Semicathartisma: Difference between revisions

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{{Infobox Interval

| Ratio = 14641/14580

~~| Monzo = -2 -6 -1 0 4~~

| Name = semicathartisma

~~| Cents = 7.2281~~

| Color name = 1o<sup>4</sup>g1, quadlo-agu unison

| Name = ~~semicanousma~~

| Comma = yes

| Color name =

| ~~FJS name =~~

~~| Sound~~ =

}}

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).

~~The '''semicanousma''', 14641/14580~~ = ~~{{monzo|~~ -2 -~~6 -1 0~~ 4 ~~}}, is an~~ [[~~11-limit~~]] [[comma]] ~~measuring about 7.2~~ [[~~cent~~]]~~s, named for it is one of the commas tempered out in the~~ [[~~semicanou~~]] ~~temperament~~. It ~~is 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]].

~~== Temperaments ==~~

See [[Semicathartismic clan]] for the clan of rank-3 temperaments where it is tempered out.

~~Tempering it out leads to the rank-4 '''semicanousmic temperament''', which splits the~~ [[~~81/80|syntonic comma~~]] ~~into two equal parts, each representing 121/120~243/242, so it can be said to be~~ the ~~undecimal counterpart~~ of ~~both [[3136/3125|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~~ ==

== Etymology ==

* [[~~Rank-4 temperament #Semicanousmic (14641/14580)]]~~

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''.

* [[Semicanousmic temperaments]], ~~a collection of rank-3 temperament where~~ it is tempered out

* [[~~Small comma~~]]

[[Category:~~11-limit~~]]

[[Category:Semicathartismic]]

[[Category:~~Small comma]]~~

[[Category:Commas named for their regular temperament properties]]

~~[[Category:Semicanousmic~~]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
 | Ratio = 14641/14580
-| Monzo = -2 -6 -1 0 4
+| Name = semicathartisma
-| Cents = 7.2281
+| Color name = 1o<sup>4</sup>g1, quadlo-agu unison
-| Name = semicanousma
+| Comma = yes
-| Color name =
-| FJS name =
-| Sound =
 }}
+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).
-The '''semicanousma''', 14641/14580 = {{monzo| -2 -6 -1 0 4 }}, is an [[11-limit]] [[comma]] measuring about 7.2 [[cent]]s, named for it is one of the commas tempered out in the [[semicanou]] temperament. It is 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]].
-== Temperaments ==
+See [[Semicathartismic clan]] for the clan of rank-3 temperaments where it is tempered out.
-Tempering it out leads to the rank-4 '''semicanousmic temperament''', which splits the [[81/80|syntonic comma]] into two equal parts, each representing 121/120~243/242, so it can be said to be the undecimal counterpart of both [[3136/3125|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 ==
+== Etymology ==
-* [[Rank-4 temperament #Semicanousmic (14641/14580)]]
+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''.
-* [[Semicanousmic temperaments]], a collection of rank-3 temperament where it is tempered out
-* [[Small comma]]
-[[Category:11-limit]]
+[[Category:Semicathartismic]]
-[[Category:Small comma]]
+[[Category:Commas named for their regular temperament properties]]
-[[Category:Semicanousmic]]