1029/1024 - Revision history

FloraC: Expand & misc. cleanup

2026-05-06T09:10:50Z

Expand & misc. cleanup

← Older revision		Revision as of 09:10, 6 May 2026
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			{{Interwiki
			\| en = 1029/1024
			\| de = 1029/1024
			}}
	{{Infobox Interval		{{Infobox Interval
	\| Name = slendric comma, gamelisma, gamelan residue		\| Name = slendric comma, gamelisma, gamelan residue
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	\| Comma = yes		\| Comma = yes
	}}		}}
	~~{{interwiki~~		'''1029/1024''', the '''slendric comma''' or '''gamelisma''', is a [[small comma\|small]] [[7-limit]] (also [[2.3.7 subgroup\|2.3.7-subgroup]]) [[comma]] measuring about 8.4 [[cent]]s. It is the amount by which a stack of three [[8/7]]'s falls short of [[3/2]], and the ratio between [[49/48]] ({{S\|7}}) and [[64/63]] ({{S\|8}}), which gives it the [[S-expression]] of S7/S8, making it an ultraparticular comma.
	~~\| de = 1029/1024~~
	~~\| en = 1029/1024~~
	}}
	'''1029/1024''', the '''slendric comma''' or '''gamelisma''', is a [[small comma\|small]] [[7-limit]] (also 2.3.7-[[subgroup]]) [[comma]] measuring about 8.4 [[cent]]s. It is the amount by which a stack of three [[8/7]]'s falls short of [[3/2]], and the ratio between ~~S7 =~~ [[49/48]] and ~~S8 =~~ [[64/63]], which gives it the [[S-expression]] of S7/S8, making it an ultraparticular comma~~. It is also the amount by which a stack of three [[garischisma]]s falls short of a [[countercomp comma]]~~.

	== Commatic relations ==		== Commatic relations ==
	This comma ~~factorizes into~~ [[~~superparticular~~]]s ~~as:~~		This comma is the difference between a [[Pythagorean limma]] and a stack of three septimal commas, as well as the difference between a [[Pythagorean countercomma]] and a stack of three [[septimal schisma]]s.
	* [[~~217/216~~]] × [[~~3969~~/~~3968~~]] (~~subgroup:~~ [[~~31-limit\|2.3.7.31~~]])
	* [[~~225~~/~~224~~]] × [[~~2401~~/~~2400~~]] (subgroup: ~~[[7-limit\|~~2.3.5.7]])		In the full 7-limit it factorizes into [[superparticular]]s as ([[225/224]])⋅([[2401/2400]]). It also factorizes into the following constituent superparticulars in the higher limits:
	* [[~~273~~/~~272~~]] × [[~~833~~/~~832~~]] (subgroup: ~~[[17-limit\|~~2.3.7.~~13.17]]~~)		* [[385/384]] and [[441/440]] (subgroup: 2.3.5.7.11)
	* [[~~343~~/~~342~~]] × [[~~513~~/~~512~~]] (subgroup: ~~[[19-limit\|~~2.3.7.~~19]]~~)		* [[343/342]] and [[513/512]] (subgroup: 2.3.7.19)
	* [[~~385~~/~~384~~]] × [[~~441~~/~~440~~]] (subgroup: ~~[[11-limit\|~~2.3.5.7.~~11]]~~).		* [[273/272]] and [[833/832]] (subgroup: 2.3.7.13.17)
			* [[217/216]] and [[3969/3968]] (subgroup: 2.3.7.31)

	Tempering out these constituent commas adds new intervals (outside of the 2.3.7 subgroup) to the chain of 8/7s while doing minimal additional damage to 2.3.7 itself.		Tempering out these constituent commas adds new intervals (outside of the 2.3.7 subgroup) to the chain of 8/7's while doing minimal additional damage to 2.3.7 itself.

