TAG / 3 ARTICLES
mathematics
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.
- ·14 min read
What Is a Musical Interval? Ratios, Tuning, and Consonance
Why musical intervals are frequency ratios, from vibration and ancient harmonic theory to octaves, fifths, tuning systems, and the limits of ratio-based explanations of consonance.