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framework:euclidean-rhythmsEuclidean Rhythms
Family of musical rhythms generated via Bjorklund's algorithm, where k onsets are distributed evenly across n time units; denoted E(k,n).
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Thinkers (1)
thinker
- Godfried ToussaintintroducesAuthor of the paper; computer scientist at McGill University studying mathematical connections between music, physics, and algorithms.
Concepts (4)
concept
- Bjorklund's AlgorithmimplementsAlgorithm developed for timing systems in neutron accelerators; generates binary sequences where pulses are distributed as evenly as possible among intervals.
- Rhythm E(5,8) = [x . x x . x x .] related to tresillo; used in jazz, 1950s rockabilly, and West African music.
- Famous rhythm E(3,8) = [x . . x . . x .] found in Cuban music, West African traditions, and 1950s rockabilly (e.g., Elvis Presley's 'Hound Dog').
- Turkish rhythm E(4,9) = [x . x . x . x . .] used by Dave Brubeck in 'Rondo a la Turk'; example of Euclidean string.
Claims (2)
claim
- Key theoretical insight: both algorithms use repeated subtraction (division) to recursively partition sequences; this structural identity justifies the term 'Euclidean rhythm'.
- Rhythmic Distribution PropertysupportsCore property of Euclidean rhythms: onset patterns are distributed as evenly as possible across the time span.
Related by similarity (8)
cosine ≥ 0.65 · no typed edgeEntities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.
- Ancient algorithm from Euclid's Elements (circa 300 B.C.) that computes greatest common divisor; shown to structurally parallel Bjorklund's rhythm generation algorithm.
- The implicit assumption of linear steering methods, which the paper argues is inappropriate for neural activation spaces