Semiporwellisma: Difference between revisions
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The '''semiporwellisma''' | 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]]. | ||
In the full 11-limit, it is the difference between [[896/891]] and [[385/384]]. | 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 the [[S-expression]] S31⋅S32<sup>2</sup>. | ||
== Temperaments == | == Temperaments == | ||
Tempering | [[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. | ||
See [[Semiporwellismic clan]] for the [[clan]] of rank-3 temperaments where it is tempered out. | |||
== Etymology == | == Etymology == | ||
Latest revision as of 09:49, 17 June 2026
| Interval information |
reduced subharmonic
The semiporwellisma (ratio: 16384/16335, monzo: [14 -3 -1 0 -2⟩) is a small 11-limit comma measuring about 5.19 cents, 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.
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)2 and gives rise to the S-expression S31⋅S322.
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.
See Semiporwellismic clan for the clan of rank-3 temperaments where it is tempered out.
Etymology
This comma was named by Flora Canou in 2021 after the semiporwell temperament, which in turn derives from porwell, the 7-limit comma shared by porcupine and orwell.