Una formulació matemàtica de les modulacions musicals

Abstract

It has always been mentioned that Mathematics and Music are deeply connected, but sometimes it can be difficult to precise the how and the why. As we all know, music transmission’s way is the sound, which can be represented by means of Fourier analysis as a sum of sinusoidal waves multiplied by amplitude factors. These factors are given by Fourier coefficients and, musically, they provide the harmonics of a fundamental sound and determine the timbre of a musical instrument. The purpose of this project is to use Fourier analysis in an alternative way in order to obtain a representation in coordinates of triad chords, by means of the Fourier transform of their characteristic functions. Since we identify a triad chord with a tonality, this work has allowed us to shape and visualize musical modulations in a different way from that of the traditional tonal harmony.