Garischisma - Revision history

TallKite: updated the comma color name

2026-04-29T04:10:51Z

updated the comma color name

← Older revision		Revision as of 04:10, 29 April 2026
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	\| Ratio = 33554432/33480783		\| Ratio = 33554432/33480783
	\| Name = garischisma, septimal schisma		\| Name = garischisma, septimal schisma
	\| Color name = ssr2, sasaru 2nd,<br>~~Sasaru comma~~		\| Color name = ssr2, sasaru 2nd,<br>ssrM, sasaruma
	\| Comma = yes		\| Comma = yes
	}}		}}

FloraC: Restore some lost details. These lists aren't clearer than prose.

2026-04-11T21:15:31Z

Restore some lost details. These lists aren't clearer than prose.

← Older revision		Revision as of 21:15, 11 April 2026
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	}}		}}

	The '''garischisma''' or '''septimal schisma''' is a very [[small comma\|small]] [[7-limit]] [[comma]] measuring about 3.80 [[cent]]s. It is ~~most well known as~~ the difference between the [[~~pythagorean~~ comma]] and the [[64/63\|septimal ~~comma~~]]. It is also the difference the ~~difference between:~~		The '''garischisma''' or '''septimal schisma''' is a very [[small comma\|small]] [[7-limit]] [[comma]] measuring about 3.80 [[cent]]s. It can be considered the septimal counterpart of the [[schisma]]: whereas the schisma is the difference between the [[Pythagorean comma]] and the [[syntonic comma]], the garischisma is the difference between the [[septimal comma]] and the Pythagorean comma. Equivalently, it can be described as the amount by which a stack of two [[2187/2048\|apotomes]] falls short of a [[8/7\|septimal whole tone]]. It is also the difference between the [[aberschisma]] and the schisma in the full 7-limit.

	* [[~~8/7]] and 2 [[2187/2048~~\|~~apotomes]]~~		It factors into the following [[11-limit\|11-]] and [[13-limit]] commas:
	* The [[hemifamity comma]] and ~~the~~ [[~~schisma~~]]		* The [[19712/19683\|symbiotic comma]] and [[131072/130977\|olympia]];
			* The [[wilschisma]] and the [[minisma]].
	~~It also factors into the following higher limit~~ commas:

	* The [[19712/19683\|symbiotic comma]] and [[131072/130977\|olympia]]
	* The [[wilschisma]] and the [[minisma]]

	== Temperaments ==		== Temperaments ==
	Tempering out this comma in the full 7-limit leads to the rank-3 '''garischismic ~~temperament~~''', or in the 2.3.7 subgroup, the rank-2 '''gary ~~temperament~~'''. See [[Garischismic family]] for the [[~~Temperament~~ families and clans\|family]] of rank-3 temperaments where it is tempered out. See [[Garischismic clan]] for the [[~~Temperament~~ families and clans\|clan]] of rank-2 temperaments where it is tempered out.		[[Tempering out]] this comma in the full 7-limit leads to the rank-3 '''garischismic''' temperament, or in the [[2.3.7 subgroup]], the rank-2 '''gary''' temperament. See [[Garischismic family]] for the [[temperament families and clans\|family]] of rank-3 temperaments where it is tempered out. See [[Garischismic clan]] for the [[temperament families and clans\|clan]] of rank-2 temperaments where it is tempered out.

	== Etymology ==		== Etymology ==
	Its name comes from the temperament [[garibaldi]] and the schisma, as it is a similarly sized interval that alongside it, defines garibaldi.		Its name comes from the temperament [[garibaldi]] and the schisma, as it is a similarly sized interval that alongside it, defines garibaldi.

	[[Category:Garischismic]]		[[Category:Garischismic]]
	[[Category:Commas named by combining multiple temperament names]]		[[Category:Commas named by combining multiple temperament names]]

Eufalesio: hotfixes!

2026-04-11T20:13:38Z

hotfixes!

← Older revision		Revision as of 20:13, 11 April 2026
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	}}		}}

	The '''garischisma''' or '''septimal schisma''' is a very [[small comma\|small]] [[7-limit]] [[comma]] measuring about 3.80 [[cent]]s. It is most well known as the difference between the ~~Pythagorean~~ comma and the [[64/63\|septimal comma]]. It is also the difference the difference between:		The '''garischisma''' or '''septimal schisma''' is a very [[small comma\|small]] [[7-limit]] [[comma]] measuring about 3.80 [[cent]]s. It is most well known as the difference between the [[pythagorean comma]] and the [[64/63\|septimal comma]]. It is also the difference the difference between:

	* [[8/7]] and 2 [[2187/2048\|apotomes]]		* [[8/7]] and 2 [[2187/2048\|apotomes]]

Eufalesio: Formatted and added extra things

2026-04-11T20:13:13Z

Formatted and added extra things

← Older revision		Revision as of 20:13, 11 April 2026
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	}}		}}

