The Euclidean Algorithm Generates Traditional Musical Rhythms

Our next paper is "The Euclidean Algorithm Generates Traditional Musical Rhythms" by Godfried Toussaint.

They say that math and music are intertwined. After centuries of studying diverse music from cultures across the globe, we have proof today better than ever. In this paper, authored by Godfried Toussaint, we explore how rhythms native to indigenous tribes and cultures across earth can be represented algebraically using a shorthand syntax, first identified by Euclid.

*The Euclidean algorithm (which comes down to us from Euclid’s Elements) computes the greatest common divisor of two given integers. It is shown here that the structure of the Euclidean algorithm may be used to generate, very efficiently, a large family of rhythms used as timelines (ostinatos), in sub-Saharan African music in particular, and world music in general. These rhythms, here dubbed Euclidean rhythms, have the property that their onset patterns are distributed as evenly as possible. Euclidean rhythms also find