Cathartic comma: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Ratio = 4802000/4782969

~~| Monzo = 4 -14 3 4~~

| Name = carthartic comma

~~| Cents = 6.8748~~

| Color name = sz<sup>4</sup>y<sup>3</sup>3, saquadzo-atriyo 3rd

| Name = ~~canousma~~

| Comma = yes

| Color name =

| ~~FJS name =~~

~~| Sound~~ =

}}

The '''cathartic comma''' (formerly ''canousma'', {{monzo|legend=1| 4 -14 3 4 }}, [[ratio]]: {{nowrap| 4 802 000 / 4 782 969 }}) is a [[small comma|small]] [[7-limit]] [[comma]] measuring about 6.9 [[cent]]s. It is the amount by which a stack of three instances of [[81/70]] falls short of [[14/9]]. It is also the interval separating the [[81/80|syntonic comma (81/80)]] from a stack of two [[245/243|sensamagic commas (245/243)]].

~~The '''canousma''', 4802000/4782969~~ = ~~{{monzo|4~~ -14 3 ~~4}} is a~~ [[~~7-limit~~]] [[~~comma~~]] ~~measuring about 6.9 cents~~. It is ~~the difference between the~~ [[81/80|~~syntonic comma (81~~/~~80)~~]] and ~~a stack of two~~ [[~~245~~/~~243|sensamagic commas~~ (~~245/243~~)]].

== Temperaments ==

[[Tempering out]] this comma leads to the rank-3 [[cathartic]] temperament, which splits the syntonic comma into two equal parts, each representing 245/243. It also splits [[5/4]] (classic major third) into two equal parts, each representing 2450/2187~2187/1960. It is similar to [[3136/3125|hemimean]] in that regard. Tempering out both equates 245/243 with [[126/125]] (septimal semicomma) and [[225/224]] (septimal kleisma) leads to [[parakleismic]].

~~== Temperament ==~~

See [[Cathartic family]] for the rank-3 family where it is tempered out. See [[Cathartic temperaments]] for a collection of rank-2 temperaments where it is tempered out.

~~Tempering it out leads to the~~ [[~~canou~~ family]] of rank-3 ~~temperaments, which splits the syntonic comma into two equal parts, each representing 245/243~~. ~~It also splits~~ [[~~5/4~~]] ~~(classic major third) into two equal parts, each representing 2450/2187~2187/1960. It~~ is ~~similar to [[3136/3125|hemimean]] in that regard. Tempering~~ out ~~both equates 245/243 with [[126/125]] (septimal semicomma) and [[225/224]] (septimal kleisma) leads to [[parakleismic]]~~.

== ~~See also~~ ==

== Etymology ==

* [[Canou ~~family~~]], the ~~rank-3 family where it is tempered out~~

This comma was first named by [[Flora Canou]] as ''canousma'' in 2020 after herself. In 2026, she disavowed that name and came up with the current name as a replacement, from the feeling she associated with the interval [[28/27]], which had the role of a basic building block in the corresponding temperament.

* [[~~Canousmic temperaments~~]], a ~~collection of rank-2 temperaments where it is tempered out~~

* [[Small comma]]

[[Category:~~7-limit~~]]

[[Category:Cathartic]]

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

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

~~[[Category:Canou~~]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
 | Ratio = 4802000/4782969
-| Monzo = 4 -14 3 4
+| Name = carthartic comma
-| Cents = 6.8748
+| Color name = sz<sup>4</sup>y<sup>3</sup>3, saquadzo-atriyo 3rd
-| Name = canousma
+| Comma = yes
-| Color name =
-| FJS name =
-| Sound =
 }}
+The '''cathartic comma''' (formerly ''canousma'', {{monzo|legend=1| 4 -14 3 4 }}, [[ratio]]: {{nowrap| 4 802 000 / 4 782 969 }}) is a [[small comma|small]] [[7-limit]] [[comma]] measuring about 6.9 [[cent]]s. It is the amount by which a stack of three instances of [[81/70]] falls short of [[14/9]]. It is also the interval separating the [[81/80|syntonic comma (81/80)]] from a stack of two [[245/243|sensamagic commas (245/243)]].
-The '''canousma''', 4802000/4782969 = {{monzo|4 -14 3 4}} is a [[7-limit]] [[comma]] measuring about 6.9 cents. It is the difference between the [[81/80|syntonic comma (81/80)]] and a stack of two [[245/243|sensamagic commas (245/243)]].
+== Temperaments ==
+[[Tempering out]] this comma leads to the rank-3 [[cathartic]] temperament, which splits the syntonic comma into two equal parts, each representing 245/243. It also splits [[5/4]] (classic major third) into two equal parts, each representing 2450/2187~2187/1960. It is similar to [[3136/3125|hemimean]] in that regard. Tempering out both equates 245/243 with [[126/125]] (septimal semicomma) and [[225/224]] (septimal kleisma) leads to [[parakleismic]].
-== Temperament ==
+See [[Cathartic family]] for the rank-3 family where it is tempered out. See [[Cathartic temperaments]] for a collection of rank-2 temperaments where it is tempered out.
-Tempering it out leads to the [[canou family]] of rank-3 temperaments, which splits the syntonic comma into two equal parts, each representing 245/243. It also splits [[5/4]] (classic major third) into two equal parts, each representing 2450/2187~2187/1960. It is similar to [[3136/3125|hemimean]] in that regard. Tempering out both equates 245/243 with [[126/125]] (septimal semicomma) and [[225/224]] (septimal kleisma) leads to [[parakleismic]].
-== See also ==
+== Etymology ==
-* [[Canou family]], the rank-3 family where it is tempered out
+This comma was first named by [[Flora Canou]] as ''canousma'' in 2020 after herself. In 2026, she disavowed that name and came up with the current name as a replacement, from the feeling she associated with the interval [[28/27]], which had the role of a basic building block in the corresponding temperament.
-* [[Canousmic temperaments]], a collection of rank-2 temperaments where it is tempered out
-* [[Small comma]]
-[[Category:7-limit]]
+[[Category:Cathartic]]
-[[Category:Small comma]]
+[[Category:Commas named for their regular temperament properties]]
-[[Category:Canou]]