Orwellismic temperaments - Revision history

Xenllium at 22:34, 21 January 2026

2026-01-21T22:34:07Z

← Older revision		Revision as of 22:34, 21 January 2026
Line 305:		Line 305:

	== 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
Line 390:		Line 390:

	[[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
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]]

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
Line 19:		Line 19:
	== 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
Line 45:		Line 49:

	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 }}
Line 60:		Line 64:

	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 }}
Line 68:		Line 72:

	== 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

Line 147:		Line 153:
	== 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
Line 196:		Line 204:

	== 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

Line 246:		Line 256:
	: ''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
Line 30:		Line 30:
	* [[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 }}
Line 46:		Line 45:
	* 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 }}
Line 62:		Line 60:
	* 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 }}
Line 78:		Line 75:
	* 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 }}
Line 94:		Line 90:
	* 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 }}
Line 113:		Line 108:
	* [[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 }}
Line 129:		Line 123:
	* 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 }}
Line 145:		Line 138:
	* 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 }}
Line 166:		Line 158:
	* [[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 }}
Line 182:		Line 173:
	* 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 }}
Line 198:		Line 188:
	* 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 }}
Line 219:		Line 208:
	* [[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 }}

FloraC: Switch to Sintel's badness, WE & CWE tunings, per community consensus (3/3)

2025-10-21T13:49:58Z

Switch to Sintel's badness, WE & CWE tunings, per community consensus (3/3)

← Older revision		Revision as of 13:49, 21 October 2025
Line 304:		Line 304:
	: mapping generators: ~15/14, ~3		: mapping generators: ~15/14, ~3

	[[Optimal tuning]] ([[POTE]]): ~15/14 = 92.308{{c}}, ~3/2 = 694.143{{c}}		[[Optimal tuning]]s:
			* [[WE]]: ~15/14 = 92.5254{{c}}, ~3/2 = 695.7801{{c}}
			: [[error map]]: {{val\| +2.831 -3.344 -10.551 +10.192 }}
			* [[CWE]]: ~15/14 = 92.3077{{c}}, ~3/2 = 695.8319{{c}}
			: 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 }}

	[[Badness]] (~~Smith~~): 0.~~219050~~		[[Badness]] (Sintel): 5.54

	=== 11-limit ===		=== 11-limit ===
Line 317:		Line 322:
	Mapping: {{mapping\| 13 0 30 16 45 \| 0 1 0 1 0 }}		Mapping: {{mapping\| 13 0 30 16 45 \| 0 1 0 1 0 }}

	Optimal ~~tuning (~~POTE): ~15/14 = 92.308{{c}}, ~3/2 = 696.296{{c}}		Optimal tunings:
			* WE: ~15/14 = 92.4364{{c}}, ~3/2 = 697.2675{{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~~, 91cd~~ }}		{{Optimal ET sequence\|legend=0\| 13d, 26 }}

	Badness (~~Smith~~): 0.~~098847~~		Badness (Sintel): 3.27

	=== 13-limit ===		=== 13-limit ===
Line 330:		Line 338:
	Mapping: {{mapping\| 13 0 30 16 45 48 \| 0 1 0 1 0 0 }}		Mapping: {{mapping\| 13 0 30 16 45 48 \| 0 1 0 1 0 0 }}

	Optimal ~~tuning (~~POTE): ~15/14 = 92.308{{c}}, ~3/2 = 695.879{{c}}		Optimal tunings:
			* WE: ~15/14 = 92.4535{{c}}, ~3/2 = 696.9785{{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~~, 91cdf~~ }}		{{Optimal ET sequence\|legend=0\| 13d, 26 }}

	Badness (~~Smith~~): 0.~~059216~~		Badness (Sintel): 2.45

	== Pentaorwell ==		== Pentaorwell ==
Line 348:		Line 359:

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[CTE]]: ~280/243 = 240.000{{c}}, ~3/2 = 704.3709{{c}} (~64/63 = 15.6291{{c}})		* [[WE]]: ~280/243 = 239.7268{{c}}, ~3/2 = 704.1103{{c}} (~64/63 = 15.0700{{c}})
	* [[POTE]]: ~280/243 = 240.000{{c}}, ~3/2 = 704.9128{{c}} (~64/63 = 15.0872{{c}})		: [[error map]]: {{val\| -1.366 +0.789 -0.013 +2.419 }}
			* [[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 }}
			<!-- * [[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 }}

	[[Badness]] (~~Smith~~): 0.~~148665~~		[[Badness]] (Sintel): 3.76

	=== 11-limit ===		=== 11-limit ===
Line 363:		Line 378:

	Optimal tunings:		Optimal tunings:
	* CTE: ~55/48 = 240.000{{c}}, ~3/2 = 704.8440{{c}} (~99/98 = 15.1560{{c}})		* WE: ~55/48 = 239.7357{{c}}, ~3/2 = 704.1025{{c}} (~99/98 = 15.1045{{c}})
	* POTE: ~55/48 = 240.000{{c}}, ~3/2 = 704.8788{{c}} (~99/98 = 15.1212{{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\| 75e, 80, 315bcdddee }}		{{Optimal ET sequence\|legend=0\| 5, 75e, 80, 315bcdddee }}

