Keegic temperaments - Revision history

FloraC: Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "

2026-09-24T12:32:35Z

Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "

← Older revision		Revision as of 12:32, 24 September 2026
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	Comma list: 121/120, 176/175, 1029/1000		Comma list: 121/120, 176/175, 1029/1000

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

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

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

	Optimal tunings:		Optimal tunings:
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	Comma list: 56/55, 1029/1000, 5632/5625		Comma list: 56/55, 1029/1000, 5632/5625

	~~Mapping:~~ {{~~mapping~~\| 1 -3 5 7 5 \| 0 12 -7 -11 -4 }}		{{Mapping\|legend=0\| 1 -3 5 7 5 \| 0 12 -7 -11 -4 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 56/55, 105/104, 512/507, 637/625		Comma list: 56/55, 105/104, 512/507, 637/625

	~~Mapping:~~ {{~~mapping~~\| 1 -3 5 7 5 6 \| 0 12 -7 -11 -4 -6 }}		{{Mapping\|legend=0\| 1 -3 5 7 5 6 \| 0 12 -7 -11 -4 -6 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 56/55, 105/104, 170/169, 221/220, 375/374		Comma list: 56/55, 105/104, 170/169, 221/220, 375/374

	~~Mapping:~~ {{~~mapping~~\| 1 -3 5 7 5 6 6 \| 0 12 -7 -11 -4 -6 -5 }}		{{Mapping\|legend=0\| 1 -3 5 7 5 6 6 \| 0 12 -7 -11 -4 -6 -5 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 56/55, 76/75, 105/104, 170/169, 190/187, 221/220		Comma list: 56/55, 76/75, 105/104, 170/169, 190/187, 221/220

	~~Mapping:~~ {{~~mapping~~\| 1 -3 5 7 5 6 6 5 \| 0 12 -7 -11 -4 -6 -5 -2 }}		{{Mapping\|legend=0\| 1 -3 5 7 5 6 6 5 \| 0 12 -7 -11 -4 -6 -5 -2 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 56/55, 76/75, 105/104, 161/160, 170/169, 190/187, 221/220		Comma list: 56/55, 76/75, 105/104, 161/160, 170/169, 190/187, 221/220

	~~Mapping:~~ {{~~mapping~~\| 1 -3 5 7 5 6 6 5 3 \| 0 12 -7 -11 -4 -6 -5 -2 4 }}		{{Mapping\|legend=0\| 1 -3 5 7 5 6 6 5 3 \| 0 12 -7 -11 -4 -6 -5 -2 4 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 56/55, 76/75, 105/104, 116/115, 145/143, 161/160, 170/169, 221/220		Comma list: 56/55, 76/75, 105/104, 116/115, 145/143, 161/160, 170/169, 221/220

	~~Mapping:~~ {{~~mapping~~\| 1 -3 5 7 5 6 6 5 3 6 \| 0 12 -7 -11 -4 -6 -5 -2 4 -3 }}		{{Mapping\|legend=0\| 1 -3 5 7 5 6 6 5 3 6 \| 0 12 -7 -11 -4 -6 -5 -2 4 -3 }}

	Optimal tunings:		Optimal tunings:

FloraC: Recategorize

2026-08-15T07:56:11Z

Recategorize

← Older revision		Revision as of 07:56, 15 August 2026
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	[[Category:Keegic temperaments\| ]] <!-- main article -->		[[Category:Keegic temperaments\| ]] <!-- main article -->
	[[Category:Temperament collections]]		[[Category:Temperament collections]]
	[[Category:~~Rank~~ 2]]		[[Category:Catalogs of rank-2 temperaments]]

FloraC: Oops. - typo

2026-07-18T18:14:40Z

Oops. - typo

← Older revision		Revision as of 18:14, 18 July 2026
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	This is a collection of rank-2 '''keegic temperaments''', which [[tempering out\|temper out]] the [[keega]] ([[ratio]]: 1029/1000, {{monzo\|legend=1\| -3 1 -3 3 }}), the difference a stack of three [[10/7]]'s and the [[3/1\|3rd harmonic]].		This is a collection of rank-2 '''keegic temperaments''', which [[tempering out\|temper out]] the [[keega]] ([[ratio]]: 1029/1000, {{monzo\|legend=1\| -3 1 -3 3 }}), the difference a stack of three [[10/7]]'s and the [[3/1\|3rd harmonic]].

