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Articles
- ·14 min read
Why Is Pitch Logarithmic? From Frequencies to the Geometry of Pitch
How logarithms turn frequency ratios into additive pitch distances, explaining octaves, cents, equal temperament, and the pitch-class circle.
- ·10 min read
The Circle of Fifths Does Not Close: A Diophantine Problem in Music
Why twelve pure fifths do not equal seven octaves, and how prime factorization turns the Pythagorean comma into a theorem.