Quartkeenlig - Revision history

Eliora: +infobox, restructure

2026-08-16T20:00:38Z

+infobox, restructure

← Older revision		Revision as of 20:00, 16 August 2026
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	Quartkeenlig is a rank-2 temperament with a generator of about 53 cents, which stands for 33/32 and 36/35 tempered together.		{{Infobox regtemp
			\| Title = Quartkeenlig
			\| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13
			\| Comma basis = [[15625/15552]], 117649/116640 (7-limit); <br>[[385/384]], [[6250/6237]], 67228/66825 (11-limit)
			\| Edo join 1 = 68 \| Edo join 2 = 159
			\| Mapping = 1; 36 30 41 -35
			\| Generators = 33/32, 36/35
			\| Generators tuning = ~52.845
			\| Optimization method = CWE
			\| Pergen = (P8, P12/36)
			\| MOS scales = [[22L 1s]]
			}}
			Quartkeenlig is a rank-2 temperament with a generator of about 53 cents, which stands for 33/32 and 36/35 tempered together. Its name is taken from a portmanteau of the commas that constitute its basis. For technical data see: [[Kleismic family#Quartkeenlig]].

	~~For technical data see:~~ [[~~Kleismic family#Quartkeenlig~~]]		Quartkeeling is notable additionally because of its relationship to [[23edo and octave stretching]]. If 23 steps of pure [[TE tuning]] quartkeenlig in the 11-limit are considered without octave equivalence, the resulting scale would have an octave of 1215.62 cents, which is almost exactly the octave recommended for harmonic stretching of 23edo. Threfore, much like [[bohpier]] can be considered to represent [[Bohlen-Pierce scale]] but with octaves, quartkeenlig similarly represents stretched 23edo but with conventional octaves.

			Other interval relationships also work. Quartkeenlig maps 5 steps to 7/6, and 6 steps to 6/5, which are the direct approximations stretched 23edo provides for these intervals.

	== Theory ==		== Theory ==
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	The fifth in the standard sense constitutes 13 steps, and it is close to the [[7edo]] fifth. In 91edo, it is exactly the 7edo fifth. However it should be noted that from a regular temperament theory perspective it is not mapped to [[3/2]]. In order to reach just 3/2, one would need to stack 36 generators.		The fifth in the standard sense constitutes 13 steps, and it is close to the [[7edo]] fifth. In 91edo, it is exactly the 7edo fifth. However it should be noted that from a regular temperament theory perspective it is not mapped to [[3/2]]. In order to reach just 3/2, one would need to stack 36 generators.

	~~=== Relationship to 23edo and octave stretching ===~~		Being a member of kleismic family, quartkeenlig supports the stacking of [[6/5]] to produce [[3/1]], and partitions 6/5 into 6 quartertone steps.

	~~If 23 steps~~ of ~~pure [[TE tuning]]~~ quartkeenlig ~~in the 11-limit are considered without octave equivalence,~~ the ~~resulting scale would have an octave~~ of ~~1215.62 cents, which is almost exactly the octave recommended for harmonic~~ [[~~23edo and octave stretching\|stretching of 23edo~~]].

	~~Other interval relationships also work. Quartkeenlig maps 5 steps~~ to 7/6, and ~~6 steps to~~ 6/5~~, which are the direct approximations stretched 23edo provides for these intervals~~. ~~In addition, such a system would be fourthless like stretched 23edo, as [[4/3]] occurs nearly halfway between the 9th and 10th steps~~

	[[Category:Quartkeenlig\| ]] <!-- main article -->		[[Category:Quartkeenlig\| ]] <!-- main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:Kleismic family]]		[[Category:Kleismic family]]

FloraC: - parent category

2025-04-28T14:35:43Z

- parent category

← Older revision		Revision as of 14:35, 28 April 2025
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	Other interval relationships also work. Quartkeenlig maps 5 steps to 7/6, and 6 steps to 6/5, which are the direct approximations stretched 23edo provides for these intervals. In addition, such a system would be fourthless like stretched 23edo, as [[4/3]] occurs nearly halfway between the 9th and 10th steps		Other interval relationships also work. Quartkeenlig maps 5 steps to 7/6, and 6 steps to 6/5, which are the direct approximations stretched 23edo provides for these intervals. In addition, such a system would be fourthless like stretched 23edo, as [[4/3]] occurs nearly halfway between the 9th and 10th steps

	[[Category:~~Temperaments~~]]		[[Category:Quartkeenlig\| ]] <!-- main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:Kleismic family]]		[[Category:Kleismic family]]
	~~[[Category:Quartismic]]~~

Lériendil at 23:40, 19 April 2025

2025-04-19T23:40:06Z

← Older revision		Revision as of 23:40, 19 April 2025
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	For technical data see: [[Kleismic family#Quartkeenlig]]		For technical data see: [[Kleismic family#Quartkeenlig]]
	==Theory==
			== Theory ==
	EDOs which support quartkeenlig: {{EDOs\|68, 91, 159}}.		EDOs which support quartkeenlig: {{EDOs\|68, 91, 159}}.
	The simplest mos of quartkeenlig is [[22L 1s]].		The simplest mos of quartkeenlig is [[22L 1s]].

