3:2 · 7 semitones
Perfect fifth. Nearly paid in full.
- Pure
- 701.96¢
- Tempered
- 700¢
- Charge
- −1.96¢
- Beat
- 0.37 Hz
Lower note 220 Hz. Pure upper 330.00 Hz. Tempered upper 329.63 Hz.
The fifth is the one interval equal temperament barely touches. The tempered fifth is about two hundredths of a semitone narrower than 3:2, and the two versions beat less than once every two seconds.
This is why the compromise exists. The reason is the Pythagorean comma: twelve pure 3:2 fifths overshoot seven octaves by about 23.5 cents, and temperament closes the circle by narrowing each of the twelve fifths by about 2 cents. The thirds are then whatever that arrangement leaves them.