Didymus rank-3 family - Revision history

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

2025-11-27T12:17:26Z

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
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Didymus rank-3 family\| ]] <!-- main article -->		[[Category:Didymus rank-3 family\| ]] <!-- main article -->
	[[Category:Didymus\| ]] <!-- key article -->		[[Category:Didymus\| ]] <!-- key article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

FloraC: Fix linking

2025-08-27T13:50:02Z

Fix linking

← Older revision		Revision as of 13:50, 27 August 2025
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	Temperaments discussed elsewhere include:		Temperaments discussed elsewhere include:
	* ''[[Urania]]'' (+243/242 or 121/120) → [[Rastmic rank ~~three~~ clan #Urania\|Rastmic rank ~~three~~ clan]]		* ''[[Urania]]'' (+243/242 or 121/120) → [[Rastmic rank-3 clan #Urania\|Rastmic rank-3 clan]]

	== Didymus ==		== Didymus ==

FloraC: - typo

2025-08-27T12:54:15Z

- typo

← Older revision		Revision as of 12:54, 27 August 2025
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	== Polyhymnia ==		== Polyhymnia ==
	Polyhymnia tempers out 385/38. It is another temperament related to meanpop.		Polyhymnia tempers out 385/384. It is another temperament related to meanpop.

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

FloraC: FloraC moved page Didymus rank three family to Didymus rank-3 family: For obvious reasons

2025-08-27T12:48:38Z

FloraC moved page Didymus rank three family to Didymus rank-3 family: For obvious reasons

← Older revision	Revision as of 12:48, 27 August 2025
(No difference)

FloraC: Sorting and + intro to each temp

2025-08-27T12:46:56Z

Sorting and + intro to each temp

Show changes

FloraC: - POTE tunings

2025-08-27T12:39:11Z

- POTE tunings

← Older revision		Revision as of 12:39, 27 August 2025
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 696.6512{{c}}, ~7/4 = 966.5654{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 696.6512{{c}}, ~7/4 = 966.5654{{c}}
	: error map: {{val\| 0.000 -5.304 +0.291 -2.261 }}		: error map: {{val\| 0.000 -5.304 +0.291 -2.261 }}
	~~<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 696.2387{{c}}, ~7/4 = 964.9090{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 12, 19, 31, 81, 112b, 143b }}		{{Optimal ET sequence\|legend=1\| 12, 19, 31, 81, 112b, 143b }}
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 696.5797{{c}}, ~7/4 = 969.7942{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 696.5797{{c}}, ~7/4 = 969.7942{{c}}
	: error map: {{val\| 0.000 -5.375 +0.005 +0.968 -4.889 }}		: error map: {{val\| 0.000 -5.375 +0.005 +0.968 -4.889 }}
	~~<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 696.1982{{c}}, ~7/4 = 968.4280{{c}} -->~~

	[[Minimax tuning]]:		[[Minimax tuning]]:
Line 60:		Line 58:
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 693.9085{{c}}, ~7/4 = 965.3621{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 693.9085{{c}}, ~7/4 = 965.3621{{c}}
	: error map: {{val\| 0.000 -8.047 -10.680 -3.464 +12.133 }}		: error map: {{val\| 0.000 -8.047 -10.680 -3.464 +12.133 }}
	~~<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 696.1982{{c}}, ~7/4 = 968.4280{{c}} -->~~

	[[Minimax tuning]]:		[[Minimax tuning]]:
Line 83:		Line 80:
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 696.6562{{c}}, ~11/8 = 548.5396{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 696.6562{{c}}, ~11/8 = 548.5396{{c}}
	: error map: {{val\| 0.000 -5.299 +0.311 -2.264 -2.778 }}		: error map: {{val\| 0.000 -5.299 +0.311 -2.264 -2.778 }}
	~~<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 696.4949{{c}}, ~11/8 = 547.0252{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 12, 19, 31, 50, 81, 112b }}		{{Optimal ET sequence\|legend=1\| 12, 19, 31, 50, 81, 112b }}
Line 99:		Line 95:
	* WE: ~2 = 1201.6213{{c}}, ~3/2 = 696.9287{{c}}, ~11/8 = 546.4190{{c}}		* WE: ~2 = 1201.6213{{c}}, ~3/2 = 696.9287{{c}}, ~11/8 = 546.4190{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 696.1573{{c}}, ~11/8 = 547.5865{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 696.1573{{c}}, ~11/8 = 547.5865{{c}}
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 695.9883{{c}}, ~11/8 = 545.6817{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 12f, 19, 31, 50, 69de, 81, 119bdde }}		{{Optimal ET sequence\|legend=0\| 12f, 19, 31, 50, 69de, 81, 119bdde }}
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 697.3350{{c}}, ~7/4 = 969.0152{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 697.3350{{c}}, ~7/4 = 969.0152{{c}}
	: error map: {{val\| 0.000 -4.620 +3.026 +0.189 -3.622 }}		: error map: {{val\| 0.000 -4.620 +3.026 +0.189 -3.622 }}
	~~<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 697.2502{{c}}, ~7/4 = 968.6295{{c}} -->~~

