pinktrombone.lib

A Faust port of Neil Thapen's Pink Trombone (2017), the bare-handed procedural speech synthesiser https://dood.al/pinktrombone/.

The original is a ~1000-line JavaScript program running in a ScriptProcessorNode. This library reproduces its DSP core:

  • Glottis — a per-period-resampled Liljencrants–Fant (LF) glottal-flow waveform driven by a single "tenseness" parameter (Rd = 3(1-tenseness)), plus aspiration noise modulated by the glottal cycle, vibrato / pitch wobble and slow tenseness drift.
  • Tract — a 44-section Kelly–Lochbaum digital waveguide of the vocal tract, run at twice the audio rate (two waveguide ticks per sample), with a 28-section nasal branch coupled at section 17 by a three-port scattering junction, glottal reflection 0.75, lip/nostril reflection -0.85, fricative turbulence injected at a movable constriction, and a decaying "transient" pulse released when a full closure opens (plosives).
  • Tract shape — the "tongue" (index / diameter) that bends the rest diameters between the blade and the lips, one or two constrictions (index / diameter, e.g. for fricatives and stops), and the velum.

Everything that was block-rate (512 samples) in the JavaScript is computed at sample rate here, with the block-rate constants converted to rates using the original's block length.

Sample rate. Each waveguide section is one tick long, so the tract's acoustic length, and with it every formant, scales with the tick rate; the original has the same property. With the default ticksPerSample = 2 the model is tuned for 44.1 and 48 kHz (at 48 kHz the formants of a given shape are about 9 % higher than at 44.1 kHz). At 88.2 or 96 kHz, override it to 1, e.g. pt[ticksPerSample=1;].pinkTrombone(...): the whole model then behaves as it does at 44.1 or 48 kHz. Other rates shift the formants in proportion. The 1-D simplex drift noises are the real thing (no.simplex1_lf, a port of the same noisejs code, with a fixed seed instead of Date.now()); the browser's uniform Math.random() white noise is replaced by scaled no.noise.

Its official prefix is pt.

Deviations from the original

  • The block-rate updates (512-sample blocks) run at sample rate, and the reflection coefficients follow the section diameters every sample instead of being interpolated across each block (which also removes the original's swapped old/new interpolation at the nose junction). The release of a closure is still detected one block late, as in the original.
  • voiced behaves like a finger on the original's pitch keyboard: voicing ramps in and out, without the pressed onset of the original's untouched "always voice" start-up.
  • UI-only behaviour is not modelled: the keyboard is replaced by freq in Hz; the tongue control's reachable-range kludge, and its side effect of acting as a wide constriction while held, are left out; at most two constrictions (tract2, pinkTrombone2); the velum is the separate nasal gate instead of a touch below the tract.
  • Up to two release transients sound at once (the original keeps a list).
  • The simplex drift uses the fixed seed noiseSeed instead of Date.now(), and the uniform white noise is scaled no.noise.
  • Waveguide state below 1e-20 is flushed to zero, so the (lossless) nose does not decay into denormals.

Against a line-by-line reference port of the JavaScript, settled tract output matches to about 1e-6 (relative) and the LF waveform to 2e-3 (absolute, float32).

Usage

pt = library("pinktrombone.lib");
process = pt.pinkTrombone(freq, tenseness, voiced, wobble, tongueIndex, tongueDiameter,
                          constrictionIndex, constrictionDiameter, constrictionOn, nasal);

Use process = dm.pink_trombone_demo; with import("stdfaust.lib"); for the demo.

Note: pass signals (or use partial application / sequential composition) for the audio-rate arguments glottalOutput, noiseModulator, fricNoise — an explicit _ argument gets duplicated wherever the parameter is used inside the function.

References

  • Neil Thapen, Pink Trombone — bare-handed procedural speech synthesis, version 1.1 (March 2017), MIT licence. https://dood.al/pinktrombone/
  • The original's bibliography: J. O. Smith III, Physical Audio Signal Processing https://ccrma.stanford.edu/~jos/pasp/; B. H. Story, "A parametric model of the vocal tract area function for vowel and consonant simulation", JASA 117(5), 2005; H.-L. Lu & J. O. Smith, "Glottal source modeling for singing voice synthesis", ICMC 2000; J. Mullen, Physical modelling of the vocal tract with the 2D digital waveguide mesh, PhD thesis, York, 2006.
  • G. Fant, "The LF-model revisited. Transformations and frequency domain analysis", STL-QPSR 36(2-3), 1995 (the Rd parametrisation used by setupWaveform).

