Orwellismic temperaments - Revision history

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

2026-09-24T12:33:16Z

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

← Older revision		Revision as of 12:33, 24 September 2026
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	Comma list: 99/98, 243/242, 385/384		Comma list: 99/98, 243/242, 385/384

	~~Mapping:~~ {{~~mapping~~\| 1 -1 12 -3 -3 \| 0 4 -15 9 10 }}		{{Mapping\|legend=0\| 1 -1 12 -3 -3 \| 0 4 -15 9 10 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 99/98, 105/104, 144/143, 243/242		Comma list: 99/98, 105/104, 144/143, 243/242

	~~Mapping:~~ {{~~mapping~~\| 1 -1 12 -3 -3 5 \| 0 4 -15 9 10 -2 }}		{{Mapping\|legend=0\| 1 -1 12 -3 -3 5 \| 0 4 -15 9 10 -2 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 441/440, 1344/1331, 1728/1715		Comma list: 441/440, 1344/1331, 1728/1715

	~~Mapping:~~ {{~~mapping~~\| 2 1 0 5 6 \| 0 7 15 2 3 }}		{{Mapping\|legend=0\| 2 1 0 5 6 \| 0 7 15 2 3 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 144/143, 351/350, 364/363, 441/440		Comma list: 144/143, 351/350, 364/363, 441/440

	~~Mapping:~~ {{~~mapping~~\| 2 1 0 5 6 4 \| 0 7 15 2 3 11 }}		{{Mapping\|legend=0\| 2 1 0 5 6 4 \| 0 7 15 2 3 11 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 144/143, 170/169, 221/220, 351/350, 441/440		Comma list: 144/143, 170/169, 221/220, 351/350, 441/440

	~~Mapping:~~ {{~~mapping~~\| 2 1 0 5 6 4 6 \| 0 7 15 2 3 11 7 }}		{{Mapping\|legend=0\| 2 1 0 5 6 4 6 \| 0 7 15 2 3 11 7 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 144/143, 153/152, 170/169, 210/209, 221/220, 400/399		Comma list: 144/143, 153/152, 170/169, 210/209, 221/220, 400/399

	~~Mapping:~~ {{~~mapping~~\| 2 1 0 5 6 4 6 2 \| 0 7 15 2 3 11 7 21 }}		{{Mapping\|legend=0\| 2 1 0 5 6 4 6 2 \| 0 7 15 2 3 11 7 21 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 121/120, 441/440, 891/875		Comma list: 121/120, 441/440, 891/875

	~~Mapping:~~ {{~~mapping~~\| 1 2 3 3 4 \| 0 -13 -21 -6 -17 }}		{{Mapping\|legend=0\| 1 2 3 3 4 \| 0 -13 -21 -6 -17 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 66/65, 121/120, 343/338, 441/440		Comma list: 66/65, 121/120, 343/338, 441/440

	~~Mapping:~~ {{~~mapping~~\| 1 2 3 3 4 4 \| 0 -13 -21 -6 -17 -9 }}		{{Mapping\|legend=0\| 1 2 3 3 4 4 \| 0 -13 -21 -6 -17 -9 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 176/175, 540/539, 1344/1331		Comma list: 176/175, 540/539, 1344/1331

	~~Mapping:~~ {{~~mapping~~\| 1 -2 3 -1 1 \| 0 16 -3 17 11 }}		{{Mapping\|legend=0\| 1 -2 3 -1 1 \| 0 16 -3 17 11 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 144/143, 176/175, 196/195, 364/363		Comma list: 144/143, 176/175, 196/195, 364/363

	~~Mapping:~~ {{~~mapping~~\| 1 -2 3 -1 1 -1 \| 0 16 -3 17 11 21 }}		{{Mapping\|legend=0\| 1 -2 3 -1 1 -1 \| 0 16 -3 17 11 21 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 896/891, 1728/1715, 2200/2187		Comma list: 896/891, 1728/1715, 2200/2187

	~~Mapping:~~ {{~~mapping~~\| 5 0 -36 22 57 \| 0 1 6 -1 -5 }}		{{Mapping\|legend=0\| 5 0 -36 22 57 \| 0 1 6 -1 -5 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 325/324, 352/351, 364/363, 1728/1715		Comma list: 325/324, 352/351, 364/363, 1728/1715