	Temperaments discussed elsewhere ~~includef~~:		Temperaments discussed elsewhere include:
	* ''[[Parakangaroo]]'' (+28/27) → [[Trienstonic clan #Parakangaroo\|Trienstonic clan]]		* ''[[Parakangaroo]]'' (+28/27) → [[Trienstonic clan #Parakangaroo\|Trienstonic clan]]
	* ''[[Progress]]'' (+64/63) → [[Archytas clan #Progress\|Archytas clan]]		* ''[[Progress]]'' (+64/63) → [[Archytas clan #Progress\|Archytas clan]]

FloraC: Intro

2026-07-18T18:14:25Z

Intro

← Older revision		Revision as of 18:14, 18 July 2026
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	This is a collection of rank-2 '''keegic temperaments''', which [[tempering out\|temper out]] the [[keega]] ([[ratio]]: 1029/1000, {{monzo\|legend=1\| -3 1 -3 3 }}), the difference a stack of three [[10/7]]'s and the [[3/1\|3rd harmonic]].		This is a collection of rank-2 '''keegic temperaments''', which [[tempering out\|temper out]] the [[keega]] ([[ratio]]: 1029/1000, {{monzo\|legend=1\| -3 1 -3 3 }}), the difference a stack of three [[10/7]]'s and the [[3/1\|3rd harmonic]].

	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 includef:
			* ''[[Parakangaroo]]'' (+28/27) → [[Trienstonic clan #Parakangaroo\|Trienstonic clan]]
			* ''[[Progress]]'' (+64/63) → [[Archytas clan #Progress\|Archytas clan]]
			* ''[[Liese]]'' (+81/80) → [[Meantone family #Liese\|Meantone family]]
			* ''[[Triton]]'' (+225/224) → [[Marvel temperaments #Triton\|Marvel temperaments]]
			* [[Keemun]] (+49/48) → [[Kleismic family #Keemun\|Kleismic family]]
			* ''[[Subklei]]'' (+36/35) → [[Mint temperaments #Subklei\|Mint temperaments]]
			* ''[[Trisected]]'' (+128/125) → [[Augmented family #Trisected\|Augmented family]]
			* ''[[Xenia]]'' (+245/243) → [[Sensamagic clan #Xenia\|Sensamagic clan]]
			* ''[[Antitonic]]'' (+9/8) → [[Very low accuracy temperaments #Antitonic\|Very low accuracy temperaments]]

			Considered below are quinkee and aurora, in the order of increasing [[badness]].

	== Quinkee ==		== Quinkee ==

FloraC: Switch to Sintel's badness, WE & CWE tunings

2026-07-18T18:05:59Z

Switch to Sintel's badness, WE & CWE tunings

← Older revision		Revision as of 18:05, 18 July 2026
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	{{Mapping\|legend=1\| 1 -3 5 7 \| 0 12 -7 -11 }}		{{Mapping\|legend=1\| 1 -3 5 7 \| 0 12 -7 -11 }}

	[[Optimal tuning]] ([[~~POTE~~]]): ~2 = 1200.~~000~~{{c}}, ~21/16 = 458.~~348~~{{c}}		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1200.6445{{c}}, ~21/16 = 458.5945{{c}}
			: [[error map]]: {{val\| +0.645 -0.755 +6.748 -8.853 }}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~21/16 = 458.3493{{c}}
			: error map: {{val\| 0.000 -1.763 +5.241 -10.668 }}

