Shimamura and Tokuda, 2017; Tokuda and Shimamura, 2017; Bouvet et al., 2020c; Bouvet et al., 2021), surface masses such as polyps and nodules (Luizard and Pelorson, 2017; Conte et al., 2021b; Motie-Shirazi et al., 2023), and augmentation injection to correct for vocal bowing (Murray et al., 2014).

+

FIG. 12.

+

FIG. 12.

+ +

(Color online) Synthetic VF models with geometric asymmetry. (a) Inferior-superior left-right level difference. (b) Left-right asymmetry via rotation about medial-lateral axis. (c) Unilateral nodules using membranous models. (d) Bowed VF model with injection holes placed laterally in the mounting plate for medialization via augmentation injections. Credits: (a) Reproduced with permission from Tokuda, I. T., and Shimamura, R. (2017). “Effect of level difference between left and right vocal folds on phonation: Physical experiment and theoretical study,” J. Acoust. Soc. Am. 142, 482-492. Copyright 2017 Acoustical Society of America. (b) Adapted with permission from Bouvet, A., Tokuda, I., Pelorson, X. and Van Hirtum, A. (2021). “Imaging of auto-oscillating vocal folds replicas with left–right level difference due to angular asymmetry,” Biomed. Signal Proces. 63, 102154. Copyright 2021, Elsevier. (c) Adapted with permission from Luizard, P. and Pelorson, X. (2017). “Threshold of oscillation of a vocal fold replica with unilateral surface growths,” J. Acoust. Soc. Am. 141, 3050-3058. Copyright 2017 Acoustical Society of America. (d) Reprinted with permission from Murray, P. R., Thomson, S. L., and Smith, M. E. (2014). “A synthetic self-oscillating vocal fold model platform for studying augmentation injection,” J. Voice 28, 133–143. Copyright 2014 The Voice Foundation.

Brief mention is here made of other applications. These include spatiotemporal analysis using empirical eigenfunctions to explore irregular vibration, including subharmonic phonation and biphonation (Berry et al., 2006); subharmonic tone generation (Kniesburges et al., 2016); the effects of surface liquid on vibration [Van Hirtum et al., 2019; Bouvet et al., 2020a,b; Yoshinaga et al., 2023; see Fig. 13(a)]; the response of an injectable biomaterial to vibration in a phonomimetic bioreactor system [Latifi et al., 2016; see Fig. 13(b)]; water resistance voice therapy (Horacek et al., 2019a,b); development of a surgical training model [Saliba and Barros, 2023; Fig. 13(c)]; and coupling synthetic VF model data with finite element data for estimating VF material properties (Hadwin et al., 2019). Finally, synthetic VF models have been used to explore non-human vocalization, including mammalian air sacs (Riede et al., 2008), the vocal membrane of non-human mammalian species (Kanaya et al., 2022) [Fig. 13(d)], and the avian syrinx (Elemans et al., 2009; Riede et al., 2019) [Fig. 13(e)].

+

FIG. 13.

+

FIG. 13.

+ +

(Color online) (a) Setup for using an optical particle sizer (OPS) to measure aerosol particle formation by self-oscillating synthetic VF models. (b) Phonomimetic bioreactor with cell-scaffold mixture imbedded within VF models. (c) Surgical training model. (d) Physical model of non-human mammalian vocal membrane. (e) Membranous structure mimicking the avian syrinx. Credits: (a) Reproduced with permission from Yoshinaga, T., Yamaya, Y., Minami, T., Obata, H., Tsuchida, H., Yoshitani, T., Tokuda, I. T., and Iida, A., “Effects of vocal fold oscillation characteristics on the aerosol droplet production,” J. Aerosol Sci. 174, 106251. Copyright 2023 Elsevier. (b) Adapted from Latifi N., Heris, H. K., Thomson, S. L., Taher, R., Kazemirad, S., Sheibani, S., Li-Jessen N. Y. K., Vali, H., Mongeau, L. (2016). “A flow perfusion bioreactor system for vocal fold tissue engineering applications,” Tissue Eng. Part C.-ME. 22, 823-838. Copyright 2016 Mary Ann Liebert, Inc. (c) Reproduced from Saliba, T. V., and Barros, R. S. M. D. (2023). “Development and validation of a 3D laryngeal model in surgical skills training,” Braz. J. Otorhinolar. 89, 128-135; licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) license (https://creativecommons.org/licenses/by/4.0/). (d) Adapted from Kanaya, M., Matsumoto, T., Uemura, T., Kawabata, R., Nishimura, T., and Tokuda, I. T. (2022). “Physical modeling of the vocal membranes and their influence on animal voice production,” JASA Express Lett. 2, 111201; licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) license (https://creativecommons.org/licenses/by/4.0/). (e) Reproduced with permission Elemans, C. P. H., Muller, M., Larsen, O. N., and van Leeuwen, J. L. (2009). “Amplitude and frequency modulation control of sound production in a mechanical model of the avian syrinx,” J. Exp. Biol. 212, 1212-1224. Copyright 2009 Company of Biologists Ltd.

VI. EXPERIMENTAL TECHNIQUES

+

With the development of synthetic VF models has been the development and application of numerous experimental techniques for their study. In this section, an overview of experimental methods specifically used for studying VF model flow, motion, and acoustics is given.

+

In all cases, self-oscillating VF model studies require a flow supply; see Fig. 14 for representative cases. This is typically provided by means of compressed air from a building supply or a standalone air tank. In contrast to excised larynx setups, neither heating nor humidification of the flow supply is required to maintain health of the VF model, although such would not be inherently problematic. As with excised larynx experiments, flow conditioning, such as a large square box plenum (e.g., Fig. 14), is often used to settle airflow prior to entering the subglottic tube and, in some cases if desired, to create an area difference between the subglottic tube and the plenum to create a well-defined, reflective acoustic boundary. Hemilarynx as well as full larynx configurations have been used in synthetic VF model experiments, with and without vocal tracts.

+

FIG. 14.

+

FIG. 14.

+ +

(Color online) Illustrations of experimental setups for membranous (a–c) and elastic solid (d–f) models. (a,b) Air supplied to large plenum with laser diode and laser sensor to measure orifice opening. Reservoir of adjustable height provided symmetric pressure to opposing liquid-filled tubes representing VFs. (c) Similar to (a,b) but with separate pressures applied to opposing VF models to create medial-lateral asymmetry. (d) Air supplied through plenum, through subglottal tube, to VF models. Vocal tract model with ventricular folds included. (e) Setup with acoustic treatment of subglottal regions. (f) Acoustical treatment of subglottal system (inset region with dashed border) and supraglottal setup for using PIV to measure flow within supraglottal channel. Credits: (a) Reproduced with permission from Ruty, N., Pelorson, X., Van Hirtum, A., Lopez-Arteaga, I., and Hirschberg, A. (2007). “An in vitro setup to test the relevance and the accuracy of low-order vocal folds models,” J. Acoust. Soc. Am. 121, 479–490. Copyright 2007 Acoustical Society of America. (b) Reproduced with permission from Bailly, L., Pelorson, X., Henrich, N., and Ruty, N. (2008). “Influence of a constriction in the near field of the vocal folds: Physical modeling and experimental validation,” J. Acoust. Soc. Am. 124, 3296–3308. Copyright 2008 Acoustical Society of America. (c) Reproduced with permission from Haas, J., Luizard, P., Pelorson, X., and Lucero, J. C. (2016). “Study of the effect of a moderate asymmetry on a replica of the vocal folds,” Acta Acust. United Ac. 102, 230–239. Copyright 2016 European Acoustics Association. (d) Reproduced with permission from Drechsel, J. S, and Thomson, S. L. (2008). “Influence of supraglottal structures on the glottal jet exiting a two-layer synthetic, self-oscillating vocal fold model,” J. Acoust. Soc. Am. 123, 4434–4445. Copyright 2008 Acoustical Society of America. (e) Reproduced with permission from Häsner, P., Prescher, A. and Birkholz, P. (2021). “Effect of wavy trachea walls on the oscillation onset pressure of silicone vocal folds,” J. Acoust. Soc. Am. 149, 466–475. Copyright 2021 Acoustical Society of America. (f) Adapted from Lodermeyer, A., Becker, S., Döllinger, M., and Kniesburges, S. (2015). “Phase-locked flow field analysis in a synthetic human larynx model,” Exp. Fluids 56, 13, with permission from SNCSC. Copyright 2015 Springer-Verlag.

