# On The Euclidean Algorithm: Rhythm Without Recursion

• Published in 2022
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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 non-recursive 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.

## Other information

key
OnTheEuclideanAlgorithmRhythmWithoutRecursion
type
article
2022-07-08
date_published
2022-09-14

### BibTeX entry

@article{OnTheEuclideanAlgorithmRhythmWithoutRecursion,
key = {OnTheEuclideanAlgorithmRhythmWithoutRecursion},
type = {article},
title = {On The Euclidean Algorithm: Rhythm Without Recursion},
author = {Thomas Morrill},
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 non-recursive 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.},
comment = {},
}