Semiporwellisma
Ratio | 16384/16335 |
Factorization | 2^{14} × 3^{-3} × 5^{-1} × 11^{-2} |
Monzo | [14 -3 -1 0 -2⟩ |
Size in cents | 5.1853988¢ |
Name | semiporwellisma |
Color name | s1uug2, Salulugu comma |
FJS name | [math]\text{m2}_{5,11,11}[/math] |
Special properties | reduced |
Tenney height (log_{2} nd) | 27.9957 |
Weil height (log_{2} max(n, d)) | 28 |
Wilson height (sopfr (nd)) | 64 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.44606 bits |
Comma size | small |
S-expression | S31 * S32^{2} |
open this interval in xen-calc |
The semiporwellisma, 16384/16335 = [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 classic 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.
Temperaments
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.
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.