Pythagorean comma: Difference between revisions
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The '''Pythagorean''' or '''ditonic comma''' (about 23.460[[Cent|¢]]) is the interval 531441/524288 or {{Monzo| -19 12 }} in [[monzo]] notation. 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)<sup>12</sup>/2<sup>7</sup> and it also can be written as the ratio between the apotome and the Pythagorean minor second, ([[2187/2048]])/([[256/243]]). 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]]. | The '''Pythagorean''' or '''ditonic comma''' (about 23.460[[Cent|¢]]) is the interval 531441/524288 or {{Monzo| -19 12 }} in [[monzo]] notation. 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)<sup>12</sup>/2<sup>7</sup> and it also can be written as the ratio between the apotome and the Pythagorean minor second, ([[2187/2048]])/([[256/243]]). 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]]. | ||
== See also == | == See also == | ||
* [[Gallery of Just Intervals]] | * [[Gallery of Just Intervals]] | ||
* [[Comma]] | * [[Comma]] | ||
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[[Category:3-limit]] | [[Category:3-limit]] | ||
[[Category: | [[Category:Small comma]] | ||
[[Category:Pythagorean]] | [[Category:Pythagorean]] | ||
Revision as of 17:34, 25 September 2020
The Pythagorean or ditonic comma (about 23.460¢) is the interval 531441/524288 or [-19 12⟩ in monzo notation. 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). 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.