	~~Mapping:~~ {{~~mapping~~\| 5 0 -36 22 57 82 \| 0 1 6 -1 -5 -8 }}		{{Mapping\|legend=0\| 5 0 -36 22 57 82 \| 0 1 6 -1 -5 -8 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 99/98, 125/121, 385/384		Comma list: 99/98, 125/121, 385/384

	~~Mapping:~~ {{~~mapping~~\| 13 0 30 16 45 \| 0 1 0 1 0 }}		{{Mapping\|legend=0\| 13 0 30 16 45 \| 0 1 0 1 0 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 78/77, 99/98, 125/121, 1200/1183		Comma list: 78/77, 99/98, 125/121, 1200/1183

	~~Mapping:~~ {{~~mapping~~\| 13 0 30 16 45 48 \| 0 1 0 1 0 0 }}		{{Mapping\|legend=0\| 13 0 30 16 45 48 \| 0 1 0 1 0 0 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 99/98, 385/384, 729/704		Comma list: 99/98, 385/384, 729/704

	~~Mapping:~~ {{~~mapping~~\| 2 0 33 -7 -12 \| 0 1 -9 4 6 }}		{{Mapping\|legend=0\| 2 0 33 -7 -12 \| 0 1 -9 4 6 }}

	Optimal tunings:		Optimal tunings:

FloraC: Recategorize

2026-09-20T03:54:22Z

Recategorize

← Older revision		Revision as of 03:54, 20 September 2026
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	* ''[[Trimabila]]'' (+268435456/263671875) → [[Mabila family #Trimabila\|Mabila family]]		* ''[[Trimabila]]'' (+268435456/263671875) → [[Mabila family #Trimabila\|Mabila family]]

	Considered below are sentinel, secant, diesic, infraorwell, pentaorwell, triskaidekic, and philips in the order of increasing [[badness]].		Considered below are sentinel, secant, diesic, infraorwell, pentaorwell, triskaidekic, and philips, in the order of increasing [[badness]].

	== Sentinel ==		== Sentinel ==
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	Badness (Sintel): 3.17		Badness (Sintel): 3.17

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

FloraC: + link to echidna; sorting

2026-09-15T08:21:10Z

+ link to echidna; sorting

← Older revision		Revision as of 08:21, 15 September 2026
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	Temperaments discussed elsewhere are:		Temperaments discussed elsewhere are:
			* [[Superpyth]] (+64/63) → [[Archytas clan #Superpyth\|Archytas clan]]
	* [[Beep]] (+21/20 or 27/25) → [[Bug family #Beep\|Bug family]]		* [[Beep]] (+21/20 or 27/25) → [[Bug family #Beep\|Bug family]]
			* [[Mothra]] (+81/80) → [[Meantone family #Mothra\|Meantone family]]
			* [[Buzzard]] (+5120/5103) → [[Buzzardsmic clan #Buzzard\|Buzzardsmic clan]]
			* ''[[Secund]]'' (+405/392 or 525/512) → [[Greenwoodmic temperaments #Secund\|Greenwoodmic temperaments]]
			* ''[[Echidna]]'' (+2048/2025) → [[Stearnsmic clan #Echidna\|Stearnsmic clan]]
			* [[Orwell]] (+225/224) → [[Semicomma family #Orwell\|Semicomma family]]
	* ''[[Doublewide]]'' (+50/49) → [[Jubilismic clan #Doublewide\|Jubilismic clan]]		* ''[[Doublewide]]'' (+50/49) → [[Jubilismic clan #Doublewide\|Jubilismic clan]]
	* [[Superpyth]] (+64/63) → [[Archytas clan #Superpyth\|Archytas clan]]
	* [[Mothra]] (+81/80) → [[Meantone family #Mothra\|Meantone family]]
	* [[Myna]] (+126/125) → [[Starling temperaments #Myna\|Starling temperaments]]		* [[Myna]] (+126/125) → [[Starling temperaments #Myna\|Starling temperaments]]
	* [[Orwell]] (+225/224) → [[Semicomma family #Orwell\|Semicomma family]]
	* ''[[Secund]]'' (+405/392 or 525/512) → [[Greenwoodmic temperaments #Secund\|Greenwoodmic temperaments]]
	* ''[[Quartonic]]'' (+4000/3969) → [[Quartonic family]]		* ''[[Quartonic]]'' (+4000/3969) → [[Quartonic family]]
	* [[Buzzard]] (+5120/5103) → [[Buzzardsmic clan #Buzzard\|Buzzardsmic clan]]
	* ''[[Trisensory]]'' (+78732/78125) → [[Sensipent family #Trisensory\|Sensipent family]]		* ''[[Trisensory]]'' (+78732/78125) → [[Sensipent family #Trisensory\|Sensipent family]]
	* ''[[Trimabila]]'' (+268435456/263671875) → [[Mabila family #Trimabila\|Mabila family]]		* ''[[Trimabila]]'' (+268435456/263671875) → [[Mabila family #Trimabila\|Mabila family]]

