Semiporwellisma: Difference between revisions

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The '''semiporwellisma''' ([[ratio]]: 16384/16335, {{monzo|legend=1| 14 -3 -1 0 -2 }}) is a [[small comma|small]] [[11-limit]] [[comma]] measuring about 5.19 [[cent]]s, named for it is one of the commas tempered out in the [[semiporwell]] temperament. It is the difference between two instances of [[33/32]], the undecimal quartertone, and [[16/15]], the classical diatonic semitone. It is also the difference between the [[rastma]] and the [[schisma]].

~~The '''semiporwellisma''', 16384/16335 = {{monzo| 14 -3 -1 0 -2 }} is a~~ [[~~Small comma|small~~]] [[11-limit]] [[~~comma~~]] ~~measuring about 5~~.19 [[~~cent~~]]~~s, named for~~ it ~~is one of the commas tempered out in the~~ [[~~semiporwell~~]] ~~temperament~~. ~~It is~~ the ~~difference between two instances of~~ [[33/32]]~~, the undecimal quartertone, and~~ [[16/15]]~~, the classic diatonic semitone. It is also the difference between the~~ [[~~rastma~~]] and ~~the~~ [[~~schisma~~]].

It factors into simpler commas as ([[4000/3993]])⋅([[5632/5625]]). In the full 11-limit, it is the difference between [[896/891]] and [[385/384]]. In the [[13-limit]] it factors into ([[2080/2079]])⋅([[3584/3575]]). In the [[31-limit]] it factors into ([[496/495]])⋅([[1024/1023]]) or ([[961/960]])⋅(1024/1023)<sup>2</sup> and gives rise to its identity as a [[lopsided comma]] of [[S-expression]] S31⋅S32<sup>2</sup>.

In the full 11-limit, ~~it is~~ the ~~difference between~~ [[~~896/891~~]] ~~and~~ [[~~385/384~~]].

== Temperaments ==

[[Tempering out]] this comma in the full 11-limit leads to the rank-4 '''semiporwellismic''' temperament (→ [[Rank-4 temperament #Semiporwellismic (16384/16335)]]), or in the [[2.3.5.11 subgroup]], the rank-3 [[semiporwellic]] temperament.

~~== Temperaments ==~~

Tempering out both 4000/3993 and 5632/5625 leads to the rank-2 [[escapade]] temperament, which does little damage to semiporwellic.

Tempering it out ~~in the full 11-limit~~ leads to the rank-~~4 semiporwellismic temperament (→~~ [[~~Rank-4 temperament #Semiporwellismic (16384/16335)~~]]), ~~or in the 2.3.5.11 subgroup, the rank-3~~ semiporwellic ~~temperament~~. See [[Semiporwellismic clan]] for ~~extensions~~ of ~~semiporwellic~~.

See [[Semiporwellismic clan]] for the [[clan]] of rank-3 temperaments where it is tempered out.

== Etymology ==

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[[Category:Semiporwellismic]]

[[Category:Commas named by combining multiple temperament names]]

[[Category:Commas named after ~~individuals~~]] ~~~~

[[Category:Commas named after other creatives]]

[[Category:Commas named after compositions]]

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+The '''semiporwellisma''' ([[ratio]]: 16384/16335, {{monzo|legend=1| 14 -3 -1 0 -2 }}) is a [[small comma|small]] [[11-limit]] [[comma]] measuring about 5.19 [[cent]]s, named for it is one of the commas tempered out in the [[semiporwell]] temperament. It is the difference between two instances of [[33/32]], the undecimal quartertone, and [[16/15]], the classical diatonic semitone. It is also the difference between the [[rastma]] and the [[schisma]].
-The '''semiporwellisma''', 16384/16335 = {{monzo| 14 -3 -1 0 -2 }} is a [[Small comma|small]] [[11-limit]] [[comma]] measuring about 5.19 [[cent]]s, named for it is one of the commas tempered out in the [[semiporwell]] temperament. It is the difference between two instances of [[33/32]], the undecimal quartertone, and [[16/15]], the classic diatonic semitone. It is also the difference between the [[rastma]] and the [[schisma]].
+It factors into simpler commas as ([[4000/3993]])⋅([[5632/5625]]). In the full 11-limit, it is the difference between [[896/891]] and [[385/384]]. In the [[13-limit]] it factors into ([[2080/2079]])⋅([[3584/3575]]). In the [[31-limit]] it factors into ([[496/495]])⋅([[1024/1023]]) or ([[961/960]])⋅(1024/1023)<sup>2</sup> and gives rise to its identity as a [[lopsided comma]] of [[S-expression]] S31⋅S32<sup>2</sup>.
-In the full 11-limit, it is the difference between [[896/891]] and [[385/384]].
+== Temperaments ==
+[[Tempering out]] this comma in the full 11-limit leads to the rank-4 '''semiporwellismic''' temperament (→ [[Rank-4 temperament #Semiporwellismic (16384/16335)]]), or in the [[2.3.5.11 subgroup]], the rank-3 [[semiporwellic]] temperament.
-== Temperaments ==
+Tempering out both 4000/3993 and 5632/5625 leads to the rank-2 [[escapade]] temperament, which does little damage to semiporwellic.
-Tempering it out in the full 11-limit leads to the rank-4 semiporwellismic temperament (→ [[Rank-4 temperament #Semiporwellismic (16384/16335)]]), or in the 2.3.5.11 subgroup, the rank-3 semiporwellic temperament. See [[Semiporwellismic clan]] for extensions of semiporwellic.
+See [[Semiporwellismic clan]] for the [[clan]] of rank-3 temperaments where it is tempered out.
 == Etymology ==
@@ Line 18: / Line 21: @@
 [[Category:Semiporwellismic]]
 [[Category:Commas named by combining multiple temperament names]]
-[[Category:Commas named after individuals]] <!-- after George Orwell -->
+[[Category:Commas named after other creatives]]
 [[Category:Commas named after compositions]]