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

	[[Badness]] (~~Smith~~): 0.~~242134~~		[[Badness]] (Sintel): 6.13

	=== 11-limit ===		=== 11-limit ===
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	Mapping: {{mapping\| 1 -3 5 7 5 \| 0 12 -7 -11 -4 }}		Mapping: {{mapping\| 1 -3 5 7 5 \| 0 12 -7 -11 -4 }}

	Optimal ~~tuning (POTE)~~: ~2 = 1200.~~000~~{{c}}, ~21/16 = 458.~~413~~{{c}}		Optimal tunings:
			* WE: ~2 = 1199.6148{{c}}, ~21/16 = 458.2655{{c}}
			* CWE: ~2 = 1200.0000{{c}}, ~21/16 = 458.4131{{c}}

	{{Optimal ET sequence\|legend=0\| ~~8bd,~~ 13, 21, 34~~, 55e, 89dee~~ }}		{{Optimal ET sequence\|legend=0\| 13, 21, 34 }}

	Badness (~~Smith~~): 0.~~116654~~		Badness (Sintel): 3.86

	=== 13-limit ===		=== 13-limit ===
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	Mapping: {{mapping\| 1 -3 5 7 5 6 \| 0 12 -7 -11 -4 -6 }}		Mapping: {{mapping\| 1 -3 5 7 5 6 \| 0 12 -7 -11 -4 -6 }}

	Optimal ~~tuning (POTE)~~: ~2 = 1200.~~000~~{{c}}, ~13/10 = 458.~~444~~{{c}}		Optimal tunings:
			* WE: ~2 = 1199.2763{{c}}, ~13/10 = 458.1671{{c}}
			* CWE: ~2 = 1200.0000{{c}}, ~13/10 = 458.4462{{c}}

	{{Optimal ET sequence\|legend=0\| ~~8bd,~~ 13, 21, 34~~, 55e, 89deef~~ }}		{{Optimal ET sequence\|legend=0\| 13, 21, 34 }}

	Badness (~~Smith~~): 0.~~066541~~		Badness (Sintel): 2.75

	=== 17-limit ===		=== 17-limit ===
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	Mapping: {{mapping\| 1 -3 5 7 5 6 6 \| 0 12 -7 -11 -4 -6 -5 }}		Mapping: {{mapping\| 1 -3 5 7 5 6 6 \| 0 12 -7 -11 -4 -6 -5 }}

	Optimal ~~tuning (POTE)~~: ~2 = 1200.~~000~~{{c}}, ~13/10 = 458.~~444~~{{c}}		Optimal tunings:
			* WE: ~2 = 1199.2758{{c}}, ~13/10 = 458.1670{{c}}
			* CWE: ~2 = 1200.0000{{c}}, ~13/10 = 458.4472{{c}}

	{{Optimal ET sequence\|legend=0\| ~~8bd,~~ 13, 21, 34~~, 55e, 89deef~~ }}		{{Optimal ET sequence\|legend=0\| 13, 21, 34 }}

	Badness (~~Smith~~): 0.~~044148~~		Badness (Sintel): 2.25

	=== 19-limit ===		=== 19-limit ===
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	Mapping: {{mapping\| 1 -3 5 7 5 6 6 5 \| 0 12 -7 -11 -4 -6 -5 -2 }}		Mapping: {{mapping\| 1 -3 5 7 5 6 6 5 \| 0 12 -7 -11 -4 -6 -5 -2 }}

	Optimal ~~tuning (POTE)~~: ~2 = 1200.~~000~~{{c}}, ~13/10 = 458.~~444~~{{c}}		Optimal tunings:
			* WE: ~2 = 1199.7718{{c}}, ~13/10 = 458.3568{{c}}
			* CWE: ~2 = 1200.0000{{c}}, ~13/10 = 458.4451{{c}}

