Pythagorean comma: Difference between revisions
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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]]. | 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]]. | ||
===Pythagorean=== | ===Pythagorean temperament=== | ||
Comma list: 531441/524288 | Comma list: 531441/524288 | ||
Revision as of 12:33, 21 April 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.
Pythagorean temperament
Comma list: 531441/524288
Mapping:
Vals: