Euclidean Rhythms Primer

[nofi]

In recent years, I have been interested in learning about polyrhythms, "the simultaneous sounding of two or more independent rhythms" (http://en.wikipedia.org/wiki/Polyrhythm) and have been utilizing them in some of my compositions.

Recently, I've been reading about Euclidean Rhythms, which is a method of using the Euclidean algorithm (http://en.wikipedia.org/wiki/Euclidean_algorithm) to compute rhythmic patterns. Briefly, this method allows one to equally distribute a number of pulses (k) in a given interval (n). For example, 5 k 9 n, or E(5,9), would look like [x . x . x . x . x]. Turns out, this rhythm is also known as the popular Arab rhythm Agsag-Samai (among other names).

To hear the results, create a clip in your DAW that is 9 steps (usually 1/16 notes) long, arrange your beats as marked above and loop it. Start combining multiple clips of Euclidean rhythms on different tracks (not necessarily just drums) and you start to hear interesting polyrhythms. Note, each pulse doesn't have to be the same note or sound. Here's a list of resources for those interested in more:

The Euclidean Algorithm Generates Traditional Musical Rhythms - http://cgm.cs.mcgill.ca/~godfried/publications/banff.pdf (PDF)
The original paper by Godfried Toussaint, which isn't as math-intensive as one might think. It also contains a good breakdown of many of the E(k,n) combinations.

Euclidean Rhythm MIDI File Resource in Ableton Live - http://www.ageofthewheel.com/2011/03/euclidean-rhythm-midi-file-resource-in.html
A good overview, including an Ableton set containing clips of every E(k,n) combination.

Generating african rhythms using the euclidean algorithm by Wesen - http://ruinwesen.com/blog?id=216
One of the earliest implementations, including code and hardware implementation.

Euclidean sequencer Max for Live version by Robin Price - http://registeringdomainnamesismorefunthandoingrealwork.com/blogs/?p=426
A M4L midi device for generating rhythms. I have used this but find making my own clips to be easier when arranging.

Eckel VST - http://www.shuriken.se/?page_id=97
A midi generating VST based on the Euclidean algorithm.

These two articles from the Create Digital Music blog give more background, compile more resources and tools:

• Euclidean Rhythms in Ableton MIDI Clips for Polyrhythmic Good Times; Microtonal Operator - http://createdigitalmusic.com/2011/03/euclidean-rhythms-in-ableton-midi-clips-for-polyrhythmic-good-times-microtonal-operator/
• Circles and Euclidean Rhythms: Off the Grid, a Few Music Makers That Go Round and Round - http://createdigitalmusic.com/2011/03/circles-and-euclidian-rhythms-off-the-grid-a-few-music-makers-that-go-round-and-round/

Drop me a line to share techniques, clips, finished tracks or if you're interested in more.

[nofi]

UPDATE: I have posted the first of several experiments with Euclidean polyrhythms at http://soundcloud.com/nofi/euclidean-polyrhythms-test-v :


A short experiment with the following Euclidean polyrhythms (in order of appearance):
1. Gnarly Kick - E(3,5)
2. Maracas - E(5,7)
3. Tambourim Open - E(5,17)
4. Bass Kick - E(2,5), half-speed
5. Soft Marimba - E(5,11)
Minimal modulation effects, granular delay, multi-band/shimmer reverb applied on some tracks

[nofi]

My second experiment, http://soundcloud.com/nofi/euclidean-polyrhythms-second-test:

[nofi]

Yet another, http://soundcloud.com/nofi/euclidean-polyrhythms-third:

[PrettyDave]

Oh hell yeah, Its very cool to see someone talking about polyrhythms especially with regards to electronic music. Ill have to check out your included "Experiments" when I get a chance(I have live open, and Im not getting any audio from the browser). This was actually one of the last things I would have thought about using when making a "beat" but I am sure it opens up a lot of new ideas.

I personally try and mess with time signatures a bit. I did one sample in 5/4, but used triplets to create a swing 4/4 feel. Essentially I could use the idea to create a mix between dubstep and house and really flip things upside down. Either way, its really nice to see someone applying some non-traditional ideas to electronic music.

Here is the link to my little sample: Its 100% 5/4 no tempo/keysignature  changes. Gotta love triplets.
http://ds.reflectgames.com/com.mp3

[JayDreamin]

This is very useful information. After a lot of experimenting I found I was able to really tie some of these rhythms together with a 4/4 beat. I know that may be common, but Euclidean Rhythms are new to me. This practice has really opened up my productions. Many possibilities exist using this approach. Thanks for the info.

[nofi]

So, let's hear it!