	Considered below are sentinel, secant, diesic, infraorwell, pentaorwell, triskaidekic, and philips.		Considered below are sentinel, secant, diesic, infraorwell, pentaorwell, triskaidekic, and philips in the order of increasing [[badness]].

	== Sentinel ==		== Sentinel ==

FloraC: /* Triskaidekic */ update

2026-07-21T03:53:06Z

Triskaidekic: update

← Older revision		Revision as of 03:53, 21 July 2026
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	== Triskaidekic ==		== Triskaidekic ==
	: ''For the 5-limit version, see [[~~13th~~-~~octave~~ temperaments #Triskaidekic]].''		: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Triskaidekic]].''

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

Xenllium at 22:34, 21 January 2026

2026-01-21T22:34:07Z

← Older revision		Revision as of 22:34, 21 January 2026
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	== Triskaidekic ==		== Triskaidekic ==
	: ''For the 5-limit version, see [[~~Miscellaneous 5~~-~~limit~~ temperaments #Triskaidekic]].''		: ''For the 5-limit version, see [[13th-octave temperaments #Triskaidekic]].''

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

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

2025-11-27T12:31:13Z

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

← Older revision		Revision as of 12:31, 27 November 2025
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	[[Category:Temperament collections]]		[[Category:Temperament collections]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Orwellismic temperaments\| ]] <!-- main article -->		[[Category:Orwellismic temperaments\| ]] <!-- main article -->
	[[Category:Orwellismic\| ]] <!-- key article -->		[[Category:Orwellismic\| ]] <!-- key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

FloraC: Update

2025-10-27T14:12:57Z

Update

← Older revision		Revision as of 14:12, 27 October 2025
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	* ''[[Secund]]'' (+405/392 or 525/512) → [[Greenwoodmic temperaments #Secund\|Greenwoodmic temperaments]]		* ''[[Secund]]'' (+405/392 or 525/512) → [[Greenwoodmic temperaments #Secund\|Greenwoodmic temperaments]]
	* ''[[Quartonic]]'' (+4000/3969) → [[Quartonic family]]		* ''[[Quartonic]]'' (+4000/3969) → [[Quartonic family]]
	* [[Buzzard]] (+5120/5103) → [[~~Vulture family~~ #Buzzard\|~~Vulture family~~]]		* [[Buzzard]] (+5120/5103) → [[Buzzardsmic clan #Buzzard\|Buzzardsmic clan]]
	* ''[[Trisensory]]'' (+78732/78125) → [[Sensipent family #Trisensory\|Sensipent family]]		* ''[[Trisensory]]'' (+78732/78125) → [[Sensipent family #Trisensory\|Sensipent family]]
	* ''[[Trimabila]]'' (+268435456/263671875) → [[Mabila family #Trimabila\|Mabila family]]		* ''[[Trimabila]]'' (+268435456/263671875) → [[Mabila family #Trimabila\|Mabila family]]

FloraC: + intro to some of these temps

2025-10-21T14:52:19Z

+ intro to some of these temps

← Older revision		Revision as of 14:52, 21 October 2025
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	== Sentinel ==		== Sentinel ==
	: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Sentinel]].''		: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Sentinel]].''

			Sentinel tempers out [[3645/3584]] and may be described as the {{nowrap\| 14 & 17 }} temperament. It is related to [[squares]], but the mappings differ for the [[5/1\|5th harmonic]]. Like squares, it splits the [[6/1\|6th harmonic]] into four subminor sixths of 11/7~14/9 (or splits a perfect eleventh into four supermajor thirds of 9/7~14/11), and uses it for a generator; its [[ploidacot]] is beta-tetracot. However, the 5th harmonic is found by -15 generator steps instead of +16 as in squares.

