My Mathematics senior thesis explores a model designed to relate chords and harmonic progression in music to arithmetic functions in mathematics. The disciplines of mathematics and music are very closely connected, overlapping in the fields of music theory and composition. Time signatures, frequency, chromaticism, and musical structures show some of the ways math is apparent in music. With inspiration from past researchers, I wondered how mathematicians could notate music in mathematical terms.
To accomplish this, I correlated notes, or tones, to integer representations based upon the tonal center, and I represented musical chords by sets of integers, called tone sets. Modular arithmetic is applied to represent the twelve-tone chromatic music system in integers without the need to worry about octave displacement. I then detailed the process of finding and applying functions to the tone sets to create harmony. I implemented the resulting model to two examples, Pachelbel’s Canon in D and Leonard Cohen’s Hallelujah.