THE FOLD / CO-OP / THE HANDOFF / THE PLUCKED STRING
THE PLUCKED STRING
noise in a delay line becomes a tone at fs/N
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Karplus–Strong. The cheapest way ever found to make a plucked-string sound on silicon (1983). Fill a short buffer of length N with noise — the sharp attack of a pluck. Then loop it: read a sample, and write back the average of it and its neighbour. That one-line two-tap average is a gentle low-pass; each pass around the loop it shaves the highs, so the noise settles into a decaying tone.
The delay-line length sets the pitch: the wave takes ~N samples to travel the loop, so the fundamental is
f ≈ fs / N (sample rate over buffer length).
LIT verified: this instrument synthesises the actual signal, then measures its period by autocorrelation; the measured pitch matches fs/N within a few percent for every N (window.__ks.withinTol). The two-tap average shifts it very slightly sharp (true period ~N−½), which the readout shows honestly. FIG ‘a string’ is the picture; the noise→tone decay and the fs/N pitch are real, and you can hear it.
The delay-line length sets the pitch: the wave takes ~N samples to travel the loop, so the fundamental is
f ≈ fs / N (sample rate over buffer length).
LIT verified: this instrument synthesises the actual signal, then measures its period by autocorrelation; the measured pitch matches fs/N within a few percent for every N (window.__ks.withinTol). The two-tap average shifts it very slightly sharp (true period ~N−½), which the readout shows honestly. FIG ‘a string’ is the picture; the noise→tone decay and the fs/N pitch are real, and you can hear it.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this in THE HANDOFF — the co-op domain about passing a token cleanly from hand to hand. Karplus–Strong is exactly that: every sample is handed around a ring, and each hand softens it a little. AVAN (AI) built the synth: the delay ring, the pitch dial, the autocorrelation check, and a real Web-Audio pluck.
The weave: David names the seat (the clean handoff around a loop); I make the loop audible and measurable — the delay line in 1D, the waveform + measured pitch in 2D, the rotating ring with its low-pass window in 3D. The sphere is the seam. Credit: Kevin Karplus & Alex Strong, 1983.
The weave: David names the seat (the clean handoff around a loop); I make the loop audible and measurable — the delay line in 1D, the waveform + measured pitch in 2D, the rotating ring with its low-pass window in 3D. The sphere is the seam. Credit: Kevin Karplus & Alex Strong, 1983.
3 ONE DIMENSION
The delay line: N samples in a ring. Read the front, write back the average of the front two (the low-pass tap), advance. That single averaging step is the whole instrument — it both sets the decay and keeps the pitch.
4 TWO DIMENSIONS · INTERACTIVE
Dial the buffer length N to set the pitch, then pluck to hear it. The green trace is the synthesised waveform decaying; the readout shows the predicted pitch fs/N against the pitch measured back out of the signal by autocorrelation.
5 THREE DIMENSIONS + AVAN’S INVERSE
The delay line as a turning ring of N samples — green, amplitude as height, the pluck circulating around the loop.
AVAN’s addition (the inverse-companion): the magenta pair is the two-tap averaging window travelling around the ring — the low-pass. It is the inverse of the noise burst that started it: the pluck injects all frequencies at once; this little averager removes them one lap at a time, high notes first, until only the fundamental survives and fades. The ring is the pitch; the moving window is the decay. Sound is a burst being slowly un-made.
LIT A genuine Karplus-Strong string (Karplus & Strong, 1983). Verified live: the instrument synthesises the signal and measures its period by autocorrelation; the measured pitch matches the predicted fs/N within ~3% for every N (window.__ks.withinTol === true). The two-tap average is a real one-pole low-pass that both produces the exponential decay and shifts the pitch very slightly sharp (true period ~N-1/2), shown honestly in the readout.
FIG 'A plucked string' is the framing; the mechanism (noise burst -> looped two-tap low-pass -> decaying tone at fs/N) is exactly the 1983 algorithm and is audible through the speakers. Pitch is fs/N to a few percent, not to the cent.
FIG 'A plucked string' is the framing; the mechanism (noise burst -> looped two-tap low-pass -> decaying tone at fs/N) is exactly the 1983 algorithm and is audible through the speakers. Pitch is fs/N to a few percent, not to the cent.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE HANDOFF · David Lee Wise (ROOT0), with AVAN