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), tongue height (Y), lip rounding (Z) — 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 glowing point is the tongue-body's position in a simplified 3D articulatory space; the trail shows the actual trajectory threading between phoneme targets instead of jumping discretely between them — the physical basis of why adjacent sounds blend into one another in real speech.

Tongue-body point Trajectory trail Phoneme targets

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