	[[Minimax tuning]]:		[[Minimax tuning]]:
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 696.3248{{c}}, ~7/4 = 964.8389{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 696.3248{{c}}, ~7/4 = 964.8389{{c}}
	: error map: {{val\| 0.000 -5.630 -1.014 -3.987 -5.131 }}		: error map: {{val\| 0.000 -5.630 -1.014 -3.987 -5.131 }}
	~~<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 696.2305{{c}}, ~7/4 = 964.8695{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 7, 12e, 19, 24, 26, 31, 81, 112b }}		{{Optimal ET sequence\|legend=1\| 7, 12e, 19, 24, 26, 31, 81, 112b }}
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 693.1206{{c}}, ~7/4 = 955.1393{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 693.1206{{c}}, ~7/4 = 955.1393{{c}}
	: error map: {{val\| 0.000 -8.834 -13.831 -13.687 -44.439 }}		: error map: {{val\| 0.000 -8.834 -13.831 -13.687 -44.439 }}
	~~<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 692.0796{{c}}, ~7/4 = 950.2565{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 5, 7, 12e, 14c, 19e, 33cdee, 52cdeee }}		{{Optimal ET sequence\|legend=1\| 5, 7, 12e, 14c, 19e, 33cdee, 52cdeee }}
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 698.9964{{c}}, ~7/4 = 962.5723{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 698.9964{{c}}, ~7/4 = 962.5723{{c}}
	: error map: {{val\| 0.000 -2.959 +9.672 -6.254 +15.269 }}		: error map: {{val\| 0.000 -2.959 +9.672 -6.254 +15.269 }}
	~~<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 699.2230{{c}}, ~7/4 = 964.2363{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 12, 17c, 19, 24, 31e, 36 }}		{{Optimal ET sequence\|legend=1\| 12, 17c, 19, 24, 31e, 36 }}
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 696.7166{{c}}, ~7/4 = 964.9479{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 696.7166{{c}}, ~7/4 = 964.9479{{c}}
	: error map: {{val\| 0.000 -5.238 +0.553 -3.878 -4.197 }}		: error map: {{val\| 0.000 -5.238 +0.553 -3.878 -4.197 }}
	~~<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 696.2358{{c}}, ~7/4 = 964.0006{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 12e, 14c, 17c, 19, 31, 81, 112b }}		{{Optimal ET sequence\|legend=1\| 12e, 14c, 17c, 19, 31, 81, 112b }}

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

2025-08-27T12:38:35Z

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

Show changes

FloraC: Cleanup and stuff

2025-08-26T12:48:11Z

Cleanup and stuff

← Older revision		Revision as of 12:48, 26 August 2025
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	The '''didymus rank-3 family''' are rank-3 temperaments tempering out the didymus comma, [[81/80]]. If nothing else is tempered out we have a [[7-limit]] [[planar temperament]], with an [[11-limit]] comma we get an 11-limit temperament, and so forth.		The '''didymus rank-3 family''' are rank-3 temperaments tempering out the didymus comma, [[81/80]]. If nothing else is tempered out we have a [[7-limit]] [[planar temperament]], with an [[11-limit]] comma we get an 11-limit temperament, and so forth.

	Most of these temperaments were named by [[Gene Ward Smith]] in 2010<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_100647.html#100648 ''Yahoo! Tuning Group \| Higher-rank meantone extensions (muse temperaments?)'']</ref>.		Most of these temperaments were named by [[Gene Ward Smith]] in 2010<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_100647.html#100648 Yahoo! Tuning Group \| ''Higher-rank meantone extensions (muse temperaments?)'']</ref>.

	Temperaments discussed elsewhere include:		Temperaments discussed elsewhere include:
Line 14:		Line 14:
	{{Mapping\|legend=1\| 1 0 -4 0 \| 0 1 4 0 \| 0 0 0 1 }}		{{Mapping\|legend=1\| 1 0 -4 0 \| 0 1 4 0 \| 0 0 0 1 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~3/2 = 696.2387, ~7/4 = 964.9090		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 696.2387{{c}}, ~7/4 = 964.9090{{c}}

	{{Optimal ET sequence\|legend=1\| 12, 19, 31, 81 }}		{{Optimal ET sequence\|legend=1\| 12, 19, 31, 81 }}

	[[Badness]]: 0.095 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.095 × 10<sup>-3</sup>

