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. It is also the difference between the 31-comma ({{nowrap|331/249}}) and seven syntonic commas ([[81/80]]). 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]]).

== Temperaments ==

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

== 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. It is also the difference between the 31-comma ({{nowrap|3<sup>31</sup>/2<sup>49</sup>}}) and seven syntonic commas ([[81/80]]). 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]]).
+== Temperaments ==
+[[Tempering out]] this comma in the 5-limit leads to the [[orson]] temperament.
 == 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?}}