Pythagorean comma: Difference between revisions
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The Pythagorean or ditonic comma (about 23. | The '''Pythagorean''' or '''ditonic comma''' (about 23.460[[Cent|¢]]) is the interval 531441/524288 or {{Monzo| -19 12 }} in [[Monzos|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)^12/2^7 and it also can be written as the ratio between the [[2187/2048|apotome]] and the [[256/243|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 | : '' See also [[Gallery of Just Intervals]], [[comma]], [http://en.wikipedia.org/wiki/Pythagorean_comma Pythagorean comma - Wikipedia]'' | ||
[ | [[Category:Comma]] | ||
[[ | [[Category:Pythagorean]] | ||
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Revision as of 18:10, 2 October 2018
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)^12/2^7 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.