Pythagorean comma
The Pythagorean or ditonic comma is the interval with the ratio 531441/524288 (= [-19 12⟩). It could also be called the 12-comma as it is the amount by which twelve fifths exceed seven octaves, or in other words (3/2)12/27 and it also can be written as the ratio between the apotome and the Pythagorean minor second, (2187/2048)/(256/243). In addition, it also equates six 9/8 major seconds with an octave.
| Interval information |
ditonic comma
reduced harmonic
Temperament
Tempering out this comma leads to the Pythagorean family of temperaments. For EDOs up to 300, it is tempered out if and only if the EDO is a multiple of 12, and hence for instance by 12edo, 24edo, 72edo and 84edo.