Pythagorean comma: Difference between revisions
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Realized that in Compton temperament, the 5-limit is represented by an independent generator, so there's actually no 3-limit version |
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| Line 11: | Line 11: | ||
| Cents = 23.46001 | | Cents = 23.46001 | ||
| Name = Pythagorean comma, <br>ditonic comma | | Name = Pythagorean comma, <br>ditonic comma | ||
| Color name = | | Color name = LLw-2, Lalawa comma | ||
| FJS name = d-2 | | FJS name = d-2 | ||
| Sound = | | Sound = | ||
Revision as of 20:09, 5 October 2021
| Interval information |
ditonic comma
reduced harmonic
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).
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.