Stefan Stelian Diaconescu

A Mathematical System of Musical Sounds Stefan Stelian Diaconescu

The relation between music and mathematics is well known for about two thousand and a half years, but new ideas can always emerge. The present paper tries to present this relation in a new perspective. First of all, we will give mathematical definitions of some musical notions like: musical sounds, musical scale, musical gamut, musical mode, relative gamut, chromatic gamut, musical piece, transposition. Secondly, we will introduce some new principles, like the dissonance principle which allows a quantitative measure of the dissonance of a set of any sounds, the principle of natural system construction which allows building a set of natural sound systems, and the third principle, the sorting principle, which explains how the natural heptatonic scale could be deduced. Based on these three principles, we will finally give a quantitative measure of the fact that temperament musical sound system is accepted today and a quantitative comparison between temperament system and natural system. This second edition of the book introduces a new chapter "The harmonic power" that gives some new explications of the "The sorting principle," that presents how the musical gamut are built.