Keegic temperaments - Revision history

FloraC: Move quinkee here

2026-06-25T10:22:32Z

Move quinkee here

← Older revision		Revision as of 10:22, 25 June 2026
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	Temperaments discussed elsewhere include [[Very low accuracy temperaments\|antitonic]], [[Trienstonic clan\|kangaroo]], [[Kleismic family\|keemun]], [[Meantone family\|liese]], [[Archytas clan\|progress]], [[Mint temperaments\|subklei]], [[Marvel temperaments\|triton]], [[Augmented family\|trisected]], and [[Sensamagic clan\|xenia]].		Temperaments discussed elsewhere include [[Very low accuracy temperaments\|antitonic]], [[Trienstonic clan\|kangaroo]], [[Kleismic family\|keemun]], [[Meantone family\|liese]], [[Archytas clan\|progress]], [[Mint temperaments\|subklei]], [[Marvel temperaments\|triton]], [[Augmented family\|trisected]], and [[Sensamagic clan\|xenia]].

			== Quinkee ==
			Quinkee has a period of 1/5 octave and tempers out the [[keega]] (1029/1000), from which it derives its name. It may be described as the {{nowrap\| 15 & 55 }} temperament. It was named by [[Xenllium]] in 2021.

			[[Subgroup]]: 2.3.5.7

			[[Comma list]]: 1029/1000, 6144/6125

			{{Mapping\|legend=1\| 5 0 9 14 \| 0 3 1 0 }}
			: mapping generators: ~8/7, ~10/7

			[[Optimal tuning]]s:
			* [[WE]]: ~8/7 = 240.0512{{c}}, ~10/7 = 633.5744{{c}} (~25/24 = 86.5794{{c}})
			: [[error map]]: {{val\| +0.256 -1.232 +7.722 -8.108 }}
			* [[CWE]]: ~8/7 = 240.0000{{c}}, ~10/7 = 633.4834{{c}} (~25/24 = 86.5160{{c}})
			: error map: {{val\| 0.000 -1.505 +7.170 -8.826 }}

			{{Optimal ET sequence\|legend=1\| 15, 40, 55 }}

			[[Badness]] (Sintel): 4.66

			=== 11-limit ===
			Subgroup: 2.3.5.7.11

			Comma list: 121/120, 176/175, 1029/1000

			Mapping: {{mapping\| 5 0 9 14 12 \| 0 3 1 0 2 }}

			Optimal tunings:
			* WE: ~8/7 = 240.0916{{c}}, ~10/7 = 633.6802{{c}} (~22/21 = 86.5947{{c}})
			* CWE: ~8/7 = 240.0000{{c}}, ~10/7 = 633.5204{{c}} (~22/21 = 86.4796{{c}})

			{{Optimal ET sequence\|legend=0\| 15, 40, 55 }}

			Badness (Sintel): 2.16

			=== 13-limit ===
			Subgroup: 2.3.5.7.11.13

			Comma list: 66/65, 105/104, 121/120, 637/625

			Mapping: {{mapping\| 5 9 12 14 18 20 \| 0 3 1 0 2 4 }}

			Optimal tunings:
			* WE: ~8/7 = 240.0392{{c}}, ~10/7 = 632.9013{{c}} (~22/21 = 87.2162{{c}})
			* CWE: ~8/7 = 240.0000{{c}}, ~10/7 = 632.8351{{c}} (~22/21 = 87.1649{{c}})

			{{Optimal ET sequence\|legend=0\| 15, 40, 55 }}

			Badness (Sintel): 2.00

	== Aurora ==		== Aurora ==

Xenllium at 06:31, 2 May 2026

2026-05-02T06:31:41Z

← Older revision		Revision as of 06:31, 2 May 2026
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	'''Keegic''' [[rank two temperament]]s temper out the keega, {{monzo\|-3 1 -3 3}} = 1029/1000, the difference three [[7/5]]s and perfect eleventh [[8/3]].		'''Keegic''' [[rank two temperament]]s temper out the keega, {{monzo\|-3 1 -3 3}} = 1029/1000, the difference three [[7/5]]s and perfect eleventh [[8/3]].

	Temperaments discussed elsewhere include [[Very low accuracy temperaments\|antitonic]], [[Trienstonic clan\|kangaroo]], [[Kleismic family\|keemun]], [[Meantone family\|liese]], [[Archytas clan\|progress]], [[Mint temperaments\|subklei]], [[Marvel temperaments\|triton]], ~~and~~ [[Augmented family\|trisected]].		Temperaments discussed elsewhere include [[Very low accuracy temperaments\|antitonic]], [[Trienstonic clan\|kangaroo]], [[Kleismic family\|keemun]], [[Meantone family\|liese]], [[Archytas clan\|progress]], [[Mint temperaments\|subklei]], [[Marvel temperaments\|triton]], [[Augmented family\|trisected]], and [[Sensamagic clan\|xenia]].

