Semicomma: Difference between revisions

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The '''semicomma''' or '''Fokker's comma''' ([[ratio]]: 2109375/2097152, [[monzo]]: {{monzo| -21 3 7 }}), is ~~an interval~~ of 10.061 [[cent]]s which is the amount by which three classic augmented second intervals of [[75/64]] exceed [[8/5]]. That means (75/64)3/(8/5), which can also be written ((9/8)(25/24))3/(8/5). In terms of commas, it factors into simpler commas as ([[15625/15552]])([[32805/32768]]), the kleisma and the schisma. ~~Tempering it out leads to~~ the [[~~Orson~~]] ~~temperament~~.

The '''semicomma''' or '''Fokker's comma''' ([[ratio]]: 2109375/2097152, [[monzo]]: {{monzo| -21 3 7 }}), is a [[small comma|small]] [[5-limit]] [[comma]] of 10.061 [[cent]]s which is the amount by which three classic augmented second intervals of [[75/64]] exceed [[8/5]]. That means (75/64)3/(8/5), which can also be written ((9/8)(25/24))3/(8/5). In terms of commas, it factors into simpler commas as ([[15625/15552]])([[32805/32768]]), the kleisma and the schisma. It is also the difference between the [[31-comma]] ({{nowrap|331/249}}) and seven syntonic commas ([[81/80]]).

~~Most notably, it is tempered~~ out in [[~~31edo~~]] as the ~~difference between~~ the ~~31-~~comma ~~({{nowrap|331/249}}) and seven syntonic commas (~~[[~~81/80~~]]).

== Temperaments ==

[[Tempering out]] this comma in the 5-limit leads to the [[orson]] temperament.

== Name ==

Given the other intervals called "semicomma", it is likely that "semicomma" refers to the comma's size as about half the size of the syntonic comma. The name "Fokker's comma" comes from [[Adriaan Fokker]].

== See also ==

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[[Category:Commas named after composers]]

[[Category:Commas named after music theorists]]

{{~~todo~~|add etymology|comment=~~explain~~ the reasoning behind the name ~~“semicomma”?~~ Why is 2109375/2097152 uniquely deserving of the name?}}

{{Todo|add etymology|comment=Explain the reasoning behind the name "semicomma". Why is 2109375/2097152 uniquely deserving of the name?}}

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-The '''semicomma''' or '''Fokker's comma''' ([[ratio]]: 2109375/2097152, [[monzo]]: {{monzo| -21 3 7 }}), is an interval of 10.061 [[cent]]s which is the amount by which three classic augmented second intervals of [[75/64]] exceed [[8/5]]. That means (75/64)<sup>3</sup>/(8/5), which can also be written ((9/8)(25/24))<sup>3</sup>/(8/5). In terms of commas, it factors into simpler commas as ([[15625/15552]])([[32805/32768]]), the kleisma and the schisma. Tempering it out leads to the [[Orson]] temperament.
+The '''semicomma''' or '''Fokker's comma''' ([[ratio]]: 2109375/2097152, [[monzo]]: {{monzo| -21 3 7 }}), is a [[small comma|small]] [[5-limit]] [[comma]] of 10.061 [[cent]]s which is the amount by which three classic augmented second intervals of [[75/64]] exceed [[8/5]]. That means (75/64)<sup>3</sup>/(8/5), which can also be written ((9/8)(25/24))<sup>3</sup>/(8/5). In terms of commas, it factors into simpler commas as ([[15625/15552]])([[32805/32768]]), the kleisma and the schisma. It is also the difference between the [[31-comma]] ({{nowrap|3<sup>31</sup>/2<sup>49</sup>}}) and seven syntonic commas ([[81/80]]).
-Most notably, it is tempered out in [[31edo]] as the difference between the 31-comma ({{nowrap|3<sup>31</sup>/2<sup>49</sup>}}) and seven syntonic commas ([[81/80]]).
+== Temperaments ==
+[[Tempering out]] this comma in the 5-limit leads to the [[orson]] temperament.
+== Name ==
+Given the other intervals called "semicomma", it is likely that "semicomma" refers to the comma's size as about half the size of the syntonic comma. The name "Fokker's comma" comes from [[Adriaan Fokker]].
 == See also ==
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 [[Category:Commas named after composers]]
 [[Category:Commas named after music theorists]]
-{{todo|add etymology|comment=explain the reasoning behind the name “semicomma”? Why is 2109375/2097152 uniquely deserving of the name?}}
+{{Todo|add etymology|comment=Explain the reasoning behind the name "semicomma". Why is 2109375/2097152 uniquely deserving of the name?}}