Keemic temperaments - Revision history

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

2026-09-24T12:32:23Z

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

← Older revision		Revision as of 12:32, 24 September 2026
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	Comma list: 100/99, 385/384, 1375/1372		Comma list: 100/99, 385/384, 1375/1372

	~~Mapping:~~ {{~~mapping~~\| 1 -9 -6 -4 8 \| 0 14 11 9 -6 }}		{{Mapping\|legend=0\| 1 -9 -6 -4 8 \| 0 14 11 9 -6 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 100/99, 196/195, 275/273, 385/384		Comma list: 100/99, 196/195, 275/273, 385/384

	~~Mapping:~~ {{~~mapping~~\| 1 -9 -6 -4 8 9 \| 0 14 11 9 -6 -7 }}		{{Mapping\|legend=0\| 1 -9 -6 -4 8 9 \| 0 14 11 9 -6 -7 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 243/242, 441/440, 625/616		Comma list: 243/242, 441/440, 625/616

	~~Mapping:~~ {{~~mapping~~\| 1 -9 -6 -4 -23 \| 0 14 11 9 35 }}		{{Mapping\|legend=0\| 1 -9 -6 -4 -23 \| 0 14 11 9 35 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 105/104, 243/242, 275/273, 325/324		Comma list: 105/104, 243/242, 275/273, 325/324

	~~Mapping:~~ {{~~mapping~~\| 1 -9 -6 -4 -23 -22 \| 0 14 11 9 35 34 }}		{{Mapping\|legend=0\| 1 -9 -6 -4 -23 -22 \| 0 14 11 9 35 34 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 245/242, 540/539, 625/616		Comma list: 245/242, 540/539, 625/616

	~~Mapping:~~ {{~~mapping~~\| 1 -10 -5 -10 -13 \| 0 19 12 21 27 }}		{{Mapping\|legend=0\| 1 -10 -5 -10 -13 \| 0 19 12 21 27 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 144/143, 196/195, 245/242, 275/273		Comma list: 144/143, 196/195, 245/242, 275/273

	~~Mapping:~~ {{~~mapping~~\| 1 -10 -5 -10 -13 -3 \| 0 19 12 21 27 11 }}		{{Mapping\|legend=0\| 1 -10 -5 -10 -13 -3 \| 0 19 12 21 27 11 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 105/104, 325/324, 15625/15379		Comma list: 105/104, 325/324, 15625/15379

	~~Mapping:~~ {{~~mapping~~\| 15 0 11 42 52 8 \| 0 1 1 0 0 2 }}		{{Mapping\|legend=0\| 15 0 11 42 52 8 \| 0 1 1 0 0 2 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 121/120, 441/440, 875/864		Comma list: 121/120, 441/440, 875/864

	~~Mapping:~~ {{~~mapping~~\| 15 0 11 42 28 \| 0 1 1 0 1 }}		{{Mapping\|legend=0\| 15 0 11 42 28 \| 0 1 1 0 1 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 105/104, 121/120, 275/273, 325/324		Comma list: 105/104, 121/120, 275/273, 325/324

	~~Mapping:~~ {{~~mapping~~\| 15 0 11 42 28 8 \| 0 1 1 0 1 2 }}		{{Mapping\|legend=0\| 15 0 11 42 28 8 \| 0 1 1 0 1 2 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 100/99, 352/343, 385/384		Comma list: 100/99, 352/343, 385/384

	~~Mapping:~~ {{~~mapping~~\| 11 0 8 31 38 \| 0 1 1 0 0 }}		{{Mapping\|legend=0\| 11 0 8 31 38 \| 0 1 1 0 0 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 85/84, 100/99, 121/119, 385/384		Comma list: 85/84, 100/99, 121/119, 385/384

	~~Mapping:~~ {{~~mapping~~\| 11 0 8 31 38 45 \| 0 1 1 0 0 0 }}		{{Mapping\|legend=0\| 11 0 8 31 38 45 \| 0 1 1 0 0 0 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 100/99, 385/384, 2420/2401		Comma list: 100/99, 385/384, 2420/2401