			As one might expect, [[31edo]] is a good tuning for this temperament, in which case it is identical to squares. Among the alternatives are [[48edo]] and [[79edo]], both in their [[patent val]]s.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	Optimal tunings:		Optimal tunings:
	* WE: ~2 = 1201.0893{{c}}, ~14/9 = 775.1534{{c}}		* WE: ~2 = 1201.0893{{c}}, ~11/7 = 775.1534{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~14/9 = 774.4564{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 774.4564{{c}}

	{{Optimal ET sequence\|legend=0\| 14, 17, 31, 79, 110e, 141e }}		{{Optimal ET sequence\|legend=0\| 14, 17, 31, 79, 110e, 141e }}
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	Optimal tunings:		Optimal tunings:
	* WE: ~2 = 1200.4045{{c}}, ~14/9 = 774.7596{{c}}		* WE: ~2 = 1200.4045{{c}}, ~11/7 = 774.7596{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~14/9 = 774.5000{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 774.5000{{c}}

	{{Optimal ET sequence\|legend=0\| 14, 17, 31 }}		{{Optimal ET sequence\|legend=0\| 14, 17, 31 }}
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	== Secant ==		== Secant ==
			Secant, the {{nowrap\| 26 & 58 }} temperament, is generated by a slightly sharp ~10/9, seven of which plus a semi-octave period give the [[3/1\|3rd harmonic]]. Its ploidacot is diploid alpha-heptacot. [[58edo]], [[84edo]] and [[142edo]] all make for excellent tunings.

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

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	== Diesic ==		== Diesic ==
	: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Diesic]].''		: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Diesic]].''

			Diesic is generated by a diesis-sized interval of ~36/35, hence the name. It may be described as the {{nowrap\| 31 & 32c }} temperament. It is related to [[slender]], both sharing the ploidacot of omega-13-cot, but the mappings differ for the [[5/1\|5th harmonic]].

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	== Infraorwell ==		== Infraorwell ==
			Infraorwell may be described as the {{nowrap\| 49 & 58 }} temperament. It is generated by a ~7/6, less sharp than the generator of [[orwell]] but still sharp of just, so that three generators make a ~8/5, but seven generators does not give the [[3/1\|3rd harmonic]]. Instead, sixteen generators give the [[12/1\|12th harmonic]]; the ploidacot for this temperament is therefore gamma-16-cot. [[58edo]] makes for a recommendable tuning, though [[49edo]] and [[67edo]] are among the possibilities.

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

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	: ''For the 5-limit version, see [[Syntonic–diatonic equivalence continuum #Counterpental]].''		: ''For the 5-limit version, see [[Syntonic–diatonic equivalence continuum #Counterpental]].''

	Named by [[User:Flirora\|+merlan #flirora]] in 2021, pentaorwell tempers out 179200/177147 and is the {{nowrap\| 75 & 80 }} temperament.		Named by [[User:Flirora\|+merlan #flirora]] in 2021, pentaorwell tempers out 179200/177147 and is the {{nowrap\| 75 & 80 }} temperament. Its ploidacot is pentaploid monocot.

