Chord Analysis in the Key of Math and Physics
By Jenny Fromme
Abstract:
Musical chords are made up of three or more unique pitches. The musical quality (major,
minor, etc.) of these chords is determined by the differences in the frequencies of the
individual pitches of the chord. These pitches are formed by acoustical energy, which
travels in waves that can be approximated by sinusoidal waves. When two pitches are
sounded simultaneously, the pitches created by the sum and difference of each sinusoidal
waves are also perceived. This research focuses on the sums and differences of each
combination of the pitches in the chord and tries to determine patterns that account for
the pleasing quality of some chords and the cacophonous quality of other chords. Also
analyzed, are the differences in the patterns created from notes formed using the just
intonation system, which utilizes rational frequencies, and the equal temperament system,
which utilizes irrational frequencies to establish the musical scale.