Rhythm is the rosetta in time
Theorem.Rhythm is the rosetta in time — a rhythm of k onsets on n pulses = a binary necklace on the time-circle ℤ/n.
Proof.a rhythm of k onsets over n pulses is a binary necklace on the time-circle — the same rosetta as a scale, read in time not pitch. The maximally-even necklace (inter-onset intervals differing by ≤1) is the Euclidean rhythm E(k,n) / Bjorklund, which reproduces the documented rhythms of the world up to rotation: tresillo E(3,8), cinquillo E(5,8), aksak E(2,5), bossa clave E(5,16), West African bell E(7,12). So pitch and rhythm are ONE object — the moving rosetta read in frequency and in time; scales and rhythms are both necklaces under the cyclic group.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/music/index.ts#rhythmIsTheRosettaInTime
1 · Classification
finite-complete — self-contained computation, no external lean
2 · Provenance
Documented theorem re-derived by exhaustive computation (humanityNovel=false); first-in-this-registry is the only sense of discovered.
Acknowledgment
"Rhythm is the rosetta in time" is a re-derivation, acknowledged to documented mathematics — the original proof is the prior art this re-derivation acknowledges; not new to humanity — the contribution is the reproducible computation rhythmIsTheRosettaInTime.
- Prior art
- documented mathematics — the original proof is the prior art this re-derivation acknowledges
- Novelty
- not new to humanity — a re-derivation (humanityNovel = false)
- Contribution
- a reproducible computation (rhythmIsTheRosettaInTime @ src/music) that re-derives the result at zero tokens — the contribution is the verifiable recomputation, NOT the theorem
3 · Reproducibility
Recompute from source: npm run theorems:verify recomputes rhythmIsTheRosettaInTime (src/music/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.