Phylogenetic Analysis of the Ancient Greek Paeonic Rhythms

Godfried T. Toussaint
Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture (2016)
Pages 363–366 Short Papers


The ancient Greek paeonic (quintuple time) family of rhythms discussed by Aristotle and Aristoxenus provides a unique and much needed opportunity to test the evolutionary efficacy of the mathematical phylogenetic tools presently available. A paeonic rhythm has durational ratio 2:3, and can be notated succinctly using binary sequences of five symbols in length such as [x - x x -], where each symbol denotes a unit of time, the symbol ‘x’ denotes a sounded pulse (note onset), and the symbol ‘-’ denotes a silent pulse (a rest). The rhythm [x - x x -], called the cretic, is the root of the paeonic genus. Seven variants of this prototype rhythm appeared gradually over a period ranging from the 7th Century BC to the 2nd Century AD. It is shown here that correlation and phylogenetic analyses of these rhythms support their documented historical evolution.