Semicomma: Difference between revisions

No edit summary
m Recategorize todo
 
(2 intermediate revisions by the same user not shown)
Line 1: Line 1:
{{Infobox Interval
{{Infobox Interval
| Ratio = 2109375/2097152
| Ratio = 2109375/2097152
| Name = semicomma, <br>orson comma, <br>Fokker's comma
| 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]]).  


Line 10: Line 11:
[[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.


== Name ==
== 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 "Fokker's comma" comes from [[Adriaan Fokker]].
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 ==
Intervals with the word "semicomma" in the name:
* [[126/125]] (aka starling comma or septimal semicomma)
* Medium semicomma, aka [[sensipent comma]]
* [[15625/15552]] (aka kleisma or semicomma majeur)
* Septimal semicomma, aka [[126/125|starling comma]]
* [[Sensipent comma]] (78732/78125, aka medium semicomma)
* Semicomma majeur, aka [[15625/15552|kleisma]]
 
== External links ==
* [http://tonalsoft.com/enc/s/semicomma.aspx Semicomma] on [[Tonalsoft Encyclopedia]]


[[Category:Orson]]
[[Category:Orson]]
Line 23: 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|add etymology|comment=Explain the reasoning behind the name "semicomma". Why is 2109375/2097152 uniquely deserving of the name?}}
{{Todo|research|comment=Explain the reasoning behind the name "semicomma". Why is 2109375/2097152 uniquely deserving of the name?}}