Ground vocal source law research
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research/vocal-source-grounding/README.md
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# Vocal Source Grounding
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This packet grounds the next cut to Aqua's graph tissue-valve source law. The
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trigger was the Warbling White-eye audition: a low-drive, smooth single-labium
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candidate finally sounded birdlike, but the route there was suspicious. The
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question is whether low drive and harmonic suppression are legitimate source
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controls or compensators that should instead fall out of morphology, pressure,
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tissue loss, aperture geometry, and acoustic load.
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Downloaded/captured source files live in `sources/`.
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## Decision Pressure
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The current graph valve lowering still gives `drive` too much authority:
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- it scales reservoir pressure, so it changes energy input;
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- it participates in oscillation gating, so it changes phonation threshold;
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- it scales modal/displacement contribution into flow, so it changes brightness;
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- it sits beside `pressure`, `damping`, `saturation`, `load_coupling`, and
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`rest_opening`, which already have clearer physical meanings.
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That is not one organ. That is a desk drawer full of half-labeled teeth.
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## Literature Anchors
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### Myoelastic-Aerodynamic Ownership
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Elemans et al. 2015 provide the cleanest cross-species authority map: bird
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syrinxes and mammal larynxes both use the myoelastic-aerodynamic mechanism.
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Airflow supplies energy; tissue elasticity/restoring forces, tissue-wave phase,
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and aerodynamic asymmetry sustain oscillation. The paper explicitly ties
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frequency and mode of oscillation to mechanical tissue properties plus
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aerodynamic driving forces, not a standalone timbre-gain parameter.
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Implementation implication: `pressure` or `reservoir_pressure` is the energy
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input. `mass`, `stiffness`, `damping`, layered phase, aperture geometry, and
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load decide what that energy becomes. A single `drive` knob should not also own
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spectral aggression.
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### Syrinx Models Use Pressure/Tension Paths, Not Timbre Rescues
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Mindlin/Laje-style syrinx work models syllables as trajectories through
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physiological parameter space, especially pressure and stiffness/tension. Their
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review emphasizes that the syrinx itself can be a source of complex acoustical
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behavior, and that smooth excursions in pressure/stiffness parameter space can
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produce recognizable syllables. The same review highlights that source-tract and
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source-source coupling can create subharmonics, period-doubling, and complex
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periodic/aperiodic behavior.
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Implementation implication: the higher-level controller can own motif gestures,
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but the lower-level source law must expose meaningful physical coordinates.
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Harmonic behavior should arise from nonlinear source dynamics and coupling
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regimes, not from a spectral smoothing knob.
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### Mechanical Syrinx Experiments Separate Bronchial Pressure And Tension
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Elemans et al. 2009 modeled the syrinx as a collapsible-tube/starling-resistor
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style mechanical system with separately controlled bronchial pressure and
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membrane tension. The captured abstract reports high-frequency self-sustained
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oscillations, tension-dependent frequency, mass-dependent lower frequency
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limits, and strong coupling to distal tube resonance.
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Implementation implication: source morphology needs separate controls for
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tension/stiffness, mass, damping/tissue loss, and tract load. Pressure should
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drive the system; distal tube/reflection should perturb it. A generic low-drive
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value is not the correct way to make a small bird source less harsh.
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### Two-Mass Vocal Fold Modeling Keeps Flow, Tissue, And Tract Separate
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Ishizaka and Flanagan's classic two-mass model approximates the vocal folds as
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two stiffness-coupled masses, uses Bernoulli flow through the glottis, and
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represents the tract as a transmission line. It calculates glottal area, glottal
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volume velocity, mouth pressure, and relationships among subglottal pressure,
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cord tension, glottal area, and duty ratio.
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Implementation implication: our layered valve law should move toward explicit
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upper/lower masses and aperture/flow equations. It should not hide duty ratio,
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open quotient, or source spectral tilt behind `drive`.
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### Self-Oscillating Fold Reviews Point To Coupled Nonlinear Physics
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The 2024 review of synthetic self-oscillating vocal fold models frames phonation
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as coupled flow dynamics, tissue motion, and acoustics. It calls out turbulence,
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flow separation, large deformation/strain, collision, acoustic coupling, and
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radiated acoustics as difficult but central nonlinear phenomena. It also
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emphasizes that stiffness and geometry are meaningful experimental controls.
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Implementation implication: if the current valve needs harmonic suppression,
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candidate owners are damping/tissue loss, collision stiffness/damping, aperture
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geometry, flow separation/loss, and radiation/load. A musical-synth style drive
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stage is the wrong default owner.
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### Vocal-Tract Loss Work Makes Area-Dependent Flow Loss A First-Class Actor
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Birkholz and Haesner 2024 propose unified viscous and kinetic pressure losses in
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discrete tube vocal-system models, including the glottis. Their measurements
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support area-dependent viscous losses and partial pressure recovery at
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expansions; the losses affect formant bandwidths, airflow, and turbulent source
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power.
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Implementation implication: some of the "harmonic suppression" we wanted by
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turning drive down should instead come from source/tract loss and radiation
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loading. For small apertures and narrow passages, area-dependent loss is not a
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post-EQ trick; it is pressure-flow physics.
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### Faust Can Express The Clean Version
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Faust has first-class tools for this lane: recursive state with `~`, filters,
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fractional delays, bidirectional waveguide primitives, mode filters, tube
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models, reed tables, and nonlinear functions. We do not need to keep a fake
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drive authority because of Faust. The hard part is choosing a source law that is
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simple enough to inspect and stable enough for realtime.