	~~Mapping:~~ {{~~mapping~~\| 1 -3 -2 2 4 \| 0 17 16 3 -2}}		{{Mapping\|legend=0\| 1 -3 -2 2 4 \| 0 17 16 3 -2}}

	Optimal tunings:		Optimal tunings:
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	Comma list: 100/99, 169/168, 275/273, 385/384		Comma list: 100/99, 169/168, 275/273, 385/384

	~~Mapping:~~ {{~~mapping~~\| 1 -3 -2 2 4 1 \| 0 17 16 3 -2 10 }}		{{Mapping\|legend=0\| 1 -3 -2 2 4 1 \| 0 17 16 3 -2 10 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 100/99, 385/384, 6655/6561		Comma list: 100/99, 385/384, 6655/6561

	~~Mapping:~~ {{~~mapping~~\| 7 0 -6 53 2 \| 0 1 2 -3 2 }}		{{Mapping\|legend=0\| 7 0 -6 53 2 \| 0 1 2 -3 2 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 100/99, 169/168, 352/351, 385/384		Comma list: 100/99, 169/168, 352/351, 385/384

	~~Mapping:~~ {{~~mapping~~\| 7 0 -6 53 2 37 \| 0 1 2 -3 2 -1 }}		{{Mapping\|legend=0\| 7 0 -6 53 2 37 \| 0 1 2 -3 2 -1 }}

	Optimal tunings:		Optimal tunings:

FloraC: Recategorize

2026-09-20T03:53:41Z

Recategorize

← Older revision		Revision as of 03:53, 20 September 2026
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	Badness (Sintel): 1.70		Badness (Sintel): 1.70

			[[Category:Keemic temperaments\| ]] <!-- main article -->
	[[Category:Temperament collections]]		[[Category:Temperament collections]]
	[[Category:~~Keemic temperaments\| ]] <!~~-~~- main article -->~~		[[Category:Catalogs of rank-2 temperaments]]
	~~[[Category:Rank~~ 2]]

FloraC: + link to wesley

2026-08-02T15:29:19Z

+ link to wesley

← Older revision		Revision as of 15:29, 2 August 2026
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	* [[Magic]] (+225/224) → [[Magic family #Septimal magic\|Magic family]]		* [[Magic]] (+225/224) → [[Magic family #Septimal magic\|Magic family]]
	* [[Keemun]] (+49/48) → [[Kleismic family #Keemun\|Kleismic family]]		* [[Keemun]] (+49/48) → [[Kleismic family #Keemun\|Kleismic family]]
			* ''[[Wesley]]'' (+405/392) → [[Wesley family #Septimal wesley\|Wesley family]]
	* ''[[Doublewide]]'' (+50/49) → [[Jubilismic clan #Doublewide\|Jubilismic clan]]		* ''[[Doublewide]]'' (+50/49) → [[Jubilismic clan #Doublewide\|Jubilismic clan]]
	* [[Superkleismic]] (+1029/1024) → [[Gamelismic clan #Superkleismic\|Gamelismic clan]]		* [[Superkleismic]] (+1029/1024) → [[Gamelismic clan #Superkleismic\|Gamelismic clan]]

FloraC: + link

2026-07-21T04:31:07Z

+ link

← Older revision		Revision as of 04:31, 21 July 2026
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	* ''[[Doublewide]]'' (+50/49) → [[Jubilismic clan #Doublewide\|Jubilismic clan]]		* ''[[Doublewide]]'' (+50/49) → [[Jubilismic clan #Doublewide\|Jubilismic clan]]
	* [[Superkleismic]] (+1029/1024) → [[Gamelismic clan #Superkleismic\|Gamelismic clan]]		* [[Superkleismic]] (+1029/1024) → [[Gamelismic clan #Superkleismic\|Gamelismic clan]]
			* ''[[Fifives]]'' (+83349/81920) → [[Fifive family #Fifives\|Fifive family]]
	* ''[[Sycamore]]'' (+686/675) → [[Sycamore family #Septimal sycamore\|Sycamore family]]		* ''[[Sycamore]]'' (+686/675) → [[Sycamore family #Septimal sycamore\|Sycamore family]]

