Clipper - Revision history

Overthink: update

2026-02-08T01:46:16Z

update

← Older revision		Revision as of 01:46, 8 February 2026
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	If c is a [[Comma\|comma]], then clipper(c) is defined as Euler(Benedetti(c)), tempered by the codimension one temperament tempering out c. Here Euler(N) is the [[Euler_genera\|Euler genus]], the divisors of the integer N reduced to the octave, and Benedetti(c) is the [[Benedetti_height\|Benedetti height]] of c = p/q, which is p*q if p/q is reduced to its lowest terms. Euler(Benedetti(c)) has exactly one interval of size c, which is removed when c is tempered out. Two [[Transversal\|transversals]] of clipper(c) are obtained by leaving out either one or the other of the pair of scale intervals separated by c.		If c is a [[Comma\|comma]], then clipper(c) is defined as Euler(Benedetti(c)), tempered by the codimension one temperament tempering out c. Here Euler(N) is the [[Euler_genera\|Euler genus]], the divisors of the integer N reduced to the octave, and Benedetti(c) is the [[Benedetti_height\|Benedetti height]] of c = p/q, which is p*q if p/q is reduced to its lowest terms. Euler(Benedetti(c)) has exactly one interval of size c, which is removed when c is tempered out. Two [[Transversal\|transversals]] of clipper(c) are obtained by leaving out either one or the other of the pair of scale intervals separated by c.

	Euler(Benedetti(c)) generates a JI group, which can be found by reducing it to a [[Normal_lists#x-Normal interval lists\|normal interval list]]. This group is characteristic of the comma, and is the group on which tempering by the comma takes place. For instance, Euler(Benedetti(225/224)) generates 2.3.5.7, the full 7-limit group, and tempering it out leads to a rank three temperament, marvel. However, Euler(Benedeti(3136/3125)) generates 2.5.7, and tempering it out generates a rank-two temperament of the 2.5.7 [[Just_intonation_subgroups\|JI subgroup]], with mapping [<1 0 -3\|, <0 2 5\|] and an approximate 28/25 generator, which ~~might be called 7-limit~~ [[~~Chromatic_pairs#Roulette\|roulette~~]] temperament.		Euler(Benedetti(c)) generates a JI group, which can be found by reducing it to a [[Normal_lists#x-Normal interval lists\|normal interval list]]. This group is characteristic of the comma, and is the group on which tempering by the comma takes place. For instance, Euler(Benedetti(225/224)) generates 2.3.5.7, the full 7-limit group, and tempering it out leads to a rank three temperament, marvel. However, Euler(Benedeti(3136/3125)) generates 2.5.7, and tempering it out generates a rank-two temperament of the 2.5.7 [[Just_intonation_subgroups\|JI subgroup]], with mapping [<1 0 -3\|, <0 2 5\|] and an approximate 28/25 generator, which is known as [[didacus]] temperament.

	== Scales ==		== Scales ==

Overthink: /* Scales */ see also the category

2026-02-08T01:43:55Z

Scales: see also the category

← Older revision		Revision as of 01:43, 8 February 2026
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	== Scales ==		== Scales ==
			{{See also\|Category:Clippers}}
	[[clipper1029\|clipper(1029/1024)]], 7 notes, 2.3.7		[[clipper1029\|clipper(1029/1024)]], 7 notes, 2.3.7

Overthink: The page itself isn't a clipper scale

2026-02-08T01:42:12Z

The page itself isn't a clipper scale

← Older revision		Revision as of 01:42, 8 February 2026
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	{{Navbox scale gallery}}		{{Navbox scale gallery}}

	~~[[Category:Clippers]]~~
	[[Category:Euler-Fokker genera]]		[[Category:Euler-Fokker genera]]
	[[Category:Regular temperament theory]]		[[Category:Regular temperament theory]]
	[[Category:Lists of scales]]		[[Category:Lists of scales]]
	[[Category:Todo:clarify]]		[[Category:Todo:clarify]]