A characteristic of VF models is the potential for coupling with subglottal acoustics to drive or assist model vibration. Zhang et al. (2006b) first identified this issue with elastic solid models in a study involving subglottic tubes of varying lengths. It was shown that the one-layer model followed quarter-wavelength resonance theory, demonstrating the importance of appropriately taking into consideration subglottic tube length [see Fig. 15(a)]. Distinct vibratory shapes for aerodynamic vs acoustically driven vibration modes were observed by Zhang et al. (2006a) [see Fig. 15(b)]. Acoustically coupled modes exhibited a “swinging-door”-type motion characterized by large inferior-superior motion, whereas aerodynamic modes were characterized by limited inferior-superior motion and greater medial-lateral motion, the latter being more characteristic of the human VF mucosal wave. Further, in general, longer tubes and VF models that produce acoustically driven modes of vibration often yield significantly lower onset pressures, but at the cost of increased vertical motion and reduced wave-like motion. The roles of VF model stiffness and acoustic loading were studied by Zhang et al. (2009), and acoustic and aerodynamic coupling was further explored by Probst et al. (2019) with a synthetic VF model and an MRI-based vocal tract replica. Given these studies which have shown the potential for model vibration to couple with subglottic resonance, it is important that studies using self-oscillating, synthetic VF models—membranous as well as elastic solid—should describe in detail the subglottic setup and address whether the model vibration was acoustically or aerodynamically coupled.

+

FIG. 15.

+

FIG. 15.

+ +

(Color online) (a) Frequency vs subglottic tube length for one-layer elastic solid VF model. Closed symbols: measured model onset frequencies; open symbols: subglottal tube resonance frequencies; solid lines: theory. Adapted with permission from Zhang, Z., Neubauer, J. and Berry, D. A. (2006a). “The influence of subglottal acoustics on laboratory models of phonation,” J. Acoust. Soc. Am. 120, 1558-1569. Copyright 2006 Acoustical Society of America. (b) Trajectories of points on homogeneous elastic solid VF model undergoing aerodynamic (left) and acoustic (right) modes of vibration. Adapted with permission from Zhang, Z., Neubauer, J., and Berry, D. A. (2006a). “Aerodynamically and acoustically driven modes of vibration in a physical model of the vocal folds,” J. Acoust. Soc. Am. 120, 2841-2849. Copyright 2006, Acoustical Society of America.

A diverse array of experimental techniques has been incorporated to study acoustics, fluid dynamics, and structural motion of self-oscillating VF models. In addition to well-known methods of processing microphone signal data to analyze radiated acoustics, human listener evaluations of model-generated acoustic data have been used to assess perceptual effects caused by changing body stiffness (Zhang et al., 2013, Signorello et al., 2016). Flow measurement techniques that have been employed include hot-wire anemometry (Thomson et al., 2005; Becker et al., 2009), laser Doppler velocimetry (Becker et al., 2009), flow visualization (Neubauer et al., 2007; Drechsel and Thomson, 2008; Horacek et al., 2011; Misun et al., 2011; Kniesburges et al., 2013; Fulcher et al., 2019), and PIV (Neubauer et al., 2007; Drechsel and Thomson, 2008; Becker et al., 2009; Pickup and Thomson, 2009; Krebs et al., 2012; Sciamarella et al., 2012; Lodermeyer et al., 2015; Lodermeyer et al., 2018; Lodermeyer et al., 2021; Sadeghi et al., 2019). In a study comparing high-speed vs phase-averaged PIV, it was shown that phase-averaging can yield useful flow information, although aeroacoustic sound generation exploration via PIV requires high-speed interrogation (Lodermeyer et al., 2016). Principal component analysis (PCA) has been a means of identifying coherent flow structures (Neubauer et al., 2007; Kniesburges et al., 2016). Analysis techniques for measuring motion of synthetic VF models include videokymography (Popolo and Titze, 2008; Spencer et al., 2008; Pickup and Thomson, 2009, 2010; Luegmair et al., 2010; Murray and Thomson, 2011, 2012; Zhang and Hieu Luu, 2012; Tokuda and Shimamura, 2017; Migimatsu and Tokuda, 2019; Motie-Shirazi et al., 2019; Bouvet et al., 2021; Greenwood and Thomson, 2021; Matsumoto et al., 2021; Matsumoto et al., 2024; Stewart and Erath, 2021; Taylor and Thomson, 2022; Hasegawa et al., 2022), modal decomposition techniques (Berry et al., 2006; Zhang et al., 2006a,b; Van Hirtum and Pelorson, 2017), direct linear transformation (DLT) to track small numbers of points on model medial surfaces (Murray and Thomson, 2012; Murray et al., 2014; Stevens et al., 2016), laser dot projection to measure superior surface motion (Luegmair et al., 2010), digital image correlation (DIC, a solid domain counterpart to PIV) to track model motion via randomly-distributed dot patterns (Spencer et al., 2008; Chen and Mongeau, 2011), MRI for simultaneous internal and external motion (Taylor et al., 2019), internal motion using optically transparent VF model materials (Motie-Shirazi, 2022), and laser Doppler vibrometry for model velocity (Spencer et al., 2008; Becker et al., 2009; Elemans et al., 2009; Lodermeyer et al., 2021; Kraxberger et al., 2023) and model frequency response (Luizard and Pelorson, 2017; Riede et al., 2019).

+

Some pitfalls and considerations of particular relevance to synthetic VF model experimentation are here noted. As discussed previously, models mounted on long subglottal tubes that produce quarter wavelengths on the order of the model in vacuo modal frequencies are prone to acoustic coupling. In some cases, acoustic coupling may be acceptable, but in studies where mucosal wave-like characteristics are central to the research question, shorter subglottal tubes for aerodynamic coupling should be utilized. In all cases, the geometric characteristics of the subglottic system should be reported because of model susceptibility to acoustic coupling.

+

The use of a vocal tract is an important consideration. Häsner et al. (2021) studied the influence of smooth vs wavy subglottal tube profile on flow and vibratory characteristics, including subglottal pressure, onset pressure, pulmonary power, and vibratory frequency (see Fig. 16). VF models with different anterior-posterior cross-sectional shapes (round, quadrilateral, and triangular) were employed along with different degrees of tracheal wall waviness and the presence or absence of a vocal tract model. They reported that including a vocal tract model decreased onset pressure by around 400 to 500 Pa, which is a significant reduction. Slight decreases in pulmonary power with waviness depth were seen. Waviness minimally affected pressures measured at the low end of the trachea at vibration onset, but significantly reduced the corresponding onset pressures at the upper end of the trachea. Model vibration frequencies were significantly higher with a vocal tract model than without, but they did not vary with waviness depth. This study demonstrated the potential influence of a vocal tract model on synthetic VF model response. Pitfalls of extrapolating conclusions based on acoustical data obtained without a vocal tract to a configuration with a vocal tract were highlighted by Signorello et al. (2016). Given these findings, the presence or absence of a vocal tract model should always be documented when presenting results using synthetic VF models, and it is recommended that vocal tract models be included where possible.

+

FIG. 16.

+

FIG. 16.

