Diminished family - Revision history

Xenllium at 03:11, 1 March 2026

2026-03-01T03:11:38Z

@@ Line 12: / Line 12: @@
 {{Mapping|legend=1| 4 0 3 | 0 1 1 }}
 [[Optimal tuning]]s:
@@ Line 226: / Line 228: @@
 Badness (Sintel): 1.26
 [[Category:Temperament families]]

FloraC at 11:47, 27 January 2026

2026-01-27T11:47:28Z

← Older revision		Revision as of 11:47, 27 January 2026
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	{{Main\| Diminished (temperament) }}		{{Main\| Diminished (temperament) }}

	Septimal diminished equates the ~~300c~~ minor third to [[7/6]] along with 6/5, and the ~~600c~~ tritone to [[7/5]].		Septimal diminished equates the 300{{c}} minor third to [[7/6]] along with 6/5, and the 600{{c}} tritone to [[7/5]][[~]][[10/7]].

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

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

2025-11-27T12:17:06Z

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

← Older revision		Revision as of 12:17, 27 November 2025
Line 228:		Line 228:

	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Diminished family\| ]] <!-- main article -->		[[Category:Diminished family\| ]] <!-- main article -->
	[[Category:Diminished\| ]] <!-- key article -->		[[Category:Diminished\| ]] <!-- key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

Lériendil at 18:14, 4 September 2025

2025-09-04T18:14:58Z

← Older revision		Revision as of 18:14, 4 September 2025
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	== Septimal diminished ==		== Septimal diminished ==
	{{Main\| Diminished (temperament) }}		{{Main\| Diminished (temperament) }}

			Septimal diminished equates the 300c minor third to [[7/6]] along with 6/5, and the 600c tritone to [[7/5]].

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

FloraC: Post-move cleanup

2025-08-21T12:13:06Z

Post-move cleanup

← Older revision		Revision as of 12:13, 21 August 2025
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	{{Technical data page}}		{{Technical data page}}
	The '''~~dimipent~~ family''' tempers out the major diesis a.k.a. diminished comma, [[648/625]], the amount by which four [[6/5]] minor thirds exceed an [[octave]], and so identifies the minor third with the quarter-octave. Hence it has the same 300-cent 6/5-approximations as [[12edo]].		The '''diminished family''' of [[regular temperament\|temperaments]] [[tempering out\|tempers out]] the major diesis a.k.a. diminished comma, [[648/625]], the amount by which four [[6/5]] minor thirds exceed an [[octave]], and so identifies the minor third with the quarter-octave. Hence it has the same 300-cent 6/5-approximations as [[12edo]].

	== ~~Dimipent~~ ==		== Diminished ==
	{{Main\| Diminished (temperament) }}		{{Main\| Diminished (temperament) }}

	The [[generator]] of ~~dimipent~~ can be taken as a fifth or a semitone, and 12edo, with its excellent fifth, is an obvious tuning, though a flatter fifth might be preferred to go with the flat minor third. Its [[ploidacot]] is tetraploid monocot.		The [[generator]] of diminished can be taken as a fifth or a semitone, and 12edo, with its excellent fifth, is an obvious tuning, though a flatter fifth might be preferred to go with the flat minor third. Its [[ploidacot]] is tetraploid monocot.

	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5
Line 23:		Line 23:
	[[Badness]] (Sintel): 1.11		[[Badness]] (Sintel): 1.11

	== ~~Diminished~~ ==		== Septimal diminished ==
	~~<div style="float: right">[[:de:Verminderte Temperaturen\|Deutsch]]</div>~~

	{{Main\| Diminished (temperament) }}		{{Main\| Diminished (temperament) }}

Line 229:		Line 227:
	[[Category:Temperament families]]		[[Category:Temperament families]]
	[[Category:Pages with mostly numerical content]]		[[Category:Pages with mostly numerical content]]
	[[Category:~~Dimipent~~ family\| ]] <!-- main article -->		[[Category:Diminished family\| ]] <!-- main article -->
	[[Category:Diminished\| ]] <!-- key article -->		[[Category:Diminished\| ]] <!-- key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

FloraC: FloraC moved page Dimipent family to Diminished family: Community consensus

2025-08-21T12:11:02Z

FloraC moved page Dimipent family to Diminished family: Community consensus

← Older revision	Revision as of 12:11, 21 August 2025
(No difference)

FloraC: + short intro to each temp

2025-08-18T15:30:52Z

+ short intro to each temp

← Older revision		Revision as of 15:30, 18 August 2025
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	{{Technical data page}}		{{Technical data page}}
	The '''dimipent family''' tempers out the major diesis ~~aka~~ diminished comma, [[648/625]], the amount by which four [[6/5]] minor thirds exceed an [[octave]], and so identifies the minor third with the quarter-octave. Hence it has the same 300-cent 6/5-approximations as [[12edo]].		The '''dimipent family''' tempers out the major diesis a.k.a. diminished comma, [[648/625]], the amount by which four [[6/5]] minor thirds exceed an [[octave]], and so identifies the minor third with the quarter-octave. Hence it has the same 300-cent 6/5-approximations as [[12edo]].

