An Introduction To Euclidean Rhythms

This video, via Voltage Control Lab, takes a look at Euclidean Rhythms, Godfried Toussaint’s theory that The Euclidean Algorithm Generates Traditional Musical Rhythms (pdf). 

The basic concept of Euclidean Rhythms is that distributing an arbitrary number of beats evenly over a larger number of pulses generates a musically useful rhythm – and that many of these rhythms are found in music around the world.

At a basic level, distributing 4 kicks over 16 pulses and 2 claps over the same 16 pulses results in one of the most common dance music patterns. But Toussaint shows that more complex relationships, like 3 beats over 8 pulses gives you the Cuban tresillo pattern, 5 over 16 gives you the bossa nova and 7 over 12 gives you a common West African bell pattern.

Here’s a deeper look at using the Mutable Instruments Yarns module to generate Euclidean Rhythms:


17 thoughts on “An Introduction To Euclidean Rhythms

  1. I’d be grateful for any links to Euclidean sequencer VST/AU out there. I know of some for Max for Live, and Reaktor, yet wondering if there are any outside of those environments. Thanks!

    1. I’ve a euclidean sampler in the team to library. Twisted Debris Sampler MKIII.

      The cat you require is the SEQ2 by by plugins. That has 6 sequencer modes. Euclidean being 1.

  2. Toussaint is a respected researcher and contributor to the field of computational geometry. He has done a fair bit of work in music similarity measurement, most recently at Harvard. He’s quoted extensively as an authoritative reference in a number of university-level texts, e.g. Computational Geometry in C (O’Rourke).

    In addition to the scholarly research and higher-level texts, there are a number of good accessible popular texts out there too on generative music / music analysis, e.g. Music and Mathematics (David Wright) and, guess what, 🙂 Mathematics and Music (Various: Fauvel et al.)

    Worth a read.

  3. Euclidean rhythms feature in the new Pyramid sequencer. That unit is very interesting to me as its hard ware but includes such functions & outputs usb, midi & cv. Poly rhythm structures with math AI side input make for interesting occurrences, whether it’s rhythmical or tonal, awesome for baselines also.

        1. You missed the point entirely.

          Understanding theory isn’t important if you want to regurgitate what you’ve heard.

          But if you want to get creative with it – and play with what you’ve heard – you have to on some level understand how music works, why a rhythm can sound completely different in a different context, why some rhythms are used more frequently than others, how to extrapolate what works in 4/4 to other meters and so on.

          This theory provides a very useful tool for analyzing and playing with rhythms.

          1. Eucldean rhythms is not about theory, at the very best it is a way to explain rhythms that have been used two thousand years now. Or do you think that in africa they were looking for the common denominator before every music event?

            1. > it is a way to explain rhythms that have been used two thousand years now

              you just described music theory. you don’t necessarily have to know the why to write a good song, but if you don’t have the inbuilt talent that truly not that many possess, it helps.

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