FloraC: Undeka 13-limit -> no-13 17-limit. Pentadecal 13-limit -> no-11 13-limit

2026-07-07T11:02:16Z

Undeka 13-limit -> no-13 17-limit. Pentadecal 13-limit -> no-11 13-limit

← Older revision		Revision as of 11:02, 7 July 2026
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	Named by [[Xenllium]] in 2021, pentadecal tempers out the 15-5/3-comma ({{monzo\| -11 -15 15 }}) in the 5-limit. This temperament can be described as {{nowrap\| 15 & 60 }} temperament, tempering out the [[cloudy comma]], 16807/16384 and the [[keema]], 875/864 in the 7-limit.		Named by [[Xenllium]] in 2021, pentadecal tempers out the 15-5/3-comma ({{monzo\| -11 -15 15 }}) in the 5-limit. This temperament can be described as {{nowrap\| 15 & 60 }} temperament, tempering out the [[cloudy comma]], 16807/16384 and the [[keema]], 875/864 in the 7-limit.

			=== 7-limit ===
	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

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	[[Badness]] (Sintel): 2.91		[[Badness]] (Sintel): 2.91

	=== ~~11-limit~~ ===		==== 2.3.5.7.13 subgroup ====
	Subgroup: 2.3.5.7.11		Subgroup: 2.3.5.7.13

	~~Comma list: 100/99, 385/384, 1372/1331~~

	~~Mapping: {{mapping\| 15 0 11 42 52 \| 0 1 1 0 0 }}~~		Comma list: 105/104, 325/324, 15625/15379

	~~Optimal tunings:~~
	* WE: ~21/20 = 80.0213{{c}}, ~3/2 = 702.9194{{c}} (~56/55 = 17.2721{{c}})
	* CWE: ~21/20 = 80.0000{{c}}, ~3/2 = 702.8751{{c}} (~56/55 = 17.1249{{c}})

	~~{{Optimal ET sequence\|legend=0\| 15, 45, 60, 75de, 135de }}~~

	~~Badness (Sintel): 2.56~~

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

	Comma list: ~~100/99,~~ 105/104, ~~144~~/~~143~~, ~~1372~~/~~1331~~

	Mapping: {{mapping\| 15 0 11 42 52 8 \| 0 1 1 0 0 2 }}		Mapping: {{mapping\| 15 0 11 42 52 8 \| 0 1 1 0 0 2 }}

	Optimal tunings:		Optimal tunings:
	* WE: ~21/20 = 80.~~0207~~{{c}}, ~3/2 = ~~701~~.~~8966~~{{c}} (~91/90 = 18.~~2900~~{{c}})		* WE: ~21/20 = 80.1133{{c}}, ~3/2 = 700.1871{{c}} (~91/90 = 20.8325{{c}})
	* CWE: ~21/20 = 80.0000{{c}}, ~3/2 = ~~701~~.~~8545~~{{c}} (~91/90 = 18.~~1455~~{{c}})		* CWE: ~21/20 = 80.0000{{c}}, ~3/2 = 700.2086{{c}} (~91/90 = 19.7914{{c}})

	{{Optimal ET sequence\|legend=0\| 15, 45f, 60~~, 135de, 195cddee~~ }}		{{Optimal ET sequence\|legend=0\| 15, 30bcff, 45f, 60 }}

	Badness (Sintel): 2.14		Badness (Sintel): 1.80

	=== Quindecal ===		=== Quindecal ===
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	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

	Comma list: 121/120, ~~196/195, 352~~/~~351~~, ~~875~~/~~864~~		Comma list: 105/104, 121/120, 275/273, 325/324

