Viola Organista

The string's shape, rebuilt from its travelling waves and sampled stroboscopically (each frame 1/48 of a period later). In Helmholtz motion it is two straight lines meeting at a corner that runs round the dashed parabolas once per period: it sticks to the wheel while the corner is on the far side and slips while the corner passes between wheel and bridge.

Helmholtz motion needs F_min < F < F_max, with F_max ∝ v_B/β and F_min ∝ v_B/β². The dot is this key now: its force (press harder, use aftertouch or ↑↓) and the wheel position. Its colour is what the string is actually doing.

Stuck, the string's surface moves with the wheel (v_B, upper line); once per period it slips back at −v_B(1 − β)/β (lower line) for a fraction β of the period. Extra dips are extra slips: surface sound below F_min, chaos above F_max.

Helmholtz motion drives the bridge with a sawtooth (harmonics ∝ 1/n); the soundboard's modes colour it.

Watch the attack: a clean start puts every harmonic in at once. Too much pressure for the speed smears noise up the column before the string settles (raucous); too little and it slips more than once a period.

How long the string takes to settle into Helmholtz motion after the key goes down, simulated here for every key travel time and final force (a Guettler diagram for a wheel that is already turning). Light: a clean start within a few periods; dark: prolonged slipping or chaos. The ring is where this key's touch lands.