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. | |||
== 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?}} | ||
Revision as of 11:12, 1 April 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.
See also
Intervals with the word "semicomma" in the name:
- Medium semicomma, aka sensipent comma
- Septimal semicomma, aka starling comma
- Semicomma majeur, aka kleisma