	== Dimipent ==		== Dimipent ==
	{{Main\| Diminished (temperament) }}		{{Main\| Diminished (temperament) }}

			The [[generator]] of dimipent can be taken as a fifth or a semitone, and 12edo, with its excellent fifth, is an obvious tuning, though a flatter fifth might be preferred to go with the flat minor third. Its [[ploidacot]] is tetraploid monocot.

	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5
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	=== Cohedim ===		=== Cohedim ===
	This ~~temperament~~ has been documented in Graham Breed's temperament finder as ''hemidim'', the same name as [[~~Dimipent family~~ #Hemidim\|11-limit 4e &~~amp;~~ 24 and 13-limit 4ef &~~amp;~~ 24]]. For 11-limit 8bce & 12 temperament, ''cohedim'' arguably makes more sense.		This extension has been documented in Graham Breed's temperament finder as ''hemidim'', the same name as [[#Hemidim\|11-limit 4e & 24 and 13-limit 4ef & 24]]. For the 11-limit 8bce & 12 temperament, ''cohedim'' arguably makes more sense. Its ploidacot is tetraploid alpha-dicot.

	Subgroup: 2.3.5.7.11		Subgroup: 2.3.5.7.11
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	== Hemidim ==		== Hemidim ==
			Hemidim tempers out 49/48 and may be described as the {{nowrap\| 4 & 24 }} temperament. Its ploidcot is tetraploid dicot.

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

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	Comma list: 49/48, 77/75, 243/242		Comma list: 49/48, 77/75, 243/242

	Mapping: {{mapping\| 4 0 3 8 -2 \| 0 2 2 1 5}}		Mapping: {{mapping\| 4 0 3 8 -2 \| 0 2 2 1 5 }}

	Optimal tunings:		Optimal tunings:
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	== Octonion ==		== Octonion ==
	It was formerly known as "semidim" but renamed to avoid confusion with another temperament of the same name.		Octonion tempers out 245/243, and may be described as the {{nowrap\| 8d & 24 }} temperament. Its ploidacot is octoploid monocot.

			It was formerly known as ''semidim'' but renamed to avoid confusion with another temperament of the same name.

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

FloraC: - CTE & POTE tunings

2025-08-18T15:11:35Z

- CTE & POTE tunings

← Older revision		Revision as of 15:11, 18 August 2025
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	* [[CWE]]: ~6/5 = 300.0000{{c}}, ~3/2 = 698.2660{{c}} (~25/24 = 98.2660{{c}})		* [[CWE]]: ~6/5 = 300.0000{{c}}, ~3/2 = 698.2660{{c}} (~25/24 = 98.2660{{c}})
	: error map: {{val\| 0.000 -3.689 +11.952 }}		: error map: {{val\| 0.000 -3.689 +11.952 }}
	~~<!-- * [[CTE]]: ~6/5 = 300.000{{c}}, ~3/2 = 696.983{{c}} (~25/24 = 96.983{{c}})~~
	~~: [[error map]]: {{val\| 0.000 -4.972 +10.670 }}~~
	* [[POTE]]: ~6/5 = 300.000{{c}}, ~3/2 = 699.507{{c}} (~25/24 = 99.507{{c}})
	~~: error map: {{val\| 0.000 -2.448 +13.193 }} -->~~

