Pythagorean comma: Difference between revisions

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The Pythagorean or ditonic comma (about 23.~~460¢~~) is the interval 531441/524288 = |-19 12~~> (see~~ [[~~monzo~~|~~monzo~~]]). 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 [[~~24edo|~~24edo]], [[~~72edo|~~72edo]] and [[~~84edo|~~84edo]].

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: [[~~Gallery_of_Just_Intervals|~~Gallery of Just Intervals]], [[~~Comma|~~comma]]

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

[~~http~~:~~//en.wikipedia.org/wiki/Pythagorean_comma Wikipedia article~~] [[Category:~~comma~~]]

[[Category:Comma]]

[[~~Category~~:~~pythagorean~~]]

[[Category:Pythagorean]]

[[de:531441/524288]]

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-The Pythagorean or ditonic comma (about 23.460¢) is the interval 531441/524288 = |-19 12&gt; (see [[monzo|monzo]]). 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 [[24edo|24edo]], [[72edo|72edo]] and [[84edo|84edo]].
+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]].
-See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]], [[Comma|comma]]
+: '' See also [[Gallery of Just Intervals]], [[comma]], [http://en.wikipedia.org/wiki/Pythagorean_comma Pythagorean comma - Wikipedia]''
-[http://en.wikipedia.org/wiki/Pythagorean_comma Wikipedia article]      [[Category:comma]]
+[[Category:Comma]]
-[[Category:pythagorean]]
+[[Category:Pythagorean]]
+<!-- interwiki -->
+[[de:531441/524288]]