s3377610: VART3492 :: Advanced Studio Technologies 2 - Bjorklund Algorithm & World Music

A new family of musical rhythms has been described, called Euclidean rhythms, which are obtained by using Bjorklund’s sequence generation algorithm, which has the same structure as the Euclidean algorithm. It was shown that many rhythms used in world music are Euclidean rhythms. Some of these Euclidean rhythms are also Euclidean strings [11]. The three groups of Euclidean rhythms listed in the preceding section reveal a tantalizing pattern. Those Euclidean rhythms that are also Euclidean strings (the first four of group one) are favoured in classical, jazz, Bulgarian, Turkish and Persian music, but are not popular in African music. The Euclidean rhythms that are neither Euclidean strings nor reverse Euclidean strings (the first two of group three) are used only in subSaharan African music. Finally, the Euclidean rhythms that are reverse Euclidean strings (the second group) appear to have a much wider appeal. Finding musicological explanations for the preferences apparent in these mathematical properties raizes an interesting ethnomusicological question. The Euclidean strings defined in [11] determine another family of rhythms, many of which are also used in world music but are not necessarily Euclidean rhythms, as for example (1221222), an Afro-Cuban bell pattern. Therefore it would be interesting to explore empirically the relation between Euclidean strings and world music rhythms, and to determine formally the exact mathematical relation between Euclidean rhythms and Euclidean strings.

The Euclidean Algorithm Generates Traditional Musical Rhythms - Godfried Toussaint (School of Computer Science, McGill University 2005)