	== Euterpe ==		== Euterpe ==
Line 27:		Line 27:
	{{Mapping\|legend=1\| 1 0 -4 0 1 \| 0 1 4 0 -2 \| 0 0 0 1 2 }}		{{Mapping\|legend=1\| 1 0 -4 0 1 \| 0 1 4 0 -2 \| 0 0 0 1 2 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~3/2 = 696.1982, ~7/4 = 968.4280		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 696.1982{{c}}, ~7/4 = 968.4280{{c}}

	[[Minimax tuning]]:		[[Minimax tuning]]:
Line 36:		Line 36:
	{{Optimal ET sequence\|legend=1\| 12, 17c, 19e, 26, 31, 88 }}		{{Optimal ET sequence\|legend=1\| 12, 17c, 19e, 26, 31, 88 }}

	[[Badness]]: 0.536 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.536 × 10<sup>-3</sup>

	== Calliope ==		== Calliope ==
Line 45:		Line 45:
	{{Mapping\|legend=1\| 1 0 -4 0 -6 \| 0 1 4 0 6 \| 0 0 0 1 0 }}		{{Mapping\|legend=1\| 1 0 -4 0 -6 \| 0 1 4 0 6 \| 0 0 0 1 0 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~3/2 = 696.1982, ~7/4 = 968.4280		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 696.1982{{c}}, ~7/4 = 968.4280{{c}}

	[[Minimax tuning]]:		[[Minimax tuning]]:
Line 54:		Line 54:
	{{Optimal ET sequence\|legend=1\| 7d, 12, 19, 26, 45 }}		{{Optimal ET sequence\|legend=1\| 7d, 12, 19, 26, 45 }}

	[[Badness]]: 0.530 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.530 × 10<sup>-3</sup>

	== Erato ==		== Erato ==
Line 63:		Line 63:
	{{Mapping\|legend=1\| 1 0 -4 -13 0 \| 0 1 4 10 0 \| 0 0 0 0 1 }}		{{Mapping\|legend=1\| 1 0 -4 -13 0 \| 0 1 4 10 0 \| 0 0 0 0 1 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~3/2 = 696.4949, ~11/8 = 547.0252		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 696.4949{{c}}, ~11/8 = 547.0252{{c}}

	{{Optimal ET sequence\|legend=1\| 12, 19, 31, 50, 81 }}		{{Optimal ET sequence\|legend=1\| 12, 19, 31, 50, 81 }}

	[[Badness]]: 0.558 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.558 × 10<sup>-3</sup>

	=== 13-limit ===		=== 13-limit ===
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	Mapping: {{mapping\| 1 0 -4 -13 0 -20 \| 0 1 4 10 0 15 \| 0 0 0 0 1 0 }}		Mapping: {{mapping\| 1 0 -4 -13 0 -20 \| 0 1 4 10 0 15 \| 0 0 0 0 1 0 }}

	Optimal tuning (POTE): ~2 = ~~1\1~~, ~3/2 = 695.9883, ~11/8 = 545.6817		Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~3/2 = 695.9883{{c}}, ~11/8 = 545.6817{{c}}

	{{Optimal ET sequence\|legend=1\| 12f, 19, 31, 50, 81 }}		{{Optimal ET sequence\|legend=0\| 12f, 19, 31, 50, 81 }}

	== Clio ==		== Clio ==
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	{{Mapping\|legend=1\| 1 0 -4 0 -12 \| 0 1 4 0 8 \| 0 0 0 1 1 }}		{{Mapping\|legend=1\| 1 0 -4 0 -12 \| 0 1 4 0 8 \| 0 0 0 1 1 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~3/2 = 697.2502, ~7/4 = 968.6295		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 697.2502{{c}}, ~7/4 = 968.6295{{c}}

	[[Minimax tuning]]:		[[Minimax tuning]]:
Line 96:		Line 96:
	{{Optimal ET sequence\|legend=1\| 7, 12, 19e, 24, 31, 105, 129 }}		{{Optimal ET sequence\|legend=1\| 7, 12, 19e, 24, 31, 105, 129 }}

	[[Badness]]: 0.738 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.738 × 10<sup>-3</sup>

	== Polyhymnia ==		== Polyhymnia ==

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11
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	{{Mapping\|legend=1\| 1 0 -4 0 11 \| 0 1 4 0 -3 \| 0 0 0 1 -1 }}		{{Mapping\|legend=1\| 1 0 -4 0 11 \| 0 1 4 0 -3 \| 0 0 0 1 -1 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~3/2 = 696.2305, ~7/4 = 964.8695		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 696.2305{{c}}, ~7/4 = 964.8695{{c}}