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Implementation implication: the next cut can stay Faust-friendly if it is a
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small set of named locals: reservoir/downstream pressure, pressure drop,
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flow-resistance/loss, upper/lower displacement and velocity, aperture,
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collision/contact, load pressure, volume velocity, and radiation flow.
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## Authority Map For The Next Cut
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Owner: `AcousticSourcePort` source morphology owns local valve dynamics;
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`AcousticNetwork` owns incident pressure/load and radiation; gesture/controller
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layers own time-varying physiological inputs.
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Inputs:
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- Controller/gesture: `pressure`, `opening`, `tension`, left/right activation.
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- Source morphology: `mass`, `upper_mass`, `lower_mass`, `stiffness`,
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`upper_stiffness`, `lower_stiffness`, `coupling_stiffness`, `damping`,
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`tissue_loss`, `collision_stiffness`, `collision_damping`,
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`rest_opening`, `aperture_shape`, `flow_loss`.
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- Graph load: incident/downstream pressure, tract impedance, tube losses,
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radiation opening/reflection/loss.
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Outputs:
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- Source volume velocity/flow injection.
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- Optional debug locals for aperture, pressure drop, contact, tissue energy,
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load pressure, and radiated flow.
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Derived state:
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- Dominant pitch, harmonic richness, phonation threshold, breathiness,
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brightness, and biphonation are outcomes of the above. They are not owned by
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`freq=` or a generic `drive`.
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Forbidden writers:
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- No hidden fixed oscillator floor when stiffness exists.
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- No direct displacement-as-audio lane except as a tiny diagnostic/legacy term.
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- No "harmonic suppression" or "bird smoothness" scalar.
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- No source-owned spectral EQ pretending to be morphology.
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## Proposed Cut, Not Yet Implemented
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1. Split `drive` into physical pieces:
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- keep `pressure`/`reservoir_pressure` as the energy input;
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- introduce or repurpose `flow_scale` only as a unit/calibration factor;
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- move threshold/ease-of-oscillation into pressure drop, aperture, damping,
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and load;
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- move spectral harshness into aperture/contact/flow-loss/radiation.
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2. Add explicit morphology fields only if they name physics:
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- `tissue_loss` or `viscous_loss` for dissipative tissue/flow losses;
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- `aperture_shape` for the nonlinear mapping from displacement to area;
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- `flow_loss` or `flow_resistance` for area-dependent pressure-flow loss;
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- keep `collision_stiffness`/`collision_damping` as the contact owner.
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3. Change the source law shape:
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- compute `pressure_drop = reservoir_pressure - downstream/load pressure`;
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- compute aperture from rest opening + controlled opening + displacement;
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- compute flow from a pressure-flow relation damped by aperture-dependent
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resistance, not from arbitrary modal gain into `tanh`;
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- use modal/two-mass tissue state to modulate aperture and flow, not as a
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parallel oscillator output;
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- let tract/radiation losses shape brightness before any post-source
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normalization.
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4. Keep a compatibility path only as explicit legacy:
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- `drive` can remain parsed for now, but it should lower to `flow_scale` or a
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deprecated alias with warnings/tests, not retain secret timbre authority.
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## Open Questions
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- Do we want `flow_scale` exposed in DSL at all, or should it be a patch
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calibration constant hidden behind morphology presets?
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- Should `aperture_shape` be a continuous scalar first, or should we jump
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directly to named aperture laws such as `slot`, `wedge`, `membrane`, and
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`reed`?
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- How aggressive should the v1 area-dependent pressure-flow loss be before we
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have a calibration set for birds?
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- Should one-mass law remain the default for realtime, with two-mass/body-cover
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reserved for richer source patches, or should syrinx defaults move directly to
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two-mass because MEAD phase asymmetry is central?
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## Source Index
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- `pmc-elemans-2015-universal-mechanisms.html` and
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`elemans-2015-universal-mechanisms.pdf`
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- `pmc-new-perspectives-birdsong-physics.html`
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- `wur-elemans-mechanical-model.html`
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- `nokia-ishizaka-flanagan-two-mass.html`
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- `pmc-self-oscillating-vocal-fold-review.html`
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- `vocaltractlab-birkholz-2024-losses.pdf` and `.txt`
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- `faust-physmodels-doc.html`, `faust-filters-doc.html`,
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`faust-noises-doc.html`
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research/vocal-source-grounding/SOURCES.md
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# Sources
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Downloaded or captured on 2026-05-28 for the vocal-source grounding pass.
