Rhythm — platter #

A reading platter for the geometry of musical rhythm: Toussaint's corpus and the wider field around it (maximal evenness, rhythmic oddity, syncopation measures, distance geometry, tiling canons, entrainment, spoken solkattu, timbre space). A sub-platter within the papers platter, parallel to jeffrey-platter, whistlegraph-platter, and corporate-graphics-platter.

The platter exists so that AC's rhythm tooling resolves "a Euclidean rhythm", "how even is this", or "how far is son from rumba" to a cited definition and a verified test vector — instead of to whichever formula seemed right the day an engine was written.

It has a specific consumer. pop/ already runs this mathematics in three places — pop/minitek/c/hypnotek.c (Bjorklund, precession, evenness, vertex distance), dubtek.c (rhythmic oddity, chord-sum evenness, off-beatness), and acidtek.c (off-beatness) — with each engine hand-rolling its own copy and none of it in pop/lib/. This platter is the digest step that comes before lifting that math into a shared library, and before the pop/bracelet/ spatial-necklace lane is built on top of it.

Posture #

Index and original restatement only. No source text is reproduced in this repo. Specifically:

• The Geometry of Musical Rhythm (CRC Press) is cited by chapter and never mirrored — no scans, no excerpts, no quoted passages, no PDF.
• Open-access papers are fetched into sources/ by fetch-sources.mjs. sources/ is gitignored — the fetch is reproducible, the mirror is not committed.
• timelines.json carries structured facts (k, n, onset sets, inter-onset intervals, necklace representatives, culture tags) with a locator back into the source. Attribution paragraphs stay in the papers.
• The digest/ entries are written in AC's own words and exist to specify code, not to summarise reading.
• The one video source (levin-2011-indian-rhythms) follows the same rule: the video and captions are fetched into gitignored sources/ by hand (yt-dlp), its on-screen overlays are OCR'd locally (macOS Vision) to sources/*.ocr.txt, and only the digest restatement is committed.
• wessel-1979-timbre-space is a hand-placed scan (shared by Sage Jenson, 2026-08-15) — no open-access URL currently resolves, so fetch-sources.mjs skips it and the local copy stays out of git like everything else in sources/.

This mirrors the corporate-graphics-platter's "third-party — research reference only" rule.

Shelves #

Full bibliography with fetch URLs and verification status: sources.json (33 entries; 9 open-access papers + 1 open video).

The catalogue #

timelines.json — 48 Euclidean rhythms extracted from Toussaint (2005) §4 with culture tags, plus 9 named timelines (the six distinguished 5-onset/16-pulse claves, the two 8-pulse Cuban patterns, and the 12-pulse bell).

Every extracted box string is cross-checked against a local Bjorklund implementation at build time. All 48 agree. That check is the acceptance test for the future pop/lib implementation, and it already passes on the reference version — so the algorithm is settled before the library is written.

What the digest changed #

Four findings that would have gone into code wrong:

1. Son clave is not a Euclidean rhythm. Its inter-onset intervals are (3,3,4,2,4); a maximally even five-in-sixteen is (3,3,3,3,4). Toussaint states plainly that E(5,16) "is also the Bossa-Nova rhythm necklace of Brazil." Of the six distinguished claves, only bossa is Euclidean. pop/minitek/thesis/dubtek.md currently says E(5,16) is "the canonical 2-3 son rotation" — that is wrong and needs correcting.
2. Compare necklaces, not strings. The published catalogue prints one arbitrary rotation per entry, and many traditional rhythms are named as a rotation of the Euclidean form. Any equality test must compare lexicographically-least rotations, or it will report false negatives on half the catalogue.
3. Off-beatness is a group-theoretic property, not a heuristic. The off-beat positions of an n-cycle are exactly the generators of C(n) — the p with gcd(p, n) = 1. For n = 12 that is {1, 5, 7, 11}. The measure degenerates for prime n (every position is a generator) and the implementation must say so rather than return a meaningless number.
4. Chronotonic distance wins. Toussaint (2004) compares five dissimilarity measures and concludes the best overall is the chronotonic distance, followed by swap distance in close second. So pop/lib should default to chronotonic and offer swap — not default to Hamming because it is easiest.

Regenerate #

node papers/rhythm-platter/fetch-sources.mjs      # → sources/ (gitignored)
node papers/rhythm-platter/build-timelines.mjs    # → timelines.json, with cross-check

# the one video source — fetched by hand, then frame-OCR'd (macOS Vision):
yt-dlp -f "bv*[height<=720]+ba/b" --write-auto-subs --sub-langs en \
  -o "papers/rhythm-platter/sources/levin-2011-indian-rhythms.%(ext)s" \
  "https://www.youtube.com/watch?v=KsvKQhOeQjQ"

build-timelines.mjs exits non-zero if any extracted rhythm disagrees with Bjorklund.

Verification debts #

Open, and deliberately visible rather than smoothed over:

• 19 of 33 sources carry "checked": false — written from working knowledge, citation details not yet confirmed against a publisher record. None may be cited in a paper until checked.
• The 9 named_timelines rows carry "checked": false. The onset sets are the standard published forms and the Euclidean-membership results are computed, but the onset strings have not been re-read out of Toussaint (2002).
• bjorklund-2003-sns has no confirmed retrieval URL.
• The digest is written against the open-access papers plus working knowledge of the book. Chapter-level citations to the 2013 book are approximate and flagged inline where they carry weight.

maintained by @jeffrey · feeds pop/lib and pop/bracelet/