Overthink: Overthink moved page Clippers to Clipper: remove plural

2026-02-08T01:41:18Z

Overthink moved page Clippers to Clipper: remove plural

← Older revision	Revision as of 01:41, 8 February 2026
(No difference)

ArrowHead294 at 15:50, 4 December 2024

2024-12-04T15:50:33Z

← Older revision		Revision as of 15:50, 4 December 2024
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	Euler(Benedetti(c)) generates a JI group, which can be found by reducing it to a [[Normal_lists#x-Normal interval lists\|normal interval list]]. This group is characteristic of the comma, and is the group on which tempering by the comma takes place. For instance, Euler(Benedetti(225/224)) generates 2.3.5.7, the full 7-limit group, and tempering it out leads to a rank three temperament, marvel. However, Euler(Benedeti(3136/3125)) generates 2.5.7, and tempering it out generates a rank-two temperament of the 2.5.7 [[Just_intonation_subgroups\|JI subgroup]], with mapping [<1 0 -3\|, <0 2 5\|] and an approximate 28/25 generator, which might be called 7-limit [[Chromatic_pairs#Roulette\|roulette]] temperament.		Euler(Benedetti(c)) generates a JI group, which can be found by reducing it to a [[Normal_lists#x-Normal interval lists\|normal interval list]]. This group is characteristic of the comma, and is the group on which tempering by the comma takes place. For instance, Euler(Benedetti(225/224)) generates 2.3.5.7, the full 7-limit group, and tempering it out leads to a rank three temperament, marvel. However, Euler(Benedeti(3136/3125)) generates 2.5.7, and tempering it out generates a rank-two temperament of the 2.5.7 [[Just_intonation_subgroups\|JI subgroup]], with mapping [<1 0 -3\|, <0 2 5\|] and an approximate 28/25 generator, which might be called 7-limit [[Chromatic_pairs#Roulette\|roulette]] temperament.

	= Scales =		== Scales ==
	[[clipper1029\|clipper(1029/1024)]], 7 notes, 2.3.7		[[clipper1029\|clipper(1029/1024)]], 7 notes, 2.3.7

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	[[clipper245\|clipper(245/243)]], 35 notes, 7-limit		[[clipper245\|clipper(245/243)]], 35 notes, 7-limit

	= Links =		== Links ==
	[http://tech.groups.yahoo.com/group/tuning-math/message/11429 http://tech.groups.yahoo.com/group/tuning-math/message/11429]		[http://tech.groups.yahoo.com/group/tuning-math/message/11429 http://tech.groups.yahoo.com/group/tuning-math/message/11429]

ArrowHead294 at 15:50, 4 December 2024

2024-12-04T15:50:23Z

← Older revision		Revision as of 15:50, 4 December 2024
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	Euler(Benedetti(c)) generates a JI group, which can be found by reducing it to a [[Normal_lists#x-Normal interval lists\|normal interval list]]. This group is characteristic of the comma, and is the group on which tempering by the comma takes place. For instance, Euler(Benedetti(225/224)) generates 2.3.5.7, the full 7-limit group, and tempering it out leads to a rank three temperament, marvel. However, Euler(Benedeti(3136/3125)) generates 2.5.7, and tempering it out generates a rank-two temperament of the 2.5.7 [[Just_intonation_subgroups\|JI subgroup]], with mapping [<1 0 -3\|, <0 2 5\|] and an approximate 28/25 generator, which might be called 7-limit [[Chromatic_pairs#Roulette\|roulette]] temperament.		Euler(Benedetti(c)) generates a JI group, which can be found by reducing it to a [[Normal_lists#x-Normal interval lists\|normal interval list]]. This group is characteristic of the comma, and is the group on which tempering by the comma takes place. For instance, Euler(Benedetti(225/224)) generates 2.3.5.7, the full 7-limit group, and tempering it out leads to a rank three temperament, marvel. However, Euler(Benedeti(3136/3125)) generates 2.5.7, and tempering it out generates a rank-two temperament of the 2.5.7 [[Just_intonation_subgroups\|JI subgroup]], with mapping [<1 0 -3\|, <0 2 5\|] and an approximate 28/25 generator, which might be called 7-limit [[Chromatic_pairs#Roulette\|roulette]] temperament.

