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Modular Synthesis is one of the more exciting intersections of science and art. The connections between mathematics and music are at our fingertips in a modular system, which is one of the fun and alluring aspects of our chosen field. One recently discovered set of musical and mathematical related phenomena, Euclidean Rhythms, have been adopted into a variety of different Eurorack modules. But what exactly are Euclidean Rhythms?

Euclidean Rhythms were discovered by Godfried Toussaint, a Computer Scientist at McGill University. In his publication from 2005, “The Euclidean Algorithm Generates Traditional Musical Rhythms” Toussaint asked…

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.

The paper goes on to detail a number of traditional rhythms heard in regions around the world, that follow the principle of evenly distributed beats over a larger repeating pattern.

Some of these rhythms can be heard in many traditional styles of music, especially African or African-influenced musical cultures such the Caribbean, the Americas and beyond. They appear in eastern European traditional music as well as Middle Eastern, Asian and Western music. Many Afro-Cuban and Brazilian bell rhythms, for instance, are Euclidean Rhythm patterns. These fundamental rhythms are universally popular, from the Bossa Nova to the classic Tresillo which appears in music from around the world. Dave Brubeck famously used a Turkish traditional rhythm which happens to be a Euclidean Rhythm in Blue Rondo A La Turk.

Euclidean Rhythms are derived from two values, a larger number which represents the length of the pattern in steps, and a smaller number representing the hits or notes to be distributed evenly across that pattern. In the video above, we examine some basic sets of numbers used to create strings of beats and rests. Patterns can also be offset by a certain number of beats, resulting in other traditional rhythms.

Bo Diddley introduced a number of Euclidean Rhythms into the Rock’n’Roll spectrum with his unique brand of rhythmic song structure. The first half of every 2 bar phrase contains either the Tresillo which can be constructed from the set of numbers E(3,8), or the Cinquillo, from the set E(5,8).

Stanton Moore spoke of the Cinquillo in an interview with Mike Dolbear…

Steve Gadd plays it all the time, you hear it in Drum’n’Bass, you hear it in Idris Muhammad, you hear it in Haiti, you hear it in the Mardi Gras Indians. They call it the Cinquillo rhythm in Haiti and Cuba because it’s 5 hits. So you start tracing these rhythms and just go back and back and back. Where did the Haitians get it from? They got it from the slaves who came over and it was probably coming over from some of the Batá stuff that was played in the Yoruba tribes of West Africa, which is where a lot of the slavery came from, so all of these rhythms came over and started morphing into their own things.

We’ll have more on Euclidean Rhythms in the near future, as it is a truly fascinating topic. If you would like to check out some modules that make use of Euclidean Rhythms, start with Mutable Instruments Grids and Yarns, the Pittsburgh Modular Game System or Pamela’s Workout from ALM, among others.

Have you composed with Euclidean Rhythms? Tell us about it in the comments!

Want to know more about Eurorack and Composition? Check out our Modular Courses!

What Are Euclidean Rhythms?