	{{Optimal ET sequence\|legend=1\| 7, 12e, 19, 24, 26, 31 }}		{{Optimal ET sequence\|legend=1\| 7, 12e, 19, 24, 26, 31 }}
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	Scales: [[polyhymnia12]]		Scales: [[polyhymnia12]]

	== Thalia ==		== Thalia ==
	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

Line 119:		Line 119:
	{{Mapping\|legend=1\| 1 0 -4 0 5 \| 0 1 4 0 -1 \| 0 0 0 1 0 }}		{{Mapping\|legend=1\| 1 0 -4 0 5 \| 0 1 4 0 -1 \| 0 0 0 1 0 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~3/2 = 692.0796, ~7/4 = 950.2565		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 692.0796{{c}}, ~7/4 = 950.2565{{c}}

	{{Optimal ET sequence\|legend=1\| 5, 7, 12e, 14c, 19e }}		{{Optimal ET sequence\|legend=1\| 5, 7, 12e, 14c, 19e }}

	== Melpomene ==		== Melpomene ==
	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

Line 130:		Line 130:
	{{Mapping\|legend=1\| 1 0 -4 0 7 \| 0 1 4 0 -4 \| 0 0 0 1 1 }}		{{Mapping\|legend=1\| 1 0 -4 0 7 \| 0 1 4 0 -4 \| 0 0 0 1 1 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~3/2 = 699.2230, ~7/4 = 964.2363		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 699.2230{{c}}, ~7/4 = 964.2363{{c}}

	{{Optimal ET sequence\|legend=1\| 7d, 12, 17c, 19, 24, 31e, 36 }}		{{Optimal ET sequence\|legend=1\| 7d, 12, 17c, 19, 24, 31e, 36 }}

			== Terpsichore ==
	== Terpsichore ==
	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

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	{{Mapping\|legend=1\| 1 0 -4 0 -2 \| 0 1 4 0 7 \| 0 0 0 1 -2 }}		{{Mapping\|legend=1\| 1 0 -4 0 -2 \| 0 1 4 0 7 \| 0 0 0 1 -2 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~3/2 = 696.2358, ~7/4 = 964.0006		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 696.2358{{c}}, ~7/4 = 964.0006{{c}}

	{{Optimal ET sequence\|legend=1\| 14c, 17c, 19, 31, 81, 112b }}		{{Optimal ET sequence\|legend=1\| 14c, 17c, 19, 31, 81, 112b }}

	[[Badness]]: 0.850 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.850 × 10<sup>-3</sup>

	[[Complexity spectrum]]: 4/3, 10/9, 9/8, 6/5, 9/7, 7/5, 7/6, 5/4, 8/7, 11/9, 12/11, 11/8, 11/10, 14/11		[[Complexity spectrum]]: 4/3, 10/9, 9/8, 6/5, 9/7, 7/5, 7/6, 5/4, 8/7, 11/9, 12/11, 11/8, 11/10, 14/11

FloraC: + naming history

2025-08-26T12:45:57Z

+ naming history

← Older revision		Revision as of 12:45, 26 August 2025
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	{{Technical data page}}		{{Technical data page}}
	The '''didymus rank-3 family''' are rank-3 temperaments tempering out the didymus comma, [[81/80]]. If nothing else is tempered out we have a [[7-limit]] [[planar temperament]], with an [[11-limit]] comma we get an 11-limit temperament, and so forth.		The '''didymus rank-3 family''' are rank-3 temperaments tempering out the didymus comma, [[81/80]]. If nothing else is tempered out we have a [[7-limit]] [[planar temperament]], with an [[11-limit]] comma we get an 11-limit temperament, and so forth.

			Most of these temperaments were named by [[Gene Ward Smith]] in 2010<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_100647.html#100648 ''Yahoo! Tuning Group \| Higher-rank meantone extensions (muse temperaments?)'']</ref>.

	Temperaments discussed elsewhere include:		Temperaments discussed elsewhere include:
Line 147:		Line 149:

	[[Complexity spectrum]]: 4/3, 10/9, 9/8, 6/5, 9/7, 7/5, 7/6, 5/4, 8/7, 11/9, 12/11, 11/8, 11/10, 14/11		[[Complexity spectrum]]: 4/3, 10/9, 9/8, 6/5, 9/7, 7/5, 7/6, 5/4, 8/7, 11/9, 12/11, 11/8, 11/10, 14/11

			== References ==

	[[Category:Temperament families]]		[[Category:Temperament families]]

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

2025-06-24T00:30:52Z

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

← Older revision		Revision as of 00:30, 24 June 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Didymus rank-3 family\| ]] <!-- main article -->		[[Category:Didymus rank-3 family\| ]] <!-- main article -->
	[[Category:Didymus\| ]] <!-- key article -->		[[Category:Didymus\| ]] <!-- key article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]