De Pitágoras a Allen Forte: algumas relações entre matemática e música

Abstract

This paper aims to study Math present in music in some moments of its history. We begin with the analysis of the Pythagorean scale formation, later adapted by Andreas Werckmeister with the creation of the temperate scale. We also studied the formation of the Greek modes and the major and minor harmonic elds, which are the basis of tonal compositions. Then we studied the basis of the mathematical theory proposed by Allen Forte to perform analysis of atonal music, those that seek a disrupition in tonalism rules. In perder to develop this theory we used two function groups named T=T I and PLR, which accomplish transpositions, inversions, and chord progression analysis when applied to a music. These two function groups are both isomorphics to the Diedral group.