Tuning & Cents
Equal-tempered vs just intonation; cents-off table; ratio ↔ cents
About this tool
Compare equal temperament with three historical tunings and convert between frequency ratios and cents.
Tunings
- Equal temperament: every semitone = 100 cents.
- 5-limit just intonation: small-integer ratios (3/2 = perfect 5th, 5/4 = major 3rd, …).
- Pythagorean: stack of pure 5ths, all ratios powers of 3/2 reduced to one octave.
- Quarter-comma meantone: fifth flattened by ¼ syntonic comma so major 3rds are pure (5/4).
cents = 1200·log₂(ratio). The famous syntonic comma is the difference between a Pythagorean and a JI major 3rd (≈ 21.5 cents).