Semicomma: Difference between revisions

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~~'''~~2109375/2097152''' = {{~~Monzo| -21 3 7~~ }}~~, called the~~ '''semicomma''' or '''Fokker comma''', is ~~an interval~~ 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)^3/(8/5), which can also be written ((9/8)*(25/24))^3/(8/5). Tempering it out leads to [[orson]] temperament.

{{Infobox Interval

| Ratio = 2109375/2097152

| Name = semicomma, orson comma, Fokker's comma

| Color name = Ly7-3, Lasepyo comma

| Comma = yes

}}

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)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]] ({{nowrap|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 ==

~~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:~~5-limit~~]]

[[Category:Orson]]

[[Category:~~Small comma~~]]

[[Category:Commas with unknown etymology]]

[[Category:Commas named after composers]]

[[Category:Commas named after music theorists]]

{{Todo|research|comment=Explain the reasoning behind the name "semicomma". Why is 2109375/2097152 uniquely deserving of the name?}}

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-'''2109375/2097152''' = {{Monzo| -21 3 7 }}, called the '''semicomma''' or '''Fokker comma''', is an interval 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)^3/(8/5), which can also be written ((9/8)*(25/24))^3/(8/5). Tempering it out leads to [[orson]] temperament.
+{{Infobox Interval
+| Ratio = 2109375/2097152
+| Name = semicomma, orson comma, Fokker's comma
+| Color name = Ly<sup>7</sup>-3, Lasepyo comma
+| 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]]).
+== 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 ==
-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:5-limit]]
+[[Category:Orson]]
-[[Category:Small comma]]
+[[Category:Commas with unknown etymology]]
+[[Category:Commas named after composers]]
+[[Category:Commas named after music theorists]]
+{{Todo|research|comment=Explain the reasoning behind the name "semicomma". Why is 2109375/2097152 uniquely deserving of the name?}}