Tipping the scales...functionally!

Abstract

Although one might be tempted to attribute the choice of notes in musical scales and chords to purely aesthetic considerations, a growing body of work seeks to establish correspondences with mathematical notions. Intriguingly, the most important musical scales turn out to be solutions to optimisation problems. In this abstract, we review mathematical characterisations which yield some of the most important musical scales. We also describe an implementation of these notions using the functional programming language Haskell, which has allowed us to conduct interactive experiments and to visualise various approaches from the literature.