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]]). | ||
== Temperaments == | == Temperaments == | ||
[[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 "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]] | ||
| Line 20: | Line 26: | ||
[[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?}} | ||
Latest revision as of 21:05, 15 July 2026
| Interval information |
orson comma,
Fokker's comma
reduced harmonic
The semicomma or Fokker's comma (ratio: 2109375/2097152, monzo: [-21 3 7⟩), is a small 5-limit comma of 10.061 cents 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 (331/249) and seven syntonic commas (81/80).
Temperaments
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 "semicomma" was given by Adriaan Fokker, while the name "Fokker's comma" refers to him directly and was likely proposed later.
See also
- 126/125 (aka starling comma or septimal semicomma)
- 15625/15552 (aka kleisma or semicomma majeur)
- Sensipent comma (78732/78125, aka medium semicomma)