ON THE EUCLIDEAN ALGORITHM: RHYTHM WITHOUT RECURSION

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...

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Vydáno v:Bulletin of the Australian Mathematical Society Ročník 107; číslo 3; s. 361 - 367
Hlavní autor: MORRILL, THOMAS
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cambridge, UK Cambridge University Press 01.06.2023
Témata:
Algorithms
Arrays
Combinatorial analysis
Composers
Modular construction
Rhythm
Software
Euclidean algorithm
computation by hand
11A05
97F60
binary rhythms
ISSN:0004-9727, 1755-1633
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0004-9727
1755-1633
DOI:10.1017/S0004972722000909