+ +

Top: Configuration for measuring effects on phonatory output of tracheal waviness, VF shape (round, quadrilateral, and triangular), and presence of vocal tract. Dimensions in mm. Bottom: Onset (solid lines) and offset (dashed lines) pressures measured at the upper pressure tap vs waviness depth for different VF shapes, with (left) and without (right) a vocal tract model, showing significant reduction in threshold pressures with a vocal tract model. Corresponding pressures measured at the lower pressure tap were affected to a significantly lesser degree by waviness. Adapted with permission from Häsner, P., Prescher, A. and Birkholz, P. (2021). “Effect of wavy trachea walls on the oscillation onset pressure of silicone vocal folds,” J. Acoust. Soc. Am. 149, 466-475. Copyright 2021 Acoustical Society of America.

For VF models themselves, environmental and temporal factors that affect properties, and hence vibratory characteristics, should be carefully observed and controlled where possible. These include model heating from intense illumination for high-speed imaging, material creep and relaxation, potential leeching of silicone thinner to adjacent regions of cured silicone in multi-layer elastic solid VF models, and changing of model geometry over time. For example, Thacker (2023) demonstrated silicone swelling/shrinking when immersed in water/mineral oil, respectively. Häsner and Birkholz (2023) systematically studied changes in elastic solid VF model vibration caused by aging over an eight-week period, finding significant variability in phonatory response measures over such an extended time. Finally, silicone is gas permeable, a potentially significant characteristic when using silicone VF models in conjunction with biological, bioengineered, or hydrogel components. Owing to considerations such as these, authors of studies using synthetic VF models should take great care to report relevant fabrication, experimental setup, and experimental procedure details.

VII. CONCLUSIONS AND FUTURE WORK

+

A comprehensive review of synthetic, self-oscillating VF models for voice production research has been provided. The designs, capabilities, and limitations of the two most common types of such models have been presented, the two types being membranous models (e.g., water-filled latex tubes), and elastic solid models (e.g., ultrasoft silicones formed into VF-like shapes). Materials and fabrication processes unique to the implementation of elastic solid models have been discussed. Applications and experimental configurations associated with both types of models have been provided. Recommendations for future studies have been given, including comparing the vibratory motion of liquid-filled elastic tube models to that of human VFs; pursuing membranous models with nonlinear and/or anisotropic material properties; further exploring the use of fibers in elastic solid VF models; using ASTM D412 for acquiring stress-strain data of synthetic model materials; acquiring Poisson's ratio data of synthetic model materials; including vocal tract models whenever possible; carefully reporting model fabrication and experimental setup and procedure details, particularly regarding subglottic configurations and resonance characteristics; measuring model geometric and material properties, ideally close to the time of model testing; and increasing utilization of synthetic VF model data for development and validation of high-fidelity computational models of phonation.

+

In addition to the previous recommendations, while significant progress has been made in recent decades to create and use models to study the biomechanical underpinnings of phonation, there remain significant opportunities to develop models with ever increasing lifelike motion that can produce even more clinically relevant results. To date, most synthetic VF models have been based on the adult human male. Female morphological characteristics, as well as those of children, remain underrepresented in VF modeling studies. Future VF modeling efforts should fill this important gap. Additionally, key success measures of modeling VF vibration include low onset pressure, mucosal wave-like motion, and glottal closure. Factors that affect these characteristics include geometric definitions, boundary conditions, and the spatial distribution of stiffness. The “M5” geometric profile of Scherer et al. (2001) has been widely used, in part because it provided the basis for early elastic solid synthetic model studies (Thomson et al., 2005) and in part because of its well-defined shape. However, more lifelike geometries can improve model response (Pickup and Thomson, 2009; Murray and Thomson, 2012). Notably, while shape variation along the anterior-posterior direction exists in the human VFs (e.g., Titze and Talkin, 1979), most synthetic VF models have been defined using uniform cross-sections. Some exceptions to this include studies by Pickup and Thomson (2009), Murray and Thomson (2012), Bouvet et al. (2021), Häsner et al. (2021), Matsumoto et al. (2021), Matsumoto et al. (2024), Van Hirtum et al. (2022), Hasegawa et al. (2022), and Tur et al. (2023). The fabrication of models with non-uniform cross-sections is slightly more complex, particularly with multi-layer models; however, this important aspect of human VF shape should be routinely incorporated in VF models. Research to quantify VF exterior profile and layer geometries with greater detail to enable more accurate modeling is needed. More lifelike boundary conditions, as opposed to rigid mounting plates, may also improve model response; see the computational study by Jones et al. (2015) and experimental incorporation by Motie-Shirazi et al. (2019), Motie-Shirazi et al. (2021a,b), Motie-Shirazi et al. (2022), Motie-Shirazi et al. (2023), and Stewart and Erath (2021). Furthermore, while elastic solid models that achieve complete closure and realistic open quotient values have been reported (e.g., Zhang, 2011; Motie-Shirazi et al., 2021a,b; Taylor and Thomson, 2022), fabrication of these models that consistently produce desired levels of glottal closure remains somewhat elusive. Owing to the significant role of collision in phonation and phonotrauma, a mature understanding of the mechanisms that govern glottal closure, followed by application in VF modeling efforts, is needed. The degree to which the epithelium layer affects VF vibration has been explored using excised human larynges and computational simulations (see Tse et al., 2015, and Deng and Peterson, 2023, respectively) but has yet to be studied using synthetic models. Methods for creating consistent and repeatable transverse isotropy and material nonlinearity are two advancements that would significantly improve VF models. Finally, neuromuscular control of the larynx plays a significant role in phonation due to the effects of intrinsic muscle activity on VF position, stiffness, and shape. VF models with artificial, soft muscle activation do not yet appear to have been reported in the literature. Consequently, this area presents a significant opportunity for VF model development, in particular by drawing upon the extensive existing studies on artificial soft actuators for robotics applications (e.g., Yang and Wang, 2024).

ACKNOWLEDGMENTS

+

The author respectfully acknowledges the contributions of the numerous students and researchers worldwide who have contributed to the ongoing advancement of synthetic, self-oscillating vocal fold models, many of whose works are cited herein. This publication was supported by the National Institute On Deafness and Other Communication Disorders (NIDCD) of the National Institutes of Health (NIH) under Award Nos. R01DC009616 and R01DC018577. The content is solely the responsibility of the author and does not necessarily represent the official views of the NIH.

+a)

Portions of this review were completed while previously affiliated with the Department of Mechanical Engineering, Brigham Young University, Provo, UT 84602, USA.

+

AUTHOR DECLARATIONS

+

Conflict of Interest

+

The author has no conflict of interest to declare.

DATA AVAILABILITY

+

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Associated Data

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This section collects any data citations, data availability statements, or supplementary materials included in this article.

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Data Availability Statement

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The data that support the findings of this study are available from the corresponding author upon reasonable request.


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+ + + + + + + DNA ligase IV binds to XRCC4 via a motif located between rather than within its BRCT domains + + + + +

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+ + The covalent rejoining of DNA ends at single-stranded or double-stranded DNA breaks is catalyzed by DNA ligases. Four DNA ligase activities (I-IV) have been identified in mammalian cells [1]. It has recently been demonstrated that DNA ligase IV interacts with and is catalytically stimulated by the XRCC4 protein [2,3], which is essential for DNA double-strand break repair and the genomic rearrangement process of V(D)J recombination [4]. Together with the finding that the yeast DNA ligase IV homologue is essential for nonhomologous DNA end joining [5-7], this has led to the hypothesis that mammalian DNA ligase IV catalyzes ligation steps in both of these processes [8]. DNA ligase IV is characterized by a unique carboxy-terminal tail comprising two BRCT (BRCA1 carboxyl terminus) domains. BRCT domains were initially identified in the breast cancer susceptibility protein BRCA1 [9], but are also found in other DNA repair proteins [10]. It has been suggested that DNA ligase IV associates with XRCC4 via its tandem BRCT domains and that this may be a general model for protein-protein interactions between DNA repair proteins [3]. We have performed a detailed deletional analysis of DNA ligase IV to define its XRCC4-binding domain and to characterize regions essential for its catalytic activity. We find that a region in the carboxy-terminal tail of DNA ligase IV located between rather than within BRCT domains is necessary and sufficient to confer binding to XRCC4. The catalytic activity of DNA ligase IV is affected by mutations within the first two-thirds of the protein including a 67 amino-acid amino-terminal region that was previously thought not to be present in human DNA ligase IV [11]. +

