Euclidean Rhythm MIDI Resource in Ableton Live

"There is geometry in the humming of the strings" - Pythagoras

The Euclidean Algorithm

In 2004, Godfried Toussaint wrote a paper titled "The Euclidean Algorithm Generates Traditional Musical Rhythms" that describes the Euclidean Algorithm in detail. In fact, his paper was the inspiration for this project. You can read it here.

Simply stated, the Euclidean Algorithm computes the greatest common divisor of two integers. In the paper, Toussaint employs this algorithm and describes a very specific process that evenly and precisely distributes some number of things (k) over any other number of things (n).

If we were to imagine (n) as equal time intervals... let's say 16th notes in a bar of music and (k) as pulses that we were interested in triggering as evenly as possible over those time intervals, then we can generate on/off patterns for any combination of pulses and time intervals using the algorithm. These patterns have the distinction of being (as Toussaint described) "Euclidean Rhythms”.

What's amazing here is that these Euclidean Rhythms happen to be the exact patterns that many cultures have traditionally defined their music by. Imagine these isolated cultures, independent of each other, with no prior knowledge of Euclid, picking up on and embracing 1 pattern from a special set of patterns defined by an algorithm 2300 years ago!

It's best understood by seeing and hearing it in action.

AMS File Utility for Ableton Live

I've finally gotten around to posting about my AMS file Utility for Ableton Live. It lets you create endless harmonic oscillators in Simpler and Sampler. It also lets you export microtonal and/or traditionally tuned zones using your own custom waveform shape. It's a little easier in Sampler because it gets the key mapping from the files themselves (just drag a bunch onto the zone editor) while Simpler makes you work for it with racks, but it's not too bad to get going since the key mapping is appended to the file name.

Circle of Fifths Chord Resource in Ableton Live

If you've turned on the radio in the last 30 years or so, you've probably noticed that almost all pop music sounds the same: rigidly formulaic, predictable and yet, oddly pleasing and familiar. This is no accident. Our Western ears have been trained to like music built around the circle of fifths.

I'm not an authority on music theory, but I've hacked together (from various resources) an Ableton Live session that can be used as a reference and compositional aid in this style. Yes, now you too can sound like a pop music hack! (Well... to be fair, a lot of really great music fits into this description as well).

The session file is just a container for several midi clips organized around the circle of fifths. Every note's major and minor key are described by the I, II, III, IV, V, VI, VII and VIII chords that are grouped under it's heading. The chords grouped under each heading all sound good in that track's key.

More exotic chord extensions are grouped under the track/note heading and can be used to substitute for any chord they're based on, in any chord progression or grouping.

The beauty of Ableton Live's session file format is that this container can be used to "inherit" from in your own session, by navigating to the session on disk, expanding individual tracks and dragging and dropping chord clips. The colors and names of the chord clips carry over into your composition. Excellent.

While Ableton Live comes with midi effect plug-ins, I find that having the chords and scales already printed and grouped into musically relevant banks suits a different work-flow.

If you use the session file and enjoy it, please consider making a donation to encourage me to make more of these types of things. Even $1 helps.

Download, unzip and enjoy!
TonysChords.zip