	{{Optimal ET sequence\|legend=1\| 4, 8, 12 }}		{{Optimal ET sequence\|legend=1\| 4, 8, 12 }}
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	* [[CWE]]: ~6/5 = 300.0000{{c}}, ~3/2 = 695.9619{{c}} (~21/20 = 95.9619{{c}})		* [[CWE]]: ~6/5 = 300.0000{{c}}, ~3/2 = 695.9619{{c}} (~21/20 = 95.9619{{c}})
	: error map: {{val\| 0.000 -5.993 +9.648 +27.136 }}		: error map: {{val\| 0.000 -5.993 +9.648 +27.136 }}
	~~<!-- * [[CTE]]: ~6/5 = 300.000{{c}}, ~3/2 = 691.955{{c}} (~21/20 = 91.955{{c}})~~
	~~: [[error map]]: {{val\| 0.000 -10.000 +5.641 +23.129 }}~~
	* [[POTE]]: ~6/5 = 300.000{{c}}, ~3/2 = 699.523{{c}} (~21/20 = 99.523{{c}})
	~~: error map: {{val\| 0.000 -2.432 +13.210 +30.698 }} -->~~

	{{Optimal ET sequence\|legend=1\| 4, 8d, 12 }}		{{Optimal ET sequence\|legend=1\| 4, 8d, 12 }}
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	* WE: ~6/5 = 297.8458{{c}}, ~3/2 = 703.9277{{c}} (~15/14 = 108.2361{{c}})		* WE: ~6/5 = 297.8458{{c}}, ~3/2 = 703.9277{{c}} (~15/14 = 108.2361{{c}})
	* CWE: ~6/5 = 300.0000{{c}}, ~3/2 = 703.5558{{c}} (~15/14 = 103.5558{{c}})		* CWE: ~6/5 = 300.0000{{c}}, ~3/2 = 703.5558{{c}} (~15/14 = 103.5558{{c}})
	~~<!-- * CTE: ~6/5 = 300.000{{c}}, ~3/2 = 691.955{{c}} (~21/20 = 91.955{{c}})~~
	* POTE: ~6/5 = 300.000{{c}}, ~3/2 = 709.109{{c}} (~15/14 = 109.109{{c}}) -->

	{{Optimal ET sequence\|legend=0\| 4, 8d, 12, 32cddee, 44cddeee }}		{{Optimal ET sequence\|legend=0\| 4, 8d, 12, 32cddee, 44cddeee }}
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	* WE: ~6/5 = 297.2520{{c}}, ~3/2 = 707.2352{{c}} (~15/14 = 112.7312{{c}})		* WE: ~6/5 = 297.2520{{c}}, ~3/2 = 707.2352{{c}} (~15/14 = 112.7312{{c}})
	* CWE: ~6/5 = 300.0000{{c}}, ~3/2 = 708.4648{{c}} (~15/14 = 108.4648{{c}})		* CWE: ~6/5 = 300.0000{{c}}, ~3/2 = 708.4648{{c}} (~15/14 = 108.4648{{c}})
	~~<!-- * CTE: ~6/5 = 300.000{{c}}, ~3/2 = 691.954{{c}} (~21/20 = 91.954{{c}})~~
	* POTE: ~6/5 = 300.000{{c}}, ~3/2 = 713.773{{c}} (~15/14 = 113.773{{c}}) -->

	{{Optimal ET sequence\|legend=0\| 4, 8d, 12f, 20cdef, 32cddeefff }}		{{Optimal ET sequence\|legend=0\| 4, 8d, 12f, 20cdef, 32cddeefff }}
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	* WE: ~6/5 = 299.6308{{c}}, ~3/2 = 689.0322{{c}} (~21/20 = 89.7707{{c}})		* WE: ~6/5 = 299.6308{{c}}, ~3/2 = 689.0322{{c}} (~21/20 = 89.7707{{c}})
	* CWE: ~6/5 = 300.0000{{c}}, ~3/2 = 688.9304{{c}} (~21/20 = 88.9304{{c}})		* CWE: ~6/5 = 300.0000{{c}}, ~3/2 = 688.9304{{c}} (~21/20 = 88.9304{{c}})
	~~<!-- * CTE: ~6/5 = 300.000{{c}}, ~3/2 = 687.747{{c}} (~21/20 = 87.747{{c}})~~
	* POTE: ~6/5 = 300.000{{c}}, ~3/2 = 689.881{{c}} (~21/20 = 89.881{{c}}) -->

