Semicathartisma: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 14641/14580 | | Ratio = 14641/14580 | ||
| Name = | | Name = semicathartisma | ||
| Color name = 1o<sup>4</sup>g1, quadlo-agu unison | | Color name = 1o<sup>4</sup>g1, quadlo-agu unison | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
The '''semicathartisma''' (formerly ''semicanousma'', {{monzo|legend=1| -2 -6 -1 0 4 }}, [[ratio]]: 14641/14580) is a [[small comma|small]] [[11-limit]] [[comma]] measuring about 7.23 [[cent]]s. It is the amount by which a stack of four [[11/9|Alpharabian artoneutral thirds (11/9)]] exceeds the [[20/9|ptolemaic major ninth (20/9)]]. It is also the difference between [[121/120]] (biyatisma) and [[243/242]] (rastma). | |||
== Temperaments == | |||
[[Tempering out]] this comma in the 11-limit leads to the rank-4 [[semicathartismic]] temperament, which splits the [[81/80|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 [[3136/3125|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''. | |||
[[Category: | [[Category:Semicathartismic]] | ||
[[Category:Commas named | [[Category:Commas named for their regular temperament properties]] | ||
Latest revision as of 12:43, 10 August 2026
| Interval information |
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).
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.