Pythagorean comma: Difference between revisions
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| Name = Pythagorean comma, <br>ditonic comma | | Name = Pythagorean comma, <br>ditonic comma | ||
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The '''Pythagorean''' or '''ditonic comma''' is the interval with the ratio '''531441/524288''' (={{Monzo| -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)<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''' is the interval with the ratio '''531441/524288''' (= {{Monzo| -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)<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]]). | ||
== 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]]. | |||
== See also == | == See also == | ||
* [[Gallery of just intervals]] | |||
* [[Gallery of | * [[Small comma]] | ||
* [[ | * [[Wikipedia: Pythagorean comma]] | ||
* [[Wikipedia: | |||
[[Category:3-limit]] | [[Category:3-limit]] | ||
[[Category:Small comma]] | [[Category:Small comma]] | ||
[[Category:Pythagorean]] | [[Category:Pythagorean]] | ||