	== Temperaments ==		== Temperaments ==
	Tempering out this comma alone in the [[2.3.7 subgroup]] leads to the rank-2 [[slendric]] temperament, or in the full 7-limit, the rank-3 [[gamelismic]] temperament. In either case, it enables the [[slendric pentad]], and the perfect fifth is split into three equal parts, one for 8/7 and two for [[21/16]]. In addition, the ~~[[256/243\|~~Pythagorean limma ~~(256/243)]]~~ is also split into three, one for 64/63[[~]]49/48 and two for [[28/27]]. It therefore provides the little interval known as a [[quark]].		[[Tempering out]] this comma alone in the 2.3.7 subgroup leads to the rank-2 [[slendric]] temperament, or in the full 7-limit, the rank-3 [[gamelismic]] temperament. In either case, it enables the [[slendric pentad]], and the perfect fifth is split into three equal parts, one for 8/7 and two for [[21/16]]. In addition, the Pythagorean limma is also split into three, one for 64/63[[~]]49/48 and two for [[28/27]]. It therefore provides the little interval known as a [[quark]].

	See [[Gamelismic family]] for the rank-3 family where it is tempered out. See [[Gamelismic clan]] for the rank-2 clan where it is tempered out.		See [[Gamelismic family]] for the rank-3 family where it is tempered out. See [[Gamelismic clan]] for the rank-2 clan where it is tempered out.

Lucius Chiaraviglio: Another way to get it — seems that a 2.3.7 equivalence continuum anchored to 41EDO should be lurking around here

2026-03-05T08:39:18Z

Another way to get it — seems that a 2.3.7 equivalence continuum anchored to 41EDO should be lurking around here

← Older revision		Revision as of 08:39, 5 March 2026
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	\| en = 1029/1024		\| en = 1029/1024
	}}		}}
	'''1029/1024''', the '''slendric comma''' or '''gamelisma''', is a [[small comma\|small]] [[7-limit]] (also 2.3.7-[[subgroup]]) [[comma]] measuring about 8.4 [[cent]]s. It is the amount by which a stack of three [[8/7]]'s falls short of [[3/2]], and the ratio between S7 = [[49/48]] and S8 = [[64/63]], which gives it the [[S-expression]] of S7/S8, making it an ultraparticular comma.		'''1029/1024''', the '''slendric comma''' or '''gamelisma''', is a [[small comma\|small]] [[7-limit]] (also 2.3.7-[[subgroup]]) [[comma]] measuring about 8.4 [[cent]]s. It is the amount by which a stack of three [[8/7]]'s falls short of [[3/2]], and the ratio between S7 = [[49/48]] and S8 = [[64/63]], which gives it the [[S-expression]] of S7/S8, making it an ultraparticular comma. It is also the amount by which a stack of three [[garischisma]]s falls short of a [[countercomp comma]].

	== Commatic relations ==		== Commatic relations ==

Hstraub: Link to German

2026-01-18T17:39:21Z

Link to German

← Older revision		Revision as of 17:39, 18 January 2026
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	\| Comma = yes		\| Comma = yes
	}}		}}
			{{interwiki
			\| de = 1029/1024
			\| en = 1029/1024
			}}
	'''1029/1024''', the '''slendric comma''' or '''gamelisma''', is a [[small comma\|small]] [[7-limit]] (also 2.3.7-[[subgroup]]) [[comma]] measuring about 8.4 [[cent]]s. It is the amount by which a stack of three [[8/7]]'s falls short of [[3/2]], and the ratio between S7 = [[49/48]] and S8 = [[64/63]], which gives it the [[S-expression]] of S7/S8, making it an ultraparticular comma.		'''1029/1024''', the '''slendric comma''' or '''gamelisma''', is a [[small comma\|small]] [[7-limit]] (also 2.3.7-[[subgroup]]) [[comma]] measuring about 8.4 [[cent]]s. It is the amount by which a stack of three [[8/7]]'s falls short of [[3/2]], and the ratio between S7 = [[49/48]] and S8 = [[64/63]], which gives it the [[S-expression]] of S7/S8, making it an ultraparticular comma.

