Tonal Optimization in Music Playing

Jiashi Hou
Bridges: Mathematical Connections in Art, Music, and Science (2002)
Pages 293–300


Music performance and enjoyment involve stylish interpretation, intonation, rhythm and specific technique associated with various instruments. While artistic interpretation is subjective - different audiences may enjoy different styles - the precision of the pitch of a certain tone, hence the harmony of a chord, is a physics phenomenon and can be determined mathematically. The enjoyment of music performances is certainly affected by whether or not the tones are generated correctly. This article attempts to explore objective criteria that can be measured mathematically for "better" or ''best'' playing of music in terms of harmonic chords and tonal relations in the melody. This measurement can be used in determining a tuning system of an instrument to "optimize" the playing of a certain piece of music. With the advancement of ever so sophisticated electronic digital keyboards and computers as a new generation of performing and recording instruments, one can predetermine the best tuning system for a specific piece of music. Some segments of classic music will be used as examples.