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 [[~~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]].

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 [[Gallery of Just Intervals]], [[~~comma~~]], [~~http~~:~~//en.wikipedia.org/wiki/~~Pythagorean_comma Pythagorean comma - Wikipedia]''

== See also ==

* [[Gallery of Just Intervals]]

* [[Comma]]

* [[Wikipedia:Pythagorean_comma|Pythagorean comma - Wikipedia]]

[[Category:3-limit]]

[[Category:Comma]]

[[Category:Pythagorean]]

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-The '''Pythagorean''' or '''ditonic comma''' (about 23.460[[Cent|&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]].
+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 [[Gallery of Just Intervals]], [[comma]], [http://en.wikipedia.org/wiki/Pythagorean_comma Pythagorean comma - Wikipedia]''
+== See also ==
+* [[Gallery of Just Intervals]]
+* [[Comma]]
+* [[Wikipedia:Pythagorean_comma|Pythagorean comma - Wikipedia]]
+[[Category:3-limit]]
 [[Category:Comma]]
 [[Category:Pythagorean]]