Semicomma: Difference between revisions
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The '''semicomma''' or '''Fokker's comma''' ([[ratio]]: 2109375/2097152, [[monzo]]: {{monzo| -21 3 7 }}), is | 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. | |||
== 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 == | == See also == | ||
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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|add etymology|comment=Explain the reasoning behind the name "semicomma". Why is 2109375/2097152 uniquely deserving of the name?}} | ||
Latest revision as of 06:41, 25 June 2025
| 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.
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
Intervals with the word "semicomma" in the name:
- Medium semicomma, aka sensipent comma
- Septimal semicomma, aka starling comma
- Semicomma majeur, aka kleisma