Cataharry comma: Difference between revisions
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The '''cataharry comma''' ( | The '''cataharry comma''' ([[ratio]]: 19683/19600, {{monzo|legend=1| -4 9 -2 -2 }}) is a [[small comma|small]] [[7-limit]] [[comma]] measuring about 6.1 [[cent]]s. It is the difference between the [[81/70|septimal ultramajor second (81/70)]] and its [[fourth complement]]. In terms of commas, it is equal to ([[81/80]])/([[245/243]]) and to ([[81/80]])<sup>2</sup>/([[49/48]]). The latter equivalence implies that if the cataharry comma is tempered out and if neither [[81/80]] nor [[49/48]] are tempered out, there will be an interval ~[[81/80]] above [[8/7]] and ~[[81/80]] below [[7/6]], and analogously for [[12/7]] and [[7/4]]. | ||
== Temperaments == | == Temperaments == | ||
Tempering out this comma leads to the rank-3 [[cataharry | Tempering out this comma leads to the rank-3 [[cataharry]] temperament, which splits the [[4/3|just perfect fourth (4/3)]] into two exact hemifourths, each representing 81/70~280/243. See [[Cataharry family]] for the rank-3 family where it is tempered out. See [[Cataharry temperaments]] for a collection of rank-2 temperaments where it is tempered out. | ||
== | == Etymology == | ||
The name ''cataharry'' was given by [[Gene Ward Smith]] in 2005 as a contraction of ''[[catakleismic]]'' and ''[[harry]]''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12900.html Yahoo! Tuning Group | ''Seven limit comma names from pairs of temperament names'']</ref>. | |||
== Notes == | |||
[[Category:Cataharry]] | [[Category:Cataharry]] | ||
Revision as of 11:49, 2 January 2024
| Interval information |
The cataharry comma (ratio: 19683/19600, monzo: [-4 9 -2 -2⟩) is a small 7-limit comma measuring about 6.1 cents. It is the difference between the septimal ultramajor second (81/70) and its fourth complement. In terms of commas, it is equal to (81/80)/(245/243) and to (81/80)2/(49/48). The latter equivalence implies that if the cataharry comma is tempered out and if neither 81/80 nor 49/48 are tempered out, there will be an interval ~81/80 above 8/7 and ~81/80 below 7/6, and analogously for 12/7 and 7/4.
Temperaments
Tempering out this comma leads to the rank-3 cataharry temperament, which splits the just perfect fourth (4/3) into two exact hemifourths, each representing 81/70~280/243. See Cataharry family for the rank-3 family where it is tempered out. See Cataharry temperaments for a collection of rank-2 temperaments where it is tempered out.
Etymology
The name cataharry was given by Gene Ward Smith in 2005 as a contraction of catakleismic and harry[1].