The complex use of tonal consonance in music: microscopic and macroscopic rules in harmony and melody (2019)
Abstract: This thesis contributes to the understanding of the connection between the tonal consonance phenomenon and the rules associated to the construction of musical pieces. It begins from the tonal consonance properties of sounds and ends with the emergence of macroscopic phenomena. The systems studied are: the marimba de chonta music, melodic lines of Western music, and secco recitatives of operas. At the microscopic level, we show how tonal consonance connects the timbre of marimba de chonta with traditional tunings and musical practices. At this level, we also extended the traditional concept of interval size, and we used chords as the unit of analysis for the harmony of secco recitatives. On the macroscopic level, we found that the new representation of intervals, together with an entropy extremalization principle, is suitable for approximately reproducing the selection of intervals in melodic lines. Besides, a conserved macroscopic quantity emerges, which is empirically related to the mean dissonance of a melodic line, hence connecting psychoacoustics with complexity.