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AT Ali Taqi
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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.

A monochord divided into the integer string-ratios (1/1, 1/2, 1/3, 1/4, 1/5) that produce the consonant musical intervals.
A monochord divided into the integer string-ratios (1/1, 1/2, 1/3, 1/4, 1/5) that produce the consonant musical intervals.
Number theoryMathematical expositionMusic theoryLaTeXR · Python

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.