No-sevens subgroup temperaments - Revision history

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

2025-11-27T12:29:17Z

← Older revision		Revision as of 12:29, 27 November 2025
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	[[Category:Temperament collections]]		[[Category:Temperament collections]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Subgroup temperaments]]		[[Category:Subgroup temperaments]]
	[[Category:Rank 2]]		[[Category:Rank 2]]

2025-09-27T16:03:07Z

2.3.5.17 temperaments: added srutal archagall

← Older revision		Revision as of 16:03, 27 September 2025
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	: ''For full 17- and 19-limit extensions, see [[Schismatic family #Quintilipyth]] or [[Schismatic family #Quintaschis]].''		: ''For full 17- and 19-limit extensions, see [[Schismatic family #Quintilipyth]] or [[Schismatic family #Quintaschis]].''
	{{Main\| Schismatic family #Quintilischis (2.3.5.17) }}		{{Main\| Schismatic family #Quintilischis (2.3.5.17) }}

			=== Srutal Archagall ===
			{{Main\|Srutal archagall}}

	== 2.3.5.19 temperaments ==		== 2.3.5.19 temperaments ==

2025-08-27T00:09:56Z

for consistency

← Older revision		Revision as of 00:09, 27 August 2025
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	[[Tp tuning #T2 tuning\|RMS error]]: 0.1171 cents		[[Tp tuning #T2 tuning\|RMS error]]: 0.1171 cents

	==== 2.3.5.13.17 ~~subgroup~~ ====		==== 2.3.5.13.17 ====
	The comma list shown here is interestingly a possible minimal [[S-expression]]-based comma list for majvam: {[[676/675\|S13/S15 = S26]], [[24576/24565\|S16/S17]], [[2601/2600\|S51]]} (though the order of the last two commas is swapped to make the commas appear in ascending prime limit).		The comma list shown here is interestingly a possible minimal [[S-expression]]-based comma list for majvam: {[[676/675\|S13/S15 = S26]], [[24576/24565\|S16/S17]], [[2601/2600\|S51]]} (though the order of the last two commas is swapped to make the commas appear in ascending prime limit).

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	[[Badness]] (Sintel): 0.301		[[Badness]] (Sintel): 0.301

	==== 2.3.5.13.19 ~~subgroup~~ ====		==== 2.3.5.13.19 ====
	Subgroup: 2.3.5.13.19		Subgroup: 2.3.5.13.19

2025-06-27T14:06:30Z

← Older revision		Revision as of 14:06, 27 June 2025
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	=== Superpine ===		=== Superpine ===
	{{see also\|Meantone family #Superpine}}		{{see also\|Meantone family #Superpine}}
			{{see also\|Meantone family #Trimean}}

	Subgroup: 2.3.5.11		Subgroup: 2.3.5.11

2025-06-26T21:46:57Z

2.3.5.11.13 subgroup

← Older revision		Revision as of 21:46, 26 June 2025
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	{{Optimal ET sequence\|legend=0\| 7, 29ce, 36, 43, 50 }}		{{Optimal ET sequence\|legend=0\| 7, 29ce, 36, 43, 50 }}

	==== 2.3.5.11.13 ~~subgroup~~ ====		==== 2.3.5.11.13 ====

	Subgroup: 2.3.5.11.13		Subgroup: 2.3.5.11.13

2025-06-26T20:17:43Z

added superpine's 13

@@ Line 142: / Line 142: @@
 * CTE: ~2 = 1200.000, ~11/10 = 167.712
 * CWE: ~2 = 1200.000, ~11/10 = 167.882
 {{Optimal ET sequence|legend=0| 7, 29ce, 36, 43, 50 }}

2025-06-26T20:14:49Z

Superpine

← Older revision		Revision as of 20:14, 26 June 2025
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	[[Tp tuning #T2 tuning\|RMS error]]: 0.2830 cents		[[Tp tuning #T2 tuning\|RMS error]]: 0.2830 cents

			=== Superpine ===
			{{see also\|Meantone family #Superpine}}

			Subgroup: 2.3.5.11

			Comma list: 81/80, 1350/1331

			Mapping: {{mapping\| 1 2 4 5 \| 0 -3 -12 -11 }}

			Optimal tunings:
			* CTE: ~2 = 1200.000, ~11/10 = 167.712
			* CWE: ~2 = 1200.000, ~11/10 = 167.882

			{{Optimal ET sequence\|legend=0\| 7, 29ce, 36, 43, 50 }}

	=== Dicot ===		=== Dicot ===

2025-06-24T00:26:50Z

← Older revision		Revision as of 00:26, 24 June 2025
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	[[Category:Temperament collections]]		[[Category:Temperament collections]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Subgroup temperaments]]		[[Category:Subgroup temperaments]]
	[[Category:Rank 2]]		[[Category:Rank 2]]

2025-06-09T10:00:53Z

← Older revision		Revision as of 10:00, 9 June 2025
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	=== Tricot ===		=== Tricot ===
	{{Main\|Tricot family #2.3.5.13 subgroup }}		{{Main\| Tricot family #2.3.5.13 subgroup }}

	=== Taylor ===		=== Taylor ===
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	=== Stützel ===		=== Stützel ===
	{{Main\| Meantone family #Stützel (2.3.5.19) }}		{{Main\| Meantone family #Stützel (2.3.5.19) }}

			== Higher-limit subgroup temperaments ==
			=== Reversed marvel ===
			As the [[Marvel\|marvel temperament]] is based on the marvel comma, [[225/224]], identifying the [[7/4\|harmonic seventh (7/4)]] as a stack of two [[15/8\|classical major sevenths (15/8)]] [[Octave reduction\|octave-reduced]] and tempering 3rd and 5th harmonics slightly flat, tempering [[226/225]] instead results in sharper 3rd and 5th harmonics, and a stack of two classical major sevenths equivalent to the 113th harmonic instead of the 7th, so it might as well be called reversed marvel.

			Subgroup: 2.3.5.113

			[[Comma list]]: 226/225

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

			: Sval mapping generators: ~2, ~3, ~5

			[[Optimal tuning]]s:
			* CTE: ~3/2 = 702.449, ~5/4 = 387.373
			* CWE: ~3/2 = 702.522, ~5/4 = 387.479

			{{Optimal ET sequence\|legend=1\| 12, 22, 31, 34, 46, 53 }}

	[[Category:Temperament collections]]		[[Category:Temperament collections]]
	[[Category:Subgroup temperaments]]		[[Category:Subgroup temperaments]]
	[[Category:Rank 2]]		[[Category:Rank 2]]

2025-06-06T16:39:41Z

Text replacement - "Badness (Dirichlet): " to "Badness (Sintel): "