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- Title
ON THE EUCLIDEAN ALGORITHM: RHYTHM WITHOUT RECURSION.
- Authors
MORRILL, THOMAS
- Abstract
A modified form of Euclid's algorithm has gained popularity among musical composers following Toussaint's 2005 survey of so-called Euclidean rhythms in world music. We offer a method to easily calculate Euclid's algorithm by hand as a modification of Bresenham's line-drawing algorithm. Notably, this modified algorithm is a nonrecursive matrix construction, using only modular arithmetic and combinatorics. This construction does not outperform the traditional divide-with-remainder method; it is presented for combinatorial interest and ease of hand computation.
- Subjects
MODULAR arithmetic; WORLD music; RHYTHM; MUSICAL meter &; rhythm; COMBINATORICS; EUCLIDEAN algorithm
- Publication
Bulletin of the Australian Mathematical Society, 2023, Vol 107, Issue 3, p361
- ISSN
0004-9727
- Publication type
Article
- DOI
10.1017/S0004972722000909