License

The Faust port is MIT-licensed, Copyright 2026 David Braun. It is a derivative work of Pink Trombone version 1.1 (March 2017) by Neil Thapen https://venuspatrol.nfshost.com; the original copyright and permission notice follows, reproduced verbatim as it requires:

Copyright 2017 Neil Thapen

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

Constants

(pt.)ticksPerSample

Waveguide ticks per sample (2). The tract's length, and so its formants, follow the tick rate: keep 2 at 44.1/48 kHz, override it to 1 at 88.2/96 kHz with explicit substitution (pt[ticksPerSample=1;]).

Usage

ticksPerSample : _

Test

import("stdfaust.lib");
pt_ticksPerSample_test = pt[ticksPerSample=1;].pinkTrombone(140, 0.6, 1, 0, 12.9, 2.43, 30, 3, 0, 0);

Utilities

(pt.)noiseSeed

Constant integer seed (12345) shared by the simplex drift streams. Override with explicit library substitution to choose another seed.

Usage

noiseSeed : _

Test

import("stdfaust.lib");
pt_noiseSeed_test = pt[noiseSeed=7;].glottis(140, 0.6, 1, 1) : _, !, !, !;

Glottis

(pt.)lfWaveform

The original's setupWaveform + normalizedLFWaveform: a Liljencrants–Fant glottal flow derivative pulse parametrised by Rd (0.5..2.7), normalised to a period of 1 and Ee = 1, evaluated at phase t in [0,1).

Usage

lfWaveform(Rd0, t) : _

Where:

  • Rd0: LF shape parameter, clamped to 0.5..2.7.
  • t: Phase in the half-open interval [0, 1).

Test

import("stdfaust.lib");
lfWaveform_test = par(i, 3, pt.lfWaveform(0.5 + i, os.lf_sawpos(100)));
lfWaveform_modulated_test = pt.lfWaveform(0.5 + 1.1*(1 + os.osc(2)), os.lf_sawpos(200));

(pt.)glottis

The Pink Trombone glottal source. Returns the glottal flow (LF pulse plus aspiration noise) that feeds the tract, together with the signals the tract needs from the glottis (noise modulator, and glottal-phase & intensity for convenience). Outputs are glottal excitation, noise modulator, intensity and phase, in that order.

Usage

glottis(freq, tenseness, voiced, wobble) : _, _, _, _

Where:

  • freq: Positive fundamental frequency in Hz; the demo spans about 87..277 Hz.
  • tenseness: Voice tenseness in 0..1; the default is 0.6.
  • voiced: Voice gate: positive is on, zero is off. It acts like a finger on the original's pitch keyboard: voicing ramps in and out, with no pressed onset.
  • wobble: Pitch wobble amount in 0..1.

Test

import("stdfaust.lib");
glottis_test = pt.glottis(140, 0.6, (ba.time < 24000), 0);
glottis_modulated_test = pt.glottis(150 + 50*os.osc(0.8), 0.5 + 0.45*os.osc(4), (ba.time % 48000) > 12000, 1);

Tract shape

(pt.)tractDiameters

The 44 time-varying section diameters (after the original's movement smoothing), as parallel signals.

Usage

tractDiameters(tongueIndex, tongueDiameter, cIndex, cDiameter, cActive) : si.bus(44)

Where:

  • tongueIndex: Tongue position in sections, 12..29 (default 12.9).
  • tongueDiameter: Tongue diameter in model units, 2.05..3.5 (default 2.43).
  • cIndex: Constriction position in sections, 2..44; position 44 lies beyond the mouth cells.
  • cDiameter: Touch diameter in model units, 0..3; at most 0.3 closes the tract, 3 leaves it open.
  • cActive: Constriction gate, 0 or 1.

Test

import("stdfaust.lib");
tractDiameters_test = pt.tractDiameters(12.9, 2.43, 30, 3, 0);
tractDiameters_constricted_test = pt.tractDiameters(20, 3.0, 30.4, 0.55, 1);

(pt.)tractDiameters2

Same with two independent constrictions, applied in order like the original's touch loop (each can only narrow what the previous ones left).

Usage

tractDiameters2(tongueIndex, tongueDiameter, c1i, c1d, c1a, c2i, c2d, c2a) : si.bus(44)

Where:

  • tongueIndex: Tongue position in sections, 12..29 (default 12.9).
  • tongueDiameter: Tongue diameter in model units, 2.05..3.5 (default 2.43).
  • c1i: First constriction position in sections, 2..44.
  • c1d: First touch diameter in model units, 0..3; at most 0.3 closes the tract.
  • c1a: First constriction gate, 0 or 1.
  • c2i: Second constriction position in sections, 2..44.
  • c2d: Second touch diameter in model units, 0..3; at most 0.3 closes the tract.
  • c2a: Second constriction gate, 0 or 1.

