Semiporwellisma

Interval information

Ratio	16384/16335
Factorization	214 × 3-3 × 5-1 × 11-2
Monzo	[14 -3 -1 0 -2⟩
Size in cents	5.185399¢
Name	semiporwellisma
Color name	s1uug2, Salulugu comma
FJS name	[math]\displaystyle{ \text{m2}_{5,11,11} }[/math]
Special properties	reduced, reduced subharmonic
Tenney norm (log2 nd)	27.9957
Weil norm (log2 max(n, d))	28
Wilson norm (sopfr(nd))	64
Comma size	small
S-expression	S31⋅S322
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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.