	{{Optimal ET sequence\|legend=0\| ~~8bd,~~ 13, 21, 34~~, 55eh, 89deefhh~~ }}		{{Optimal ET sequence\|legend=0\| 13, 21, 34 }}

	Badness (~~Smith~~): 0.~~037621~~		Badness (Sintel): 2.29

	=== 23-limit ===		=== 23-limit ===
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	Mapping: {{mapping\| 1 -3 5 7 5 6 6 5 3 \| 0 12 -7 -11 -4 -6 -5 -2 4 }}		Mapping: {{mapping\| 1 -3 5 7 5 6 6 5 3 \| 0 12 -7 -11 -4 -6 -5 -2 4 }}

	Optimal ~~tuning (POTE)~~: ~2 = 1200.~~000~~{{c}}, ~13/10 = 458.~~430~~{{c}}		Optimal tunings:
			* WE: ~2 = 1199.6512{{c}}, ~13/10 = 458.2963{{c}}
			* CWE: ~2 = 1200.0000{{c}}, ~13/10 = 458.4307{{c}}

	{{Optimal ET sequence\|legend=0\| ~~8bd,~~ 13, 21, 34~~, 55eh, 89deefhh~~ }}		{{Optimal ET sequence\|legend=0\| 13, 21, 34 }}

	Badness (~~Smith~~): 0.~~030236~~		Badness (Sintel): 2.16

	=== 29-limit ===		=== 29-limit ===
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	Mapping: {{mapping\| 1 -3 5 7 5 6 6 5 3 6 \| 0 12 -7 -11 -4 -6 -5 -2 4 -3 }}		Mapping: {{mapping\| 1 -3 5 7 5 6 6 5 3 6 \| 0 12 -7 -11 -4 -6 -5 -2 4 -3 }}

	Optimal ~~tuning (POTE)~~: ~2 = 1200.~~000~~{{c}}, ~13/10 = 458.~~426~~{{c}}		Optimal tunings:
			* WE: ~2 = 1199.7786{{c}}, ~13/10 = 458.3411{{c}}
			* CWE: ~2 = 1200.0000{{c}}, ~13/10 = 458.4265{{c}}

	{{Optimal ET sequence\|legend=0\| ~~8bd,~~ 13, 21, 34~~, 55eh, 89deefhh~~ }}		{{Optimal ET sequence\|legend=0\| 13, 21, 34 }}

	Badness (~~Smith~~): 0.~~025201~~		Badness (Sintel): 2.11

	[[Category:Keegic temperaments\| ]] <!-- main article -->		[[Category:Keegic temperaments\| ]] <!-- main article -->
	[[Category:Temperament collections]]		[[Category:Temperament collections]]
	[[Category:Rank 2]]		[[Category:Rank 2]]

FloraC: Misc. cleanup

2026-07-18T17:31:04Z

Misc. cleanup

← Older revision		Revision as of 17:31, 18 July 2026
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	{{Technical data page}}		{{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]].		This is a collection of rank-2 '''keegic temperaments''', which [[tempering out\|temper out]] the [[keega]] ([[ratio]]: 1029/1000, {{monzo\|legend=1\| -3 1 -3 3 }}), the difference a stack of three [[10/7]]'s and the [[3/1\|3rd harmonic]].

	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]].
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	: ''For the 5-limit version, see [[Diaschismic–gothmic equivalence continuum #Goldis]].''		: ''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.		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 (subfourths/ultramajor third) or sharp fifths (superfifths/ultraminor 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

	[[Comma list]]: 1029/1000, 28672/28125		[[Comma list]]: 1029/1000, 28672/28125

	~~[[Mapping]]: [~~{{~~val~~\|1 -3 5 7~~}}, {{val~~\|0 12 -7 -11}}]		{{Mapping\|legend=1\| 1 -3 5 7 \| 0 12 -7 -11 }}

	[[POTE ~~generator~~]]: ~21/16 = 458.348		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~21/16 = 458.348{{c}}