	== Aurora ==		== Aurora ==

Overthink: + trisected

2026-03-19T04:13:38Z

+ trisected

← Older revision		Revision as of 04:13, 19 March 2026
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	'''Keegic''' [[rank two temperament]]s temper out the keega, {{monzo\|-3 1 -3 3}} = 1029/1000, the difference three [[7/5]]s and perfect eleventh [[8/3]].		'''Keegic''' [[rank two temperament]]s temper out the keega, {{monzo\|-3 1 -3 3}} = 1029/1000, the difference three [[7/5]]s and perfect eleventh [[8/3]].

	Temperaments discussed elsewhere include [[Very low accuracy temperaments\|antitonic]], [[Trienstonic clan\|kangaroo]], [[Kleismic family\|keemun]], [[Meantone family\|liese]], [[Archytas clan\|progress]], [[Mint temperaments\|subklei]], ~~and~~ [[Marvel temperaments\|triton]].		Temperaments discussed elsewhere include [[Very low accuracy temperaments\|antitonic]], [[Trienstonic clan\|kangaroo]], [[Kleismic family\|keemun]], [[Meantone family\|liese]], [[Archytas clan\|progress]], [[Mint temperaments\|subklei]], [[Marvel temperaments\|triton]], and [[Augmented family\|trisected]].

	== Aurora ==		== Aurora ==

FloraC: Text replacement - "Category:Temperament collections↵Category:Pages with mostly numerical content" to "Category:Temperament collections"

2025-11-27T12:29:30Z

Text replacement - "Category:Temperament collections↵Category:Pages with mostly numerical content" to "Category:Temperament collections"

← Older revision		Revision as of 12:29, 27 November 2025
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	[[Category:Temperament collections]]		[[Category:Temperament collections]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Keegic]]		[[Category:Keegic]]
	[[Category:Rank 2]]		[[Category:Rank 2]]

Lériendil: Text replacement - "Category:Temperament collections" to "Category:Temperament collections Category:Pages with mostly numerical content"

2025-06-24T00:37:35Z

Text replacement - "Category:Temperament collections" to "Category:Temperament collections Category:Pages with mostly numerical content"

← Older revision		Revision as of 00:37, 24 June 2025
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	[[Category:Temperament collections]]		[[Category:Temperament collections]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Keegic]]		[[Category:Keegic]]
	[[Category:Rank 2]]		[[Category:Rank 2]]

FloraC: Linking & cleanup

2025-06-14T16:07:19Z

Linking & cleanup

← Older revision		Revision as of 16:07, 14 June 2025
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	== Aurora ==		== Aurora ==
	The ''aurora'' temperament (13&~~amp;~~21) is very strongly related to the ~~'''~~[[Logarithmic phi\|golden oneirotonic tuning]]~~'''~~ (generator: ~~<math>\frac~~{3-\sqrt{5}}~~{2}</math>~~ octave = 458.3592135001 cents). It has a temperament structure superficially similar to [[~~Father family\|~~father]], with extremely flat fourths (sub-fourths/ultra-major third) or sharp fifths (super-fifths/ultra-minor sixths). However, unlike father, 12 of these bad fourths reach a more in tune fifth, which is useful for creating resolutions when using a large enough gamut, such as the [[13L 8s]] ~~MOS~~ which has two good major &~~amp;~~ minor chords.		: ''For the 5-limit version, see [[Diaschismic–gothmic equivalence continuum #Goldis]].''

			The ''aurora'' temperament ({{nowrap\| 13 & 21 }}) is very strongly related to the [[Logarithmic phi\|golden oneirotonic tuning]] (generator: {{nowrap\| (3 - sqrt(5))/2 }} octave = 458.3592135001 cents). It has a temperament structure superficially similar to [[father]], with extremely flat fourths (sub-fourths/ultra-major third) or sharp fifths (super-fifths/ultra-minor sixths). However, unlike father, 12 of these bad fourths reach a more in tune fifth, which is useful for creating resolutions when using a large enough gamut, such as the [[13L 8s]] mos which has two good major & minor chords.

	Subgroup: 2.3.5.7		Subgroup: 2.3.5.7

VectorGraphics at 05:14, 12 June 2025

2025-06-12T05:14:53Z

← Older revision		Revision as of 05:14, 12 June 2025
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	[[Mapping]]: [{{val\|1 -3 5 7}}, {{val\|0 12 -7 -11}}]		[[Mapping]]: [{{val\|1 -3 5 7}}, {{val\|0 12 -7 -11}}]