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+ +. 2017 Sep;27(9):092101. + +
+ + + + + doi: 10.1063/1.4986932. + + + + + + + +
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+ + + + + + + Nonlinear dynamics in the study of birdsong + + + + +

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+ + + + + + + Nonlinear dynamics in the study of birdsong + + + + +

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+ + + + Gabriel B Mindlin. + + + + + + + Chaos. + + + + 2017 Sep. + + + + +
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+ Abstract + +

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+ + Birdsong, a rich and complex behavior, is a stellar model to understand a variety of biological problems, from motor control to learning. It also enables us to study how behavior emerges when a nervous system, a biomechanical device and the environment interact. In this review, I will show that many questions in the field can benefit from the approach of nonlinear dynamics, and how birdsong can inspire new directions for research in dynamics. +

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+ Figures +

+ +
+ +
+ + FIG. 1. + + + + + + + + + + +
+ + + + + + + + FIG. 1. + + + + +
The syrinx, the trachea and the oroesopharingeal cavity (a). Muscles controlling the oscine syrinx. See text for full description (b).
+ + + + +
+ + +
+ +
+ + FIG. 2. + + + + + + + + + + +
+ + + + + + + + FIG. 2. + + + + +
Isofrequencies in the parameter space of a simple model for labial dynamics. The slowly changing parameters during the production of a syllable are the coordinates of a trajectory in the parameter space. Pressure and tension are (β,k) in the model.
+ + + + +
+ + +
+ +
+ + FIG. 3. + + + + + + + + + + +
+ + + + + + + + FIG. 3. + + + + +
Experimental recordings during the production of a canary syllable. The sound (first panel), the air sac pressure (second panel), the electromyography of the right muscle syringealis ventralis (third panel) and the sonogram (fourth panel).
+ + + + +
+ + +
+ +
+ + FIG. 4. + + + + + + + + + + +
+ + + + + + + + FIG. 4. + + + + +
The modes of labia during one cycle.
+ + + + +
+ + +
+ +
+ + FIG. 5. + + + + + + + + + + +
+ + + + + + + + FIG. 5. + + + + +
Parameter space for the model described in the text. The red curves correspond to saddle node bifurcations and the blue curve to a Hopf (a). The sonogram of a recorded song (top panel) and the sonogram of a synthetic sound produced by the model (bottom panel) (b).
+ + + + +
+ + +
+ +
+ + FIG. 6. + + + + + + + + + + +
+ + + + + + + + FIG. 6. + + + + +
The relationship between the spectral content and the frequency for syllables, recorded from different birds. The continuous curve is obtained with our model: an oscillation born in a SNILC (saddle node in limit cycle), filtered with a tube.
+ + + + +
+ + +
+ +
+ + FIG. 7. + + + + + + + + + + +
+ + + + + + + + FIG. 7. + + + + +
A recorded song (top panel) and a synthetic sound (bottom panel) generated by the model described in the text.
+ + + + +
+ + +
+ +
+ + FIG. 8. + + + + + + + + + + +
+ + + + + + + + FIG. 8. + + + + +
Testing the response of highly selective neurons to synthetic sounds generated by the model, with slightly different parameters.
+ + + + +
+ + +
+ +
+ + FIG. 9. + + + + + + + + + + +
+ + + + + + + + FIG. 9. + + + + +
Asymmetric labia can generate sounds with distinctive timbre (notice the side bands in the sonograms). In the top panel is the bifurcation diagram. The recorded sonogram of the picazuro pigeon song and the synthetic sound generated with symmetric labia (left), compared with the song of maculosa pigeon and sound generated with asymmetric labia (right).
+ + + + +
+ + +
+ +
+ + FIG. 10. + + + + + + + + + + +
+ + + + + + + + FIG. 10. + + + + +
The spectrum of a song (first panel), synthetic sound with an added vortex sound (middle panel) and the synthetic sound without a vortex sound (bottom panel). There is a significant difference for frequencies higher than 10 kHz.
+ + + + +
+ + +
+ +
+ + FIG. 11. + + + + + + + + + + +
+ + + + + + + + FIG. 11. + + + + +
A schematic diagram of the nuclei in the oscine song system.
+ + + + +
+ + +
+ +
+ + FIG. 12. + + + + + + + + + + +
+ + + + + + + + FIG. 12. + + + + +
Recorded air sac pressure in a singing canary (a). A neural oscillator, i.e., a population of excitatory neurons coupled to a population of inhibitory ones (top). The bifurcation diagram showing the different regions of the parameter space presenting qualitatively different flows (bottom). The parameters are the inputs to the neural oscillator (b). The synthetic time series emulating air sac pressure (c). The syllables are generated changing the parameters along the trajectories displayed in (b).
+ + + + +
+ + +
+ +
+ + FIG. 13. + + + + + + + + + + +
+ + + + + + + + FIG. 13. + + + + +
One-way of generating synthetic pressure gestures similar to the recorded ones. The dynamical system is written in terms of the activities of interconnected nuclei.
+ + + + +
+ + +
+ +
+ + FIG. 14. + + + + + + + + + + +
+ + + + + + + + FIG. 14. + + + + +
Parameter space regions of the average model.
+ + + + +
+ + +
+ +
+ + +
+ +
+ + + + + + + +
+ + + + + + + + +
+

+ References +

+
+ +
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    2. + +
    +
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+ +. 1988 Apr;83(4):1536-52. + +
+ + + + + doi: 10.1121/1.395910. + + + + + + + +
+ + +

+ + + + + + + The physics of small-amplitude oscillation of the vocal folds + + + + +

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  • + + + + PMID: + + + + + 3372869 + + + + + +
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  • + + + + DOI: + + + + + + 10.1121/1.395910 + + + + + + +
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+ + + + + + + The physics of small-amplitude oscillation of the vocal folds + + + + +

+ + + + + +
+ + + + I R Titze. + + + + + + + J Acoust Soc Am. + + + + 1988 Apr. + + + + +
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+ Abstract + +

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+ + A theory of vocal fold oscillation is developed on the basis of the body-cover hypothesis. The cover is represented by a distributed surface layer that can propagate a mucosal surface wave. Linearization of the surface-wave displacement and velocity, and further small-amplitude approximations, yields closed-form expressions for conditions of oscillation. The theory predicts that the lung pressure required to sustain oscillation, i.e., the oscillation threshold pressure, is reduced by reducing the mucosal wave velocity, by bringing the vocal folds closer together and by reducing the convergence angle in the glottis. The effect of vocal tract acoustic loading is included. It is shown that vocal tract inertance reduces the oscillation threshold pressure, whereas vocal tract resistance increases it. The treatment, which is applicable to falsetto and breathy voice, as well as onset or release of phonation in the absence of vocal fold collision, is harmonized with former treatments based on two-mass models and collapsible tubes. +

