Independent Project · Number Theory × Music · 2022 · Solo, self-directed
Music of the Primes
A book-length mathematical treatise that reconstructs music theory by climbing the number systems — the harmonic series, octaves, interval ratios, the primes behind the major chord, and the irrationals of equal temperament — into a constructive arithmetic of pitch and harmony.
This is a self-directed treatise that rebuilds Western music theory from the ground up — not by convention, but by climbing the number systems one at a time. The harmonic series lives in the natural numbers (ℕ); octave equivalence brings in the integers (ℤ); the consonant intervals are small rational ratios (ℚ); the primes (ℙ) sit behind the major chord; and twelve-tone equal temperament is finally an irrational (ℝ) approximation to all of it.
From those foundations it develops a constructive arithmetic of pitch — how accidentals, scales, and diatonic harmony fall out of the underlying number theory — supported by companion code in R and Python and appendices on algorithms and consonance.
Typeset as a full book in LaTeX, it’s the project where my mathematics and my music meet most directly — and the one I’d most want a curious reader to actually open.