	Mapping: {{mapping\| 15 0 11 42 28 ~~103~~ \| 0 1 1 0 1 -2 }}		Mapping: {{mapping\| 15 0 11 42 28 8 \| 0 1 1 0 1 2 }}

	Optimal tunings:		Optimal tunings:
	* WE: ~21/20 = 80.~~1015~~{{c}}, ~3/2 = ~~702~~.~~5374~~{{c}} (~~~126~~/~~125~~ = 18.~~3763~~{{c}})		* WE: ~21/20 = 80.1359{{c}}, ~3/2 = 700.2567{{c}} (~91/90 = 20.9661{{c}})
	* CWE: ~21/20 = 80.0000{{c}}, ~3/2 = ~~701~~.~~8504~~{{c}} (~~~126~~/~~125~~ = 18.~~1496~~{{c}})		* CWE: ~21/20 = 80.0000{{c}}, ~3/2 = 700.2955{{c}} (~91/90 = 19.7045{{c}})

	{{Optimal ET sequence\|legend=0\| ~~15f~~, 60e~~, 135deef~~ }}		{{Optimal ET sequence\|legend=0\| 15, 30bceff, 45ef, 60e }}

	Badness (Sintel): 2.29		Badness (Sintel): 1.34

	== Undeka ==		== Undeka ==
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	Badness (Sintel): 2.27		Badness (Sintel): 2.27

	=== ~~13-limit~~ ===		=== 2.3.5.7.11.17 subgroup ===
	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.17

	Comma list: 65/63, 100/99, ~~169~~/~~165~~, ~~352~~/~~343~~		Comma list: 85/84, 100/99, 121/119, 385/384

	Mapping: {{mapping\| 11 0 8 31 38 23 \| 0 1 1 0 0 1 }}		Mapping: {{mapping\| 11 0 8 31 38 45 \| 0 1 1 0 0 0 }}

	Optimal tunings:		Optimal tunings:
	* WE: ~13/12 = 109.~~1184~~{{c}}, ~3/2 = ~~707~~.~~9422~~{{c}}		* WE: ~17/16 = 109.0232{{c}}, ~3/2 = 706.5074{{c}}
	* CWE: ~13/12 = 109.0909{{c}}, ~3/2 = ~~707~~.~~9065~~{{c}}		* CWE: ~17/16 = 109.0909{{c}}, ~3/2 = 706.6786{{c}}

	{{Optimal ET sequence\|legend=0\| ~~11cf~~, 22 }}		{{Optimal ET sequence\|legend=0\| 11c, 22 }}

	Badness (Sintel): 2.34		Badness (Sintel): 1.82

	== Hyperkleismic ==		== Hyperkleismic ==

FloraC: /* Undeka */ + link

2026-07-05T11:04:00Z

Undeka: + link

← Older revision		Revision as of 11:04, 5 July 2026
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	== Undeka ==		== Undeka ==
			: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Undeka]].''

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

FloraC: Move undeka here

2026-07-05T10:30:01Z

Move undeka here

@@ Line 12: / Line 12: @@
 * [[Superkleismic]] (+1029/1024) → [[Gamelismic clan #Superkleismic|Gamelismic clan]]
 * ''[[Sycamore]]'' (+686/675) → [[Sycamore family #Septimal sycamore|Sycamore family]]
-Discussed below are quasitemp, chromo, barbad, pentadecal, hyperkleismic, and sevond, in the order of increasing [[TE logflat badness]].
+Discussed below are quasitemp, chromo, barbad, pentadecal, undeka, hyperkleismic, and sevond, in the order of increasing [[TE logflat badness]].
 == Quasitemp ==
@@ Line 255: / Line 254: @@
 Badness (Sintel): 2.29
 == Hyperkleismic ==