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

FloraC: Sort by badness

2025-10-21T13:53:27Z

Sort by badness

Show changes

FloraC: - CTE & POTE tunings

2025-10-21T13:51:05Z

- CTE & POTE tunings

← Older revision		Revision as of 13:51, 21 October 2025
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	* [[CWE]]: ~567/400 = 600.0000{{c}}, ~10/9 = 185.8618{{c}}		* [[CWE]]: ~567/400 = 600.0000{{c}}, ~10/9 = 185.8618{{c}}
	: error map: {{val\| 0.000 -0.922 +1.613 +2.898 }}		: error map: {{val\| 0.000 -0.922 +1.613 +2.898 }}
	~~<!-- * [[POTE]]: ~567/400 = 600.000{{c}}, ~10/9 = 185.885{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 26, 58, 84, 142, 368cd }}		{{Optimal ET sequence\|legend=1\| 26, 58, 84, 142, 368cd }}
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	* WE: ~99/70 = 599.5785{{c}}, ~10/9 = 185.8332{{c}}		* WE: ~99/70 = 599.5785{{c}}, ~10/9 = 185.8332{{c}}
	* CWE: ~99/70 = 600.0000{{c}}, ~10/9 = 185.9140{{c}}		* CWE: ~99/70 = 600.0000{{c}}, ~10/9 = 185.9140{{c}}
	~~<!-- * POTE: ~99/70 = 600.000{{c}}, ~10/9 = 185.962{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 26, 58, 142e, 200cdee }}		{{Optimal ET sequence\|legend=0\| 26, 58, 142e, 200cdee }}
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	* WE: ~55/39 = 599.5432{{c}}, ~10/9 = 185.8136{{c}}		* WE: ~55/39 = 599.5432{{c}}, ~10/9 = 185.8136{{c}}
	* CWE: ~55/39 = 600.0000{{c}}, ~10/9 = 185.9012{{c}}		* CWE: ~55/39 = 600.0000{{c}}, ~10/9 = 185.9012{{c}}
	~~<!-- * POTE: ~99/70 = 600.000{{c}}, ~10/9 = 185.955{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 26, 58, 84, 142ef }}		{{Optimal ET sequence\|legend=0\| 26, 58, 84, 142ef }}
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	* WE: ~17/12 = 599.7117{{c}}, ~10/9 = 185.8270{{c}}		* WE: ~17/12 = 599.7117{{c}}, ~10/9 = 185.8270{{c}}
	* CWE: ~17/12 = 600.0000{{c}}, ~10/9 = 185.8834{{c}}		* CWE: ~17/12 = 600.0000{{c}}, ~10/9 = 185.8834{{c}}
	~~<!-- * POTE: ~17/12 = 600.000{{c}}, ~10/9 = 185.916{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 26, 58, 84 }}		{{Optimal ET sequence\|legend=0\| 26, 58, 84 }}
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	* WE: ~17/12 = 599.7288{{c}}, ~10/9 = 185.7738{{c}}		* WE: ~17/12 = 599.7288{{c}}, ~10/9 = 185.7738{{c}}
	* CWE: ~17/12 = 600.0000{{c}}, ~10/9 = 185.8279{{c}}		* CWE: ~17/12 = 600.0000{{c}}, ~10/9 = 185.8279{{c}}
	~~<!-- * POTE: ~17/12 = 600.000{{c}}, ~10/9 = 185.858{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 26, 58h, 84 }}		{{Optimal ET sequence\|legend=0\| 26, 58h, 84 }}
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/6 = 268.9844{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/6 = 268.9844{{c}}
	: error map: {{val\| 0.000 +1.796 +6.733 +3.909 }}		: error map: {{val\| 0.000 +1.796 +6.733 +3.909 }}
	~~<!-- * POTE: ~2 = 1200.000{{c}}, ~7/6 = 269.032{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 9, 40bd, 49, 58, 165cd, 223bccd, 281bcccdd }}		{{Optimal ET sequence\|legend=1\| 9, 40bd, 49, 58, 165cd, 223bccd, 281bcccdd }}
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	* WE: ~2 = 1198.2928{{c}}, ~7/6 = 268.6532{{c}}		* WE: ~2 = 1198.2928{{c}}, ~7/6 = 268.6532{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~7/6 = 268.9825{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~7/6 = 268.9825{{c}}
	~~<!-- * POTE: ~2 = 1200.000{{c}}, ~7/6 = 269.036{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 9, 40bde, 49, 58, 165cdee, 223bccdeee, 281bcccddeee }}		{{Optimal ET sequence\|legend=0\| 9, 40bde, 49, 58, 165cdee, 223bccdeee, 281bcccddeee }}
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	* WE: ~2 = 1198.2216{{c}}, ~7/6 = 268.6220{{c}}		* WE: ~2 = 1198.2216{{c}}, ~7/6 = 268.6220{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~7/6 = 268.9616{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~7/6 = 268.9616{{c}}
	~~<!-- * POTE: ~2 = 1200.000{{c}}, ~7/6 = 269.021{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 9, 40bdef, 49f, 58, 223bccdeeefff, 281bcccddeeeffff }}		{{Optimal ET sequence\|legend=0\| 9, 40bdef, 49f, 58, 223bccdeeefff, 281bcccddeeeffff }}
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~14/9 = 774.4021{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~14/9 = 774.4021{{c}}
	: error map: {{val\| 0.000 -4.347 -2.345 +0.793 }}		: error map: {{val\| 0.000 -4.347 -2.345 +0.793 }}
	~~<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~14/9 = 774.404{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 14, 17, 31, 110, 141, 172b }}		{{Optimal ET sequence\|legend=1\| 14, 17, 31, 110, 141, 172b }}
