Mathematics and soft computing in music

Teresa Leon

Vicente Liern

pp. 451-465

in: Rudolf Seising, Veronica Sanz González (eds), Soft computing in humanities and social sciences, Berlin, Springer, 2012

Abstract

Mathematics is the fundamental tool for dealing with the physical processes that explain music but it is also in the very essence of this art. Musical notes, the first elements which music works with, are defined for each tuning system as very specific frequencies; however, instrumentalists know that small changes in these values do not have serious consequences. In fact, sometimes consensus is only reached if the entire orchestra alters the theoretical pitches. The explanation for this contradiction is that musicians implicitly handle very complex mathematical processes involving some uncertainty in the concepts and this is better explained in terms of fuzzy logic. Modelling the notes as fuzzy sets and extending the concept of tuning systems lead us to a better understanding on how musicians work in real-life. The notes offered by a musician during a performance should be compatible with the theoretical ones but not necessarily equal. A numerical experiment, conducted with the help of a saxophonist, illustrates our approach and also points to the need for considering sequential uncertainty.