Semicathartisma

The semicathartisma (formerly semicanousma, monzo: [-2 -6 -1 0 4⟩, ratio: 14641/14580) is a small 11-limit comma measuring about 7.23 cents. It is the amount by which a stack of four Alpharabian artoneutral thirds (11/9) exceeds the ptolemaic major ninth (20/9). It is also the difference between 121/120 (biyatisma) and 243/242 (rastma).

Interval information

Ratio	14641/14580
Factorization	2-2 × 3-6 × 5-1 × 114
Monzo	[-2 -6 -1 0 4⟩
Size in cents	7.22805¢
Name	semicathartisma
Color name	1o4g1, quadlo-agu unison
FJS name	[math]\displaystyle{ \text{dd1}^{11,11,11,11}_{5} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	27.6694
Weil norm (log2 max(n, d))	27.6755
Wilson norm (sopfr(nd))	71
Comma size	small
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Temperaments

Tempering out this comma in the 11-limit leads to the rank-4 semicathartismic 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 cathartic comma. 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 Semicathartismic clan for the clan of rank-3 temperaments where it is tempered out.

Etymology

This comma was first named by Flora Canou as semicanousma in 2020, for the fact that it is one of the commas tempered out in the semicanou (now semicathart) temperament. In 2026, she disavowed that name and came up with the current name as a replacement, following the rename of semicanou to semicathart.