Modeling Musical Rhythm Mutations with Geometric Quantization

A mathematical analysis of musical rhythm presupposes what exactly a musical rhythm is and how it is represented. In the music literature, there are more than 50 ways to define musical rhythm. This chapter is concerned with transforming rhythms from one category of rhythms to another. Two classes of rhythms are referred to as binary and ternary. Several binarization algorithms that result from geometric quantization schemes are examined using the transformation of the fume-fume into the clave son as a case study. The chapter sheds some light on the likelihood of musical rhythm mutation between these two rhythms and that it suggests psychological experiments to determine which binarization algorithm is the better predictor of human perceived similarity. There are many ways to measure rhythm similarity. One natural approach is to sum the discrepancies between all the corresponding pairs of onsets.