What Are "Good" Rhythms? Generating Rhythms Based on the Properties Set Out in The Geometry of Musical Rhythm

We propose in this article to generate good rhythms from geometric properties. This approach is based on the work by Toussaint, who investigated the properties that make a "good" rhythm good in his book The Geometry of Musical Rhythm. To do this, he analyzed the shapes of polygons corresponding to certain rhythms to derive geometric properties of a good rhythm. In this article, we propose to quantify these properties using original mathematical formulas. This scores each rhythm against several properties to measure how good a rhythm is, resulting in the generation of rhythms with k onsets and n pulses. When k = 5 and n = 16, we reveal that the son rhythm obtains the best score, as predicted by Toussaint at the end of his book. Applying the method for other values of k and n, we demonstrate that some of the rhythms with the highest scores are musically important rhythms, such as the tresillo rhythm with k = 3 and n = 8, the fume-fume rhythm with k = 5 and n = 12, the samba rhythm with k = 7 and n = 16 or the Steve Reich's signature rhythm with k = 8 and n = 12.