	The '''garischisma''' or '''septimal schisma''' is a [[small comma\|small]] [[7-limit]] [[comma]] measuring about 3.80 [[cent]]s. ~~While the [[schisma]] is the difference between the [[Pythagorean comma]] and the [[81/80\|syntonic comma]], the garischisma, in contrast,~~ is the difference between the Pythagorean comma and the [[64/63\|septimal comma]]. It ~~can~~ also ~~be described as~~ the difference between ~~the [[8/7\|septimal whole tone]] and a stack of two [[2187/2048\|apotomes]].~~		The '''garischisma''' or '''septimal schisma''' is a very [[small comma\|small]] [[7-limit]] [[comma]] measuring about 3.80 [[cent]]s. It is most well known as the difference between the Pythagorean comma and the [[64/63\|septimal comma]]. It is also the difference the difference between:

	In the ~~11-limit, it~~ factors into ~~simpler~~ commas ~~as (~~[[19712/19683]])([[131072/130977]]).		* [[8/7]] and 2 [[2187/2048\|apotomes]]
			* The [[hemifamity comma]] and the [[schisma]]

			It also factors into the following higher limit commas:

			* The [[19712/19683\|symbiotic comma]] and [[131072/130977\|olympia]]
			* The [[wilschisma]] and the [[minisma]]

	== Temperaments ==		== Temperaments ==
	Tempering out this comma in the full 7-limit leads to the rank-3 '''garischismic temperament''', or in the 2.3.7 subgroup, the rank-2 '''gary temperament'''. See [[Garischismic family]] for the [[Temperament families and clans\|family]] of rank-3 temperaments where it is tempered out. See [[Garischismic clan]] for the [[Temperament families and clans\|clan]] of rank-2 temperaments where it is tempered out.		Tempering out this comma in the full 7-limit leads to the rank-3 '''garischismic temperament''', or in the 2.3.7 subgroup, the rank-2 '''gary temperament'''. See [[Garischismic family]] for the [[Temperament families and clans\|family]] of rank-3 temperaments where it is tempered out. See [[Garischismic clan]] for the [[Temperament families and clans\|clan]] of rank-2 temperaments where it is tempered out.

			== Etymology ==
			Its name comes from the temperament [[garibaldi]] and the schisma, as it is a similarly sized interval that alongside it, defines garibaldi.
	[[Category:Garischismic]]		[[Category:Garischismic]]
	[[Category:Commas named by combining multiple temperament names]]		[[Category:Commas named by combining multiple temperament names]]

Xenllium at 12:37, 21 March 2025

2025-03-21T12:37:56Z

← Older revision		Revision as of 12:37, 21 March 2025
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	[[Category:Garischismic]]		[[Category:Garischismic]]
			[[Category:Commas named by combining multiple temperament names]]

FloraC: Expand and update links

2024-04-11T10:13:22Z

Expand and update links

← Older revision		Revision as of 10:13, 11 April 2024
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	}}		}}

	The '''garischisma''' or '''septimal schisma''' is a [[7-limit]] [[comma]] measuring about 3.80 [[cent]]s. While the [[schisma]] is the difference between the [[Pythagorean comma]] and the [[81/80\|syntonic comma]], the garischisma, in contrast, is the difference between the Pythagorean comma and the [[64/63\|septimal comma]]. It can also be described as the difference between the [[8/7\|septimal whole tone]] and a stack of two [[2187/2048\|apotomes]].		The '''garischisma''' or '''septimal schisma''' is a [[small comma\|small]] [[7-limit]] [[comma]] measuring about 3.80 [[cent]]s. While the [[schisma]] is the difference between the [[Pythagorean comma]] and the [[81/80\|syntonic comma]], the garischisma, in contrast, is the difference between the Pythagorean comma and the [[64/63\|septimal comma]]. It can also be described as the difference between the [[8/7\|septimal whole tone]] and a stack of two [[2187/2048\|apotomes]].

			In the 11-limit, it factors into simpler commas as ([[19712/19683]])([[131072/130977]]).

	== Temperaments ==		== Temperaments ==
	Tempering out this comma in the full 7-limit leads to the rank-3 '''garischismic temperament''', or in the 2.3.7 subgroup, the rank-2 '''gary temperament'''. See [[~~Olympic clan #Cassaschismic~~]] for the rank-3 ~~temperament~~. See [[Garischismic clan]] for the [[Temperament families and clans\|clan]] of rank-2 temperaments where it is tempered out.		Tempering out this comma in the full 7-limit leads to the rank-3 '''garischismic temperament''', or in the 2.3.7 subgroup, the rank-2 '''gary temperament'''. See [[Garischismic family]] for the [[Temperament families and clans\|family]] of rank-3 temperaments where it is tempered out. See [[Garischismic clan]] for the [[Temperament families and clans\|clan]] of rank-2 temperaments where it is tempered out.