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| Local file | Source | Use |
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| --- | --- | --- |
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| `sources/pmc-elemans-2015-universal-mechanisms.html` | <https://pmc.ncbi.nlm.nih.gov/articles/PMC4674827/> | Cross-species MEAD evidence for birds and mammals. |
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| `sources/elemans-2015-universal-mechanisms.pdf` | <https://findresearcher.sdu.dk/ws/portalfiles/portal/137389098/Universal_mechanisms_of_sound_production_and_control_in_birds_and_mammals.pdf> | Local PDF copy of the same paper. |
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| `sources/pmc-new-perspectives-birdsong-physics.html` | <https://pmc.ncbi.nlm.nih.gov/articles/PMC3263773/> | Mindlin/Laje birdsong physics review: pressure/tension parameter trajectories, nonlinear syrinx, source-tract/source-source coupling. |
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| `sources/pubmed-mindlin-birdsong-nonlinear-dynamics.html` | <https://pubmed.ncbi.nlm.nih.gov/28964148/> | PubMed metadata for Mindlin's nonlinear dynamics of birdsong review. |
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| `sources/pubmed-fee-nonlinear-dynamics-birdsong.html` | <https://pubmed.ncbi.nlm.nih.gov/9705934/> | PubMed metadata for Fee et al. nonlinear dynamics in birdsong. |
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| `sources/wur-elemans-mechanical-model.html` | <https://research.wur.nl/en/publications/amplitude-and-frequency-modulation-control-of-sound-production-in/> | Mechanical syrinx model metadata and abstract. |
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| `sources/nokia-ishizaka-flanagan-two-mass.html` | <https://www.nokia.com/bell-labs/publications-and-media/publications/synthesis-of-voiced-sounds-from-a-two-mass-model-of-the-vocal-chords/> | Classic two-mass model summary from Bell Labs/Nokia. |
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| `sources/pubmed-titze-1988-small-amplitude.html` | <https://pubmed.ncbi.nlm.nih.gov/3372869/> | PubMed metadata for Titze's small-amplitude vocal fold oscillation paper. |
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| `sources/pmc-self-oscillating-vocal-fold-review.html` | <https://pmc.ncbi.nlm.nih.gov/articles/PMC11348498/> | 2024 review of synthetic self-oscillating vocal fold models. |
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| `sources/vocaltractlab-birkholz-2024-losses.pdf` | <https://www.vocaltractlab.de/publications/birkholz-2024-interspeech.pdf> | Birkholz/Haesner 2024 vocal-system pressure-loss model. |
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| `sources/faust-physmodels-doc.html` | <https://faustlibraries.grame.fr/libs/physmodels/> | Faust physical modeling primitives. |
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| `sources/faust-filters-doc.html` | <https://faustlibraries.grame.fr/libs/filters/> | Faust filters for loss/radiation/source shaping. |
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| `sources/faust-noises-doc.html` | <https://faustlibraries.grame.fr/libs/noises/> | Faust noise primitives for turbulence. |
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Note: two attempted URLs resolved to unrelated pages during collection and were
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removed from the packet.
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<li class="nav-item" data-level="3"><a href="#normultinoise" class="nav-link">(no.)rmultinoise</a>
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<li class="nav-item" data-level="3"><a href="#nornoises" class="nav-link">(no.)rnoises</a>
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<li class="nav-item" data-level="3"><a href="#nopink_noise" class="nav-link">(no.)pink_noise</a>
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<ul class="nav flex-column">
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</ul>
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</li>
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<li class="nav-item" data-level="3"><a href="#nopink_noise_vm" class="nav-link">(no.)pink_noise_vm</a>
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</ul>
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</li>
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<li class="nav-item" data-level="3"><a href="#nolfnoise-nolfnoise0-and-nolfnoisen" class="nav-link">(no.)lfnoise, (no.)lfnoise0 and (no.)lfnoiseN</a>
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</ul>
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</ul>
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<li class="nav-item" data-level="3"><a href="#novelvet_noise_vm" class="nav-link">(no.)velvet_noise_vm</a>
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<div class="col-md-9 main-container" role="main">
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|
||||
<h1 id="noiseslib">noises.lib</h1>
|
||||
<p>Noises library. Its official prefix is <code>no</code>.</p>
|
||||
<p>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.</p>
|
||||
<p>The Noises library is organized into 1 section:</p>
|
||||
<ul>
|
||||
<li><a href="#functions-reference">Functions Reference</a></li>
|
||||
</ul>
|
||||
<h4 id="references">References</h4>
|
||||
<ul>
|
||||
<li><a href="https://github.com/grame-cncm/faustlibraries/blob/master/noises.lib">https://github.com/grame-cncm/faustlibraries/blob/master/noises.lib</a></li>
|
||||
</ul>
|
||||
<h2 id="functions-reference">Functions Reference</h2>
|
||||
<hr />
|
||||
<h3 id="nonoise"><code>(no.)noise</code></h3>
|
||||
<p>White noise generator (outputs random number between -1 and 1).
