Euclidean Rhythms
Euclidean rhythms — Bjorklund’s even distribution
Bjorklund’s algorithm for E(5,13), E(7,16), E(5,16), E(4,9), E(5,8) and E(3,8), drawn as Toussaint’s concentric rhythm-necklaces — onsets spaced on a circle and joined into a polygon. Each ring is also an audible rhythm.
Paper / citationGodfried T. Toussaint, “The Euclidean Algorithm Generates Traditional Musical Rhythms,” Bridges 2005, pp. 47–56.
https://archive.bridgesmathart.org/2005/bridges2005-47.html
https://archive.bridgesmathart.org/2005/bridges2005-47.html
◈Made by real computation — every vertex is produced by the algorithm’s own math, integrated or iterated from the paper’s equations. No tracing, no decoration, no image model.