Bjorklund algorithm and Euclidean Rhythms
I came across an article on CDM the other day that really grabbed my interest. The bit that grabbed me was the talk about rhythm generation using a form of the Euclidean algorithm. Looking at all the various computer based implementations though, I found that non of them really hit the spot for me (as interesting and impressive as they are). After a ponder I decided that what I would like was method of generating rhythms that were longer than 16 steps, simply, from within live. (If you don’t know about Euclidean algorithms you should probably go and read that CDM article if you want to understand this post.)
So, I set about modifying the Step Sequencer patch that comes with Max For Live. Initially I picked out the algorithm from work done by Robin Prince here, in his M4L patch most of the logic was handled by JavaScript which was a good start. Unfortunately I found the implementation to be broken, over 16 steps and things started going out of whack. I realised that most of the other implementations were using the same basic logic (Java, Flash/Actionscript, Ruby) so all exhibited the same behaviour. As an example for a pattern with 17 steps and 13 pulses all the above have a function that will return something like this (I have formatted the output so it is easier to read):
[x.x.x.x.xxxxxxxx.]
There are two things wrong with this, firstly this does not look like an even distribution of pulses to me, secondly there is a pulse missing! Now, I am no mega brained uber genius, so I am more that willing to accept that I have missed some detail or just plain don’t get it and it does seem odd that so many implementation are wrong… That said, I took it upon myself to create a ‘fixed’ version and decided to go in search of the original paper that Bjorklund wrote and then attempt to extract the algorithm from that port it to Javascript myself. After some work I came up with the code below.
Using our previous example of 17 steps and 13 pulses this code will generate the following sequence:
[x.xxx.xxx.xxx.xxx]
now this is more like it, it looks much more even (because this is a cyclical rhythm it doesn’t matter that it is not ‘balanced’) and it has all 13 pulses :)
I plugged the Javascript into a M4L Patch to create a simple step sequencer (it is pretty rough and I considered not posting it). Create a new M4L Midi patch and paste the below in (NOTE: you will need bjorklund.js in you Max search path, or simply in the same folder as the .amxd file you create).
----------begin_max5_patcher----------
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-----------end_max5_patcher-----------
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