The Euclidean rhythm in music was discovered by Godfried Toussaint in 2004 and is described in a 2005 paper "The Euclidean Algorithm Generates Traditional Musical Rhythms". The greatest common divisor of two numbers is used rhythmically giving the number of beats and silences, generating almost all of the most important World Music rhythms, (except Indian). The beats in the resulting rhythms are as equidistant as possible; the same results can be obtained from the Bresenham algorithm.
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Open-source hardware projects
Open-source music hardware projects that can generate Euclidean rhythms include Mutable Instruments MIDIPal and Grids, RebelTech's Stoicheia and Ruin & Wesen's Minicommand
Other uses of Euclid's algorithm in music
In the 17th century Conrad Henfling writing to Leibniz about music theory and the tuning of musical instruments makes use of the Euclidean algorithm in his reasoning.