	The fifth in the standard sense constitutes 13 steps, and it is close to the [[7edo]] fifth. In 91edo, it is exactly the 7edo fifth. However it should be noted that from a regular temperament theory perspective it is not mapped to [[3/2]]. In order to reach just 3/2, one would need to stack 36 generators.		The fifth in the standard sense constitutes 13 steps, and it is close to the [[7edo]] fifth. In 91edo, it is exactly the 7edo fifth. However it should be noted that from a regular temperament theory perspective it is not mapped to [[3/2]]. In order to reach just 3/2, one would need to stack 36 generators.

	=== Relationship to 23edo and octave stretching ===		=== Relationship to 23edo and octave stretching ===

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	Other interval relationships also work. Quartkeenlig maps 5 steps to 7/6, and 6 steps to 6/5, which are the direct approximations stretched 23edo provides for these intervals. In addition, such a system would be fourthless like stretched 23edo, as [[4/3]] occurs nearly halfway between the 9th and 10th steps		Other interval relationships also work. Quartkeenlig maps 5 steps to 7/6, and 6 steps to 6/5, which are the direct approximations stretched 23edo provides for these intervals. In addition, such a system would be fourthless like stretched 23edo, as [[4/3]] occurs nearly halfway between the 9th and 10th steps



	[[Category:Temperaments]]		[[Category:Temperaments]]
			[[Category:Rank-2 temperaments]]
	[[Category:Kleismic family]]		[[Category:Kleismic family]]
	[[Category:Quartismic]]		[[Category:Quartismic]]

Eliora: /* Theory */

2023-03-20T01:06:12Z

Theory

← Older revision		Revision as of 01:06, 20 March 2023
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	If 23 steps of pure [[TE tuning]] quartkeenlig in the 11-limit are considered without octave equivalence, the resulting scale would have an octave of 1215.62 cents, which is almost exactly the octave recommended for harmonic [[23edo and octave stretching\|stretching of 23edo]].		If 23 steps of pure [[TE tuning]] quartkeenlig in the 11-limit are considered without octave equivalence, the resulting scale would have an octave of 1215.62 cents, which is almost exactly the octave recommended for harmonic [[23edo and octave stretching\|stretching of 23edo]].

	Other interval relationships also work. Quartkeenlig maps 5 steps to 7/6, and 6 steps to 6/5, which are the direct approximations stretched 23edo provides for these intervals. In addition, such a system would be fourthless, as [[4/3]] occurs nearly halfway between the 9th and 10th steps.		Other interval relationships also work. Quartkeenlig maps 5 steps to 7/6, and 6 steps to 6/5, which are the direct approximations stretched 23edo provides for these intervals. In addition, such a system would be fourthless like stretched 23edo, as [[4/3]] occurs nearly halfway between the 9th and 10th steps

Eliora: new page, created after a discussion

2022-12-18T19:21:45Z

new page, created after a discussion

@@ Line 1: / Line 1: @@
-#REDIRECT [[Kleismic family #Quartkeenlig]]
+Quartkeenlig is a rank-2 temperament with a generator of about 53 cents, which stands for 33/32 and 36/35 tempered together.
 [[Category:Temperaments]]
 [[Category:Kleismic family]]

FloraC: Changed redirect target from The Quartercache#Quartkeenlig to Kleismic family#Quartkeenlig

2022-09-12T15:06:18Z

Changed redirect target from The Quartercache#Quartkeenlig to Kleismic family#Quartkeenlig

← Older revision		Revision as of 15:06, 12 September 2022
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	#REDIRECT [[~~The Quartercache~~#Quartkeenlig]]		#REDIRECT [[Kleismic family #Quartkeenlig]]

			[[Category:Temperaments]]
			[[Category:Kleismic family]]

Eliora: Redirected page to The Quartercache#Quartkeenlig

2022-09-09T19:33:11Z

Redirected page to The Quartercache#Quartkeenlig

New page

#REDIRECT [[The Quartercache#Quartkeenlig]]