FloraC: Move pentadecal here

2026-06-25T10:21:38Z

Move pentadecal here

@@ Line 14: / Line 14: @@
 * ''[[Undeka]]'' (+3200/3087) → [[11th-octave temperaments #Undeka|11th-octave temperaments]]
-Discussed below are quasitemp, chromo, barbad, hyperkleismic, and sevond, in the order of increasing [[TE logflat badness]].
+Discussed below are quasitemp, chromo, barbad, pentadecal, hyperkleismic, and sevond, in the order of increasing [[TE logflat badness]].
 == Quasitemp ==
@@ Line 173: / Line 173: @@
 Badness (Sintel): 1.62
 == Hyperkleismic ==

FloraC: + link to mujannabic

2026-05-29T10:17:08Z

+ link to mujannabic

← Older revision		Revision as of 10:17, 29 May 2026
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	Full [[7-limit]] keemic temperaments discussed elsewhere are:		Full [[7-limit]] keemic temperaments discussed elsewhere are:
	* [[Flattone]] (+81/80) → [[Meantone family #Flattone\|Meantone family]]		* [[Flattone]] (+81/80) → [[Meantone family #Flattone\|Meantone family]]
			* ''[[Mujannabic]]'' (+25/24) → [[Dicot family #Dicot\|Dicot family]]
	* [[Porcupine]] (+64/63) → [[Porcupine family #Septimal porcupine\|Porcupine family]]		* [[Porcupine]] (+64/63) → [[Porcupine family #Septimal porcupine\|Porcupine family]]
	* [[Monkey]] (+5120/5103) → [[Tetracot family #Monkey\|Tetracot family]]		* [[Monkey]] (+5120/5103) → [[Tetracot family #Monkey\|Tetracot family]]

FloraC: + link to monkey. Sort links by ploidacot

2026-04-15T18:07:31Z

+ link to monkey. Sort links by ploidacot

← Older revision		Revision as of 18:07, 15 April 2026
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	This is a collection of [[rank-2 temperament\|linear]] [[regular temperament\|temperaments]] that [[tempering out\|temper out]] the [[keema]] ({{monzo\|legend=1\| -5 -3 3 1 }}, [[ratio]]: 875/864), with [[S-expression]] S5/S6. Its fundamental equivalence entails that [[6/5]] is sharpened so that it stacks three times to reach [[7/4]], and the interval between 6/5 and [[5/4]] is compressed so that [[7/6]]–6/5–5/4–[[9/7]] are set equidistant from each other. As the canonical extension of rank-3 [[keemic]] to the [[11-limit]] tempers out the commas [[100/99]] and [[385/384]] (whereby ([[6/5]])<sup>2</sup> is identified with [[16/11]]), this provides a clean way to extend the various keemic temperaments to the 11-limit as well.		This is a collection of [[rank-2 temperament\|linear]] [[regular temperament\|temperaments]] that [[tempering out\|temper out]] the [[keema]] ({{monzo\|legend=1\| -5 -3 3 1 }}, [[ratio]]: 875/864), with [[S-expression]] S5/S6. Its fundamental equivalence entails that [[6/5]] is sharpened so that it stacks three times to reach [[7/4]], and the interval between 6/5 and [[5/4]] is compressed so that [[7/6]]–6/5–5/4–[[9/7]] are set equidistant from each other. As the canonical extension of rank-3 [[keemic]] to the [[11-limit]] tempers out the commas [[100/99]] and [[385/384]] (whereby ([[6/5]])<sup>2</sup> is identified with [[16/11]]), this provides a clean way to extend the various keemic temperaments to the 11-limit as well.