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+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/research/vocal-source-grounding/sources/vocaltractlab-birkholz-2024-losses.pdf b/research/vocal-source-grounding/sources/vocaltractlab-birkholz-2024-losses.pdf new file mode 100644 index 0000000..9caaae3 Binary files /dev/null and b/research/vocal-source-grounding/sources/vocaltractlab-birkholz-2024-losses.pdf differ diff --git a/research/vocal-source-grounding/sources/vocaltractlab-birkholz-2024-losses.txt b/research/vocal-source-grounding/sources/vocaltractlab-birkholz-2024-losses.txt new file mode 100644 index 0000000..8484376 --- /dev/null +++ b/research/vocal-source-grounding/sources/vocaltractlab-birkholz-2024-losses.txt @@ -0,0 +1,660 @@ +Interspeech 2024 +1-5 September 2024, Kos, Greece + +Measurement and simulation of pressure losses due to airflow in vocal tract +models +Peter Birkholz, Patrick Häsner +Institute of Acoustics and Speech Communication, TU Dresden, Germany +peter.birkholz@tu-dresden.de + +the length l remains constant, then ∆Pv ∝ A−3 . Fulcher et +al. [7] proposed a modification to the viscous term, which better fitted their own data from flow experiments with a physical +replica of the glottis, namely + +λ +w +12µ +∆Pv = ∆x 3 +U, +(2) +lw +wref + +Abstract +We propose a unified model for viscous and kinetic energy +losses in a discrete tube model of the vocal system including +the glottis. In this model, a lossless Bernoulli flow is assumed +at each transition between two tube sections if the downstream +section has a smaller diameter than the upstream section, and +otherwise the recovery of a fixed fraction of the dynamic pressure. For viscous losses, we propose a general equation according to which the pressure drop within a tube section is inversely +proportional to a certain power of its cross-sectional area. The +parameters of the model were adjusted to reproduce the results +of measurements with physical replicas of the glottis and the +vocal tract. The best agreement with the experimental data was +achieved when 29% of the dynamic pressure were recovered at +tube expansions, and when the viscous losses were proportional +to the tube area to the power of -2.9. These results may improve +articulatory speech synthesis. +Index Terms: one-dimensional flow model, flow resistance + +where wref = 0.01 cm and λ = 0.41. With this modification +the viscous pressure loss becomes proportional to A−2.59 . +The term ∆Pk in Eq. (1) represents the loss of kinetic energy, where % is the density of the air, and kent and kexit describe the effects responsible for energy losses at the glottal +entrance and the effect of pressure recovery at the glottal exit, +respectively. The case kent = 1 and kexit = 0 would correspond to a lossless conversion of static to dynamic pressure at +the entrance of the glottis according to Bernoulli’s equation, and +a loss of all dynamic pressure at the exit of the glottis. Potential energy losses during the conversion from static to dynamic +pressure can be considered by setting kent > 1. Furthermore, a +certain percentage of dynamic pressure is usually recovered at +the glottal exit, which can be considered by setting kexit > 0. +The coefficients are frequently set to the values obtained by van +den Berg et al. [6], namely kent = 1.375 and kexit = 0.5. +However, there is no consensus on these values. For example, +Ishizaka et al. [8] proposed to calculate kexit based on the conservation of momentum at the glottal exit, which makes kexit a +function of the cross-sectional area of the glottis and the area +immediately downstream from the glottis. The resulting coefficient is typically in the order of 0.05 to 0.4. With respect to the +entrance coefficient, Pelorson et al. [9, 10] argue that kent = 1 +instead of 1.375 because the human glottis has a smooth entrance at which no significant flow separation should occur. +In the vocal tract above the glottis, viscous losses are often +modeled as distributed pressure losses using Poiseuille’s equation, which describes the pressure drop across a cylindrical tube +section of length ∆x and cross-sectional area A under the assumption of a fully developed laminar flow [11, 12]: + +1. Introduction +Articulatory speech synthesizers mostly use one-dimensional +aerodynamic-acoustic simulations of the vocal tract, because +they are much faster than two-dimensional or three-dimensional +simulations and physically valid up to frequencies of about +4 kHz [1, 2, 3, 4]. An important element for realistic simulations is the modeling of energy losses. For voiced speech +sounds they determine the bandwidths of the formants, and for +unvoiced sounds they determine the airflow rate for a certain +subglottal pressure, which in turn affects the power spectrum of +turbulent noise sources [5]. +Currently, the energy loss at the glottis is usually modeled +differently than losses further downstream in the vocal tract. +With regard to the glottis, the transglottal pressure drop ∆P +is often modeled as +12µ +% +∆P = ∆x 3 U + (kent − kexit ) 2 U 2 +lw +2A +| {z } | +{z +} +∆Pv + +(1) + +∆Pk + +∆Pv = ∆x + +based on a study by van den Berg et al. [6]. The term ∆Pv +represents the viscous pressure loss of a fully developed laminar flow through a rectangular duct (the glottis), where ∆x is +the length of the duct (axial glottal length), l is the long side of +the rectangle (anterior-posterior glottal length), w is the short +side of the rectangle (glottal width), µ is the viscosity of the air, +and U is the volume velocity through the glottis. The area of +the glottis is A = lw, hence the viscous pressure loss can be +rewritten as ∆Pv = ∆x12µl2 /A3 . When we assume that the +glottal area changes mainly due to changes of its width w, and + +8µπ +U. +A2 + +(3) + +In contrast to ∆Pv in Eqs. (1) and (2), here ∆Pv ∝ A−2 . +A supraglottal kinetic energy loss is usually only considered locally at the site of a critical constriction with the area Ac +(e.g. in fricatives) as +∆Pk = kc · + +% +U 2, +2A2c + +(4) + +where kc is an empirical coefficient [13, 1]. However, using +a lumped loss at constrictions can cause acoustic artifacts in + +3105 + +10.21437/Interspeech.2024-1970 + + Cylinder + +/a/ + +// + +/e/ + +/i/ + +/o/ + +Laptop + +/u/ + +l = 16 mm + +Trachea + +Pressure +transducer + +Vocal tract + +Data +acquisition + +Single-board +computer + +w = 4 mm + +Figure 1: Back row: Tube models of the vocal tract. The mouth +opening is at the upper end. Front row, from left to right: Glottis +models with glottal widths of 1, 2, 4, 8, and 16 mm. + +Lung + +Pressure +tap + +Glottis +Larynx + +Blower + +Airflow +sensor + +Trachea + +Figure 2: Measurement setup. The right side shows a cutaway +view of the vocal tract for /a/, the glottis replica (“Larynx”), +and the upper part of the trachea. + +aerodynamic-acoustic simulations of running speech, where the +constriction sites change dynamically [14]. +The above overview shows that there are several ways of +modeling the viscous and kinetic energy losses in the vocal +tract. However, there is little experimental evidence for onedimensional flow models of the vocal tract [15], especially +when they include both the glottis and the supraglottal cavities. +The goal of the present study was to propose a unified approach +to modeling viscous and kinetic energy losses in the vocal tract, +which is suitable to be included in one-dimensional models for +articulatory speech synthesis. In this model, not only the viscous losses but also the kinetic energy losses are distributed +(as opposed to localized losses in previous studies). The model +has three parameters that were adjusted to reproduce flow data +obtained with physical replicas of the vocal tract including the +glottis. + +1.7 cm. Further details about these models can be found in [16]. +The glottis models consist of three regions: a short cylindrical part with a diameter of 1.8 cm that represents the upper part of the trachea, a 7 mm long section that represents the +conus elasticus where the cross-section tapers towards that of +the actual glottis, which is represented as a rectangular duct +(with slightly rounded edges) with a length of 3 mm (glottal +depth), a long side (glottal length) of 16 mm and a short side +of the glottal width w. We made five glottis models with glottal widths of 1, 2, 4, 8, and 16 mm. For the width of 16 mm, +the glottal area became a full circle with a diameter of 16 mm, +as shown in Figure 1. Glottal widths of w = 1 mm and +w = 2 mm roughly represent intermediate and maximal areas +during phonation, w = 4 mm and w = 8 mm correspond to +glottal areas used for voiceless fricatives [5], and w = 16 mm +corresponds to an area of 201 mm2 typical for breathing [17]. +The area functions and 3D-printable STL files of all models are +provided in the supplemental material1 . +The glottis and vocal tract replicas were used in the measurement setup shown in Figure 2. Here, air was fed