COLS Sound Lab — Listening to Integers (v24)

Turn integers into sound. Each prime-power p^e becomes a voice; its period is estimated on the arithmetic signal and mapped to a frequency f = K / T. Optional 12-TET quantisation, chord tools, tempo-sync arpeggios, and WAV export — all in a self-contained HTML.

Interactive audio lab

🎧 Sound Lab (multi-voice pe)

Analyse → select voices → map f=K/T → play chords/arpeggios → export WAV. Self-contained; works offline.
Open HTML Self-contained

📄 Listening to Integers — Paper

Theory: period estimators (Hann + ACF promotion), acoustic density, practical recipes.
Open PDF Research paper

📘 User Manual (V4)

Guided explorations: truth at octave-0, timbre of primes vs squares, pq beats, chord detection.
Open DOCX Manual

For everyone — Why “listening to integers” matters

Two and a half millennia after Pythagoras plucked a monochord and heard whole numbers as pure consonances, we still wonder: how can arithmetic, so digital and discrete, give birth to continuous harmony? The Coupled Order Lattice System (COLS) answers by building a formal bridge: modular residues (discrete) generate audible harmonic combs (continuous). Each prime-power acts as a voice whose period is read in arithmetic space and rendered as a frequency in acoustic space — a direct passage from integer logic to geometry and sound.

What you hear is not a metaphor: it is the structure of the number, made audible. The lab estimates per-factor periods with a Hann-windowed sinusoidal scan and promotes the fundamental via ACF, then maps f = K / T with optional 12-TET. You can blend voices into chords, sweep arpeggios synced to tempo, and export WAV — a reproducible, browser-native experiment where mathematics becomes music.