Cathartic comma: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 4802000/4782969 | | Ratio = 4802000/4782969 | ||
| Name = | | Name = carthartic comma | ||
| Color name = sz<sup>4</sup>y<sup>3</sup>3, saquadzo-atriyo 3rd | | Color name = sz<sup>4</sup>y<sup>3</sup>3, saquadzo-atriyo 3rd | ||
| Comma = yes | | 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 ''' | |||
== Temperaments == | == Temperaments == | ||
Tempering | [[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 [[ | 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 == | == 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. | ||
[[Category: | [[Category:Cathartic]] | ||
[[Category:Commas named | [[Category:Commas named for their regular temperament properties]] | ||
Latest revision as of 12:42, 10 August 2026
| Interval information |
The cathartic comma (formerly canousma, monzo: [4 -14 3 4⟩, ratio: 4 802 000 / 4 782 969) is a small 7-limit comma measuring about 6.9 cents. 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 syntonic comma (81/80) from a stack of two 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 hemimean in that regard. Tempering out both equates 245/243 with 126/125 (septimal semicomma) and 225/224 (septimal kleisma) leads to parakleismic.
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 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.