CAYLEY II // octonion harmonic sequencer

integer ladders · wave mixtures · haunted

tap POWER — fano nodes show each component's harmonic number

VOICES — sine → triangle → saw

ROOT

WAVE

FAN

SEQUENCE — patterns on the harmonic series

RATE

RANGE

GLIDE

GATE

ENV

OCTONION RING — Z = Y·X

SPIN

DRIFT

DEPTH

SHIFT — Re[(I+jQ)·e^{jΔωt}]

SHIFT Δ

BALANCE

FEEDBACK

FB TIME

SHIFT MIX

MEMORY

HAUNT

OUT

ladder: harmonics climb, levels taper — a quiet Shepard staircase. prime: only the unfactorable overtones. fractal: ruler-sequence octaves, self-similar at every zoom.
gate low + env high = pointillism scattered through 8D by the rotor. glide high + walk = the lattice melts. envelopes hit X before Y·X — every pluck is smeared across components by the rotation.

CAYLEY — the octonions from message one, now an instrument.

CAYLEY // octonion ring machine

8 voices · non-associative · haunted

tap POWER — the scope is a tumbling 2D shadow of the 8D trajectory

VOICES — X = x₀e₀ + … + x₇e₇

ROOT

SPREAD

TIMBRE

OCTONION RING — Z = Y·X

SPIN

DRIFT

DEPTH

SHIFT — Re[(I+jQ)·e^{jΔωt}]

SHIFT Δ

BALANCE

FEEDBACK

FB TIME

SHIFT MIX

MEMORY

HAUNT

OUT

rotate: Y·X swirls energy through the 8 voices — |Y·X| = |X|, nothing gained, everything moved. assoc: plays (WY)X − W(YX) — zero for ℂ and ℍ; whatever you hear is pure non-associativity. haunt: ghost / memory / swap / stasis intrude on sound and image, each differently.
audio-rate SPIN = octonionic ring mod · slow SPIN + SHIFT feedback = a barberpole that breathes through eight voices.

SHIFT // bode frequency shifter

Δf, not Δpitch

tap POWER — the circle is the complex plane: x = I, y = Q = Hilbert(I)

DRONE HZ

SHIFT Δ

BALANCE

DRY/WET

FEEDBACK

FB TIME

OUT

out = Re[ (I + jQ) · e^±jΔωt ]  —  complex multiplication, audible.
barberpole: feedback .80–.90, Δ 1–8 Hz, fb time ~150 ms, full UP. ring mod: balance dead center. mic + speaker = acoustic loop — headphones, or embrace it.