	Badness (~~Smith~~): 0.~~071702~~		Badness (Sintel): 2.37

	=== 13-limit ===		=== 13-limit ===
Line 378:		Line 395:

	Optimal tunings:		Optimal tunings:
	* ~~CTE~~: ~55/48 = 240.~~000~~{{c}}, ~3/2 = 704.~~7636~~{{c}} (~99/98 = 15.~~2364~~{{c}})		* WE: ~55/48 = 239.7711{{c}}, ~3/2 = 704.0302{{c}} (~99/98 = 15.2830{{c}})
	* ~~CWE~~: ~55/48 = 240.000{{c}}, ~3/2 = 704.~~7112~~{{c}} (~99/98 = 15.~~2882~~{{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\| 75e, 80, 155de }}		{{Optimal ET sequence\|legend=0\| 5f, 75e, 80, 155de }}

	Badness (~~Smith~~): 0.~~0557~~		Badness (Sintel): 2.30

	[[Category:Temperament collections]]		[[Category:Temperament collections]]

FloraC: Switch to Sintel's badness, WE & CWE tunings, per community consensus (2/)

2025-10-21T13:36:01Z

Switch to Sintel's badness, WE & CWE tunings, per community consensus (2/)

Show changes

FloraC: Switch to Sintel's badness, WE & CWE tunings, per community consensus (1/)

2025-10-21T13:09:24Z

Switch to Sintel's badness, WE & CWE tunings, per community consensus (1/)

← Older revision		Revision as of 13:09, 21 October 2025
Line 25:		Line 25:
	: mapping generators: ~567/400, ~10/9		: mapping generators: ~567/400, ~10/9

	[[Optimal tuning]] ([[POTE]]): ~567/400 = 600.000{{c}}, ~10/9 = 185.885{{c}}		[[Optimal tuning]]s:
			* [[WE]]: ~567/400 = 599.8218{{c}}, ~10/9 = 185.8303{{c}}
			: [[error map]]: {{val\| -0.356 -1.321 +1.141 +1.944 }}
			* [[CWE]]: ~567/400 = 600.0000{{c}}, ~10/9 = 185.8618{{c}}
			: 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 }}

	[[Badness]] (~~Smith~~): 0.~~095278~~		[[Badness]] (Sintel): 2.41

	=== 11-limit ===		=== 11-limit ===
Line 38:		Line 43:
	Mapping: {{mapping\| 2 1 0 5 6 \| 0 7 15 2 3 }}		Mapping: {{mapping\| 2 1 0 5 6 \| 0 7 15 2 3 }}

	Optimal ~~tuning (~~POTE): ~99/70 = 600.000{{c}}, ~10/9 = 185.962{{c}}		Optimal tunings:
			* WE: ~99/70 = 599.5785{{c}}, ~10/9 = 185.8332{{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 }}

	Badness (~~Smith~~): 0.~~046373~~		Badness (Sintel): 1.53

	=== 13-limit ===		=== 13-limit ===
Line 51:		Line 59:
	Mapping: {{mapping\| 2 1 0 5 6 4 \| 0 7 15 2 3 11 }}		Mapping: {{mapping\| 2 1 0 5 6 4 \| 0 7 15 2 3 11 }}

	Optimal ~~tuning (~~POTE): ~99/70 = 600.000{{c}}, ~10/9 = 185.955{{c}}		Optimal tunings:
			* WE: ~55/39 = 599.5432{{c}}, ~10/9 = 185.8136{{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 }}

	Badness (~~Smith~~): 0.~~025035~~		Badness (Sintel): 1.03

	=== 17-limit ===		=== 17-limit ===
Line 64:		Line 75:
	Mapping: {{mapping\| 2 1 0 5 6 4 6 \| 0 7 15 2 3 11 7 }}		Mapping: {{mapping\| 2 1 0 5 6 4 6 \| 0 7 15 2 3 11 7 }}

	Optimal ~~tuning (~~POTE): ~17/12 = 600.000{{c}}, ~10/9 = 185.916{{c}}		Optimal tunings:
			* WE: ~17/12 = 599.7117{{c}}, ~10/9 = 185.8270{{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~~, 142ef~~ }}		{{Optimal ET sequence\|legend=0\| 26, 58, 84 }}

	Badness (~~Smith~~): 0.~~021642~~		Badness (Sintel): 1.10

	=== 19-limit ===		=== 19-limit ===
Line 77:		Line 91:
	Mapping: {{mapping\| 2 1 0 5 6 4 6 2 \| 0 7 15 2 3 11 7 21 }}		Mapping: {{mapping\| 2 1 0 5 6 4 6 2 \| 0 7 15 2 3 11 7 21 }}

