Cataharry comma - Revision history

BudjarnLambeth at 02:23, 4 November 2024

2024-11-04T02:23:20Z

← Older revision		Revision as of 02:23, 4 November 2024
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	[[Category:Cataharry]]		[[Category:Cataharry]]
	[[Category:Commas named by combining multiple temperament names]]		[[Category:Commas named by combining multiple temperament names]]
	[[Category:Commas named after ~~individuals~~]]		[[Category:Commas named after composers]]
			[[Category:Commas named after music theorists]]

BudjarnLambeth at 13:04, 3 November 2024

2024-11-03T13:04:37Z

← Older revision		Revision as of 13:04, 3 November 2024
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	[[Category:Cataharry]]		[[Category:Cataharry]]
	[[Category:Commas named ~~for their regular~~ temperament ~~properties~~]]		[[Category:Commas named by combining multiple temperament names]]
	[[Category:Commas named after individuals]]		[[Category:Commas named after individuals]]

BudjarnLambeth at 12:48, 3 November 2024

2024-11-03T12:48:08Z

← Older revision		Revision as of 12:48, 3 November 2024
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	[[Category:Cataharry]]		[[Category:Cataharry]]
			[[Category:Commas named for their regular temperament properties]]
			[[Category:Commas named after individuals]]

FloraC: Expansion

2024-01-02T11:49:40Z

Expansion

← Older revision		Revision as of 11:49, 2 January 2024
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	}}		}}

	The '''cataharry comma''' (~~'''~~19683/19600~~'''~~) is a [[7-limit]] [[comma]] measuring about 6.1 ~~cents~~. 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]].		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 ~~family~~]] ~~of temperaments~~, which splits the [[4/3\|just perfect fourth (4/3)]] into two exact hemifourths, each representing 81/70~280/243.		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.

	== ~~See also~~ ==		== Etymology ==
	* [[~~Cataharry family~~]]~~, the rank-3 family where it is tempered out~~		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>.
	* [[~~Cataharry temperaments~~]]~~, a collection of rank-2 temperaments where it is tempered out~~
	* [[~~Small~~ comma]]		== Notes ==

	[[Category:Cataharry]]		[[Category:Cataharry]]

TallKite: added color name

2022-12-29T03:00:15Z

added color name

← Older revision		Revision as of 03:00, 29 December 2022
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	\| Ratio = 19683/19600		\| Ratio = 19683/19600
	\| Name = cataharry comma		\| Name = cataharry comma
			\| Color name = Lrrgg-2, Labirugu comma
	\| Comma = yes		\| Comma = yes
	}}		}}

Plumtree: Normalising usage of Infobox Interval

2022-10-25T17:30:39Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 17:30, 25 October 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Icon =~~
	\| Ratio = 19683/19600		\| Ratio = 19683/19600
	~~\| Monzo = -4 9 -2 -2~~
	~~\| Cents = 7.31577~~
	\| Name = cataharry comma		\| Name = cataharry comma
	\| ~~Color name =~~		\| Comma = yes
	~~\| FJS name =~~
	~~\| Sound~~ =
	}}		}}

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	* [[Small comma]]		* [[Small comma]]

	~~[[Category:7-limit]]~~
	~~[[Category:Small commas]]~~
	[[Category:Cataharry]]		[[Category:Cataharry]]

Fredg999 category edits: Moving from Category:Small comma to Category:Small commas using Cat-a-lot

2022-03-20T21:59:58Z

Moving from Category:Small comma to Category:Small commas using Cat-a-lot

← Older revision		Revision as of 21:59, 20 March 2022
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	[[Category:7-limit]]		[[Category:7-limit]]
	[[Category:Small ~~comma~~]]		[[Category:Small commas]]
	[[Category:Cataharry]]		[[Category:Cataharry]]

Godtone: explanation of meaning

2021-11-09T15:09:57Z

explanation of meaning

← Older revision		Revision as of 15:09, 9 November 2021
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	}}		}}

	The '''cataharry comma''' ('''19683/19600''') is a [[7-limit]] [[comma]] measuring about 6.1 cents. It is the difference between the [[81/70\|septimal ultramajor second (81/70)]] and its [[fourth complement]]. In terms of commas, it is the ~~difference between~~ [[81/80]] and [[~~245~~/~~243~~]].		The '''cataharry comma''' ('''19683/19600''') is a [[7-limit]] [[comma]] measuring about 6.1 cents. 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 ==

Aura: placed a link for "fourth complement", as this concept will hopefully be fleshed out

2021-06-06T19:22:26Z

placed a link for "fourth complement", as this concept will hopefully be fleshed out

← Older revision		Revision as of 19:22, 6 June 2021
Line 10:		Line 10:
	}}		}}

	The '''cataharry comma''' ('''19683/19600''') is a [[7-limit]] [[comma]] measuring about 6.1 cents. It is the difference between the [[81/70\|septimal ultramajor second (81/70)]] and its fourth complement. In terms of commas, it is the difference between [[81/80]] and [[245/243]].		The '''cataharry comma''' ('''19683/19600''') is a [[7-limit]] [[comma]] measuring about 6.1 cents. It is the difference between the [[81/70\|septimal ultramajor second (81/70)]] and its [[fourth complement]]. In terms of commas, it is the difference between [[81/80]] and [[245/243]].

	== Temperaments ==		== Temperaments ==

FloraC: Created page with "{{Infobox Interval | Icon = | Ratio = 19683/19600 | Monzo = -4 9 -2 -2 | Cents = 7.31577 | Name = cataharry comma | Color name = | FJS name = | Sound = }} The '''cataharry..."

2021-06-06T12:09:23Z

Created page with "{{Infobox Interval | Icon = | Ratio = 19683/19600 | Monzo = -4 9 -2 -2 | Cents = 7.31577 | Name = cataharry comma | Color name = | FJS name = | Sound = }} The '''cataharry..."

New page

{{Infobox Interval
| Icon =
| Ratio = 19683/19600
| Monzo = -4 9 -2 -2
| Cents = 7.31577
| Name = cataharry comma
| Color name =
| FJS name =
| Sound =
}}

The '''cataharry comma''' ('''19683/19600''') is a [[7-limit]] [[comma]] measuring about 6.1 cents. It is the difference between the [[81/70|septimal ultramajor second (81/70)]] and its fourth complement. In terms of commas, it is the difference between [[81/80]] and [[245/243]].

== Temperaments ==
Tempering out this comma leads to the rank-3 [[cataharry family]] of temperaments, which splits the [[4/3|just perfect fourth (4/3)]] into two exact hemifourths, each representing 81/70~280/243.

== See also ==
* [[Cataharry family]], the rank-3 family where it is tempered out
* [[Cataharry temperaments]], a collection of rank-2 temperaments where it is tempered out
* [[Small comma]]

[[Category:7-limit]]
[[Category:Small comma]]
[[Category:Cataharry]]