Kelly–Lochbaum Vocal Tract Explorer
Waveguide mesh simulation with gesture-timed keyboard articulation
Tract Geometry & Wave Propagation
Tube Parameters
17.5
44
0.10
0.80
0.30
0.50
Excitation & Output
150
0.50
1.00
rn = reflection coeff at junction n.
An = cross-sectional area of section n.
Output is taken from the lip end (right boundary).
An = cross-sectional area of section n.
Output is taken from the lip end (right boundary).
Articulatory Modspace
rate 1.00× ·
IOI 260 ms ·
voice 0.00 ·
x 0.00 y 0.00 z 0.00
live: pos 0.50 · constrict 0.30 · lip 0.80
live: pos 0.50 · constrict 0.30 · lip 0.80
Vowel keys: UIOP close · JKL; mid · M,./ open.
Columns run front to back; the second and fourth are lip-rounded.
Hold two keys to sit between them, overlap them to glide, tap briefly to undershoot.
Reflection Coefficients
How It Works
The Kelly–Lochbaum model discretizes the vocal tract into N cylindrical sections of varying cross-sectional area An. At each junction between sections, acoustic waves partially reflect and transmit according to the reflection coefficient:
rn = (An − An+1) / (An + An+1)
Forward and backward traveling pressure waves p+ and p− are scattered at each junction. Section count is derived from tract length: each section is one half-sample of propagation delay, so N = L / (c / 2fs).
In keyboard mode, held keys act as attractors in a three-dimensional articulatory space. The cursor settles at their weighted centroid via a critically damped second-order integrator, so the articulators carry mass. Source gating uses a much faster one-pole, which is what makes the response feel immediate even though the tongue is still moving.
rn = (An − An+1) / (An + An+1)
Forward and backward traveling pressure waves p+ and p− are scattered at each junction. Section count is derived from tract length: each section is one half-sample of propagation delay, so N = L / (c / 2fs).
In keyboard mode, held keys act as attractors in a three-dimensional articulatory space. The cursor settles at their weighted centroid via a critically damped second-order integrator, so the articulators carry mass. Source gating uses a much faster one-pole, which is what makes the response feel immediate even though the tongue is still moving.