Keemic temperaments - Revision history

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
Line 4:		Line 4:
	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
Line 2:		Line 2:
	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 ==

FloraC: /* Quasitemp */ comparison with myna

2026-02-19T16:20:06Z

Quasitemp: comparison with myna

← Older revision		Revision as of 16:20, 19 February 2026
Line 17:		Line 17:
	: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Quasitemp]].''		: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Quasitemp]].''

	Quasitemp tempers out [[2401/2400]] in addition to 875/864 and may be described as the {{nowrap\| 37 & 41 }} temperament. It can be thought of as a [[strong extension]] of the 2.5/3.7/3 subgroup temperament called [[gariberttet]], which is defined by tempering out [[3125/3087]]. In gariberttet, three generators reach [[5/3]] and five reach [[7/3]], so that the generator itself has the interpretation of [[25/21]]. This implies that 3:5:7 and 5:6:7 chords are reached rather quickly. Quasitemp tempering out 875/864 entails that [[8/7]] is found after 9 generators, from which the mappings of 3 and 5 follow.		Quasitemp tempers out [[2401/2400]] in addition to 875/864 and may be described as the {{nowrap\| 37 & 41 }} temperament. It is characterized by equating the interval between the pental and septimal thirds ([[36/35]]) with the classical chromatic semitone ([[25/24]]), and by tempering together the septimal dieses of [[49/48]] and [[50/49]]. In that sense, it is opposed to [[orwellismic temperaments]], in particular [[myna]], where the distance between the pental and septimal thirds is the same as the septimal dieses and different from the classical chromatic semitone.

			Quasitemp can also be thought of as a [[strong extension]] of the 2.5/3.7/3-subgroup temperament called [[gariberttet]], which is defined by tempering out [[3125/3087]]. In gariberttet, three generators reach [[5/3]] and five reach [[7/3]], so that the generator itself has the interpretation of [[25/21]]. This implies that 3:5:7 and 5:6:7 chords are reached rather quickly. Quasitemp tempering out 875/864 entails that [[8/7]] is found after 9 generators, from which the mappings of 3 and 5 follow.

	Note that the generator is given as 25/21's octave complement, 42/25, in the data that follow, since a stack of 14 such generators octave-reduced is the perfect fifth, whence the temperament's [[ploidacot]] is iota-14-cot. This generator is equated to [[22/13]] for the 13-limit extension, tempering out [[275/273]].		Note that the generator is given as 25/21's octave complement, 42/25, in the data that follow, since a stack of 14 such generators octave-reduced is the perfect fifth, whence the temperament's [[ploidacot]] is iota-14-cot. This generator is equated to [[22/13]] for the 13-limit extension, tempering out [[275/273]].

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

2025-11-27T12:20:41Z

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

← Older revision		Revision as of 12:20, 27 November 2025
Line 271:		Line 271:

	[[Category:Temperament collections]]		[[Category:Temperament collections]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Keemic temperaments\| ]] <!-- main article -->		[[Category:Keemic temperaments\| ]] <!-- main article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

FloraC: Temp rename followup

2025-10-12T10:58:10Z

Temp rename followup

← Older revision		Revision as of 10:58, 12 October 2025
Line 1:		Line 1:
	{{Technical data page}}		{{Technical data page}}
	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 ~~[[Keemic family #Undecimal supermagic\|~~canonical extension]] of ~~[[Keemic family#Supermagic\|~~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:

Lériendil: /* Quasitemp */

2025-10-10T14:02:08Z

Quasitemp

← Older revision		Revision as of 14:02, 10 October 2025
Line 17:		Line 17:
	: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Quasitemp]].''		: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Quasitemp]].''

	Quasitemp tempers out [[2401/2400]] in addition to 875/864 and may be described as the {{nowrap\| 37 & 41 }} temperament. It ~~has~~ a [[strong ~~restriction~~]] to the 2.5/3.7/3 subgroup, called [[gariberttet]], which is defined by tempering out [[3125/3087]]. In gariberttet, three generators reach [[5/3]] and five reach [[7/3]], so that the generator itself has the interpretation of [[25/21]]. This implies that 3:5:7 and 5:6:7 chords are reached rather quickly. ~~In quasitemp,~~ tempering out 875/864 entails that [[8/7]] is found after 9 generators, from which the mappings of 3 and 5 follow.		Quasitemp tempers out [[2401/2400]] in addition to 875/864 and may be described as the {{nowrap\| 37 & 41 }} temperament. It can be thought of as a [[strong extension]] of the 2.5/3.7/3 subgroup temperament called [[gariberttet]], which is defined by tempering out [[3125/3087]]. In gariberttet, three generators reach [[5/3]] and five reach [[7/3]], so that the generator itself has the interpretation of [[25/21]]. This implies that 3:5:7 and 5:6:7 chords are reached rather quickly. Quasitemp tempering out 875/864 entails that [[8/7]] is found after 9 generators, from which the mappings of 3 and 5 follow.