FloraC: Update

2025-06-11T12:41:07Z

Update

← Older revision		Revision as of 12:41, 11 June 2025
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	== Etymology ==		== Etymology ==
	This comma was known as the ''gamelan residue'' no later than May 2001. It was allegedly named by [[Adriaan Fokker]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_22907.html Yahoo! Tuning Group\| ''Re: "Miracle Scale" -- comparing notes on an exciting week'']</ref>.		This comma was known as the ''gamelan residue'' no later than May 2001. It was allegedly named by [[Adriaan Fokker]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_22907.html Yahoo! Tuning Group\| ''Re: "Miracle Scale" -- comparing notes on an exciting week'']</ref>. The name ''gamelisma'', a contracted form of ''gamelan residue'', appeared somewhat later.

	~~The name~~ ''[[slendrisma~~]],~~'' ~~despite being the correct~~ systematic ~~derivation from~~ ''slendric,'' ~~is not used due to being the name of a different comma (the slendric schisma)~~.		It may also be called the ''slendrisma'' or ''gamelic comma'', as systematic derivations of ''slendric comma'' and ''gamelisma'', respectively.

	== Notes ==		== Notes ==

VectorGraphics at 08:22, 11 June 2025

2025-06-11T08:22:18Z

← Older revision		Revision as of 08:22, 11 June 2025
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	== Etymology ==		== Etymology ==
	This comma was known as the ''gamelan residue'' no later than May 2001. It was allegedly named by [[Adriaan Fokker]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_22907.html Yahoo! Tuning Group\| ''Re: "Miracle Scale" -- comparing notes on an exciting week'']</ref>.		This comma was known as the ''gamelan residue'' no later than May 2001. It was allegedly named by [[Adriaan Fokker]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_22907.html Yahoo! Tuning Group\| ''Re: "Miracle Scale" -- comparing notes on an exciting week'']</ref>.

			The name ''[[slendrisma]],'' despite being the correct systematic derivation from ''slendric,'' is not used due to being the name of a different comma (the slendric schisma).

	== Notes ==		== Notes ==

Lériendil: /* Commatic relations */Added marvél

2025-03-04T20:23:09Z

Commatic relations: Added marvél

← Older revision		Revision as of 20:23, 4 March 2025
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	This comma factorizes into [[superparticular]]s as:		This comma factorizes into [[superparticular]]s as:
	* [[217/216]] × [[3969/3968]] (subgroup: [[31-limit\|2.3.7.31]])		* [[217/216]] × [[3969/3968]] (subgroup: [[31-limit\|2.3.7.31]])
			* [[225/224]] × [[2401/2400]] (subgroup: [[7-limit\|2.3.5.7]])
	* [[273/272]] × [[833/832]] (subgroup: [[17-limit\|2.3.7.13.17]])		* [[273/272]] × [[833/832]] (subgroup: [[17-limit\|2.3.7.13.17]])
	* [[343/342]] × [[513/512]] (subgroup: [[19-limit\|2.3.7.19]])		* [[343/342]] × [[513/512]] (subgroup: [[19-limit\|2.3.7.19]])

Lériendil at 17:58, 8 February 2025

2025-02-08T17:58:56Z

← Older revision		Revision as of 17:58, 8 February 2025
Line 5:		Line 5:
	}}		}}

	'''1029/1024''', the '''slendric comma''' or '''gamelisma''', is a [[small comma\|small]] [[7-limit]] (also 2.3.7-[[subgroup]]) [[comma]] measuring about 8.4 [[cent]]s. It is the amount by which a stack of three [[8/7]]'s falls short of [[3/2]].		'''1029/1024''', the '''slendric comma''' or '''gamelisma''', is a [[small comma\|small]] [[7-limit]] (also 2.3.7-[[subgroup]]) [[comma]] measuring about 8.4 [[cent]]s. It is the amount by which a stack of three [[8/7]]'s falls short of [[3/2]], and the ratio between S7 = [[49/48]] and S8 = [[64/63]], which gives it the [[S-expression]] of S7/S8, making it an ultraparticular comma.