	~~{{Multival\|legend=1\|12 -7 -11 -39 -51 -6}}~~

	[[POTE generator]]: ~21/16 = 458.348		[[POTE generator]]: ~21/16 = 458.348

VectorGraphics: golden father -> golden oneirotonic

2025-04-26T21:29:40Z

golden father -> golden oneirotonic

← Older revision		Revision as of 21:29, 26 April 2025
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	== Aurora ==		== Aurora ==
	The ''aurora'' temperament (13&21) is very strongly related to the '''[[Logarithmic phi\|golden ~~father~~ tuning]]''' (generator: <math>\frac{3-\sqrt{5}}{2}</math> octave = 458.3592135001 cents). It has a temperament structure superficially similar to [[Father family\|father]], with extremely flat fourths (sub-fourths/ultra-major third) or sharp fifths (super-fifths/ultra-minor sixths). However, unlike father, 12 of these bad fourths reach a more in tune fifth, which is useful for creating resolutions when using a large enough gamut, such as the [[13L 8s]] MOS which has two good major & minor chords.		The ''aurora'' temperament (13&21) is very strongly related to the '''[[Logarithmic phi\|golden oneirotonic tuning]]''' (generator: <math>\frac{3-\sqrt{5}}{2}</math> octave = 458.3592135001 cents). It has a temperament structure superficially similar to [[Father family\|father]], with extremely flat fourths (sub-fourths/ultra-major third) or sharp fifths (super-fifths/ultra-minor sixths). However, unlike father, 12 of these bad fourths reach a more in tune fifth, which is useful for creating resolutions when using a large enough gamut, such as the [[13L 8s]] MOS which has two good major & minor chords.

	Subgroup: 2.3.5.7		Subgroup: 2.3.5.7

BudjarnLambeth: {{Technical data page}}

2025-04-13T14:33:14Z

← Older revision		Revision as of 14:33, 13 April 2025
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	Keegic rank-two ~~temperaments~~ temper out the keega, {{monzo\|-3 1 -3 3}} = 1029/1000, the difference three [[7/5]]s and perfect eleventh [[8/3]].		{{Technical data page}}
			'''Keegic''' [[rank two temperament]]s temper out the keega, {{monzo\|-3 1 -3 3}} = 1029/1000, the difference three [[7/5]]s and perfect eleventh [[8/3]].

	Temperaments discussed elsewhere include [[Very low accuracy temperaments\|antitonic]], [[Trienstonic clan\|kangaroo]], [[Kleismic family\|keemun]], [[Meantone family\|liese]], [[Archytas clan\|progress]], [[Mint temperaments\|subklei]], and [[Marvel temperaments\|triton]].		Temperaments discussed elsewhere include [[Very low accuracy temperaments\|antitonic]], [[Trienstonic clan\|kangaroo]], [[Kleismic family\|keemun]], [[Meantone family\|liese]], [[Archytas clan\|progress]], [[Mint temperaments\|subklei]], and [[Marvel temperaments\|triton]].

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

2023-05-07T16:14:47Z

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

← Older revision		Revision as of 16:14, 7 May 2023
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	[[POTE generator]]: ~21/16 = 458.348		[[POTE generator]]: ~21/16 = 458.348

	{{~~Val list~~\|legend=1\| 8bd, 13, 21, 34, 55, 89d, 144cdd }}		{{Optimal ET sequence\|legend=1\| 8bd, 13, 21, 34, 55, 89d, 144cdd }}

	[[Badness]]: 0.242134		[[Badness]]: 0.242134
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	POTE generator: ~21/16 = 458.413		POTE generator: ~21/16 = 458.413

	Optimal ~~GPV~~ sequence~~: {{Val list~~\| 8bd, 13, 21, 34, 55e, 89dee }}		{{Optimal ET sequence\|legend=1\| 8bd, 13, 21, 34, 55e, 89dee }}

	Badness: 0.116654		Badness: 0.116654
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	POTE generator: ~13/10 = 458.444		POTE generator: ~13/10 = 458.444

	Optimal ~~GPV~~ sequence~~: {{Val list~~\| 8bd, 13, 21, 34, 55e, 89deef }}		{{Optimal ET sequence\|legend=1\| 8bd, 13, 21, 34, 55e, 89deef }}

	Badness: 0.066541		Badness: 0.066541
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	POTE generator: ~13/10 = 458.444		POTE generator: ~13/10 = 458.444

	Optimal ~~GPV~~ sequence~~: {{Val list~~\| 8bd, 13, 21, 34, 55e, 89deef }}		{{Optimal ET sequence\|legend=1\| 8bd, 13, 21, 34, 55e, 89deef }}

	Badness: 0.044148		Badness: 0.044148
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	POTE generator: ~13/10 = 458.444		POTE generator: ~13/10 = 458.444

	Optimal ~~GPV~~ sequence~~: {{Val list~~\| 8bd, 13, 21, 34, 55eh, 89deefhh }}		{{Optimal ET sequence\|legend=1\| 8bd, 13, 21, 34, 55eh, 89deefhh }}

	Badness: 0.037621		Badness: 0.037621
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	POTE generator: ~13/10 = 458.430		POTE generator: ~13/10 = 458.430

	Optimal ~~GPV~~ sequence~~: {{Val list~~\| 8bd, 13, 21, 34, 55eh, 89deefhh }}		{{Optimal ET sequence\|legend=1\| 8bd, 13, 21, 34, 55eh, 89deefhh }}

	Badness: 0.030236		Badness: 0.030236
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	POTE generator: ~13/10 = 458.426		POTE generator: ~13/10 = 458.426

	Optimal ~~GPV~~ sequence~~: {{Val list~~\| 8bd, 13, 21, 34, 55eh, 89deefhh }}		{{Optimal ET sequence\|legend=1\| 8bd, 13, 21, 34, 55eh, 89deefhh }}

	Badness: 0.025201		Badness: 0.025201