The Euclidean Algorithm Generates Traditional Musical Rhythms

What do African rhythms, spallation neutron source accelerators in nuclear physics, string theory in computer science, and an ancient algorithm described by Euclid have in common? Godfried Toussaint, Professor of Computer Science and the Head of the Computer Science Program at New York University Abu Dhabi, reveals the answer.

Abstract

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 application in nuclear physics accelerators and in computer science, and are closely related to several families of words and sequences of interest in the study of the combinatorics of words, such as Euclidean strings, to which the Euclidean rhythms are compared.

1. Introduction

What do African rhythms, spallation neutron source (SNS) accelerators in nuclear physics, string theory (stringology) in computer science, and an ancient algorithm described by Euclid have in common? The short answer is: patterns distributed as evenly as possible. For the long answer please read on.

----------------------------------------------------

The rest of this article is reserved for members only. If you have a subscription, please sign in here. Otherwise, why not Subscribe today?

 

Get the Full Experience
Read the rest of this article, and view all articles in full from just £10 for 3 months.

Subscribe Today

, , ,

No comments yet.

You must be a subscriber and logged in to leave a comment. Users of a Site License are unable to comment.

Log in Now | Subscribe Today