Dozens of traditional world-music timelines are rotations of Euclidean rhythms

Toussaint’s paper catalogues more than 98 Euclidean rhythms (k and n relatively prime) that match named rhythmic timelines used across African, Latin American, Middle Eastern, Balkan, Indian, and other traditions — either directly or as a rotation (necklace member). Examples: E(3,8) = Cuban tresillo and West African atoke bell; E(5,8) = Cuban cinquillo, Egyptian Malfuf, Korean NongP’yong; E(5,16) = (33334) = the Bossa-Nova necklace of Brazil (usually started on the third onset) and a common EDM timeline; E(7,16) = Samba necklace; E(5,12) = Venda clapping and Aka Pygmy patterns. The correspondence is not thought to be coincidental: independent cultures converge on maximally even distributions, plausibly because such patterns feel most balanced to human perception. A notable exception is Indian classical music, whose long talas use a wider variety of durations and so violate maximal evenness.

Examples

E(7,12) started on its third onset = the ‘Standard Pattern’ / African Signature Tune, the most internationally known African timeline — the same pattern as the pitch sequence of the major diatonic scale. Bossa Nova = E(5,16) started on the third onset.

Assessment

Name three distinct cultures that use E(3,8) under different names. Explain why E(7,12) coinciding with both a world-music timeline and the major-scale pitch pattern is considered striking.