Coarticulation & Speech Target Undershoot

Speech Sequence

Dynamics Parameters

Speech rate 5.0 phones/s

Articulator stiffness ω 18 rad/s

Damping ratio ζ 1.00

Live Readouts

Current target

/i/

Time in phone

0.00 s

Last undershoot

Phone duration

0.20 s

How it works

This is a task-dynamic model of speech production (after Saltzman & Munhall, 1989): each articulatory dimension — tongue backness (X, horizontal), tongue height (Y, vertical) and lip rounding (Z, the side gauge) — behaves as an independent, critically-tunable mass-spring system pulled toward the target position of whichever phoneme is currently being produced:

ẍ = −2ζω ẋ − ω²(x − x_target)

Integrated every frame with a clamped timestep (semi-implicit Euler):

v += dt · (−2ζω·v − ω²·(x − target))
x += dt · v

Speech rate sets how much time each phoneme gets (duration = 1 / rate). Faster speech leaves less time to reach the target.
Stiffness ω is how fast the articulator "wants" to move toward its target — a stiffer gesture reaches its goal sooner.
Damping ζ shapes the approach: ζ = 1 is critically damped (fastest approach with no overshoot, the typical value used in speech-motor-control models), ζ < 1 overshoots and oscillates, ζ > 1 approaches sluggishly.
Undershoot is measured at the instant a target's time budget expires: the fraction of the straight-line distance from the previous target that the articulator failed to close. At slow rates it is near 0%; at fast rates with low stiffness it rises sharply — this is exactly the acoustic vowel reduction and coarticulation effect measured in real speech (Lindblom, 1963).

The main map is the front–back / height plane of the articulatory space — drag to pan, scroll/pinch to zoom. The right-hand gauge is the third, rounding dimension. The bottom strip logs the undershoot percentage of every phone the sequence has already passed through, so you can watch coarticulation build up run after run.

Tongue-body point Trajectory trail Phoneme targets

drag to pan · scroll to zoom