|
||||
<code>noise</code> is a standard Faust function.</p>
|
||||
<h4 id="usage">Usage</h4>
|
||||
<pre><code>noise : _
|
||||
</code></pre>
|
||||
<p>Where:</p>
|
||||
<ul>
|
||||
<li>output: white noise signal in [-1, 1].</li>
|
||||
</ul>
|
||||
<h4 id="test">Test</h4>
|
||||
<pre><code>no = library("noises.lib");
|
||||
noise_test = no.noise;
|
||||
</code></pre>
|
||||
<hr />
|
||||
<h3 id="nomultirandom"><code>(no.)multirandom</code></h3>
|
||||
<p>Generates multiple decorrelated random numbers in parallel.</p>
|
||||
<h4 id="usage_1">Usage</h4>
|
||||
<pre><code>multirandom(N) : si.bus(N)
|
||||
</code></pre>
|
||||
<p>Where:</p>
|
||||
<ul>
|
||||
<li><code>N</code>: the number of decorrelated random numbers in parallel, a constant numerical expression</li>
|
||||
</ul>
|
||||
<h4 id="test_1">Test</h4>
|
||||
<pre><code>no = library("noises.lib");
|
||||
multirandom_test = no.multirandom(3);
|
||||
</code></pre>
|
||||
<hr />
|
||||
<h3 id="nomultinoise"><code>(no.)multinoise</code></h3>
|
||||
<p>Generates multiple decorrelated noises in parallel.</p>
|
||||
<h4 id="usage_2">Usage</h4>
|
||||
<pre><code>multinoise(N) : si.bus(N)
|
||||
</code></pre>
|
||||
<p>Where:</p>
|
||||
<ul>
|
||||
<li><code>N</code>: the number of decorrelated random numbers in parallel, a constant numerical expression</li>
|
||||
</ul>
|
||||
<h4 id="test_2">Test</h4>
|
||||
<pre><code>no = library("noises.lib");
|
||||
multinoise_test = no.multinoise(3);
|
||||
</code></pre>
|
||||
<hr />
|
||||
<h3 id="nonoises"><code>(no.)noises</code></h3>
|
||||
<p>A convenient wrapper around multinoise.</p>
|
||||
<h4 id="usage_3">Usage</h4>
|
||||
<pre><code>noises(N,i) : _
|
||||
</code></pre>
|
||||
<p>Where:</p>
|
||||
<ul>
|
||||
<li><code>N</code>: the number of decorrelated random numbers in parallel, a constant numerical expression</li>
|
||||
<li><code>i</code>: the selected random number (i in [0..N[)</li>
|
||||
</ul>
|
||||
<h4 id="test_3">Test</h4>
|
||||
<pre><code>no = library("noises.lib");
|
||||
noises_test = no.noises(4, 2);
|
||||
</code></pre>
|
||||
<hr />
|
||||
<h3 id="nodnoise"><code>(no.)dnoise</code></h3>
|
||||
<p>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.</p>
|
||||
<h4 id="usage_4">Usage</h4>
|
||||
<pre><code>dnoise(t,sx) : _
|
||||
</code></pre>
|
||||
<p>Where:</p>
|
||||
<ul>
|
||||
<li><code>t</code>: is a noise burst trigger</li>
|
||||
<li><code>sx</code>: defines the range of integer seed multipliers. </li>
|
||||
</ul>
|
||||
<h4 id="test_4">Test</h4>
|
||||
<pre><code>no = library("noises.lib");
|
||||
ba = library("basics.lib");
|
||||
dnoise_test = (trigger, seedRange) : no.dnoise
|
||||
with {
|
||||
trigger = 1 : ba.impulsify;
|
||||
seedRange = 10.0;
|
||||
};
|
||||
</code></pre>
|
||||
<h4 id="example">Example</h4>
|
||||
<p>This expression <code>sx = hslider("seed multiplier",1,1,1000,1)</code> allows 1000 distinct seed variations.
|
||||
To generate a burst with a fixed length, use <code>ba.spulse(bLength, t)</code> (as trigger for the <code>t</code> parameter), where <code>bLength</code> is the burst duration in samples and <code>t</code> is a trigger.</p>
|
||||
<hr />
|
||||
<h3 id="norandomseed"><code>(no.)randomseed</code></h3>
|
||||
<p>A random seed based on the foreign function <code>arc4random</code>
|
||||
(see man arc4random). Used in <code>rnoise</code>, <code>rmultirandom</code>, etc. to
|
||||
avoid having the same pseudo random sequence at each run.</p>
|
||||
<p>WARNING: using the foreign function <code>arc4random</code>, so only available in C/C++ and LLVM backends.</p>
|
||||
<h4 id="usage_5">Usage</h4>
|
||||
<pre><code>randomseed : _
|
||||
</code></pre>
|
||||
<p>Where:</p>
|
||||
<ul>
|
||||
<li>output: platform-specific random seed value.</li>
|
||||
</ul>
|
||||
<h4 id="test_5">Test</h4>
|
||||
<pre><code>no = library("noises.lib");
|
||||
randomseed_test = no.randomseed;
|
||||
</code></pre>
|
