By Paul Lascabettes, Isabelle Bloch.
Mathematics and Computation in Music, Jun 2024, Coimbra, Portugal. pp.45-57.
Abstract: 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.