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	* WE: ~2 = 1201.0893{{c}}, ~14/9 = 775.1534{{c}}		* WE: ~2 = 1201.0893{{c}}, ~14/9 = 775.1534{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~14/9 = 774.4564{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~14/9 = 774.4564{{c}}
	~~<!-- * POTE: ~2 = 1200.000{{c}}, ~14/9 = 774.450{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 14, 17, 31, 79, 110e, 141e }}		{{Optimal ET sequence\|legend=0\| 14, 17, 31, 79, 110e, 141e }}
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	* WE: ~2 = 1200.4045{{c}}, ~14/9 = 774.7596{{c}}		* WE: ~2 = 1200.4045{{c}}, ~14/9 = 774.7596{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~14/9 = 774.5000{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~14/9 = 774.5000{{c}}
	~~<!-- * POTE: ~2 = 1200.000{{c}}, ~14/9 = 774.499{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 14, 17, 31 }}		{{Optimal ET sequence\|legend=0\| 14, 17, 31 }}
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~36/35 = 38.5603{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~36/35 = 38.5603{{c}}
	: error map: {{val\| 0.000 -3.239 +3.920 -0.188 }}		: error map: {{val\| 0.000 -3.239 +3.920 -0.188 }}
	~~<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~36/35 = 38.567{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 1c, 30bc, 31, 156c }}		{{Optimal ET sequence\|legend=1\| 1c, 30bc, 31, 156c }}
Line 235:		Line 223:
	* WE: ~2 = 1200.4923{{c}}, ~36/35 = 38.5806{{c}}		* WE: ~2 = 1200.4923{{c}}, ~36/35 = 38.5806{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~36/35 = 38.5397{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~36/35 = 38.5397{{c}}
	~~<!-- * POTE: ~2 = 1200.000{{c}}, ~36/35 = 38.565{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 1ce, 30bce, 31 }}		{{Optimal ET sequence\|legend=0\| 1ce, 30bce, 31 }}
Line 251:		Line 238:
	* WE: ~2 = 1199.3005{{c}}, ~36/35 = 38.4213{{c}}		* WE: ~2 = 1199.3005{{c}}, ~36/35 = 38.4213{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~36/35 = 38.4764{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~36/35 = 38.4764{{c}}
	~~<!-- * POTE: ~2 = 1200.000{{c}}, ~36/35 = 38.444{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 1ce, 30bce, 31 }}		{{Optimal ET sequence\|legend=0\| 1ce, 30bce, 31 }}
Line 272:		Line 258:
	* [[CWE]]: ~81/56 = 600.0000{{c}}, ~3/2 = 691.1141{{c}}		* [[CWE]]: ~81/56 = 600.0000{{c}}, ~3/2 = 691.1141{{c}}
	: error map: {{val\| 0.000 -10.841 -6.340 -4.370 }}		: error map: {{val\| 0.000 -10.841 -6.340 -4.370 }}
	~~<!-- * [[POTE]]: ~81/56 = 600.000{{c}}, ~3/2 = 691.174{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 14, 26, 66b, 92bc }}		{{Optimal ET sequence\|legend=1\| 14, 26, 66b, 92bc }}
Line 288:		Line 273:
	* WE: ~63/44 = 601.2349{{c}}, ~3/2 = 692.4623{{c}}		* WE: ~63/44 = 601.2349{{c}}, ~3/2 = 692.4623{{c}}
	* CWE: ~63/44 = 600.0000{{c}}, ~3/2 = 691.0383{{c}}		* CWE: ~63/44 = 600.0000{{c}}, ~3/2 = 691.0383{{c}}
	~~<!-- * POTE: ~63/44 = 600.000{{c}}, ~3/2 = 691.040{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 14, 26, 40, 66b }}		{{Optimal ET sequence\|legend=0\| 14, 26, 40, 66b }}
Line 309:		Line 293:
	* [[CWE]]: ~15/14 = 92.3077{{c}}, ~3/2 = 695.8319{{c}}		* [[CWE]]: ~15/14 = 92.3077{{c}}, ~3/2 = 695.8319{{c}}
	: error map: {{val\| 0.000 -6.123 -17.083 +3.929 }}		: error map: {{val\| 0.000 -6.123 -17.083 +3.929 }}
	~~<!-- * [[POTE]]: ~15/14 = 92.308{{c}}, ~3/2 = 694.143{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 13d, 26 }}		{{Optimal ET sequence\|legend=1\| 13d, 26 }}
Line 325:		Line 308:
	* WE: ~15/14 = 92.4364{{c}}, ~3/2 = 697.2675{{c}}		* WE: ~15/14 = 92.4364{{c}}, ~3/2 = 697.2675{{c}}
	* CWE: ~15/14 = 92.3077{{c}}, ~3/2 = 697.0548{{c}}		* CWE: ~15/14 = 92.3077{{c}}, ~3/2 = 697.0548{{c}}
	~~<!-- * POTE: ~15/14 = 92.308{{c}}, ~3/2 = 696.296{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 13d, 26 }}		{{Optimal ET sequence\|legend=0\| 13d, 26 }}
Line 341:		Line 323:
	* WE: ~15/14 = 92.4535{{c}}, ~3/2 = 696.9785{{c}}		* WE: ~15/14 = 92.4535{{c}}, ~3/2 = 696.9785{{c}}
	* CWE: ~15/14 = 92.3077{{c}}, ~3/2 = 696.5711{{c}}		* CWE: ~15/14 = 92.3077{{c}}, ~3/2 = 696.5711{{c}}
	~~<!-- * POTE: ~15/14 = 92.308{{c}}, ~3/2 = 695.879{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 13d, 26 }}		{{Optimal ET sequence\|legend=0\| 13d, 26 }}
Line 363:		Line 344:
	* [[CWE]]: ~280/243 = 240.0000{{c}}, ~3/2 = 704.7723{{c}} (~64/63 = 15.2277{{c}})		* [[CWE]]: ~280/243 = 240.0000{{c}}, ~3/2 = 704.7723{{c}} (~64/63 = 15.2277{{c}})
	: error map: {{val\| 0.000 +2.817 +2.320 +6.402 }}		: error map: {{val\| 0.000 +2.817 +2.320 +6.402 }}
	~~<!-- * [[CTE]]: ~280/243 = 240.000{{c}}, ~3/2 = 704.3709{{c}} (~64/63 = 15.6291{{c}})~~
	* [[POTE]]: ~280/243 = 240.000{{c}}, ~3/2 = 704.9128{{c}} (~64/63 = 15.0872{{c}}) -->