	Note that the generator is given as 25/21's octave complement, 42/25, in the data that follow, since a stack of 14 such generators octave-reduced is the perfect fifth, whence the temperament's [[ploidacot]] is iota-14-cot. This generator is equated to [[22/13]] for the 13-limit extension, tempering out [[275/273]].		Note that the generator is given as 25/21's octave complement, 42/25, in the data that follow, since a stack of 14 such generators octave-reduced is the perfect fifth, whence the temperament's [[ploidacot]] is iota-14-cot. This generator is equated to [[22/13]] for the 13-limit extension, tempering out [[275/273]].

Lériendil at 13:58, 10 October 2025

2025-10-10T13:58:48Z

← Older revision		Revision as of 13:58, 10 October 2025
Line 1:		Line 1:
	{{Technical data page}}		{{Technical data page}}
	This is a collection of [[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 [[Keemic family #Undecimal supermagic\|canonical extension]] of [[Keemic family#Supermagic\|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 [[Keemic family #Undecimal supermagic\|canonical extension]] of [[Keemic family#Supermagic\|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:

Lériendil at 13:58, 10 October 2025

2025-10-10T13:58:10Z

← Older revision		Revision as of 13:58, 10 October 2025
Line 1:		Line 1:
	{{Technical data page}}		{{Technical data page}}
	This is a collection of [[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 [[Keemic family #Undecimal supermagic\|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 [[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 [[Keemic family #Undecimal supermagic\|canonical extension]] of [[Keemic family#Supermagic\|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:

FloraC: - POTE tunings

2025-10-10T10:59:22Z

- POTE tunings

← Older revision		Revision as of 10:59, 10 October 2025
Line 33:		Line 33:
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~42/25 = 907.3471{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~42/25 = 907.3471{{c}}
	: error map: {{val\| 0.000 +0.905 -5.495 -2.702 }}		: error map: {{val\| 0.000 +0.905 -5.495 -2.702 }}
	~~<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~42/25 = 907.290{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 4, …, 37, 41 }}		{{Optimal ET sequence\|legend=1\| 4, …, 37, 41 }}
Line 49:		Line 48:
	* WE: ~2 = 1199.9585{{c}}, ~42/25 = 907.4221{{c}}		* WE: ~2 = 1199.9585{{c}}, ~42/25 = 907.4221{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~42/25 = 907.4521{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~42/25 = 907.4521{{c}}
	~~<!-- * POTE: ~2 = 1200.000{{c}}, ~42/25 = 907.453{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 4, 37, 41, 119 }}		{{Optimal ET sequence\|legend=0\| 4, 37, 41, 119 }}
Line 65:		Line 63:
	* WE: ~2 = 1199.4376{{c}}, ~22/13 = 907.1175{{c}}		* WE: ~2 = 1199.4376{{c}}, ~22/13 = 907.1175{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~22/13 = 907.5314{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~22/13 = 907.5314{{c}}
	~~<!-- * POTE: ~2 = 1200.000{{c}}, ~22/13 = 907.543{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 4, 37, 41, 78, 119f }}		{{Optimal ET sequence\|legend=0\| 4, 37, 41, 78, 119f }}
Line 81:		Line 78:
	* WE: ~2 = 1201.2729{{c}}, ~42/25 = 908.1116{{c}}		* WE: ~2 = 1201.2729{{c}}, ~42/25 = 908.1116{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~42/25 = 907.2109{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~42/25 = 907.2109{{c}}
	~~<!-- * POTE: ~2 = 1200.000{{c}}, ~42/25 = 907.149{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 41, 127cd, 168cd }}		{{Optimal ET sequence\|legend=0\| 41, 127cd, 168cd }}
Line 97:		Line 93:
	* WE: ~2 = 1201.4078{{c}}, ~42/25 = 908.1362{{c}}		* WE: ~2 = 1201.4078{{c}}, ~42/25 = 908.1362{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~42/25 = 907.1370{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~42/25 = 907.1370{{c}}
	~~<!-- * POTE: ~2 = 1200.000{{c}}, ~22/13 = 907.072{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 41, 86ce }}		{{Optimal ET sequence\|legend=0\| 41, 86ce }}
Line 122:		Line 117:
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~36/35 = 53.9055{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~36/35 = 53.9055{{c}}
	: error map: {{val\| 0.000 -1.183 -8.975 +1.474 }}		: error map: {{val\| 0.000 -1.183 -8.975 +1.474 }}
	~~<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~36/35 = 53.816{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 22, 45, 67c }}		{{Optimal ET sequence\|legend=1\| 22, 45, 67c }}
Line 141:		Line 135:
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~75/49 = 731.7183{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~75/49 = 731.7183{{c}}
	: error map: {{val\| 0.000 +0.692 -5.694 -2.742 }}		: error map: {{val\| 0.000 +0.692 -5.694 -2.742 }}
	~~<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~75/49 = 731.669{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 18, 23d, 41 }}		{{Optimal ET sequence\|legend=0\| 18, 23d, 41 }}
Line 157:		Line 150:
	* WE: ~2 = 1200.8513{{c}}, ~75/49 = 732.1519{{c}}		* WE: ~2 = 1200.8513{{c}}, ~75/49 = 732.1519{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~75/49 = 731.6740{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~75/49 = 731.6740{{c}}
	~~<!-- * POTE: ~2 = 1200.000{{c}}, ~75/49 = 731.633{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 18e, 23de, 41 }}		{{Optimal ET sequence\|legend=0\| 18e, 23de, 41 }}
Line 173:		Line 165:
	* WE: ~2 = 1199.7960{{c}}, ~20/13 = 731.6053{{c}}		* WE: ~2 = 1199.7960{{c}}, ~20/13 = 731.6053{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~20/13 = 731.7208{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~20/13 = 731.7208{{c}}
	~~<!-- * POTE: ~2 = 1200.000{{c}}, ~20/13 = 731.730{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 18e, 23de, 41 }}		{{Optimal ET sequence\|legend=0\| 18e, 23de, 41 }}
Line 192:		Line 183:
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~6/5 = 323.7816{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~6/5 = 323.7816{{c}}
	: error map: {{val\| 0.000 +2.332 -5.808 +2.519 }}		: error map: {{val\| 0.000 +2.332 -5.808 +2.519 }}
	~~<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~6/5 = 323.780{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 26, 37, 63 }}		{{Optimal ET sequence\|legend=1\| 26, 37, 63 }}
Line 208:		Line 198:
	* WE: ~2 = 1199.9010{{c}}, ~6/5 = 323.7691{{c}}		* WE: ~2 = 1199.9010{{c}}, ~6/5 = 323.7691{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 323.7931{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 323.7931{{c}}
	~~<!-- * POTE: ~2 = 1200.000{{c}}, ~6/5 = 323.796{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 26, 37, 63 }}		{{Optimal ET sequence\|legend=0\| 26, 37, 63 }}
Line 224:		Line 213:
	* WE: ~2 = 1200.0524{{c}}, ~6/5 = 323.8039{{c}}		* WE: ~2 = 1200.0524{{c}}, ~6/5 = 323.8039{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 323.7912{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 323.7912{{c}}
	~~<!-- * POTE: ~2 = 1200.000{{c}}, ~6/5 = 323.790{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 26, 37, 63 }}		{{Optimal ET sequence\|legend=0\| 26, 37, 63 }}
Line 247:		Line 235:
	* [[CWE]]: ~10/9 = 171.4286{{c}}, ~3/2 = 705.6057{{c}}		* [[CWE]]: ~10/9 = 171.4286{{c}}, ~3/2 = 705.6057{{c}}
	: error map: {{val\| 0.000 +3.651 -3.674 +0.071 }}		: error map: {{val\| 0.000 +3.651 -3.674 +0.071 }}
	~~<!-- * [[POTE]]: ~10/9 = 171.429{{c}}, ~3/2 = 705.613{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 7, …, 56, 63, 119 }}		{{Optimal ET sequence\|legend=1\| 7, …, 56, 63, 119 }}
Line 263:		Line 250:
	* WE: ~11/10 = 171.3859{{c}}, ~3/2 = 705.3421{{c}}		* WE: ~11/10 = 171.3859{{c}}, ~3/2 = 705.3421{{c}}
	* CWE: ~11/10 = 171.4286{{c}}, ~3/2 = 705.4973{{c}}		* CWE: ~11/10 = 171.4286{{c}}, ~3/2 = 705.4973{{c}}
	~~<!-- * POTE: ~11/10 = 171.429{{c}}, ~3/2 = 705.518{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 7, 56, 63, 119 }}		{{Optimal ET sequence\|legend=0\| 7, 56, 63, 119 }}
Line 279:		Line 265:
	* WE: ~11/10 = 171.4163{{c}}, ~3/2 = 705.2930{{c}}		* WE: ~11/10 = 171.4163{{c}}, ~3/2 = 705.2930{{c}}
	* CWE: ~11/10 = 171.4286{{c}}, ~3/2 = 705.3402{{c}}		* CWE: ~11/10 = 171.4286{{c}}, ~3/2 = 705.3402{{c}}
	~~<!-- * POTE: ~10/9 = 171.429{{c}}, ~3/2 = 705.344{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 7, 56, 63, 119 }}		{{Optimal ET sequence\|legend=0\| 7, 56, 63, 119 }}

← Older revision		Revision as of 10:17, 29 May 2026
Line 4:		Line 4:
	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]]

← Older revision		Revision as of 18:07, 15 April 2026
Line 2:		Line 2:
	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 ==