Test

import("stdfaust.lib");
tractDiameters2_test = pt.tractDiameters2(20, 3.0, 36.3, 0.5, 1, 20.6, 0.8, 1);

Tract waveguide

(pt.)tract

The Pink Trombone vocal tract: 44-section Kelly–Lochbaum waveguide with a 28-section nasal branch, ticked twice per sample. Diameters, constriction and velum drive the reflection coefficients; fricative noise and closure-release transients are injected into the waveguide.

Usage

tract(tongueIndex, tongueDiameter, cIndex, cDiameter, cActive, nasal, glottalOutput, noiseModulator) : _

Where:

  • tongueIndex: Tongue position in sections, 12..29 (default 12.9).
  • tongueDiameter: Tongue diameter in model units, 2.05..3.5 (default 2.43).
  • cIndex: Constriction position in sections, 2..44; position 44 lies beyond the mouth cells.
  • cDiameter: Touch diameter in model units, 0..3; at most 0.3 closes the tract, 3 leaves it open.
  • cActive: Constriction gate, 0 or 1.
  • nasal: Velum gate: positive selects diameter 0.4; zero selects 0.01.
  • glottalOutput: Audio excitation from glottis or an external source.
  • noiseModulator: Turbulence amplitude modulator, normally the second output of glottis.

Test

import("stdfaust.lib");
tract_test = (os.lf_imptrain(140), 0.3) : pt.tract(12.9, 2.43, 30, 3, 0, 0);
tract_nasal_test = (os.lf_imptrain(140), 0.3) : pt.tract(27, 2.2, 30, 3, 0, 1);
tract_closure_test = (os.lf_imptrain(140), 0.3) : pt.tract(12.9, 2.43, 40, 0, 1, 0);
tract_release_test = (os.lf_imptrain(140), 0.3) : pt.tract(12.9, 2.43, 30, 0, ba.time < 12000, 0);

(pt.)tract2

tract with two independent constrictions (the original is multi-touch: each touch narrows the tract and injects its own turbulence). Useful for consonant clusters and double articulations.

Usage

tract2(tongueIndex, tongueDiameter, c1i, c1d, c1a, c2i, c2d, c2a, nasal, glottalOutput, noiseModulator) : _

Where:

  • tongueIndex: Tongue position in sections, 12..29 (default 12.9).
  • tongueDiameter: Tongue diameter in model units, 2.05..3.5 (default 2.43).
  • c1i: First constriction position in sections, 2..44.
  • c1d: First touch diameter in model units, 0..3; at most 0.3 closes the tract.
  • c1a: First constriction gate, 0 or 1.
  • c2i: Second constriction position in sections, 2..44.
  • c2d: Second touch diameter in model units, 0..3; at most 0.3 closes the tract.
  • c2a: Second constriction gate, 0 or 1.
  • nasal: Velum gate: positive selects diameter 0.4; zero selects 0.01.
  • glottalOutput: Audio excitation from glottis or an external source.
  • noiseModulator: Turbulence amplitude modulator, normally the second output of glottis.

Test

import("stdfaust.lib");
tract2_test = (os.lf_imptrain(140), 0.3) : pt.tract2(12.9, 2.43, 36.3, 0.5, 1, 20.6, 0.8, 1, 0);

(pt.)tractExt

Same as tract / tract2 but with an explicit turbulence noise source (the original's 1 kHz, Q 0.5 bandpassed white noise) as first argument, for testing.

With fricNoise = 0 and constant articulation arguments, tractExt/tract2Ext reduce to the bare linear waveguide, which is exactly LTI from glottalOutput to the output: _moveTowards starts on its target, so constant articulation never ramps, the reflection coefficients are constants, and no release transient can fire. Its impulse response then characterises it completely (useful for FIR/formant analysis of a fixed vocal-tract shape).

Usage

tractExt(fricNoise, tongueIndex, tongueDiameter, cIndex, cDiameter, cActive, nasal, glottalOutput, noiseModulator) : _

Where:

  • fricNoise: External turbulence signal, typically white noise bandpassed at 1 kHz with Q 0.5; zero disables turbulence.
  • tongueIndex: Tongue position in sections, 12..29 (default 12.9).
  • tongueDiameter: Tongue diameter in model units, 2.05..3.5 (default 2.43).
  • cIndex: Constriction position in sections, 2..44; position 44 lies beyond the mouth cells.
  • cDiameter: Touch diameter in model units, 0..3; at most 0.3 closes the tract, 3 leaves it open.
  • cActive: Constriction gate, 0 or 1.
  • nasal: Velum gate: positive selects diameter 0.4; zero selects 0.01.
  • glottalOutput: Audio excitation from glottis or an external source.
  • noiseModulator: Turbulence amplitude modulator, normally the second output of glottis.

