The landscape

Every point on the plane is a possible vowel — F₂ across (front to the left), F₁ down (close at the top). Colour is harmony: the brighter it is, the fewer the violations. Nudge the weights and watch the terrain shift; click anywhere (or hit drop it) and a candidate slides downhill to the bottom of the valley.

perceptual target tongue's rest ×optimum candidate

The road from rest to target

Follow the straight line joining the tongue's rest to the perceptual target: harmony along it is a single valley. The bottom of that valley — the optimum — is always a weighted average of the two points, and it slides toward whichever one pulls harder.