	{{Optimal ET sequence\|legend=0\| 4e, 8dee, 12, 28 }}		{{Optimal ET sequence\|legend=0\| 4e, 8dee, 12, 28 }}
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	* WE: ~6/5 = 298.7799{{c}}, ~11/7 = 795.0744{{c}} (~12/11 = 101.2653{{c}})		* WE: ~6/5 = 298.7799{{c}}, ~11/7 = 795.0744{{c}} (~12/11 = 101.2653{{c}})
	* CWE: ~6/5 = 300.0000{{c}}, ~11/7 = 796.0102{{c}} (~12/11 = 103.9898{{c}})		* CWE: ~6/5 = 300.0000{{c}}, ~11/7 = 796.0102{{c}} (~12/11 = 103.9898{{c}})
	~~<!-- * CTE: ~6/5 = 300.000{{c}}, ~11/7 = 793.423{{c}} (~12/11 = 106.577{{c}})~~
	* POTE: ~6/5 = 300.000{{c}}, ~11/7 = 798.421{{c}} (~12/11 = 101.679{{c}}) -->

	{{Optimal ET sequence\|legend=0\| 8bce, 12 }}		{{Optimal ET sequence\|legend=0\| 8bce, 12 }}
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	* WE: ~6/5 = 298.4646{{c}}, ~11/7 = 793.6185{{c}} (~12/11 = 101.7754{{c}})		* WE: ~6/5 = 298.4646{{c}}, ~11/7 = 793.6185{{c}} (~12/11 = 101.7754{{c}})
	* CWE: ~6/5 = 300.0000{{c}}, ~11/7 = 794.7323{{c}} (~12/11 = 105.2677{{c}})		* CWE: ~6/5 = 300.0000{{c}}, ~11/7 = 794.7323{{c}} (~12/11 = 105.2677{{c}})
	~~<!-- * CTE: ~6/5 = 300.000{{c}}, ~11/7 = 791.375{{c}} (~12/11 = 108.625{{c}})~~
	* POTE: ~6/5 = 300.000{{c}}, ~11/7 = 797.701{{c}} (~12/11 = 102.299{{c}}) -->

	{{Optimal ET sequence\|legend=0\| 8bcef, 12f }}		{{Optimal ET sequence\|legend=0\| 8bcef, 12f }}
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	* [[CWE]]: ~6/5 = 300.0000{{c}}, ~7/4 = 948.2575{{c}} (~36/35 = 48.2575{{c}})		* [[CWE]]: ~6/5 = 300.0000{{c}}, ~7/4 = 948.2575{{c}} (~36/35 = 48.2575{{c}})
	: error map: {{val\| 0.000 -5.440 +10.201 -20.568 }}		: error map: {{val\| 0.000 -5.440 +10.201 -20.568 }}
	~~<!-- * [[CTE]]: ~6/5 = 300.000{{c}}, ~7/4 = 949.540{{c}} (~36/35 = 49.540{{c}})~~
	~~: [[error map]]: {{val\| 0.000 -2.875 +12.766 -19.286 }}~~
	* [[POTE]]: ~6/5 = 300.000{{c}}, ~7/4 = 947.445{{c}} (~36/35 = 47.445{{c}})
	~~: error map: {{val\| 0.000 -7.065 +8.576 -21.381 }} -->~~

	{{Optimal ET sequence\|legend=1\| 4, …, 20c, 24 }}		{{Optimal ET sequence\|legend=1\| 4, …, 20c, 24 }}
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	* WE: ~6/5 = 300.4282{{c}}, ~7/4 = 949.6958{{c}} (~36/35 = 48.4112{{c}})		* WE: ~6/5 = 300.4282{{c}}, ~7/4 = 949.6958{{c}} (~36/35 = 48.4112{{c}})
	* CWE: ~6/5 = 300.0000{{c}}, ~7/4 = 948.9065{{c}} (~36/35 = 48.9065{{c}})		* CWE: ~6/5 = 300.0000{{c}}, ~7/4 = 948.9065{{c}} (~36/35 = 48.9065{{c}})
	~~<!-- * CTE: ~6/5 = 300.000{{c}}, ~7/4 = 949.872{{c}} (~36/35 = 49.872{{c}})~~
	* POTE: ~6/5 = 300.000{{c}}, ~7/4 = 948.342{{c}} (~36/35 = 48.342{{c}}) -->

	{{Optimal ET sequence\|legend=0\| 4e, 20ce, 24 }}		{{Optimal ET sequence\|legend=0\| 4e, 20ce, 24 }}
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	* WE: ~6/5 = 300.4282{{c}}, ~7/4 = 949.2440{{c}} (~36/35 = 47.8487{{c}})		* WE: ~6/5 = 300.4282{{c}}, ~7/4 = 949.2440{{c}} (~36/35 = 47.8487{{c}})
	* CWE: ~6/5 = 300.0000{{c}}, ~7/4 = 948.3581{{c}} (~36/35 = 48.3581{{c}})		* CWE: ~6/5 = 300.0000{{c}}, ~7/4 = 948.3581{{c}} (~36/35 = 48.3581{{c}})
	~~<!-- * CTE: ~6/5 = 300.000{{c}}, ~7/4 = 949.366{{c}} (~36/35 = 49.366{{c}})~~
	* POTE: ~6/5 = 300.000{{c}}, ~7/4 = 947.775{{c}} (~36/35 = 47.775{{c}}) -->