	~~== See also ==~~
	* [[Small comma]]

	[[Category:Garischismic]]		[[Category:Garischismic]]

FloraC: Cleanup

2023-10-04T05:20:49Z

Cleanup

← Older revision		Revision as of 05:20, 4 October 2023
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	}}		}}

	The '''garischisma''' or '''septimal schisma''' is a [[7-limit]] [[comma]] measuring about 3.80 ~~cents~~. While the [[schisma]] is the difference between the [[Pythagorean comma]] and the [[81/80\|syntonic comma]], the garischisma, in contrast, is the difference between the Pythagorean comma and the [[64/63\|septimal comma]]. It can also be described as the difference between the [[8/7\|septimal whole tone]] and two [[2187/2048\|apotomes]].		The '''garischisma''' or '''septimal schisma''' is a [[7-limit]] [[comma]] measuring about 3.80 [[cent]]s. While the [[schisma]] is the difference between the [[Pythagorean comma]] and the [[81/80\|syntonic comma]], the garischisma, in contrast, is the difference between the Pythagorean comma and the [[64/63\|septimal comma]]. It can also be described as the difference between the [[8/7\|septimal whole tone]] and a stack of two [[2187/2048\|apotomes]].

	== Temperaments ==		== Temperaments ==
	Tempering it out in the full 7-limit leads to the rank-3 '''garischismic temperament'''.		Tempering out this comma in the full 7-limit leads to the rank-3 '''garischismic temperament''', or in the 2.3.7 subgroup, the rank-2 '''gary temperament'''. See [[Olympic clan #Cassaschismic]] for the rank-3 temperament. See [[Garischismic clan]] for the [[Temperament families and clans\|clan]] of rank-2 temperaments where it is tempered out.

	~~=== Garischismic (41 & 53 & 270) ===~~
	~~Subgroup:~~ 2.3.5.7

	[[~~Comma list~~]]~~: 33554432/33480783~~

	[[~~Mapping~~]]: [~~{{val~~\| ~~1 0 0 25 }}, {{val\| 0 1 0 -14 }}, {{val\| 0 0 1 0 }}~~]

	~~[[POTE generator~~]~~]s: ~3/~~2 ~~= 702.2079, ~5/4 = 386~~.~~5100~~

	~~{{Optimal ET sequence\|legend=1\| 12, 29, 41, 53, 94, 164, 176, 217, 229, 270, 593, 863, 1133, 1996d, 2037, 2307, 2900bd, 3170bd, 4303bcd }}~~

	~~[[Badness]]: 1.313 × 10<sup>-3</sup>~~

	== See also ==		== See also ==
	* [[Garischismic clan]], the rank-2 clan where it is tempered out
	* [[Small comma]]		* [[Small comma]]

	[[Category:Garischismic]]		[[Category:Garischismic]]

Cmloegcmluin: "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

2023-05-07T18:31:42Z

"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

← Older revision		Revision as of 18:31, 7 May 2023
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	[[POTE generator]]s: ~3/2 = 702.2079, ~5/4 = 386.5100		[[POTE generator]]s: ~3/2 = 702.2079, ~5/4 = 386.5100

	{{~~Val list~~\|legend=1\| 12, 29, 41, 53, 94, 164, 176, 217, 229, 270, 593, 863, 1133, 1996d, 2037, 2307, 2900bd, 3170bd, 4303bcd }}		{{Optimal ET sequence\|legend=1\| 12, 29, 41, 53, 94, 164, 176, 217, 229, 270, 593, 863, 1133, 1996d, 2037, 2307, 2900bd, 3170bd, 4303bcd }}

	[[Badness]]: 1.313 × 10<sup>-3</sup>		[[Badness]]: 1.313 × 10<sup>-3</sup>

TallKite at 07:44, 14 January 2023

2023-01-14T07:44:01Z

← Older revision		Revision as of 07:44, 14 January 2023
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	\| Ratio = 33554432/33480783		\| Ratio = 33554432/33480783
	\| Name = garischisma, septimal schisma		\| Name = garischisma, septimal schisma
	\| Color name = ssr2, sasaru 2nd		\| Color name = ssr2, sasaru 2nd,<br>Sasaru comma
	\| Comma = yes		\| Comma = yes
	}}		}}

Plumtree: Normalising usage of Infobox Interval

2022-10-25T17:38:09Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 17:38, 25 October 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| JI glyph =~~
	\| Ratio = 33554432/33480783		\| Ratio = 33554432/33480783
	~~\| Monzo = 25 -14 0 -1~~		\| Name = garischisma, septimal schisma
	~~\| Cents = 3.8041~~
	\| Name = garischisma, ~~<br>~~septimal schisma
	\| Color name = ssr2, sasaru 2nd		\| Color name = ssr2, sasaru 2nd
	\| ~~FJS name = d2<sub>7</sub>~~		\| Comma = yes
	~~\| Sound~~ =
	}}		}}

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

	~~[[Category:7-limit]]~~
	~~[[Category:Small commas]]~~
	~~[[Category:Unnoticeable commas]]~~
	[[Category:Garischismic]]		[[Category:Garischismic]]