	=Scales=		= Scales =
	[[clipper1029\|clipper(1029/1024)]], 7 notes, 2.3.7		[[clipper1029\|clipper(1029/1024)]], 7 notes, 2.3.7

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	[[clipper245\|clipper(245/243)]], 35 notes, 7-limit		[[clipper245\|clipper(245/243)]], 35 notes, 7-limit

	=Links=		= Links =
	[http://tech.groups.yahoo.com/group/tuning-math/message/11429 http://tech.groups.yahoo.com/group/tuning-math/message/11429]		[http://tech.groups.yahoo.com/group/tuning-math/message/11429 http://tech.groups.yahoo.com/group/tuning-math/message/11429]

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	[http://tech.groups.yahoo.com/group/tuning-math/message/11441 http://tech.groups.yahoo.com/group/tuning-math/message/11441]		[http://tech.groups.yahoo.com/group/tuning-math/message/11441 http://tech.groups.yahoo.com/group/tuning-math/message/11441]

	~~<br>~~		{{Navbox scale gallery}}
	{{~~Scale~~ gallery}}

	[[Category:Clippers]]		[[Category:Clippers]]

BudjarnLambeth: /* Links */

2024-12-02T04:42:27Z

Links

← Older revision		Revision as of 04:42, 2 December 2024
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	[http://tech.groups.yahoo.com/group/tuning-math/message/11441 http://tech.groups.yahoo.com/group/tuning-math/message/11441]		[http://tech.groups.yahoo.com/group/tuning-math/message/11441 http://tech.groups.yahoo.com/group/tuning-math/message/11441]

			<br>
	{{Scale gallery}}		{{Scale gallery}}

BudjarnLambeth: {{Scale gallery}}

2024-12-02T04:42:15Z

← Older revision		Revision as of 04:42, 2 December 2024
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	[http://tech.groups.yahoo.com/group/tuning-math/message/11441 http://tech.groups.yahoo.com/group/tuning-math/message/11441]		[http://tech.groups.yahoo.com/group/tuning-math/message/11441 http://tech.groups.yahoo.com/group/tuning-math/message/11441]

			{{Scale gallery}}

	[[Category:Clippers]]		[[Category:Clippers]]
	[[Category:Euler-Fokker genera]]		[[Category:Euler-Fokker genera]]

BudjarnLambeth: Removed from category “scales by family” because “lists of scales” is more appropriate

2023-07-01T15:02:52Z

Removed from category “scales by family” because “lists of scales” is more appropriate

← Older revision		Revision as of 15:02, 1 July 2023
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	[[Category:Euler-Fokker genera]]		[[Category:Euler-Fokker genera]]
	[[Category:Regular temperament theory]]		[[Category:Regular temperament theory]]
	~~[[Category:Scales by family]]~~
	[[Category:Lists of scales]]		[[Category:Lists of scales]]
	[[Category:Todo:clarify]]		[[Category:Todo:clarify]]

BudjarnLambeth at 09:39, 1 May 2023

2023-05-01T09:39:34Z

← Older revision		Revision as of 09:39, 1 May 2023
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	[http://tech.groups.yahoo.com/group/tuning-math/message/11441 http://tech.groups.yahoo.com/group/tuning-math/message/11441]		[http://tech.groups.yahoo.com/group/tuning-math/message/11441 http://tech.groups.yahoo.com/group/tuning-math/message/11441]
	[[Category:~~Clipper~~]]		[[Category:Clippers]]
	[[Category:Euler-Fokker genera]]		[[Category:Euler-Fokker genera]]
	[[Category:Regular temperament theory]]		[[Category:Regular temperament theory]]