Ready to make your Ableton Live pattern programming a bit more polyrhythmic with the power of math?

In Monday’s reflections and round-up of cycles and circles, I mentioned Euclidean evenness and Godfried Toussaint’s research. The basic idea is that a mathematical algorithm for spacing pulses has a lot in common with traditional preferences for polyrhythms spanning everything from rock hits to conga patterns and musical cultures around the world.

Reader Tony Wheeler has turned those patterns into MIDI clips so you can drop patterns into Ableton Live. Drum patterns and dance music are obvious applications, but this could be an idea starter for melodic patterns or music in a variety of idioms.

Each individual pattern will sound like an isolated cycle; it’s often when you put them together that they’re most compelling. Here’s an example; Tony added a regular bass drum just to make things more grounded (it actually calls attention to the asymmetry of the other patterns).

ScaledKit by wheelmaker

Tony has another terrific tool for Ableton Live that generates the AMS files used by Operator to tune oscillators to alternative pitches, as we covered previously:
Free Utility Makes Endless Oscillators for Ableton Live Simpler, Sampler
Direct link: AMS File Utility for Ableton Live

And for harmonic experimentation, see the Circle of Fifths Chord Resource:
Circle of Fifths Chord Resource in Ableton Live

This is all fairly academic stuff, but the funny thing about it is there’s nothing stopping you from making either a dance music hit or some experimental new kind of music that doesn’t sound like it came from Ableton.

Alternative tunings for Operator oscillators and Euclidean polyrhythms? There are many tools aside from Ableton that will work, too, but whatever your tool, this could be a great way to jump-start a musical idea. Airport layover, meet musical productivity.

Updated: Another great way to go is the Eckel VST plug-in, also donationware. It works on Mac (Universal) and Windows, and since you can dial up parameters, may be easier to use than the MIDI clips, depending on your workflow – especially since you can still choose pitch. (Or, hey, grab both!) Thanks to John Larsby for the reminder: VST – Eckel

For Dr. Toussaint’s part, you can glance over his syllabus on Discrete Mathematics — and find a reference to Tony’s Ableton experiments.

Grab the download and read more on this topic (free, donations welcome):
Euclidean Rhythm MIDI File Resource in Ableton Live [Age of the Wheel]

  • I tried to read that Wolfram link about the algorithm and my head just about exploded. Good reminder that I am fairly math-retarded.

    Great subject though… Tony Wheeler's site makes it more clear. I'm definitely going to make use of that Ableton Project.


  • ChoChos

    links to the AMS app are dead

  • barfBarfer

    AMS app is on the same site:

    There's also a circle of fifths collection there that is the tits.

  • dumafuji

    very cool. i was doing this by hand for non-periodic patterns…but this is so much more helpful and complete.

    the circle of fifths set is really cool, too. coming back to the basics of (pop) music through techno…this is fun stuff:

    very interesting way of working to build out scales, chords, and patterns in clips and not in presets for scale and chord live midi effects. can be more informative and instructive. using the eckel vst to record midi events is awesome fun.

    thanks for the post(s).

  • Awesome post! Music is math, and we should math a lot more. Gonna study all this thoroughly. Very useful!

  • barfBarfer

    dumafuji: that picture just blew my mind

  • ChoChos

    Thanks barbarfer but I should have specified I was referring to the AMS app for OSX users.

    The link provided in the article here brings you to the previous article AMS was highlighted. But the links in that article are now dead…

    so if anyone knows where the original OSX version is, maybe they could host it and/or let Peter Kirn know where it is so he can update his links.

    The original app was a max patch, I believe, written by Robert Henke ?

  • Johnny

    Cheers Peter. Useful and inspiring article.

  • I was thinking about this Euclidean stuff w/regard to melody and found this crazy study done on the melodic oral tradition of Hungarian folk music. I don't fully grasp the intricacies of the method used for the mapping, but the graphs they come up with are pretty fascinating. Patterns created by the Euclidean algorithm really are beautiful.

