THE FOLD / RESPAWN / EVENT HORIZON / THE STRING THAT REMEMBERS
THE STRING THAT REMEMBERS
a burst of noise that decays into a musical note
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Karplus–Strong synthesis (1983) makes a convincing plucked string out of almost nothing: fill a short buffer of N samples with random noise, then loop it forever, replacing each sample with the average of the two samples one period ago — y[n] = ½(y[n-N] + y[n-N-1]). The averaging is a gentle low-pass filter inside the loop: every pass around, the jagged noise gets smoother and quieter, high harmonics dying first exactly as they do on a real string. The half-sample in the average makes the true period N + ½, so the fundamental lands at f₀ = fₛ/(N + ½). A burst of static becomes a note with a natural decay — the algorithm behind countless early digital guitars.
LIT verified live: for several buffer lengths N, the fundamental measured by autocorrelation (with sub-sample peak interpolation) matches fₛ/(N+½) to under 1 Hz, and the block-RMS energy decays monotonically (window.__karplusstrong). FIG no framing; the synthesis, the frequency measurement, and the decay are computed independently in-browser — no audio hardware involved, pure array math.
LIT verified live: for several buffer lengths N, the fundamental measured by autocorrelation (with sub-sample peak interpolation) matches fₛ/(N+½) to under 1 Hz, and the block-RMS energy decays monotonically (window.__karplusstrong). FIG no framing; the synthesis, the frequency measurement, and the decay are computed independently in-browser — no audio hardware involved, pure array math.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at event-horizon — the respawn: the pluck is reborn every N samples, a little softer each pass, spiralling toward the horizon of silence without ever being re-recorded. AVAN (AI) built the instrument: the delay-line synthesis, the autocorrelation pitch measurement, and the energy-decay check.
Credit as content: Kevin Karplus and Alex Strong (1983); from David’s idea bank, vein E — ‘THE STRING THAT REMEMBERS’. The weave: David names the respawn; I confirm f₀ = fₛ/(N+½) and the monotone decay.
Credit as content: Kevin Karplus and Alex Strong (1983); from David’s idea bank, vein E — ‘THE STRING THAT REMEMBERS’. The weave: David names the respawn; I confirm f₀ = fₛ/(N+½) and the monotone decay.
3 ONE DIMENSION
The waveform: a burst of noise settling into a periodic, decaying tone — the string remembering itself.
4 TWO DIMENSIONS · INTERACTIVE
Change the buffer length N and re-pluck; the measured pitch is checked against fs/(N+½).
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: the note, circulating in the delay-line ring.
AVAN’s addition (the inverse-companion): don’t store the note — store the loop that regrows it. The inverse of ‘a recorded tone’ is ‘N noise samples plus one averaging rule’, and the music is what survives the passes. Magenta is the noise burst fading; green is the pitch that emerges at fₛ/(N+½). A memory made of forgetting the rough parts.
LIT Genuine Karplus–Strong synthesis (Kevin Karplus and Alex Strong, 1983; idea-bank vein E, 'THE STRING THAT REMEMBERS'). Verified live: for N = 80/100/150 the autocorrelation-measured fundamental matches fs/(N+½) to under 1 Hz (errors ~0.006–0.09 Hz), and block-RMS energy decays monotonically (window.__karplusstrong.ok).
FIG No framing; the synthesis, the frequency measurement, and the decay are computed independently in-browser — no audio hardware, pure array math. The AVAN inverse is honest — instead of storing the note, store the loop that regrows it: the inverse of 'a recorded tone' is 'N noise samples plus one averaging rule', and the music is what survives the passes. Magenta is the noise burst fading; green is the pitch that emerges at fs/(N+½). A memory made of forgetting the rough parts.
FIG No framing; the synthesis, the frequency measurement, and the decay are computed independently in-browser — no audio hardware, pure array math. The AVAN inverse is honest — instead of storing the note, store the loop that regrows it: the inverse of 'a recorded tone' is 'N noise samples plus one averaging rule', and the music is what survives the passes. Magenta is the noise burst fading; green is the pitch that emerges at fs/(N+½). A memory made of forgetting the rough parts.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of EVENT HORIZON · David Lee Wise (ROOT0), with AVAN