	Optimal ~~tuning (~~POTE): ~17/12 = 600.000{{c}}, ~10/9 = 185.858{{c}}		Optimal tunings:
			* WE: ~17/12 = 599.7288{{c}}, ~10/9 = 185.7738{{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~~, 142efh, 226deefgh~~ }}		{{Optimal ET sequence\|legend=0\| 26, 58h, 84 }}

	Badness (~~Smith~~): 0.~~018565~~		Badness (Sintel): 1.13

	== Infraorwell ==		== Infraorwell ==
Line 88:		Line 105:
	[[Comma list]]: 1728/1715, 28672/28125		[[Comma list]]: 1728/1715, 28672/28125

	{{Mapping\|legend=1\| 1 14 0 16 ~~\| 0~~ -16 3 -17 }}		{{Mapping\|legend=1\| 1 -2 3 -1 \| 0 16 -3 17 }}
	: mapping generators: ~2, ~12/7		: mapping generators: ~2, ~7/6

	[[Optimal tuning]] ([[~~POTE~~]]): ~2 = 1200.000{{c}}, ~7/6 = 269.032{{c}}		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1198.4649{{c}}, ~7/6 = 268.6878{{c}}
			: [[error map]]: {{val\| -1.535 +0.120 +3.018 +0.401 }}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/6 = 268.9844{{c}}
			: 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, 49, 58, 165cd, ~~223bcd~~ }}		{{Optimal ET sequence\|legend=1\| 9, 40bd, 49, 58, 165cd, 223bccd, 281bcccdd }}

	[[Badness]] (~~Smith~~): 0.~~117073~~		[[Badness]] (Sintel): 2.96

	=== 11-limit ===		=== 11-limit ===
Line 102:		Line 124:
	Comma list: 176/175, 540/539, 1344/1331		Comma list: 176/175, 540/539, 1344/1331

	Mapping: {{mapping\| 1 14 0 16 ~~12 \| 0~~ -16 3 -17 -11 }}		Mapping: {{mapping\| 1 -2 3 -1 1 \| 0 16 -3 17 11 }}

	Optimal ~~tuning (~~POTE): ~2 = 1200.000{{c}}, ~7/6 = 269.036{{c}}		Optimal tunings:
			* WE: ~2 = 1198.2928{{c}}, ~7/6 = 268.6532{{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, 49, 58, 165cdee }}		{{Optimal ET sequence\|legend=0\| 9, 40bde, 49, 58, 165cdee, 223bccdeee, 281bcccddeee }}

	Badness (~~Smith~~): 0.~~040721~~		Badness (Sintel): 1.35

	=== 13-limit ===		=== 13-limit ===
Line 115:		Line 140:
	Comma list: 144/143, 176/175, 196/195, 364/363		Comma list: 144/143, 176/175, 196/195, 364/363

	Mapping: {{mapping\| 1 14 0 16 ~~12 20 \| 0~~ -16 3 -17 -11 -21 }}		Mapping: {{mapping\| 1 -2 3 -1 1 -1 \| 0 16 -3 17 11 21 }}

	Optimal ~~tuning (~~POTE): ~2 = 1200.000{{c}}, ~7/6 = 269.021{{c}}		Optimal tunings:
			* WE: ~2 = 1198.2216{{c}}, ~7/6 = 268.6220{{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, 49f, 58 }}		{{Optimal ET sequence\|legend=0\| 9, 40bdef, 49f, 58, 223bccdeeefff, 281bcccddeeeffff }}

	Badness (~~Smith~~): 0.~~023683~~		Badness (Sintel): 0.979

	== Sentinel ==		== Sentinel ==

FloraC at 12:39, 21 October 2025

2025-10-21T12:39:34Z

← Older revision		Revision as of 12:39, 21 October 2025
Line 2:		Line 2:
	This is a collection of [[rank-2 temperament\|rank-2]] [[regular temperament\|temperaments]] that [[tempering out\|temper out]] the [[orwellisma]] ({{monzo\|legend=1\| 6 3 -1 -3 }}, [[ratio]]: 1728/1715).		This is a collection of [[rank-2 temperament\|rank-2]] [[regular temperament\|temperaments]] that [[tempering out\|temper out]] the [[orwellisma]] ({{monzo\|legend=1\| 6 3 -1 -3 }}, [[ratio]]: 1728/1715).

	Temperaments ~~considered below are secant, infraorwell, quartonic, sentinel, diesic, philips, triskaidekic, and pentaorwell. Discussed~~ elsewhere are:		Temperaments discussed elsewhere are:
	* [[Beep]] (+21/20 or 27/25) → [[Bug family #Beep\|Bug family]]		* [[Beep]] (+21/20 or 27/25) → [[Bug family #Beep\|Bug family]]
	* ''[[Doublewide]]'' (+50/49) → [[Jubilismic clan #Doublewide\|Jubilismic clan]]		* ''[[Doublewide]]'' (+50/49) → [[Jubilismic clan #Doublewide\|Jubilismic clan]]
Line 14:		Line 14:
	* ''[[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 secant, infraorwell, quartonic, sentinel, diesic, philips, triskaidekic, and pentaorwell.

	== Secant ==		== Secant ==

← 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]]