from a +radial blower (U71HX-024KX-6 by micronel, Tagelswangen, +Switzerland) through a 2 m long tube into a box representing +the lungs and from there through a model of the trachea. The +glottis and vocal tract models were mounted on the upper end +of the trachea, as shown in the cutaway view at the right side +of the figure. A pressure transducer (DMU4, Kalinsky Sensor +Elektronik, Erfurt, Germany) was used to capture the subglottal +pressure at the upper end of the trachea, and an airflow sensor (AWM720-P1, Honeywell, Charlotte, North Carolina) was +used to capture the flow rate at the entrance to the “lung box”. +The sensor values were digitized by a data acquisition device +(DataTranslation 9837C, Norton, MA) with a sampling rate of +48 kHz and 24 bits quantization per channel and sent to a laptop. The laptop was running a custom software to display the +data and control the power of the radial blower. +For each combination of a glottis model and a vocal tract +model, the blower power was adjusted sequentially to generate 7 fluid power levels: 100, 200, 400, 700, 1100, 1600, and + +2. Method +2.1. Measurements with physical tube models +To obtain reference data for the proposed theoretical model (see +Sec. 2.2), we performed flow experiments with physical replicas +of the glottis and the vocal tract. Glottis models with different +glottal areas were combined with tube models of the vocal tract +for different vowels, and the pressure drop across these models +was measured for multiple airflow rates. +A photograph of all vocal tract and glottis models is shown +in Figure 1. They were designed with the software Autodesk +Inventor (version 2019) and 3D-printed on an Ultimaker 5S +printer using the material polylactic acid. The vocal tract models comprise a cylinder as well as straight axisymmetric tubes +with area functions of the vowels /a, E, e, i, o, u/. The area +functions were exported from the articulatory speech synthesizer VocalTractLab 2.3 (www.vocaltractlab.de) based +on the respective vocal tract shapes of the standard speaker +model. The tube models were chosen because they cover a +range of conditions with different numbers of constrictions and +constrictions of different lengths. For example, the models for +/e/ and /i/ have a single relatively long constriction in the anterior part, while the models for /o/ and /u/ have two shorter +constrictions in the middle and at the anterior end. The smallest +cross-sectional areas of these models are in the range of 0.25 +to 0.36 cm2 . The diameter at the glottal end is 1.7 cm for all +models, which tapers to a diameter of about 0.68 cm (area of +0.36 cm2 ) at the upper end of the epilaryngeal tube. The cylinder model has a length of 17 cm and a uniform diameter of + +1 https://www.vocaltractlab.de/index.php?page= +birkholz-supplements + +3106 + + 6 + +a) + +Mouth opening + +Glottis + +Area in cm + +2 + +5 +Glottis + +4 +3 +2 + +Oral cavity + +Pressure in Pa + +1 +0 +b) 300 + +R1 ++ +Psub +- + +200 + +Q1 + +R2 + +Q2 + +... + +QN-2 RN-1 QN-1 + +RN + +U + +100 + +Figure 4: Discrete tube model and fluidic network. + +0 +-2 + +0 + +2 + +4 + +6 +8 +10 +Position in cm + +12 + +14 + +16 + +between these sections, namely + +Figure 3: a) Continuous (black) and discrete (red) area functions for the glottis model (glottal width of 2 mm) concatenated +with the tube model for /a/. b) Simulated distribution of the +static pressure for a flow rate of 500 cm3 /s. + + + +2200 mW. At each power level, the pressure and airflow rate +were measured. The measurements were carried out three times +on different days and averaged over the repetitions. Since the +results for the glottal widths of 8 mm and 16 mm were nearly +identical (less than 5% deviation for all measurements), the data +with the 16 mm glottis were excluded from further analysis. +2.2. Theoretical model +Our approach to model viscous and kinetic losses in a uniform +way assumes that the vocal tract (including the glottis and subglottis) is represented as a sequence of short abutting cylindrical +tube sections [18]. The lengths and cross-sectional areas of the +tube sections are given in terms of a discrete area function. As +an example, the red curve in Figure 3a shows the discrete area +function that was derived from the combined continuous area +function (black curve) of the physical replicas of the glottis and +the vocal tract for /a/. As proposed in [19], the areas of the +discrete sections assume the minimum of the continuous area +function in the regions of the sections. +As shown in Section 1, previous approaches to model the +viscous pressure loss ∆Pv over a short tube section of length +∆x have in common that they are proportional to the airflow +rate U , to ∆x and to a (negative) power of the cross-sectional +area. However, the proportionality factor and the area exponent +differ between the equations. Here we propose the following +general equation for the viscous loss over a tube section i, +∆Pv,i = li Rref · (Aref /Ai )α U, + +kc · (%/2)(1/A2i+1 − 1/A2i )U 2 +ke · (%/2)(1/A2i+1 − 1/A2i )U 2 + +for Ai+1 < Ai +otherwise, +(6) +where the proportionality factors kc and ke account for potential +losses at tube contractions and expansions, respectively. With +this approach, the total kinetic pressure change across a tube +contraction or expansion that extends over multiple tube sections (sum of the involved ∆Pk,i ) depends only on the initial +and final cross-sectional areas of the expansion or contraction. +This makes the results independent of the discretization step +size of the area function. +A summation of all ∆Pk,i for the whole tube furthermore +shows that the overall kinetic pressure loss is essentially a function of the difference (kc − ke ) of the coefficients, so that their +individual values cannot be independently determined from our +experimental data. Hence, following [9] we set kc = 1 in this +study, assuming a lossless conversion from static to dynamic +pressure at tube contractions. This leaves ke as the only parameter to be determined for the kinetic energy losses. +With these considerations, the pressure changes in the vocal +tract can be represented in terms of the fluidic network shown +in Figure 4. Here, Psub is the subglottal pressure, N is the number of tube sections, Rn are linear resistors that cause a pressure change proportional to U according to Eq. (5), and Qn are +non-linear resistors that cause a pressure change proportional +to U 2 according to Eq. (6). Note that QN = 0, because there +is no pressure recovery at the tube exit [20]. The network allows to determine the complete pressure distribution along the +tube axis for steady flows and can be readily combined with +the transmission-line circuit representation of the vocal tract to +model both aerodynamics and acoustics [18, 14]. +∆Pk,i = + +(5) + +2.3. Determination of model parameters + +where li and Ai are the length and cross-sectional area of the +tube section, and Rref , Aref and α are free parameters. Aref was +fixed to 1 cm2 , so that Rref can be interpreted as the flow resistance (ratio of pressure drop to volume flow) per unit length for +an area of 1 cm2 , and α models the variation of the resistance +with the area. Both Rref and α were adjusted to fit the simulations to our experimental data (see Section 2.3). +Inspired by [14], kinetic energy losses are distributed along +the entire vocal system and depend on whether the tube is +locally contracting or expanding. Specifically, the pressure +change at each transition between two tube sections i and i + 1 +is assumed to be proportional to that of a lossless Bernoulli flow + +To find values for the three model parameters Rref , α and ke +that minimize the deviation between measurements and simulations, we performed a complete grid search in the intervals +Rref ∈ [800; 2.6 · 106 ] Pa·s/m4 , α ∈ [2; 3], and ke ∈ [0; 0.8]. +For each setting of the parameters, the subglottal pressure was +simulated for all airflow rates and tube models used in the experiments in Section 2.1 based on the discretized area functions. +The overall deviation between simulations and measurements +for a certain parameter setting was then calculated as the root +mean square percentage error E [21] between simulated and +measured subglottal pressure values across all tube models and +flow rates. + +3107 + + Pressure Psub in Pa + +2500 Glottis only +2000 (no vocal tract) +1500 +1000 +500 +0 + +Uniform cylinder + +/a/ + +Pressure Psub in Pa + +2500 // +2000 +1500 +1000 +500 +0 + +/e/ + +/i/ + +Pressure Psub in Pa + +2500 /o/ +2000 +1500 +1000 +500 +0 +0 + +/u/ + +0 + +500 +1000 +Flow U in cm3/s + +1500 + +0 + +500 +1000 +Flow U in cm3/s + +500 +1000 +Flow U in cm3/s + +1500 + +1500 + +Flow resistance per unit length in Pa∙s/m4 + +Figure 5: Measured flow-pressure points (circles) and simulated flow-pressure curves with optimized parameters. The black, red, green, +and blue curves were obtained for glottal widths of 1 mm, 2 mm, 4 