	== Commatic relations ==		== Commatic relations ==
Line 17:		Line 17:

	== Temperaments ==		== Temperaments ==
	Tempering out this comma alone in the [[2.3.7 subgroup]] leads to the rank-2 [[slendric]] temperament, or in the full 7-limit, the rank-3 [[gamelismic]] temperament. In either case, it enables the [[slendric pentad]], and the perfect fifth is split into three equal parts, one for 8/7 and two for [[21/16]]. In addition, the [[256/243\|Pythagorean limma (256/243)]] is also split into three, one for [[64/63]][[~]][[49/48]] and two for [[28/27]]. It therefore provides the little interval known as a [[quark]].		Tempering out this comma alone in the [[2.3.7 subgroup]] leads to the rank-2 [[slendric]] temperament, or in the full 7-limit, the rank-3 [[gamelismic]] temperament. In either case, it enables the [[slendric pentad]], and the perfect fifth is split into three equal parts, one for 8/7 and two for [[21/16]]. In addition, the [[256/243\|Pythagorean limma (256/243)]] is also split into three, one for 64/63[[~]]49/48 and two for [[28/27]]. It therefore provides the little interval known as a [[quark]].

	See [[Gamelismic family]] for the rank-3 family where it is tempered out. See [[Gamelismic clan]] for the rank-2 clan where it is tempered out.		See [[Gamelismic family]] for the rank-3 family where it is tempered out. See [[Gamelismic clan]] for the rank-2 clan where it is tempered out.

Lériendil: added more factorizations

2025-02-08T17:56:26Z

added more factorizations

← Older revision		Revision as of 17:56, 8 February 2025
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	== Commatic relations ==		== Commatic relations ==
	This comma factorizes into [[superparticular]]s as:		This comma factorizes into [[superparticular]]s as:
	* [[273/272]] × [[833/832]] (subgroup: 2.3.7.13.17)		* [[217/216]] × [[3969/3968]] (subgroup: [[31-limit\|2.3.7.31]])
	* [[385/384]] × [[441/440]] (subgroup: 2.3.5.7.11).		* [[273/272]] × [[833/832]] (subgroup: [[17-limit\|2.3.7.13.17]])
			* [[343/342]] × [[513/512]] (subgroup: [[19-limit\|2.3.7.19]])
			* [[385/384]] × [[441/440]] (subgroup: [[11-limit\|2.3.5.7.11]]).

	Tempering out these constituent commas adds new intervals (outside of the 2.3.7 subgroup) to the chain of 8/7s while doing minimal additional damage to 2.3.7 itself.		Tempering out these constituent commas adds new intervals (outside of the 2.3.7 subgroup) to the chain of 8/7s while doing minimal additional damage to 2.3.7 itself.

Lériendil: added some factorizations

2025-02-08T17:42:20Z

added some factorizations

← Older revision		Revision as of 17:42, 8 February 2025
Line 6:		Line 6:

	'''1029/1024''', the '''slendric comma''' or '''gamelisma''', is a [[small comma\|small]] [[7-limit]] (also 2.3.7-[[subgroup]]) [[comma]] measuring about 8.4 [[cent]]s. It is the amount by which a stack of three [[8/7]]'s falls short of [[3/2]].		'''1029/1024''', the '''slendric comma''' or '''gamelisma''', is a [[small comma\|small]] [[7-limit]] (also 2.3.7-[[subgroup]]) [[comma]] measuring about 8.4 [[cent]]s. It is the amount by which a stack of three [[8/7]]'s falls short of [[3/2]].

			== Commatic relations ==
			This comma factorizes into [[superparticular]]s as:
			* [[273/272]] × [[833/832]] (subgroup: 2.3.7.13.17)
			* [[385/384]] × [[441/440]] (subgroup: 2.3.5.7.11).

			Tempering out these constituent commas adds new intervals (outside of the 2.3.7 subgroup) to the chain of 8/7s while doing minimal additional damage to 2.3.7 itself.

	== Temperaments ==		== Temperaments ==
	Tempering out this comma alone in the 2.3.7 [[subgroup]] leads to the rank-2 [[slendric]] temperament, or in the full 7-limit, the rank-3 [[gamelismic]] temperament. In either case, it enables the [[slendric pentad]], and the perfect fifth is split into three equal parts, one for [[8/7]] and two for [[21/16]]. In addition, the [[256/243\|Pythagorean limma (256/243)]] is also split into three, one for [[64/63]][[~]][[49/48]] and two for [[28/27]]. It therefore provides the little interval known as a [[quark]].		Tempering out this comma alone in the [[2.3.7 subgroup]] leads to the rank-2 [[slendric]] temperament, or in the full 7-limit, the rank-3 [[gamelismic]] temperament. In either case, it enables the [[slendric pentad]], and the perfect fifth is split into three equal parts, one for 8/7 and two for [[21/16]]. In addition, the [[256/243\|Pythagorean limma (256/243)]] is also split into three, one for [[64/63]][[~]][[49/48]] and two for [[28/27]]. It therefore provides the little interval known as a [[quark]].

