ⰔⰀⰜⰓⰅⰄ ⰔⰑⰖⰐⰄ

ⰔⰀⰜⰓⰅⰄ ⰔⰑⰖⰐⰄ — ⰔⰘⰑⰂⰐ ⰋⰐ ⰗⰖⰎⰎ ⰄⰅⰕⰀⰋⰎ, ⰂⰋⰕⰘ ⰋⰕⰔ ⰒⰓⰑⰑⰗ: Ⰰ ⰄⰅⰕⰅⰓⰏⰋⰐⰋⰔⰕⰋⰜ ⰜⰑⰐⰕⰅⰐⰕ-ⰀⰄⰄⰓⰅⰔⰔ ⰓⰅⰜⰑⰏⰒⰖⰕⰀⰁⰎⰅ ⰗⰓⰑⰏ ⰕⰘⰅ ⰜⰑⰏⰒⰑⰐⰅⰐⰕ'Ⱄ ⰐⰀⰏⰅ.

Sacred sound · the harmonic series, computed

Sacred sound decoded — the a432 thread deepened into real acoustics, all computed. The harmonic series is exact integer multiples of a fundamental (overtone n at n × 432 Hz), and the consonant intervals ARE its low overtones: the octave is 2:1, the perfect fifth 3:2, the major third 5:4. Just intonation tunes by those small whole-number ratios (the fifth at 702¢, the major third at 386¢, computed as 1200·log2). Equal temperament tempers them onto twelve equal semitones of the twelfth root of two, so only the octave stays pure — the fifth is two cents flat, the major third about fourteen cents sharp. The Pythagorean comma (23.46¢, twelve fifths overshooting seven octaves) is why no tuning is perfect. And a432 has a genuine history — Verdi asked Italy to standardise A = 432 in 1884 before 440 became the international standard — sitting about 32 cents below 440.

△ harmonic series — overtone n at n × 432 Hz1× = 432 Hz (fundamental) · 2× = 864 Hz (octave) · 3× = 1296 Hz (octave + fifth) · 4× = 1728 Hz (2 octaves) · 5× = 2160 Hz (2 oct + major third) · 6× = 2592 Hz (2 oct + fifth). The octave (2:1), the fifth (3:2) and the major third (5:4) ARE the low overtones — consonance is the small whole numbers.
♪ just intonation — the small whole-number ratiosoctave 2:1 = 1200¢ · perfect fifth 3:2 = 702¢ · perfect fourth 4:3 = 498¢ · major third 5:4 = 386.3¢ · minor third 6:5 = 315.6¢
⚖ equal temperament tempers them — only the octave stays puretwelve equal semitones of the 12th root of 2 (≈1.05946): the ET fifth (700¢) is ~2¢ flat of just (702¢), the ET major third (400¢) is ~14¢ SHARP of just (386¢). A trade: every key equally usable, no interval (but the octave) exact.
↻ the Pythagorean comma = 23.46¢twelve just fifths overshoot seven octaves by this much — the gap that proves no tuning is perfect, and the error equal temperament spreads evenly across the twelve.
432 — real history, flagged metaphysicsVerdi asked Italy to standardise A = 432 in 1884; 440 won (London 1939, ISO 1955); 432 sits 31.8¢ below 440. The history is real; the cosmic/healing "432 Hz" claims are flagged, not asserted — a sound is a pressure wave, not a medicine.
▶ the engine — one shared context, 119 contexts savedEvery player shares ONE AudioContext (useTones): lazy on first sound, resumed on the user gesture, never closed. The old code minted a context per component (20+) and per play — past the browser's ~6-context cap, so playback silently failed and each phrase paid a context startup (the dominant latency). Now 1 ≤ 6: no churn, no leak, less latency. Pitch and envelope are byte-for-byte unchanged.

Boundary: HONEST and computed: every cents value is 1200·log2(ratio); the ratios, the comma and the temperament deviations are exact acoustics (HyperPhysics, the microtonal/Wikipedia tuning sources). The 432 HISTORY is real (Verdi 1884; 440 at London 1939 and ISO 1955) — but the cosmic/healing/"432 = the frequency of the universe" claims are flagged, not folded (inherited from a432(), whose woo is flagged). A sound is a pressure wave, not a colour or a medicine; the consonance of small ratios is real psychoacoustics, the metaphysics is not.

✓ proven · content-address 6308f067-1d4a-807a-adde-3f5637993239 — declared, placed, mounted, and recomputable from the component's name.