Understanding Euclidean Rhythms

Some ideas to play with.

The latest episode of Sound + Voltage takes a look at Euclidean Rhythms – a way of using math to describe beats that are distributed as evenly as possible, and how this is a feature of many common musical rhythms from around the world.

See also: Tool idea: Euclidean rhythm generator


Why would you say you are dumb for not liking a compositional method? Just because it’s not readily apparent to you doesn’t make you dumb. If you are not understanding of the method, it could be a good idea to take the time to learn about it. An extra tool in the tool-box is always handy to have!

The Euclidian method is actually quite popular outside of typical music, as it places great emphasis on beat rotation and how to vary parts in a natural, cyclical way. In a way, it’s very trance-inducing. Bossa-nova patterns, samba patterns - very common, very groovy!

Finally, as an actual drummer (my primary instrument), this is how one would go about not being typical. Learning these types of patterns can make one a better musician. This is also why I’ve spent the last 27 years of my life learning/working on how to compose electronic music. I didn’t want to be ‘just another drummer’, and have to listen to my bandmates tell me how stupid I am :smiley:


3+3+2= dnb= euclidian 3/8

Just another lens through which to view rhythm :upside_down_face:


I like math combined with music.
For example, creation using chaotic attractors is unlimited.
Applying a simple mathematical algorithm can completely change the sound and rhythm.

A simple case:
Take the number, if it is even then divide it by 2 / round to whole numbers please/
if it is odd then multiply it by 3 and add 1.
Then continue until the resulting number is equal to 1.
That is the whole algorithm. This way you get different lengths of sequences.

the conversion to notes consists in the fact that the obtained number, for example, modifies 140 by 24 / 2 octaves/ add 48 (C3) to the result and voila :slight_smile: then you can use it with a quantizer, etc.

note picture for number 47

in text: (140 % 24)


Cool. I think I never heard of the term “euclidean rhythm”, but it’s pretty much the same what I did when I started creating music to get a feeling for beats. Especially when using a tracker math is always part of the game. Pattern length, LPB, BPM and so on, everything requires math. But personally I approach the matter less scientifically, I don’t use any formulars. :slightly_smiling_face:

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Look for math behind everything :slight_smile:


I do. Have you seen “Pi”? Highly recommended. :slightly_smiling_face:

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Yes of course, but long time ago.
Have you listen how PI sounds like ?


Anyone want to write a tool for generating euclidian rhythms? @joule’s New tool (3.1): Place selected notes evenly comes close, and with a little tweaking could make a very flexible euclidian rhythm generator.
I have a bunch of euclidian rhythms saved as phrases, but it would be nice to be able to generate exotic ones on the fly, using flexible divisions against a selected number of pattern lines…

Gotta learn to code so I can write tools myself, but in the meantime, this seems like some tasty, low-hanging fruit if anyone wants a little coding project


I’m using dAnushri sometimes


The xStream tool has a proper model for generating euclidean rhythms. (It’s a simple algorithm, but not quite as easy as rounding to grid iirc. I think of it as a ‘musical rounding algorithm’.)

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Oh, that’s great. Didn’t realize/remember that was in xstream. I’ll check out the implementation. I still think a dedicated euclidian tool would be great, but good to know it’s there! Thanks

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What an irony.
I remembered that I used to do something like that.
I also found the old source files on the disk :slight_smile:
The generator uses the Bresenham algorithm to distribute the pulses.
It has never been used.



Euclidean rhythms are fun. And quite common in the modular synth world. Edit: seems that get mentioned in the first few moments of the video. :sweat_smile:

from another non-coder.


I’ve been diving pretty deep into this, making a personal tool for song arrangements - and a sandbox for understanding the pulse and rhythm dimension of music.

What I’ve concluded is that you can pretty much formalize everything that happens (onsets) in an arrangement by combinations of harmonic and dissonant pulses. Think of it as naive “DFT”, but more compatible with counterpoint principles. Dissonant pulses is my own invention that I won’t go into right now, and harmonic pulses are very close or equivalent to euclidean rhythms (bresenham).

However, I do believe that pure bresenham is suboptimal for generating harmonic pulses, but I am not sure about this yet. The issue can be illustrated by the fact that 6/16 will just generate two cycles of 3/8, meaning that you don’t really get a new harmony/overtone to play with in your jigsaw of polyrhythm. Better would probably be a rasterization that favours symmetry instead of cyclicity.

3/8 or tresillo, clave is the ursatz of latin rhythm. In my mind, ideally 6/16 should generate a pattern like this: 1001001001010010 (or any phase/rotation thereof). This way we would get the ursatz of african rhythm, if I’m not misinformed. Basically, it’s the standard pop flow overtone that is not latin. A modified bresenham should be able to do this?

Some other hypothesis/conclusions I’ve made during my research. I’m just writing them here in case there is someone else on this forum interested in these things. Sadly, Godfried Toussaint died in 2019 so I don’t have anyone to talk to :confused:

  • Two counterpoint pulses form the illusion of a phrase. A musical phrase is a combination of either two harmonic pulses or one harmonic and one dissonant pulse. That’s why you most of the time can clearly find a somewhat “steady” pulse engrained in a melody - perhaps you’ve noticed.
  • Some people are easily provoked by music theory because they want to believe in the hypnosis and remain on the visceral/physical plane. That’s kind of the point in listening to music, so it’s only human.
  • Pop music is best seen as instrumented polyrhythm with post-processing (pulse switch, omit et c). I could say it’s just a way to formalize music, but since this perspective is very aligned with “harmonicity” we might as well call it a “truth” :wink:
  • The current theories about rhythm and arrangement seem incredibly archaic and underdeveloped in comparison to pitch theory. My impression is that even the scientists haven’t yet broken free from the “hypnosis” and visceral response that instrumented polyrhythm provokes.
  • A big part of good arrangement and flow is, at the most fundamental plane, the art of masking the rounding errors that happen between pure harmonicity and the 2n grid. This can be done with various techniques. Microtiming (rhythmic intonation), phase shifting, instrumentation and polymeter.

Very inspiration lecture about Shillinger system.

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