	{{Optimal ET sequence\|legend=1\| 5, 75, 80 }}		{{Optimal ET sequence\|legend=1\| 5, 75, 80 }}
Line 380:		Line 359:
	* WE: ~55/48 = 239.7357{{c}}, ~3/2 = 704.1025{{c}} (~99/98 = 15.1045{{c}})		* WE: ~55/48 = 239.7357{{c}}, ~3/2 = 704.1025{{c}} (~99/98 = 15.1045{{c}})
	* CWE: ~55/48 = 240.0000{{c}}, ~3/2 = 704.8440{{c}} (~99/98 = 15.1560{{c}})		* CWE: ~55/48 = 240.0000{{c}}, ~3/2 = 704.8440{{c}} (~99/98 = 15.1560{{c}})
	~~<!-- * CTE: ~55/48 = 240.000{{c}}, ~3/2 = 704.8440{{c}} (~99/98 = 15.1560{{c}})~~
	* POTE: ~55/48 = 240.000{{c}}, ~3/2 = 704.8788{{c}} (~99/98 = 15.1212{{c}}) -->

	{{Optimal ET sequence\|legend=0\| 5, 75e, 80, 315bcdddee }}		{{Optimal ET sequence\|legend=0\| 5, 75e, 80, 315bcdddee }}
Line 397:		Line 374:
	* WE: ~55/48 = 239.7711{{c}}, ~3/2 = 704.0302{{c}} (~99/98 = 15.2830{{c}})		* WE: ~55/48 = 239.7711{{c}}, ~3/2 = 704.0302{{c}} (~99/98 = 15.2830{{c}})
	* CWE: ~55/48 = 240.0000{{c}}, ~3/2 = 704.7112{{c}} (~99/98 = 15.2888{{c}})		* CWE: ~55/48 = 240.0000{{c}}, ~3/2 = 704.7112{{c}} (~99/98 = 15.2888{{c}})
	~~<!-- * CTE: ~55/48 = 240.000{{c}}, ~3/2 = 704.7636{{c}} (~99/98 = 15.2364{{c}}) -->~~

	{{Optimal ET sequence\|legend=0\| 5f, 75e, 80, 155de }}		{{Optimal ET sequence\|legend=0\| 5f, 75e, 80, 155de }}