Test

import("stdfaust.lib");
tractExt_test = pt.tractExt(no.noise, 12.9, 2.43, 30.4, 0.55, 1, 0, os.lf_imptrain(140), 0.3);

(pt.)tract2Ext

Vocal tract with two independent constrictions and an explicit turbulence source. With zero turbulence and constant articulation, this is a linear time-invariant filter of the glottal excitation. Constant articulation starts on its target.

Usage

tract2Ext(fricNoise, tongueIndex, tongueDiameter, c1i, c1d, c1a, c2i, c2d, c2a, nasal, glottalOutput, noiseModulator) : _

Where:

  • fricNoise: External turbulence signal, typically white noise bandpassed at 1 kHz with Q 0.5; zero disables turbulence.
  • tongueIndex: Tongue position in sections, 12..29 (default 12.9).
  • tongueDiameter: Tongue diameter in model units, 2.05..3.5 (default 2.43).
  • c1i: First constriction position in sections, 2..44.
  • c1d: First touch diameter in model units, 0..3; at most 0.3 closes the tract.
  • c1a: First constriction gate, 0 or 1.
  • c2i: Second constriction position in sections, 2..44.
  • c2d: Second touch diameter in model units, 0..3; at most 0.3 closes the tract.
  • c2a: Second constriction gate, 0 or 1.
  • nasal: Velum gate: positive selects diameter 0.4; zero selects 0.01.
  • glottalOutput: Audio excitation from glottis or an external source.
  • noiseModulator: Turbulence amplitude modulator, normally the second output of glottis.

Test

import("stdfaust.lib");
tract2Ext_test = pt.tract2Ext(no.noise, 12.9, 2.43, 36.3, 0.5, 1, 20.6, 0.8, 1, 0, os.lf_imptrain(140), 0.3);

Full instrument

(pt.)pinkTrombone

Glottis + tract. Mono output.

Usage

pinkTrombone(freq, tenseness, voiced, wobble, tongueIndex, tongueDiameter, cIndex, cDiameter, cActive, nasal) : _

Where:

  • freq: Positive fundamental frequency in Hz; the demo spans about 87..277 Hz.
  • tenseness: Voice tenseness in 0..1; the default is 0.6.
  • voiced: Voice gate: positive is on, zero is off. It acts like a finger on the original's pitch keyboard: voicing ramps in and out, with no pressed onset.
  • wobble: Pitch wobble amount in 0..1.
  • tongueIndex: Tongue position in sections, 12..29 (default 12.9).
  • tongueDiameter: Tongue diameter in model units, 2.05..3.5 (default 2.43).
  • cIndex: Constriction position in sections, 2..44; position 44 lies beyond the mouth cells.
  • cDiameter: Touch diameter in model units, 0..3; at most 0.3 closes the tract, 3 leaves it open.
  • cActive: Constriction gate, 0 or 1.
  • nasal: Velum gate: positive selects diameter 0.4; zero selects 0.01.

Test

import("stdfaust.lib");
pinkTrombone_test = pt.pinkTrombone(140, 0.6, 1, 0, 12.9, 2.43, 30, 3, 0, 0);

(pt.)pinkTrombone2

Glottis + tract with two constrictions. Mono output.

Usage

pinkTrombone2(freq, tenseness, voiced, wobble, tongueIndex, tongueDiameter, c1i, c1d, c1a, c2i, c2d, c2a, nasal) : _

Where:

  • freq: Positive fundamental frequency in Hz; the demo spans about 87..277 Hz.
  • tenseness: Voice tenseness in 0..1; the default is 0.6.
  • voiced: Voice gate: positive is on, zero is off. It acts like a finger on the original's pitch keyboard: voicing ramps in and out, with no pressed onset.
  • wobble: Pitch wobble amount in 0..1.
  • tongueIndex: Tongue position in sections, 12..29 (default 12.9).
  • tongueDiameter: Tongue diameter in model units, 2.05..3.5 (default 2.43).
  • c1i: First constriction position in sections, 2..44.
  • c1d: First touch diameter in model units, 0..3; at most 0.3 closes the tract.
  • c1a: First constriction gate, 0 or 1.
  • c2i: Second constriction position in sections, 2..44.
  • c2d: Second touch diameter in model units, 0..3; at most 0.3 closes the tract.
  • c2a: Second constriction gate, 0 or 1.
  • nasal: Velum gate: positive selects diameter 0.4; zero selects 0.01.

Test

import("stdfaust.lib");
pinkTrombone2_test = pt.pinkTrombone2(140, 0.6, 1, 0, 12.9, 2.43, 40, 0.2, 1, 20, 1.0, 1, 1);