Euclidean Rhythm

Bjorklund algorithm · maximally even · Bresenham

8
3
0
Physics: Euclidean rhythm E(k,n): distribute k onsets in n slots as evenly as possible, using the Björklund/Euclidean GCD algorithm (Toussaint 2005). Identical to Bresenham's line-drawing algorithm. E(3,8) = [1,0,0,1,0,0,1,0] = Cuban tresillo; E(5,8) = bossa nova clave; E(5,12) = Afro-Cuban clave; E(7,12) = West African bell pattern; E(13,24) = Arab rhythm. Connection to Farey sequences and Stern-Brocot trees — these patterns minimize the maximum gap between onsets.