An implementation of Bjorklund's algorithm applied to rhythm.

examples/euclid.rb

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+# An implementation of Bjorklund's algorithm applied to rhythm.
+# Inspired by http://ruinwesen.com/blog?id=216
+
+require 'music'
+
+include Music
+
+module Euclid
+  module_function
+  def euclid(k, n)
+    bjorklund Array.new(k, [true]) + Array.new(n - k, [false])
+  end
+
+  def bjorklund(seqs)
+    real, rem = split_rem(seqs)
+    if rem.size <= 1
+      (real + rem).flatten
+    else
+      bjorklund(interleave(real, rem))
+    end
+  end
+
+  def split_rem(seq)
+    rem, real  = seq.partition { |x| x == seq.last }
+    if rem.size == real.size
+      return seq, []
+    else
+      return real, rem
+    end
+  end
+
+  def interleave(list1, list2)
+    res = []
+    l1  = list1.dup
+    l2  = list2.dup
+    until l1.empty? && l2.empty?
+      e1 = l1.shift || []
+      e2 = l2.shift || []
+      res.push(e1 + e2)
+    end
+    res
+  end
+end
+
+def cresc(factor, score)
+  group(score,
+    :velocity => env { |v0, ph|
+       v1 = (v0 + ph * ((v0 * factor) - v0)).round # Linear interpolation
+       v1.clip(0..127) })
+end
+
+def kick(*args)
+  n(35, *args)
+end
+
+def snare(*args)
+  n(38, *args)
+end
+
+def rhythm(k, n)
+  bits = Euclid.euclid(k, n)
+  s(bits.map { |pulse| pulse ? kick(SN) : r(SN) }) * 2
+end
+
+def tick
+  (r & snare(1)) * 2
+end
+
+def score
+  ks = rhythm(3, 8) & rhythm(7, 8) & rhythm(5, 8) & rhythm(7, 8)
+  ss = tick * 4
+  ks | ss
+end
+
+SMFWriter.new(:tempo => 136).
+  track(score, :name => 'Euclidean Etude').
+  save('euclid')