A mathematical analysis on the flamenco rhythm
José Miguel Díaz-Báñez
Departamento de Matemática Aplicada II, Universidad de Sevilla
Math and music are intertwined in many different ways and more recently, in the computer science area. Surprisingly, although the flamenco music is very popular all over the world, no exhaustive studies are known. The flamenco music is characterized by hand clapping patterns in which the underlying meter is manifested through accented claps. In this talk, we present a phylogenetic analysis of the five 12/8 time metric timelines used in Flamenco music. To carry out the phylogenetic analysis of the flamenco rhythms we first compute the distance (or dissimilarity) between every pair of rhythms. We consider two distance measures: the chronotonic distance of Gustafson and a new distance measure called the directed swap distance. Several techniques exist for generating phylogenetic trees from distance matrices. We will propose the SplitsTree tool. The results support several established musicological tenets. For example, the fandango and soleá are ”centers” of this family of rhythmic patterns. Finally, we also show some mathematical measures of preference in the flamenco world.