  • Random Chance

    Fascinating that after all this time I get to read to abou other people digging the simple idea of adapting the Bjorklund algorithm from generating firing patterns for particle accelerators to generating rhythms. The original paper was a bit skimpy on connecting this with the (extended) Euclidean algorithm in my opinion. It lacked mathematical rigour so to speak. But what's even more fascinating than the fact that the world's first (non trivial) algorithm is also somehow at the heart of rhythmic patterns that are of similar vintage or older is that people actually dig this stuff.

    Peter, you're on to something here. There's a lot of other interesting (and simple) math applications for music.

  • loopstationzebra

    I'm glad that so many readers find this kind of antiseptic and scientific approach to making music so fascinating.

    I'm also glad that people like Stevie Wonder, James Brown, and Coltrain would have recoiled at the very notion of approaching music in this fashion.

    When some people say that electronic music has no soul, this is exactly the kind of thing they are talking about. Congrats.

  • JCB


    You do realize that about everything in music is maths? From the Pythagorean tuning system still exclusively used in occidental pop music 2500 years after its creation to just about every rhythms… If music has soul or not is of course a subjective matter, and I would think it has more to do in the execution (the machine being too tight?) timbre (robot sounds?) etc., than the fact that music is approached by a mathematical angle. Lots of great composers used maths to make fantastic music. Take a look at Iannis Xenakis, for example, who used architectural concepts to create orchestral music…

    Info on the maths behind Pythagoras tuning system :

    Info on Xenakis :

  • p(lk)-

    Euclidean sequencer max4live version


  • Random Chance

    @Loopstationzeb: Intersting, did you by chance work with any of the musicians you mentioned or had a good long talk about life, the universe, and everything else (including music, theory, and technology)? Or is your statement about their views on science as a tool for creating music based on any sources you'd care to cite? 

  • drrn

    Eckel is loads of fun but I've never been able to figure out what the hell it's actually doing. I just twiddle knobs until things sound cool.

  • Peter Kirn

    Yes, the math is just convenience – we're talking pretty fundamental, basic music theory. The whole point is that musicians *do* tend to do these things intuitively and may not be aware of mathematical views of the topics – and the reverse is often true; many mathematicians or (in this case) physicists would be even more unaware of musical applications of topics. The idea is to have a conversation between people and how they work, not to proscribe a specific way of working.

    Anyway, the Circle of Fifths and Euclidean algorithms are going to each give you very common musical building blocks. We're not in chin-stroking territory at all.

  • JCB

    I entirely agree!

  • mat

    I love polyrhythmic stuff!
    Although I do not think that you need any math for it. You can also do it intuitive. Ableton gives you the great opportunitiy to edit your pattern length – just use it. Tip: I found out that polyrhythmic variations based on 4th and 8th length variations of a bar (e.g. 3/4 or 7/8) work fine, while based on 16th (e.g. 15/16) sound really weird (but might be also nice)
    @ p (lk)- great work!!

  • Darthen

    As a matter Coltrane worked an awful lot with a very "dry" and "mathematical" book namely: Nicolas Slonimsky’s Thesaurus of Scales and Melodic Patterns.

  • tony wheeler

    @loopstationzeb, you're entitled to that opinion but i think this is a tired debate. life's too short to hate on style, technique or really anything else for that matter. as long as people are making their art using technology, musicianship or any combination of the 2, we should be celebrating.

    the euclidean project was a way to explore the connection between math, beauty and the natural world. it's practical application, in my opinion, isn't as important as raising awareness of this connection. it's magic and it's real.

  • Peter Kirn

    I'll defend loopstationzeb's comment in part by saying this:

    If you apply theory — any theory — and don't *also* use your ears, you're pretty much sunk. Nine out of ten theorists, even, agree.

  • BellectroniQ

    Good stuff. 

  • Ranch

    loopstationzeb know the deal. this kind of music making can be very cold. as long as there is some africa in there the vibe will be cool.