Semicomma: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 2109375/2097152 | | Ratio = 2109375/2097152 | ||
| Name = semicomma, | | Name = semicomma, orson comma, Fokker's comma | ||
| Color name = Ly<sup>7</sup>-3, Lasepyo comma | | Color name = Ly<sup>7</sup>-3, Lasepyo comma | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
{{Wikipedia}} | |||
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]]). | 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]]). | ||
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[[Tempering out]] this comma in the 5-limit leads to the [[orson]] temperament. | [[Tempering out]] this comma in the 5-limit leads to the [[orson]] temperament. | ||
== | == Etymology == | ||
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 " | 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 "semicomma" was given by [[Adriaan Fokker]], while the name "Fokker's comma" refers to him directly and was likely proposed later. | ||
== See also == | == See also == | ||
* [[126/125]] (aka starling comma or septimal semicomma) | |||
* | * [[15625/15552]] (aka kleisma or semicomma majeur) | ||
* | * [[Sensipent comma]] (78732/78125, aka medium semicomma) | ||
* Semicomma | |||
== External links == | |||
* [http://tonalsoft.com/enc/s/semicomma.aspx Semicomma] on [[Tonalsoft Encyclopedia]] | |||
[[Category:Orson]] | [[Category:Orson]] | ||
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[[Category:Commas named after composers]] | [[Category:Commas named after composers]] | ||
[[Category:Commas named after music theorists]] | [[Category:Commas named after music theorists]] | ||
{{Todo| | {{Todo|research|comment=Explain the reasoning behind the name "semicomma". Why is 2109375/2097152 uniquely deserving of the name?}} | ||