||||
<hr />
|
||||
<h3 id="nornoise"><code>(no.)rnoise</code></h3>
|
||||
<p>A randomized white noise generator (outputs random number between -1 and 1).</p>
|
||||
<p>WARNING: using the foreign function <code>arc4random</code>, so only available in C/C++ and LLVM backends.</p>
|
||||
<h4 id="usage_6">Usage</h4>
|
||||
<pre><code>rnoise : _
|
||||
</code></pre>
|
||||
<h4 id="test_6">Test</h4>
|
||||
<pre><code>no = library("noises.lib");
|
||||
rnoise_test = no.rnoise;
|
||||
</code></pre>
|
||||
<hr />
|
||||
<h3 id="normultirandom"><code>(no.)rmultirandom</code></h3>
|
||||
<p>Generates multiple decorrelated random numbers in parallel.</p>
|
||||
<p>WARNING: using the foreign function <code>arc4random</code>, so only available in C/C++ and LLVM backends.</p>
|
||||
<h4 id="usage_7">Usage</h4>
|
||||
<pre><code>rmultirandom(N) : _
|
||||
</code></pre>
|
||||
<p>Where:</p>
|
||||
<ul>
|
||||
<li><code>N</code>: the number of decorrelated random numbers in parallel, a constant numerical expression</li>
|
||||
</ul>
|
||||
<h4 id="test_7">Test</h4>
|
||||
<pre><code>no = library("noises.lib");
|
||||
rmultirandom_test = no.rmultirandom(3);
|
||||
</code></pre>
|
||||
<hr />
|
||||
<h3 id="normultinoise"><code>(no.)rmultinoise</code></h3>
|
||||
<p>Generates multiple decorrelated noises in parallel.</p>
|
||||
<p>WARNING: using the foreign function <code>arc4random</code>, so only available in C/C++ and LLVM backends.</p>
|
||||
<h4 id="usage_8">Usage</h4>
|
||||
<pre><code>rmultinoise(N) : _
|
||||
</code></pre>
|
||||
<p>Where:</p>
|
||||
<ul>
|
||||
<li><code>N</code>: the number of decorrelated random numbers in parallel, a constant numerical expression</li>
|
||||
</ul>
|
||||
<h4 id="test_8">Test</h4>
|
||||
<pre><code>no = library("noises.lib");
|
||||
rmultinoise_test = no.rmultinoise(3);
|
||||
</code></pre>
|
||||
<hr />
|
||||
<h3 id="nornoises"><code>(no.)rnoises</code></h3>
|
||||
<p>A convenient wrapper around rmultinoise.</p>
|
||||
<p>WARNING: using the foreign function <code>arc4random</code>, so only available in C/C++ and LLVM backends.</p>
|
||||
<h4 id="usage_9">Usage</h4>
|
||||
<pre><code>rnoises(N,i) : _
|
||||
</code></pre>
|
||||
<p>Where:</p>
|
||||
<ul>
|
||||
<li><code>N</code>: the number of decorrelated random numbers in parallel</li>
|
||||
<li><code>i</code>: the selected random number (i in [0..N[)</li>
|
||||
</ul>
|
||||
<h4 id="test_9">Test</h4>
|
||||
<pre><code>no = library("noises.lib");
|
||||
rnoises_test = no.rnoises(4, 1);
|
||||
</code></pre>
|
||||
<hr />
|
||||
<h3 id="nopink_noise"><code>(no.)pink_noise</code></h3>
|
||||
<p>Pink noise (1/f noise) generator (third-order approximation covering the audio band well).
|
||||
<code>pink_noise</code> is a standard Faust function.</p>
|
||||
<h4 id="usage_10">Usage</h4>
|
||||
<pre><code>pink_noise : _
|
||||
</code></pre>
|
||||
<p>Where:</p>
|
||||
<ul>
|
||||
<li>output: pink (1/f) noise signal.</li>
|
||||
</ul>
|
||||
<h4 id="test_10">Test</h4>
|
||||
<pre><code>no = library("noises.lib");
|
||||
pink_noise_test = no.pink_noise;
|
||||
</code></pre>
|
||||
<h4 id="alternatives">Alternatives</h4>
|
||||
<p>Higher-order approximations covering any frequency band can be obtained using</p>
|
||||
<pre><code>no.noise : fi.spectral_tilt(order,lowerBandLimit,Bandwidth,p)
|
||||
</code></pre>
|
||||
<p>where <code>p=-0.5</code> means filter rolloff <code>f^(-1/2)</code> which gives 1/f rolloff in the
|
||||
power spectral density, and can be changed to other real values.</p>
|
||||
<h4 id="example_1">Example</h4>
|
||||
<p>pink_noise_compare.dsp - compare three pinking filters</p>
|
||||
<pre><code>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
|
||||
};
|
||||
</code></pre>
|
||||
<h4 id="output-of-example">Output of Example</h4>
|
||||
<pre><code>faust2octave pink_noise_compare.dsp
|
||||
Octave:1> semilogx(20*log10(abs(fft(faustout,8192))(1:4096,:)));
|
||||
...
