Abstract
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.
