Calculating Euclidean Rhythmns using the Bresenham Algorithm

Nikolaus Gradwohl2017-11-24T06:43:52+00:00

Recently I started playing with euclidean rhythms and implemented the bjorklund algorithm shown in the paper by Godfired Toussaint in ruby. The implementation isn't really rocket science (actually it's ring accelerator science :-)) but it uses recursive function calls, two arrays, multiple stages, ... and I had the feeling that this is far more complicated than it needs to be. After reading several posts, blogs and papers about the implementations of the algorithm I read somewhere that the algorithm produces the same result as the bresenham algorithm - at first I ignored the sentence and unfortunately I have no idea anymore where I read it but today I implemented a simple version of it an the results I get are the same as my recursive version - or rotations, which is fine because you usually loop over the sequences and are free to choose a starting point - so in case anyone is interested here is my bresenhamish method for calculating euclidean rhythms in ruby - shouldn't be too complicated to port it to different languages

def eucledean(k,n)
    f = 1.0*n/k
    res = Array.new(n,0);
    a = 0
    k.times do |i|
        res[a.to_i] = 1
        a += f
    end
    return res
end

(1..8).each do |i|
print eucledian(i,8)
print "\n"
end

and this are the results I get for the 8 possible rhythms with 8 steps

[1, 0, 0, 0, 0, 0, 0, 0]
[1, 0, 0, 0, 1, 0, 0, 0]
[1, 0, 1, 0, 0, 1, 0, 0]
[1, 0, 1, 0, 1, 0, 1, 0]
[1, 1, 0, 1, 1, 0, 1, 0]
[1, 1, 1, 0, 1, 1, 1, 0]
[1, 1, 1, 1, 1, 1, 1, 0]
[1, 1, 1, 1, 1, 1, 1, 1]
Tweet This! submit to reddit Digg! Tags: | no comments | no trackbacks

See also:

Sonic Pi beatslicing livecoding session
creating midifiles using ruby
New Song - A Target you can't see
Welcome Lil Erebus
New Song - Turn into a Tune

Trackbacks

Comments

Leave a response

Leave a comment