|
||||
</code></pre>
|
||||
<p><img alt="pink_noise_demo figure" src="https://ccrma.stanford.edu/wiki/Images/8/86/Tpinkd.jpg" width="600" /></p>
|
||||
<h4 id="references_1">References</h4>
|
||||
<ul>
|
||||
<li><a href="https://ccrma.stanford.edu/~jos/sasp/Example_Synthesis_1_F_Noise.html">https://ccrma.stanford.edu/~jos/sasp/Example_Synthesis_1_F_Noise.html</a></li>
|
||||
</ul>
|
||||
<hr />
|
||||
<h3 id="nopink_noise_vm"><code>(no.)pink_noise_vm</code></h3>
|
||||
<p>Multi pink noise generator.</p>
|
||||
<h4 id="usage_11">Usage</h4>
|
||||
<pre><code>pink_noise_vm(N) : _
|
||||
</code></pre>
|
||||
<p>Where:</p>
|
||||
<ul>
|
||||
<li><code>N</code>: number of latched white-noise processes to sum,
|
||||
not to exceed sizeof(int) in C++ (typically 32).</li>
|
||||
</ul>
|
||||
<h4 id="test_11">Test</h4>
|
||||
<pre><code>no = library("noises.lib");
|
||||
pink_noise_vm_test = no.pink_noise_vm(4);
|
||||
</code></pre>
|
||||
<h4 id="references_2">References</h4>
|
||||
<ul>
|
||||
<li><a href="http://www.dsprelated.com/showarticle/908.php">http://www.dsprelated.com/showarticle/908.php</a></li>
|
||||
<li><a href="http://www.firstpr.com.au/dsp/pink-noise/#Voss-McCartney">http://www.firstpr.com.au/dsp/pink-noise/#Voss-McCartney</a></li>
|
||||
</ul>
|
||||
<hr />
|
||||
<h3 id="nolfnoise-nolfnoise0-and-nolfnoisen"><code>(no.)lfnoise</code>, <code>(no.)lfnoise0</code> and <code>(no.)lfnoiseN</code></h3>
|
||||
<p>Low-frequency noise generators (Butterworth-filtered downsampled white noise).</p>
|
||||
<h4 id="usage_12">Usage</h4>
|
||||
<pre><code>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)
|
||||
</code></pre>
|
||||
<h4 id="example_2">Example</h4>
|
||||
<p>(view waveforms in faust2octave):</p>
|
||||
<pre><code>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
|
||||
</code></pre>
|
||||
<h4 id="test_12">Test</h4>
|
||||
<pre><code>no = library("noises.lib");
|
||||
lfnoise0_test = no.lfnoise0(10.0);
|
||||
</code></pre>
|
||||
<hr />
|
||||
<h3 id="nosparse_noise"><code>(no.)sparse_noise</code></h3>
|
||||
<p>Sparse noise generator.</p>
|
||||
<h4 id="usage_13">Usage</h4>
|
||||
<pre><code>sparse_noise(f0) : _
|
||||
</code></pre>
|
||||
<p>Where:</p>
|
||||
<ul>
|
||||
<li><code>f0</code>: average frequency of noise impulses per second</li>
|
||||
</ul>
|
||||
<p>Random impulses in the amplitude range -1 to 1 are generated
|
||||
at an average rate of f0 impulses per second.</p>
|
||||
<h4 id="test_13">Test</h4>
|
||||
<pre><code>no = library("noises.lib");
|
||||
sparse_noise_test = no.sparse_noise(5.0);
|
||||
</code></pre>
|
||||
<h4 id="references_3">References</h4>
|
||||
<ul>
|
||||
<li>See velvet_noise</li>
|
||||
</ul>
|
||||
<hr />
|
||||
<h3 id="novelvet_noise_vm"><code>(no.)velvet_noise_vm</code></h3>
|
||||
<p>Velvet noise generator.</p>
|
||||
<h4 id="usage_14">Usage</h4>
|
||||
<pre><code>velvet_noise(amp, f0) : _
|
||||
</code></pre>
|
||||
<p>Where:</p>
|
||||
<ul>
|
||||
<li><code>amp</code>: amplitude of noise impulses (positive and negative)</li>
|
||||
<li><code>f0</code>: average frequency of noise impulses per second</li>
|
||||
</ul>
|
||||
<h4 id="test_14">Test</h4>
|
||||
<pre><code>no = library("noises.lib");
|
||||
velvet_noise_test = no.velvet_noise(0.5, 5.0);
|
||||
</code></pre>
|
||||
<h4 id="references_4">References</h4>
|
||||
<ul>
|
||||
<li>Matti Karjalainen and Hanna Jarvelainen,
|
||||
"Reverberation Modeling Using Velvet Noise",
|
||||
in Proc. 30th Int. Conf. Intelligent Audio Environments (AES07),
|
||||
March 2007.</li>
|
||||
</ul>
|
||||
<hr />
|
||||
<h3 id="nognoise"><code>(no.)gnoise</code></h3>
|
||||
<p>Approximate zero-mean, unit-variance Gaussian white noise generator.</p>
|
||||
<h4 id="usage_15">Usage</h4>
|
||||
<pre><code>gnoise(N) : _
|
||||
</code></pre>
|
||||
<p>Where:</p>
|
||||
<ul>
|
||||
<li><code>N</code>: number of uniform random numbers added to approximate Gaussian white noise</li>
|
||||
</ul>
|
||||
<h4 id="test_15">Test</h4>
|
||||
<pre><code>no = library("noises.lib");
|
||||
gnoise_test = no.gnoise(8);
|
||||
</code></pre>
|
||||
<h4 id="references_5">References</h4>
|
||||
<ul>
|
||||
<li>See Central Limit Theorem</li>
|
||||
</ul>
|
||||
<hr />
|
||||
<h3 id="nocolored_noise"><code>(no.)colored_noise</code></h3>
|
||||
<p>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.</p>
|
||||
<h4 id="usage_16">Usage</h4>
|
||||
<pre><code>colored_noise(N,alpha) : _
|
||||
</code></pre>
|
||||
<p>Where:</p>
|
||||
<ul>
|
||||
<li><code>N</code>: desired integer filter order (constant numerical expression)</li>
|
||||
<li><code>alpha</code>: 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.</li>
|
||||
</ul>
|
||||
<h4 id="test_16">Test</h4>
|
||||
<pre><code>no = library("noises.lib");
|
||||
colored_noise_test = no.colored_noise(4, 0.0);
|
||||
</code></pre>
|
||||
<h4 id="examples">Examples</h4>
|
||||
<p>See <code>dm.colored_noise_demo</code>.</p></div>
|
||||
</div>
|
||||
</div>
|
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3742
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|
|
@ -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,
|
||||
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|
||||
[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
|
||||
|
||||
|
||||
|
|
@ -0,0 +1,855 @@
|
|||
|
||||
|
||||
|
||||
|
||||
<!DOCTYPE html>
|
||||
<html lang="en" class="nexus-font-support">
|
||||
|
||||
|
||||
<head>
|
||||
<meta charset="utf-8"/>
|
||||
<meta http-equiv="X-UA-Compatible" content="IE=edge"/>
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1"/>
|
||||
<meta name="google" content="nositelinkssearchbox"/>
