paper
active
2021
paper:2021-11-17-stefan-lesser-banff-pdf-a9e313The Euclidean Algorithm Generates Traditional Musical Rhythms
ByGodfried Toussaint
Findings (2)
- Many rhythms used in world music are Euclidean rhythms generated by Bjorklund's algorithm.
- Euclidean string status correlates with cultural musical preference
Empirical observation: Euclidean strings favored in classical/jazz/Persian music; reverse Euclidean strings have wider appeal; non-Euclidean rhythms used in sub-Saharan African music.
Claims (3)
- Euclidean strings are favored in classical, jazz, Bulgarian, Turkish and Persian music but not popular in African music.
- Bjorklund's algorithm has identical structure to Euclidean algorithm
Key theoretical insight: both algorithms use repeated subtraction (division) to recursively partition sequences; this structural identity justifies the term 'Euclidean rhythm'.
- Rhythmic Distribution Property
Core property of Euclidean rhythms: onset patterns are distributed as evenly as possible across the time span.
Questions (2)
- What musicological explanations exist for cultural preferences apparent in mathematical properties of rhythms?
- Why do different musical cultures prefer different mathematical properties in rhythms?
Open ethnomusicological question raised by observed pattern of cultural preferences for Euclidean vs. reverse Euclidean vs. non-Euclidean rhythms.
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