	{{Optimal ET sequence\|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]] (Smith): 0.242134

	=== 11-limit ===		=== 11-limit ===
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	Comma list: 56/55, 1029/1000, 5632/5625		Comma list: 56/55, 1029/1000, 5632/5625

	Mapping: [{{~~val~~\|1 -3 5 7 5~~}}, {{val~~\|0 12 -7 -11 -4}}]		Mapping: {{mapping\| 1 -3 5 7 5 \| 0 12 -7 -11 -4 }}

	POTE ~~generator~~: ~21/16 = 458.413		Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~21/16 = 458.413{{c}}

	{{Optimal ET sequence\|legend=1\| 8bd, 13, 21, 34, 55e, 89dee }}		{{Optimal ET sequence\|legend=0\| 8bd, 13, 21, 34, 55e, 89dee }}

	Badness: 0.116654		Badness (Smith): 0.116654

	=== 13-limit ===		=== 13-limit ===
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	Comma list: 56/55, 105/104, 512/507, 637/625		Comma list: 56/55, 105/104, 512/507, 637/625

	Mapping: [{{~~val~~\|1 -3 5 7 5 6~~}}, {{val~~\|0 12 -7 -11 -4 -6}}]		Mapping: {{mapping\| 1 -3 5 7 5 6 \| 0 12 -7 -11 -4 -6 }}

	POTE ~~generator~~: ~13/10 = 458.444		Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~13/10 = 458.444{{c}}

	{{Optimal ET sequence\|legend=1\| 8bd, 13, 21, 34, 55e, 89deef }}		{{Optimal ET sequence\|legend=0\| 8bd, 13, 21, 34, 55e, 89deef }}

	Badness: 0.066541		Badness (Smith): 0.066541

	=== 17-limit ===		=== 17-limit ===
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	Comma list: 56/55, 105/104, 170/169, 221/220, 375/374		Comma list: 56/55, 105/104, 170/169, 221/220, 375/374

	Mapping: [{{~~val~~\|1 -3 5 7 5 6 6~~}}, {{val~~\|0 12 -7 -11 -4 -6 -5}}]		Mapping: {{mapping\| 1 -3 5 7 5 6 6 \| 0 12 -7 -11 -4 -6 -5 }}

	POTE ~~generator~~: ~13/10 = 458.444		Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~13/10 = 458.444{{c}}

	{{Optimal ET sequence\|legend=1\| 8bd, 13, 21, 34, 55e, 89deef }}		{{Optimal ET sequence\|legend=0\| 8bd, 13, 21, 34, 55e, 89deef }}

	Badness: 0.044148		Badness (Smith): 0.044148

	=== 19-limit ===		=== 19-limit ===
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	Comma list: 56/55, 76/75, 105/104, 170/169, 190/187, 221/220		Comma list: 56/55, 76/75, 105/104, 170/169, 190/187, 221/220

	Mapping: [{{~~val~~\|1 -3 5 7 5 6 6 5~~}}, {{val~~\|0 12 -7 -11 -4 -6 -5 -2}}]		Mapping: {{mapping\| 1 -3 5 7 5 6 6 5 \| 0 12 -7 -11 -4 -6 -5 -2 }}

	POTE ~~generator~~: ~13/10 = 458.444		Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~13/10 = 458.444{{c}}

	{{Optimal ET sequence\|legend=1\| 8bd, 13, 21, 34, 55eh, 89deefhh }}		{{Optimal ET sequence\|legend=0\| 8bd, 13, 21, 34, 55eh, 89deefhh }}

	Badness: 0.037621		Badness (Smith): 0.037621

	=== 23-limit ===		=== 23-limit ===
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	Comma list: 56/55, 76/75, 105/104, 161/160, 170/169, 190/187, 221/220		Comma list: 56/55, 76/75, 105/104, 161/160, 170/169, 190/187, 221/220