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<div class="rendering"><h1><span>Amplitude and frequency modulation control of sound production in a mechanical model of the avian syrinx</span></h1></div>
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<div class="rendering rendering_researchoutput rendering_researchoutput_associatespersonsclassifiedportal rendering_contributiontojournal rendering_associatespersonsclassifiedportal rendering_contributiontojournal_associatespersonsclassifiedportal"><ul class="relations persons"><li>C.P.H. Elemans</li><li>, M. Muller</li><li>, O.N. Larsen</li><li>, <a rel="Person" href="https://research.wur.nl/en/persons/johan-van-leeuwen/" class="link person"><span>J.L. van Leeuwen</span></a></li></div>
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<h2 class="subheader">Abstract</h2>
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<div class="rendering rendering_researchoutput rendering_researchoutput_abstractportal rendering_contributiontojournal rendering_abstractportal rendering_contributiontojournal_abstractportal"><div class="textblock">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</div></div>
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<div class="rendering rendering_researchoutput rendering_researchoutput_detailsportal rendering_contributiontojournal rendering_detailsportal rendering_contributiontojournal_detailsportal"><div class="article"><table class="properties"><tbody><tr class="language"><th scope="row">Original language</th><td>English</td></tr><tr><th scope="row">Pages (from-to)</th><td>1212-1224</td></tr><tr><th scope="row">Journal</th><td><a rel="Journal" href="#" class="link"><span>Journal of Experimental Biology</span></a></td></tr><tr><th scope="row">Volume</th><td>212</td></tr><tr><th scope="row">Issue number</th><td>8</td></tr><tr class="digital_object_identifiers"><th scope="row">DOIs</th><td><ul class="relations digital_object_identifiers"><li><a onclick="window.open(this.href, '_blank','noopener,noreferrer'); return false;" href="https://doi.org/10.1242/jeb.026872" class="link"><span>https://doi.org/10.1242/jeb.026872</span></a> </li></ul></td></tr><tr class="status"><th scope="row">Publication status</th><td><span class="prefix">Published - </span><span class="date">2009</span></td></tr></tbody></table></div></div>
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<div class="rendering rendering_keywordable rendering_expertkeywordgrouspbytypeportal rendering_keywordable_expertkeywordgrouspbytypeportal"><div class="keyword-group"><h2 class="subheader">Keywords</h2><ul class="relations keywords"><li class="userdefined-keyword"><span>voice-producing element</span></li><li class="userdefined-keyword"><span>self-excited oscillations</span></li><li class="userdefined-keyword"><span>vocal-fold vibration</span></li><li class="userdefined-keyword"><span>collapsible tubes</span></li><li class="userdefined-keyword"><span>nonlinear dynamics</span></li><li class="userdefined-keyword"><span>numerical-simulation</span></li><li class="userdefined-keyword"><span>2-mass model</span></li><li class="userdefined-keyword"><span>flow-through</span></li><li class="userdefined-keyword"><span>zebra finch</span></li><li class="userdefined-keyword"><span>laryngectomized patients</span></li></ul></div></div>
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<div class="rendering rendering_researchoutput rendering_researchoutput_publicationaccessrenderer rendering_contributiontojournal rendering_publicationaccessrenderer rendering_contributiontojournal_publicationaccessrenderer"><ul class="dois"><li><div class="doi"><a onclick="window.open(this.href, '_blank','noopener,noreferrer'); return false;" href="https://doi.org/10.1242/jeb.026872" class="link"><span>10.1242/jeb.026872</span></a></div></li></ul></div>
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<div class="rendering rendering_researchoutput rendering_researchoutput_apa rendering_contributiontojournal rendering_apa rendering_contributiontojournal_apa">Elemans, C. P. H., Muller, M., Larsen, O. N.<a rel="Person" href="https://research.wur.nl/en/persons/johan-van-leeuwen/" class="link"><span>, & van Leeuwen, J. L.</span></a> (2009). <a rel="ContributionToJournal" href="https://research.wur.nl/en/publications/amplitude-and-frequency-modulation-control-of-sound-production-in/" class="link"><span>Amplitude and frequency modulation control of sound production in a mechanical model of the avian syrinx</span></a>. <a rel="Journal" href="#" class="link"><span><em>Journal of Experimental Biology</em></span></a>, <em>212</em>(8), 1212-1224. <a onclick="window.open(this.href, '_blank','noopener,noreferrer'); return false;" href="https://doi.org/10.1242/jeb.026872" class="link"><span>https://doi.org/10.1242/jeb.026872</span></a></div>
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<div class="rendering rendering_researchoutput rendering_researchoutput_author rendering_contributiontojournal rendering_author rendering_contributiontojournal_author">Elemans, C.P.H. ; Muller, M. ; Larsen, O.N. et al. / <a rel="ContributionToJournal" href="https://research.wur.nl/en/publications/amplitude-and-frequency-modulation-control-of-sound-production-in/" class="link"><span><strong>Amplitude and frequency modulation control of sound production in a mechanical model of the avian syrinx</strong></span></a>. In: <a rel="Journal" href="#" class="link"><span>Journal of Experimental Biology</span></a>. 2009 ; Vol. 212, No. 8. pp. 1212-1224.</div>
