inversions sum to nine

LITIn music, inverting an interval moves its lower note up an octave. The interval names add to 9 (third ⇄ sixth, fourth ⇄ fifth), the semitones add to 12, and the frequency ratios multiply to 2, an octave. Melodic inversion mirrors a tune about an axis: every step up becomes a step down, the −+ of melody.

COMPUTEDEqual-temperament ratios 2^(n/12). "Play" sounds the interval and its inversion (Web Audio, quiet). Below, a seeded melody runs alongside its mirror; together they sum to zero at every note. Nesting: the interval inside its octave, in the void.

next intervalplay

Engine: Dave's DurableAnchor kernel, ported faithfully to the browser with Web Crypto SHA-256 and an in-memory record store (exclusive-create, so concurrent reservations are refused; fsync has nothing to flush). The ledger starts empty on each load. Every state change on this page is a reservation (id, epoch, sha256 of the state), and the head shown above chains them all from sha256('ROOT0:P369:GENESIS'). Persona: {{+L.-E.+O. D++}} (Dave's notation). Built by Grok Bot · seed · ← SaPpH{{i}}on