mm, and 8 mm, respectively. + +1012 + +10 + +With regard to viscous losses, we obtained an area exponent of 2.9, which is close to the value of 3 assumed in many +studies for the glottis, and higher than the value of 2.59 obtained by Fulcher et al. [7] or the value of 2 in Poiseuille’s law. +Figure 6 compares the flow resistance as a function of the tube +area between the proposed Eq. (5) with the optimized parameters (red curve), Eq. (2) proposed for the glottis by Fulcher et +al. (light gray curve), the viscous resistance for the glottis in +Eq. (1) (gray curve), and Poiseuille’s law (black curve). This +shows that Poiseuille’s law, which is often used to model viscous losses in the vocal tract, strongly underestimates the losses +for small cross-sectional areas. This in turn leads to an underestimation of formant bandwidths in acoustic simulations [22]. + +Propsed +Glottis (Fulcher) +Glottis (van den Berg) +Poiseuille's law + +11 + +10 + +10 + +109 +8 + +10 + +107 +106 +105 +10 + +4 + +10-2 + +10-1 +Area in cm2 + +100 + +Figure 6: Variation of the flow resistance per unit length as a +function of the cross-sectional area for different equations. + +The fluidic network shown in Figure 4 and the optimized +model parameters allow to calculate the pressure distribution +along the tube axis for any given area function and airflow rate. +As an example, Figure 3b shows the pressure distribution for the +glottis with a width of 2 mm connected to the vocal tract for /a/ +at a flow rate of 500 cm3 /s. For the three tube contractions and +expansions in the posterior part, the associated pressure drops +and (partial) recoveries can be clearly seen. In future studies, +it would be interesting to compare such pressure profiles with +distributed pressure measurements along the whole tube axis. + +3. Results and discussion +The parameter values that minimize the deviation between the +measured and simulated subglottal pressure values across all +models and flow rates are Rref = 347, 922 Pa·s/m4 , α = 2.9 +and ke = 0.29 with an error of E = 14.9%. Figure 5 shows +the measured flow-pressure pairs as circles along with the simulated flow-pressure curves. Different glottal widths are represented by different colors (black for 1 mm, red for 2 mm, green +for 4 mm, and blue for 8 mm), while each panel represents one +vocal tract model (including the absence of a vocal tract in the +top left panel). The simulations approximate the measured data +points reasonably well. +With regard to the kinetic energy losses, the difference of +the contraction and expansion factors is kc − ke = 0.71 in our +model. This value is somewhat lower than 0.875 as determined +by van den Berg for the glottis [6], and lower than the value of +1.0 assumed by Birkholz et al. [14]. Hence, the overall kinetic +energy losses in the proposed model are lower than in these earlier models. + +Finally, we would like to compare the error of 14.9% between measurements and simulations for the optimized model +parameters with other choices for the model parameters. If we +model viscous losses with Poiseuille’s law and set ke = 0 for +tube expansions as in [14], the error increases to 20.9%. When +the viscous loss according to Poiseuille’s law is combined with +ke = 0.29, the error becomes 28.0%, and when the optimized +viscous resistance is combined with ke = 0, the error becomes +31.2%. This shows that the parameters for both viscous and kinetic losses must be set correctly to achieve optimum agreement +with the experimental data. + +3108 + + 4. Acknowledgements +We thank Mario Fleischer for useful discussions about this +study. + +[17] A. Scheinherr, L. Bailly, O. Boiron, A. Lagier, T. Legou, +M. Pichelin, G. Caillibotte, and A. Giovanni, “Realistic glottal +motion and airflow rate during human breathing,” Medical Engineering & Physics, vol. 37, no. 9, pp. 829–839, 2015. + +5. References + +[18] J. L. Flanagan, Speech Analysis, Synthesis and Perception. +Springer-Verlag, Berlin, 1965. +[19] P. Birkholz, “Enhanced area functions for noise source modeling in the vocal tract,” in Proc. of the 10th International Seminar +on Speech Production (ISSP 2014), Cologne, Germany, 2014, pp. +37–40. + +[1] A. J. S. Teixeira, R. Martinez, L. N. Silva, L. M. T. Jesus, J. C. +Principe, and F. A. C. Vaz, “Simulation of human speech production applied to the study and synthesis of European Portuguese,” +EURASIP Journal on Applied Signal Processing, vol. 9, pp. 1435– +1448, 2005. + +[20] A. C. Yunus and C. J.M., Fluid Mechanics: Fundamentals and +Applications (SI Units). McGraw Hill, 2006. + +[2] S. Fels, J. E. Lloyd, K. Van Den Doel, F. Vogt, I. Stavness, and +E. Vatikiotis-Bateson, “Developing physically-based, dynamic +vocal tract models using ArtiSynth,” in Proc. of the 7th International Seminar on Speech Production (ISSP 2006), Ubatuba, +Brazil, 2006, pp. 419–426. + +[21] M. V. Shcherbakov, A. Brebels, N. L. Shcherbakova, A. P. Tyukov, +T. A. Janovsky, V. A. Kamaev et al., “A survey of forecast error +measures,” World Applied Sciences Journal, vol. 24, no. 24, pp. +171–176, 2013. + +[3] P. Birkholz, “Modeling consonant-vowel coarticulation for articulatory speech synthesis,” PLOS ONE, vol. 8, no. 4, p. e60603, +2013. + +[22] P. Birkholz, R. Blandin, and S. Kürbis, “Bandwidths of vocal tract +resonances in physical models compared to transmission-line simulations,” The Journal of the Acoustical Society of America, vol. +153, no. 6, pp. 3281–3281, 2023. + +[4] R. Blandin, M. Arnela, S. Félix, J.-B. Doc, and P. Birkholz, “Efficient 3D acoustic simulation of the vocal tract by combining the +multimodal method and finite elements,” IEEE Access, vol. 10, +pp. 69 922–69 938, 2022. +[5] K. N. Stevens, Acoustic Phonetics. + +The MIT Press, 1998. + +[6] J. Van Den Berg, J. T. Zantema, and P. J. Doornenbal, “On the +air resistance and the Bernoulli effect of the human larynx,” The +Journal of the Acoustical Society of America, vol. 29, no. 5, pp. +626–631, 1957. +[7] L. P. Fulcher, R. C. Scherer, and T. Powell, “Viscous effects in a +static physical model of the uniform glottis,” The Journal of the +Acoustical Society of America, vol. 134, no. 2, pp. 1253–1260, +2013. +[8] K. Ishizaka and J. L. Flanagan, “Synthesis of voiced sounds from +a two-mass model of the vocal cords,” The Bell System Technical +Journal, vol. 51, no. 6, pp. 1233–1268, 1972. +[9] X. Pelorson, A. Hirschberg, R. R. van Hassel, A. P. J. Wijnands, and Y. Auregan, “Theoretical and experimental study of +quasisteady-flow separation within the glottis during phonation. +application to a modified two-mass model,” The Journal of the +Acoustical Society of America, vol. 96, no. 6, pp. 3416–3431, +1994. +[10] X. Pelorson, C. Vescovi, E. Castelli, A. Hirschberg, A. P. J. Wijnands, and H. M. A. Bailliet, “Description of the flow through invitro models of the glottis during phonation. application to voiced +sound synthesis,” Acta Acustica, vol. 82, pp. 358–361, 1996. +[11] S. Maeda, “A digital simulation method of the vocal-tract system,” +Speech Communication, vol. 1, pp. 199–229, 1982. +[12] B. Elie and Y. Laprie, “Extension of the single-matrix formulation +of the vocal tract: Consideration of bilateral channels and connection of self-oscillating models of the vocal folds with a glottal +chink,” Speech Communication, vol. 82, pp. 85–96, 2016. +[13] M. M. Sondhi and J. Schroeter, “A hybrid time-frequency domain +articulatory speech synthesizer,” IEEE Transactions on Acoustics, +Speech and Signal Processing, vol. 35, no. 7, pp. 955–967, 1987. +[14] P. Birkholz, D. Jackèl, and B. J. Kröger, “Simulation of losses due +to turbulence in the time-varying vocal system,” IEEE Transactions on Audio, Speech and Language Processing, vol. 15, no. 4, +pp. 1218–1226, 2007. +[15] A. V. Hirtum, X. Pelorson, O. Estienne, and H. Bailliet, “Experimental validation of flow models for a rigid vocal tract replica,” +The Journal of the Acoustical Society of America, vol. 130, no. 4, +pp. 2128–2138, 2011. +[16] P. Birkholz, P. Häsner, and S. Kürbis, “Acoustic comparison of +physical vocal tract models with hard and soft walls,” in International Conference on Acoustics, Speech, and Signal Processing +(ICASSP 2022), Singapore, 2022, pp. 8242–8246. + +3109 + + \ No newline at end of file diff --git a/research/vocal-source-grounding/sources/wur-elemans-mechanical-model.html b/research/vocal-source-grounding/sources/wur-elemans-mechanical-model.html new file mode 100644 index 0000000..33beece --- /dev/null +++ b/research/vocal-source-grounding/sources/wur-elemans-mechanical-model.html @@ -0,0 +1,855 @@ + + + + + + + + + + + + + + + + Amplitude and frequency modulation control of sound production in a mechanical model of the avian syrinx + - Research Portal - Wageningen University & Research + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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Amplitude and frequency modulation control of sound production in a mechanical model of the avian syrinx

