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| "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.