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<div class="rendering rendering_researchoutput rendering_researchoutput_bibtex rendering_contributiontojournal rendering_bibtex rendering_contributiontojournal_bibtex"><div>@article{fbd3f2af867a46fb82bd3d4636628706,</div><div> title = "Amplitude and frequency modulation control of sound production in a mechanical model of the avian syrinx",</div><div> abstract = "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",</div><div> 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",</div><div> author = "C.P.H. Elemans and M. Muller and O.N. Larsen and \{van Leeuwen\}, J.L.",</div><div> year = "2009",</div><div> doi = "10.1242/jeb.026872",</div><div> language = "English",</div><div> volume = "212",</div><div> pages = "1212--1224",</div><div> journal = "Journal of Experimental Biology",</div><div> issn = "0022-0949",</div><div> publisher = "Company of Biologists",</div><div> number = "8",</div><p>}</p></div>
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<div class="rendering rendering_researchoutput rendering_researchoutput_harvard rendering_contributiontojournal rendering_harvard rendering_contributiontojournal_harvard">Elemans, CPH, Muller, M, Larsen, ON<a rel="Person" href="https://research.wur.nl/en/persons/johan-van-leeuwen/" class="link"><span> & van Leeuwen, JL</span></a> 2009, '<a rel="ContributionToJournal" href="https://research.wur.nl/en/publications/amplitude-and-frequency-modulation-control-of-sound-production-in/" class="link harvard_title"><span>Amplitude and frequency modulation control of sound production in a mechanical model of the avian syrinx</span></a>', <a rel="Journal" href="#" class="link"><span><em>Journal of Experimental Biology</em></span></a>, vol. 212, no. 8, pp. 1212-1224. <a onclick="window.open(this.href, '_blank','noopener,noreferrer'); return false;" href="https://doi.org/10.1242/jeb.026872" class="link"><span>https://doi.org/10.1242/jeb.026872</span></a></div>
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<div class="rendering rendering_researchoutput rendering_researchoutput_standard rendering_contributiontojournal rendering_standard rendering_contributiontojournal_standard"><a rel="ContributionToJournal" href="https://research.wur.nl/en/publications/amplitude-and-frequency-modulation-control-of-sound-production-in/" class="link"><span><strong>Amplitude and frequency modulation control of sound production in a mechanical model of the avian syrinx.</strong></span></a> / Elemans, C.P.H.; Muller, M.; Larsen, O.N. et al. <br />In: <a rel="Journal" href="#" class="link"><span>Journal of Experimental Biology</span></a>, Vol. 212, No. 8, 2009, p. 1212-1224.<p class="type"><span class="type_family">Research output<span class="type_family_sep">: </span></span><span class="type_classification_parent">Contribution to journal<span class="type_parent_sep"> › </span></span><span class="type_classification">Article</span><span class="type_classification"><span class="type_parent_sep"> › </span>Academic</span><span class="type_classification"><span class="type_parent_sep"> › </span>peer-review</span></p></div>
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<div class="rendering rendering_researchoutput rendering_researchoutput_ris rendering_contributiontojournal rendering_ris rendering_contributiontojournal_ris"><p>TY - JOUR</p><p>T1 - Amplitude and frequency modulation control of sound production in a mechanical model of the avian syrinx</p><p>AU - Elemans, C.P.H.</p><p>AU - Muller, M.</p><p>AU - Larsen, O.N.</p><p>AU - van Leeuwen, J.L.</p><p>PY - 2009</p><p>Y1 - 2009</p><p>N2 - 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</p><p>AB - 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</p><p>KW - voice-producing element</p><p>KW - self-excited oscillations</p><p>KW - vocal-fold vibration</p><p>KW - collapsible tubes</p><p>KW - nonlinear dynamics</p><p>KW - numerical-simulation</p><p>KW - 2-mass model</p><p>KW - flow-through</p><p>KW - zebra finch</p><p>KW - laryngectomized patients</p><p>U2 - 10.1242/jeb.026872</p><p>DO - 10.1242/jeb.026872</p><p>M3 - Article</p><p>SN - 0022-0949</p><p>VL - 212</p><p>SP - 1212</p><p>EP - 1224</p><p>JO - Journal of Experimental Biology</p><p>JF - Journal of Experimental Biology</p><p>IS - 8</p><p>ER - </p></div>
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<div class="rendering rendering_researchoutput rendering_researchoutput_vancouver rendering_contributiontojournal rendering_vancouver rendering_contributiontojournal_vancouver">Elemans CPH, Muller M, Larsen ON<a rel="Person" href="https://research.wur.nl/en/persons/johan-van-leeuwen/" class="link"><span>, van Leeuwen JL</span></a>. <span class="title"><a rel="ContributionToJournal" href="https://research.wur.nl/en/publications/amplitude-and-frequency-modulation-control-of-sound-production-in/" class="link"><span>Amplitude and frequency modulation control of sound production in a mechanical model of the avian syrinx</span></a></span>. <a rel="Journal" href="#" class="link"><span>Journal of Experimental Biology</span></a>. 2009;212(8):1212-1224. doi: 10.1242/jeb.026872</div>
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{"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"}
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{"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"}
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{"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"}
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{"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"}
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