Cathartic comma: Difference between revisions

(5 intermediate revisions by 2 users not shown)

Line 1:

{{Infobox Interval

| Ratio = 4802000/4782969

| Name = ~~canousma~~

| Name = carthartic comma

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

| Comma = yes

}}

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~~''' ({{monzo|legend=1| 4 -14 3 4 }}, [[ratio]]: ~~4802000~~/~~4782969~~) is a [[7-limit]] [[comma]] measuring about 6.9 [[cent]]s. It is ~~notable as~~ the amount by which a stack ~~consisting~~ of ~~[[112/81]] and~~ three instances of [[35/27]] ~~exceeds a~~ [[~~perfect twelfth~~]]. It is also the interval separating the [[81/80|syntonic comma (81/80)]] from a stack of two [[245/243|sensamagic commas (245/243)]].

== Temperaments ==

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]].

[[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]].

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

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.

== Etymology ==

This comma was named by [[Flora Canou]] in 2020 after herself.

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.

~~== See also ==~~

* [[~~Small comma~~]]

[[Category:~~Canou~~]]

[[Category:Cathartic]]

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

@@ Line 1: / Line 1: @@
 {{Infobox Interval
 | Ratio = 4802000/4782969
-| Name = canousma
+| Name = carthartic comma
 | Color name = sz<sup>4</sup>y<sup>3</sup>3, saquadzo-atriyo 3rd
 | Comma = yes
 }}
+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''' ({{monzo|legend=1| 4 -14 3 4 }}, [[ratio]]: 4802000/4782969) is a [[7-limit]] [[comma]] measuring about 6.9 [[cent]]s. It is notable as the amount by which a stack consisting of [[112/81]] and three instances of [[35/27]] exceeds a [[perfect twelfth]].  It is also the interval separating the [[81/80|syntonic comma (81/80)]] from a stack of two [[245/243|sensamagic commas (245/243)]].
 == Temperaments ==
-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]].
+[[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]].
-See [[Canou family]] for the rank-3 family where it is tempered out. See [[Canousmic temperaments]] for a collection of rank-2 temperaments where it is tempered out.
+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.
 == Etymology ==
-This comma was named by [[Flora Canou]] in 2020 after herself.
+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.
-== See also ==
-* [[Small comma]]
-[[Category:Canou]]
+[[Category:Cathartic]]
+[[Category:Commas named for their regular temperament properties]]