Semicanousma
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Ratio | 14641/14580 |
Factorization | 2^{-2} × 3^{-6} × 5^{-1} × 11^{4} |
Monzo | [-2 -6 -1 0 4⟩ |
Size in cents | 7.2280504¢ |
Name | semicanousma |
Color name | 1o^{4}g1, quadlo-agu unison |
FJS name | [math]\text{dd1}^{11,11,11,11}_{5}[/math] |
Special properties | reduced |
Tenney height (log_{2} nd) | 27.6694 |
Weil height (log_{2} max(n, d)) | 27.6755 |
Wilson height (sopfr (nd)) | 71 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.67269 bits |
Comma size | small |
open this interval in xen-calc |
The semicanousma, 14641/14580 = [-2 -6 -1 0 4⟩, is an 11-limit comma measuring about 7.2 cents, named for the fact that it is one of the commas tempered out in the semicanou temperament. It is the amount by which a stack of four Alpharabian artoneutral thirds (11/9) exceeds the ptolemaic ninth (20/9). It is also the difference between 121/120 (biyatisma) and 243/242 (rastma).
Temperaments
Tempering it out leads to the rank-4 semicanousmic temperament, which splits the syntonic comma into two equal parts, each representing 121/120~243/242, so the comma can be said to be the undecimal counterpart of both hemimean and canousma. It also identifies 20/11 by three 11/9's stacked, so an octave is divided into 11/9-11/9-11/9-11/10.
See also
- Rank-4 temperament #Semicanousmic (14641/14580)
- Semicanousmic clan, the clan of rank-3 temperaments where it is tempered out
- Small comma