	{{Optimal ET sequence\|legend=0\| 4ef, 24 }}		{{Optimal ET sequence\|legend=0\| 4ef, 24 }}
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	* [[CWE]]: ~15/14 = 150.0000{{c}}, ~3/2 = 704.9636{{c}} (~36/35 = 45.0364{{c}})		* [[CWE]]: ~15/14 = 150.0000{{c}}, ~3/2 = 704.9636{{c}} (~36/35 = 45.0364{{c}})
	: error map: {{val\| 0.000 +3.008 +18.650 -8.899 }}		: error map: {{val\| 0.000 +3.008 +18.650 -8.899 }}
	~~<!-- * [[CTE]]: ~15/14 = 150.000{{c}}, ~3/2 = 702.765{{c}} (~36/35 = 47.235{{c}})~~
	* [[POTE]]: ~15/14 = 150.000{{c}}, ~3/2 = 707.014{{c}} (~36/35 = 42.986{{c}}) -->

	{{Optimal ET sequence\|legend=1\| 8d, 16d, 24, 32c }}		{{Optimal ET sequence\|legend=1\| 8d, 16d, 24, 32c }}
Line 229:		Line 201:
	* WE: ~12/11 = 149.7102{{c}}, ~3/2 = 705.2799{{c}} (~36/35 = 43.2712{{c}})		* WE: ~12/11 = 149.7102{{c}}, ~3/2 = 705.2799{{c}} (~36/35 = 43.2712{{c}})
	* CWE: ~12/11 = 150.0000{{c}}, ~3/2 = 704.9285{{c}} (~36/35 = 45.0715{{c}})		* CWE: ~12/11 = 150.0000{{c}}, ~3/2 = 704.9285{{c}} (~36/35 = 45.0715{{c}})
	~~<!-- * CTE: ~12/11 = 150.000{{c}}, ~3/2 = 702.662{{c}} (~36/35 = 47.338{{c}})~~
	* POTE: ~12/11 = 150.000{{c}}, ~3/2 = 706.645{{c}} (~36/35 = 43.355{{c}}) -->

	{{Optimal ET sequence\|legend=0\| 8d, 16d, 24, 32c }}		{{Optimal ET sequence\|legend=0\| 8d, 16d, 24, 32c }}
Line 246:		Line 216:
	* WE: ~12/11 = 149.6311{{c}}, ~3/2 = 705.6367{{c}} (~36/35 = 42.5188{{c}})		* WE: ~12/11 = 149.6311{{c}}, ~3/2 = 705.6367{{c}} (~36/35 = 42.5188{{c}})
	* CWE: ~12/11 = 150.0000{{c}}, ~3/2 = 705.2777{{c}} (~36/35 = 44.7223{{c}})		* CWE: ~12/11 = 150.0000{{c}}, ~3/2 = 705.2777{{c}} (~36/35 = 44.7223{{c}})
	~~<!-- * CTE: ~12/11 = 150.000{{c}}, ~3/2 = 701.952{{c}} (~36/35 = 48.048{{c}})~~
	* POTE: ~12/11 = 150.000{{c}}, ~3/2 = 707.376{{c}} (~36/35 = 42.624{{c}}) -->

	{{Optimal ET sequence\|legend=0\| 8d, 16d, 24, 32cf }}		{{Optimal ET sequence\|legend=0\| 8d, 16d, 24, 32cf }}

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

2025-08-18T15:10:50Z

Switch to Sintel's badness, WE & CWE tunings, per community consensus

Show changes

Lériendil: Text replacement - "Category:Temperament families" to "Category:Temperament families Category:Pages with mostly numerical content"

2025-06-24T00:32:21Z

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

← Older revision		Revision as of 00:32, 24 June 2025
Line 220:		Line 220:

	[[Category:Temperament families]]		[[Category:Temperament families]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Dimipent family\| ]] <!-- main article -->		[[Category:Dimipent family\| ]] <!-- main article -->
	[[Category:Diminished\| ]] <!-- key article -->		[[Category:Diminished\| ]] <!-- key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]