	Full [[7-limit]] keemic temperaments discussed elsewhere are:		Full [[7-limit]] keemic temperaments discussed elsewhere are:
			* [[Flattone]] (+81/80) → [[Meantone family #Flattone\|Meantone family]]
			* [[Porcupine]] (+64/63) → [[Porcupine family #Septimal porcupine\|Porcupine family]]
			* [[Monkey]] (+5120/5103) → [[Tetracot family #Monkey\|Tetracot family]]
			* [[Magic]] (+225/224) → [[Magic family #Septimal magic\|Magic family]]
	* [[Keemun]] (+49/48) → [[Kleismic family #Keemun\|Kleismic family]]		* [[Keemun]] (+49/48) → [[Kleismic family #Keemun\|Kleismic family]]
	* ''[[Doublewide]]'' (+50/49) → [[Jubilismic clan #Doublewide\|Jubilismic clan]]		* ''[[Doublewide]]'' (+50/49) → [[Jubilismic clan #Doublewide\|Jubilismic clan]]
	* [[~~Porcupine~~]] (+64/63) → [[~~Porcupine family~~ #~~Septimal porcupine~~\|~~Porcupine family]]~~		* [[Superkleismic]] (+1029/1024) → [[Gamelismic clan #Superkleismic\|Gamelismic clan]]
	* [[Flattone]] (+81/80) → [[Meantone family #Flattone\|Meantone family]]
	* [[Magic]] (+225/224) → [[Magic family #Septimal magic\|Magic family]]
	* ''[[Sycamore]]'' (+686/675) → [[Sycamore family #Septimal sycamore\|Sycamore family]]		* ''[[Sycamore]]'' (+686/675) → [[Sycamore family #Septimal sycamore\|Sycamore family]]
	* [[Superkleismic]] (+1029/1024) → [[Gamelismic clan #Superkleismic\|Gamelismic clan]]
	* ''[[Undeka]]'' (+3200/3087) → [[11th-octave temperaments #Undeka\|11th-octave temperaments]]		* ''[[Undeka]]'' (+3200/3087) → [[11th-octave temperaments #Undeka\|11th-octave temperaments]]

	Discussed below are quasitemp, chromo, barbad, hyperkleismic, and sevond.		Discussed below are quasitemp, chromo, barbad, hyperkleismic, and sevond, in the order of increasing [[TE logflat badness]].

	== Quasitemp ==		== Quasitemp ==

← Older revision		Revision as of 15:29, 2 August 2026
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	* [[Magic]] (+225/224) → [[Magic family #Septimal magic\|Magic family]]		* [[Magic]] (+225/224) → [[Magic family #Septimal magic\|Magic family]]
	* [[Keemun]] (+49/48) → [[Kleismic family #Keemun\|Kleismic family]]		* [[Keemun]] (+49/48) → [[Kleismic family #Keemun\|Kleismic family]]
			* ''[[Wesley]]'' (+405/392) → [[Wesley family #Septimal wesley\|Wesley family]]
	* ''[[Doublewide]]'' (+50/49) → [[Jubilismic clan #Doublewide\|Jubilismic clan]]		* ''[[Doublewide]]'' (+50/49) → [[Jubilismic clan #Doublewide\|Jubilismic clan]]
	* [[Superkleismic]] (+1029/1024) → [[Gamelismic clan #Superkleismic\|Gamelismic clan]]		* [[Superkleismic]] (+1029/1024) → [[Gamelismic clan #Superkleismic\|Gamelismic clan]]

← Older revision		Revision as of 10:17, 29 May 2026
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	Full [[7-limit]] keemic temperaments discussed elsewhere are:		Full [[7-limit]] keemic temperaments discussed elsewhere are:
	* [[Flattone]] (+81/80) → [[Meantone family #Flattone\|Meantone family]]		* [[Flattone]] (+81/80) → [[Meantone family #Flattone\|Meantone family]]
			* ''[[Mujannabic]]'' (+25/24) → [[Dicot family #Dicot\|Dicot family]]
	* [[Porcupine]] (+64/63) → [[Porcupine family #Septimal porcupine\|Porcupine family]]		* [[Porcupine]] (+64/63) → [[Porcupine family #Septimal porcupine\|Porcupine family]]
	* [[Monkey]] (+5120/5103) → [[Tetracot family #Monkey\|Tetracot family]]		* [[Monkey]] (+5120/5103) → [[Tetracot family #Monkey\|Tetracot family]]