← Older revision		Revision as of 08:21, 15 September 2026
Line 3:		Line 3:

	Temperaments discussed elsewhere are:		Temperaments discussed elsewhere are:
			* [[Superpyth]] (+64/63) → [[Archytas clan #Superpyth\|Archytas clan]]
	* [[Beep]] (+21/20 or 27/25) → [[Bug family #Beep\|Bug family]]		* [[Beep]] (+21/20 or 27/25) → [[Bug family #Beep\|Bug family]]
			* [[Mothra]] (+81/80) → [[Meantone family #Mothra\|Meantone family]]
			* [[Buzzard]] (+5120/5103) → [[Buzzardsmic clan #Buzzard\|Buzzardsmic clan]]
			* ''[[Secund]]'' (+405/392 or 525/512) → [[Greenwoodmic temperaments #Secund\|Greenwoodmic temperaments]]
			* ''[[Echidna]]'' (+2048/2025) → [[Stearnsmic clan #Echidna\|Stearnsmic clan]]
			* [[Orwell]] (+225/224) → [[Semicomma family #Orwell\|Semicomma family]]
	* ''[[Doublewide]]'' (+50/49) → [[Jubilismic clan #Doublewide\|Jubilismic clan]]		* ''[[Doublewide]]'' (+50/49) → [[Jubilismic clan #Doublewide\|Jubilismic clan]]
	* [[Superpyth]] (+64/63) → [[Archytas clan #Superpyth\|Archytas clan]]
	* [[Mothra]] (+81/80) → [[Meantone family #Mothra\|Meantone family]]
	* [[Myna]] (+126/125) → [[Starling temperaments #Myna\|Starling temperaments]]		* [[Myna]] (+126/125) → [[Starling temperaments #Myna\|Starling temperaments]]
	* [[Orwell]] (+225/224) → [[Semicomma family #Orwell\|Semicomma family]]
	* ''[[Secund]]'' (+405/392 or 525/512) → [[Greenwoodmic temperaments #Secund\|Greenwoodmic temperaments]]
	* ''[[Quartonic]]'' (+4000/3969) → [[Quartonic family]]		* ''[[Quartonic]]'' (+4000/3969) → [[Quartonic family]]
	* [[Buzzard]] (+5120/5103) → [[Buzzardsmic clan #Buzzard\|Buzzardsmic clan]]
	* ''[[Trisensory]]'' (+78732/78125) → [[Sensipent family #Trisensory\|Sensipent family]]		* ''[[Trisensory]]'' (+78732/78125) → [[Sensipent family #Trisensory\|Sensipent family]]
	* ''[[Trimabila]]'' (+268435456/263671875) → [[Mabila family #Trimabila\|Mabila family]]		* ''[[Trimabila]]'' (+268435456/263671875) → [[Mabila family #Trimabila\|Mabila family]]

	Considered below are sentinel, secant, diesic, infraorwell, pentaorwell, triskaidekic, and philips.		Considered below are sentinel, secant, diesic, infraorwell, pentaorwell, triskaidekic, and philips in the order of increasing [[badness]].

	== Sentinel ==		== Sentinel ==

← Older revision		Revision as of 14:12, 27 October 2025
Line 11:		Line 11:
	* ''[[Secund]]'' (+405/392 or 525/512) → [[Greenwoodmic temperaments #Secund\|Greenwoodmic temperaments]]		* ''[[Secund]]'' (+405/392 or 525/512) → [[Greenwoodmic temperaments #Secund\|Greenwoodmic temperaments]]
	* ''[[Quartonic]]'' (+4000/3969) → [[Quartonic family]]		* ''[[Quartonic]]'' (+4000/3969) → [[Quartonic family]]
	* [[Buzzard]] (+5120/5103) → [[~~Vulture family~~ #Buzzard\|~~Vulture family~~]]		* [[Buzzard]] (+5120/5103) → [[Buzzardsmic clan #Buzzard\|Buzzardsmic clan]]
	* ''[[Trisensory]]'' (+78732/78125) → [[Sensipent family #Trisensory\|Sensipent family]]		* ''[[Trisensory]]'' (+78732/78125) → [[Sensipent family #Trisensory\|Sensipent family]]
	* ''[[Trimabila]]'' (+268435456/263671875) → [[Mabila family #Trimabila\|Mabila family]]		* ''[[Trimabila]]'' (+268435456/263671875) → [[Mabila family #Trimabila\|Mabila family]]