	Mapping: [{{~~val~~\|1 -3 5 7 5 6 6 5 3~~}}, {{val~~\|0 12 -7 -11 -4 -6 -5 -2 4}}]		Mapping: {{mapping\| 1 -3 5 7 5 6 6 5 3 \| 0 12 -7 -11 -4 -6 -5 -2 4 }}

	POTE ~~generator~~: ~13/10 = 458.430		Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~13/10 = 458.430{{c}}

	{{Optimal ET sequence\|legend=1\| 8bd, 13, 21, 34, 55eh, 89deefhh }}		{{Optimal ET sequence\|legend=0\| 8bd, 13, 21, 34, 55eh, 89deefhh }}

	Badness: 0.030236		Badness (Smith): 0.030236

	=== 29-limit ===		=== 29-limit ===
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	Comma list: 56/55, 76/75, 105/104, 116/115, 145/143, 161/160, 170/169, 221/220		Comma list: 56/55, 76/75, 105/104, 116/115, 145/143, 161/160, 170/169, 221/220

	Mapping: [{{~~val~~\|1 -3 5 7 5 6 6 5 3 6~~}}, {{val~~\|0 12 -7 -11 -4 -6 -5 -2 4 -3}}]		Mapping: {{mapping\| 1 -3 5 7 5 6 6 5 3 6 \| 0 12 -7 -11 -4 -6 -5 -2 4 -3 }}

	POTE ~~generator~~: ~13/10 = 458.426		Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~13/10 = 458.426{{c}}

	{{Optimal ET sequence\|legend=1\| 8bd, 13, 21, 34, 55eh, 89deefhh }}		{{Optimal ET sequence\|legend=0\| 8bd, 13, 21, 34, 55eh, 89deefhh }}

	Badness: 0.025201		Badness (Smith): 0.025201

			[[Category:Keegic temperaments\| ]] <!-- main article -->
	[[Category:Temperament collections]]		[[Category:Temperament collections]]
	~~[[Category:Keegic]]~~
	[[Category:Rank 2]]		[[Category:Rank 2]]

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]]

← Older revision		Revision as of 18:14, 18 July 2026
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	This is a collection of rank-2 '''keegic temperaments''', which [[tempering out\|temper out]] the [[keega]] ([[ratio]]: 1029/1000, {{monzo\|legend=1\| -3 1 -3 3 }}), the difference a stack of three [[10/7]]'s and the [[3/1\|3rd harmonic]].		This is a collection of rank-2 '''keegic temperaments''', which [[tempering out\|temper out]] the [[keega]] ([[ratio]]: 1029/1000, {{monzo\|legend=1\| -3 1 -3 3 }}), the difference a stack of three [[10/7]]'s and the [[3/1\|3rd harmonic]].

	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 includef:
			* ''[[Parakangaroo]]'' (+28/27) → [[Trienstonic clan #Parakangaroo\|Trienstonic clan]]
			* ''[[Progress]]'' (+64/63) → [[Archytas clan #Progress\|Archytas clan]]
			* ''[[Liese]]'' (+81/80) → [[Meantone family #Liese\|Meantone family]]
			* ''[[Triton]]'' (+225/224) → [[Marvel temperaments #Triton\|Marvel temperaments]]
			* [[Keemun]] (+49/48) → [[Kleismic family #Keemun\|Kleismic family]]
			* ''[[Subklei]]'' (+36/35) → [[Mint temperaments #Subklei\|Mint temperaments]]
			* ''[[Trisected]]'' (+128/125) → [[Augmented family #Trisected\|Augmented family]]
			* ''[[Xenia]]'' (+245/243) → [[Sensamagic clan #Xenia\|Sensamagic clan]]
			* ''[[Antitonic]]'' (+9/8) → [[Very low accuracy temperaments #Antitonic\|Very low accuracy temperaments]]

			Considered below are quinkee and aurora, in the order of increasing [[badness]].

	== Quinkee ==		== Quinkee ==