	See [[Gamelismic family]] for the rank-3 family where it is tempered out. See [[Gamelismic clan]] for the rank-2 clan where it is tempered out.		See [[Gamelismic family]] for the rank-3 family where it is tempered out. See [[Gamelismic clan]] for the rank-2 clan where it is tempered out.

FloraC: Rework to address temperament properties in the "temperaments" section

2025-01-26T09:25:20Z

Rework to address temperament properties in the "temperaments" section

← Older revision		Revision as of 09:25, 26 January 2025
Line 5:		Line 5:
	}}		}}

	'''1029/1024''', the '''slendric comma''' or '''gamelisma''', is a [[7-limit]] (also 2.3.7 subgroup) [[~~small~~ comma]] measuring about 8.4 ~~cents~~. It is the amount by which a stack of three [[8/7]]s falls short of [[3/2]]. Tempering out this comma for the 2.3.7 subgroup leads to [[slendric]] temperament. In addition to the perfect fifth being split into three equal parts, the [[256/243\|Pythagorean limma (256/243)]] is also split into three in the same way, one for [[64/63]]~[[49/48]] and two for [[28/27]]. It therefore provides the little interval known as a [[quark]].		'''1029/1024''', the '''slendric comma''' or '''gamelisma''', is a [[small comma\|small]] [[7-limit]] (also 2.3.7-[[subgroup]]) [[comma]] measuring about 8.4 [[cent]]s. It is the amount by which a stack of three [[8/7]]'s falls short of [[3/2]].

	== Temperaments ==		== Temperaments ==
	Tempering out this comma alone in the 7~~-limit~~ leads to the rank-3 [[~~gamelismic~~]] temperament, or in the ~~2.3.~~7 ~~[[subgroup]]~~, the rank-2 [[~~slendric~~]] temperament. In either case, it enables the [[slendric pentad]]. See [[Gamelismic family]] for the rank-3 family where it is tempered out. See [[Gamelismic clan]] for the rank-2 clan where it is tempered out.		Tempering out this comma alone in the 2.3.7 [[subgroup]] leads to the rank-2 [[slendric]] temperament, or in the full 7-limit, the rank-3 [[gamelismic]] temperament. In either case, it enables the [[slendric pentad]], and the perfect fifth is split into three equal parts, one for [[8/7]] and two for [[21/16]]. In addition, the [[256/243\|Pythagorean limma (256/243)]] is also split into three, one for [[64/63]][[~]][[49/48]] and two for [[28/27]]. It therefore provides the little interval known as a [[quark]].

			See [[Gamelismic family]] for the rank-3 family where it is tempered out. See [[Gamelismic clan]] for the rank-2 clan where it is tempered out.

	== Etymology ==		== Etymology ==

← Older revision		Revision as of 20:23, 4 March 2025
Line 10:		Line 10:
	This comma factorizes into [[superparticular]]s as:		This comma factorizes into [[superparticular]]s as:
	* [[217/216]] × [[3969/3968]] (subgroup: [[31-limit\|2.3.7.31]])		* [[217/216]] × [[3969/3968]] (subgroup: [[31-limit\|2.3.7.31]])
			* [[225/224]] × [[2401/2400]] (subgroup: [[7-limit\|2.3.5.7]])
	* [[273/272]] × [[833/832]] (subgroup: [[17-limit\|2.3.7.13.17]])		* [[273/272]] × [[833/832]] (subgroup: [[17-limit\|2.3.7.13.17]])
	* [[343/342]] × [[513/512]] (subgroup: [[19-limit\|2.3.7.19]])		* [[343/342]] × [[513/512]] (subgroup: [[19-limit\|2.3.7.19]])