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Research output: Contribution to journal › Article › Academic › peer-review

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Abstract

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Birdsong has developed into one of the important models for motor control of learned behaviour and shows many parallels with speech acquisition in humans. However, there are several experimental limitations to studying the vocal organ – the syrinx – in vivo. The multidisciplinary approach of combining experimental data and mathematical modelling has greatly improved the understanding of neural control and peripheral motor dynamics of sound generation in birds. Here, we present a simple mechanical model of the syrinx that facilitates detailed study of vibrations and sound production. Our model resembles the `starling resistor', a collapsible tube model, and consists of a tube with a single membrane in its casing, suspended in an external pressure chamber and driven by various pressure patterns. With this design, we can separately control `bronchial' pressure and tension in the oscillating membrane and generate a wide variety of `syllables' with simple sweeps of the control parameters. We show that the membrane exhibits high frequency, self-sustained oscillations in the audio range (>600 Hz fundamental frequency) using laser Doppler vibrometry, and systematically explore the conditions for sound production of the model in its control space. The fundamental frequency of the sound increases with tension in three membranes with different stiffness and mass. The lower-bound fundamental frequency increases with membrane mass. The membrane vibrations are strongly coupled to the resonance properties of the distal tube, most likely because of its reflective properties to sound waves. Our model is a gross simplification of the complex morphology found in birds, and more closely resembles mathematical models of the syrinx. Our results confirm several assumptions underlying existing mathematical models in a complex geometry
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Original languageEnglish
Pages (from-to)1212-1224
JournalJournal of Experimental Biology
Volume212
Issue number8
DOIs
Publication statusPublished - 2009
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Keywords

  • voice-producing element
  • self-excited oscillations
  • vocal-fold vibration
  • collapsible tubes
  • nonlinear dynamics
  • numerical-simulation
  • 2-mass model
  • flow-through
  • zebra finch
  • laryngectomized patients
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+ + + + + + + + + + + + + + + + + + + diff --git a/state/evidence.jsonl b/state/evidence.jsonl index b8a8894..9161e60 100644 --- a/state/evidence.jsonl +++ b/state/evidence.jsonl @@ -213,3 +213,4 @@ {"evidence":"Listening/spectrogram audit showed the first tissue-valve batches were mostly faint noise and DC-like startup energy. Replaced the non-self-sustaining noise-resonator seed with a pressure-gated tissue oscillator whose frequency is derived from stiffness/mass/tension and bounded load detune, and bounded source-load pressure feedback with `tanh` so the tract can perturb instead of fully quench the source. Added an explicit subglottal wall terminal to `human-larynx-graph.aqua` so folds at the larynx junction have an upstream trachea segment instead of a source node with no incident wave port. Human modal, bird, and alien graph patches now render sustained harmonic stacks in spectrograms under `artifacts/listening/vocal-core-squawk-20260528T211222944`.","claim":"The graph machine can now produce audible vocalizations through reusable tissue-valve semantics. The next work is no longer basic audibility; it is shaping morphology, gestures, and source coupling into credible speech and bird articulation.","timestamp":"2026-05-28T21:16:00+01:00","topic":"tissue-valve-squawk-audit"} {"evidence":"Warbling White-eye visual audition exposed two source-ownership errors: graph tissue-valve lowering still let `freq=` impose a stiffness floor even when stiffness was explicit/parameter-bound, and direct displacement voicing injected low-frequency junk instead of only shaping aperture. Fixed graph lowering so explicit stiffness owns effective stiffness, lifted the graph tissue modal ceiling to 10 kHz for small syrinx/alien sources, and reduced modal/displacement flow drive to avoid square-wave broadband saturation. New audition artifacts under `artifacts/listening/warbling-white-eye-20260528T220500961` include five WAVs plus reference/candidate spectrogram comparisons; `05-single-trace.wav` is the clearest Warbling White-eye-shaped candidate by eye.","claim":"Bird-like graph vocalization now depends on visible phrase gestures, realtime stiffness/pressure/opening curves, and source-flow ownership rather than metrics or a fixed `freq=` rail. Future syrinx fitting should start from single-dominant-labium traces, then add bilateral behavior only when the spectrogram needs it.","timestamp":"2026-05-28T22:32:00+01:00","topic":"warbling-white-eye-visual-audition"} {"evidence":"A visual review of the Warbling White-eye comparison showed the previous best candidate still failed the reference: its contours were piecewise straight and its harmonic ladder was too strong. Added `interp=smooth` control curves lowered to Faust `seg_smooth` smoothstep segments, then rerendered the Warbling White-eye audition with smooth pressure/opening/tension/stiffness gestures and a low-drive single-labium candidate. `artifacts/listening/warbling-white-eye-20260528T220500961/06-smooth-low-drive.compare.png` now shows curved motif contours and much weaker harmonics, though it is still only a rough birdlike gesture, not a species-quality match.","claim":"Smooth realtime gesture semantics are required for vocal modeling. Straight spectral contours are often authored linear control curves leaking through the physical model, so future bird/human fitting should use smooth motor gestures before adding morphology changes or spectral compensators.","timestamp":"2026-05-28T22:50:00+01:00","topic":"smooth-vocal-gestures"} +{"evidence":"Created `research/vocal-source-grounding` with downloaded/captured references on MEAD source physics, syrinx modeling, two-mass vocal fold modeling, self-oscillating vocal fold experiments, Birkholz 2024 pressure losses, and Faust physical modeling primitives. The grounding pass found `drive` is currently split-brained: it scales reservoir pressure, phonation gate, and modal/displacement brightness. Literature points instead to pressure as energy input, tissue mass/stiffness/damping/collision as source morphology, aperture/area-dependent flow loss as pressure-flow shaping, and tract/radiation load as spectral/acoustic coupling.","claim":"The next valve-law cut should demote generic `drive` into a calibration/compatibility alias, then make harmonic richness and ease of oscillation emerge from explicit morphology, pressure-flow loss, collision/contact, damping, and graph load rather than a timbre rescue knob.","timestamp":"2026-05-28T23:12:00+01:00","topic":"vocal-source-grounding"}