Porcupine rank-3 family - Revision history

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

2025-11-27T12:19:16Z

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

← Older revision		Revision as of 12:19, 27 November 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Porcupine rank-3 family\| ]] <!-- main article -->		[[Category:Porcupine rank-3 family\| ]] <!-- main article -->
	[[Category:Porcupine\| ]] <!-- key article -->		[[Category:Porcupine\| ]] <!-- key article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

FloraC: - POTE tunings

2025-09-06T12:17:35Z

- POTE tunings

← Older revision		Revision as of 12:17, 6 September 2025
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = 164.0621{{c}}, ~7/4 = 969.4180{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = 164.0621{{c}}, ~7/4 = 969.4180{{c}}
	: error map: {{val\| 0.000 +5.859 -6.624 +0.592 }}		: error map: {{val\| 0.000 +5.859 -6.624 +0.592 }}
	~~<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~10/9 = 163.9504{{c}}, ~7/4 = 970.0552{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 7d, 8d, 14c, 15, 22, 37, 51, 73c }}		{{Optimal ET sequence\|legend=1\| 7d, 8d, 14c, 15, 22, 37, 51, 73c }}
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/10 = 163.9951{{c}}, ~7/4 = 968.2673{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/10 = 163.9951{{c}}, ~7/4 = 968.2673{{c}}
	: error map: {{val\| 0.000 +6.060 -6.289 -0.559 -7.298 }}		: error map: {{val\| 0.000 +6.060 -6.289 -0.559 -7.298 }}
	~~<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~11/10 = 164.0777{{c}}, ~7/4 = 967.8413{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 7d, 8d, 14c, 15, 22, 37, 51, 88b }}		{{Optimal ET sequence\|legend=1\| 7d, 8d, 14c, 15, 22, 37, 51, 88b }}
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/10 = 162.1977{{c}}, ~7/4 = 964.6202{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/10 = 162.1977{{c}}, ~7/4 = 964.6202{{c}}
	: error map: {{val\| 0.000 +11.452 +2.698 -4.206 +24.291 }}		: error map: {{val\| 0.000 +11.452 +2.698 -4.206 +24.291 }}
	~~<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~10/9 = 161.5193{{c}}, ~7/4 = 971.0457{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 7d, 8d, 15, 30dee, 37ee, 52bee }}		{{Optimal ET sequence\|legend=1\| 7d, 8d, 15, 30dee, 37ee, 52bee }}

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

2025-09-06T12:17:21Z

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

← Older revision		Revision as of 12:17, 6 September 2025
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	: mapping generators: ~2, ~10/9, ~7		: mapping generators: ~2, ~10/9, ~7

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~10/9 = 163.9504, ~7/4 = 970.0552		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1199.5444{{c}}, ~10/9 = 163.8881{{c}}, ~7/4 = 969.6868{{c}}
			: [[error map]]: {{val\| -0.456 +5.469 -7.121 -0.050 }}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = 164.0621{{c}}, ~7/4 = 969.4180{{c}}
			: error map: {{val\| 0.000 +5.859 -6.624 +0.592 }}
			<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~10/9 = 163.9504{{c}}, ~7/4 = 970.0552{{c}} -->

	{{Optimal ET sequence\|legend=1\| 7d, 8d, 14c, 15, 22, 37, 51, 73c }}		{{Optimal ET sequence\|legend=1\| 7d, 8d, 14c, 15, 22, 37, 51, 73c }}

	[[Badness]]: 0.~~535 × 10<sup>-3</sup>~~		[[Badness]] (Sintel): 2.36

	== Sonic ==		== Sonic ==
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	{{Mapping\|legend=1\| 1 2 3 0 4 \| 0 -3 -5 0 -4 \| 0 0 0 1 0 }}		{{Mapping\|legend=1\| 1 2 3 0 4 \| 0 -3 -5 0 -4 \| 0 0 0 1 0 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~11/10 = 164.0777, ~7/4 = 967.8413		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1200.3290{{c}}, ~11/10 = 164.1227{{c}}, ~7/4 = 968.1067{{c}}
			: [[error map]]: {{val\| +0.329 +6.335 -5.940 -0.061 -6.492 }}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/10 = 163.9951{{c}}, ~7/4 = 968.2673{{c}}
			: error map: {{val\| 0.000 +6.060 -6.289 -0.559 -7.298 }}
			<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~11/10 = 164.0777{{c}}, ~7/4 = 967.8413{{c}} -->

	{{Optimal ET sequence\|legend=1\| 7d, 8d, 14c, 15, 22, 37, 51, 88b }}		{{Optimal ET sequence\|legend=1\| 7d, 8d, 14c, 15, 22, 37, 51, 88b }}

	[[Badness]]: 0.~~523 × 10<sup>-3</sup>~~		[[Badness]] (Sintel): 0.629

	== Tikal ==		== Tikal ==
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	{{Mapping\|legend=1\| 1 2 3 0 0 \| 0 -3 -5 0 5 \| 0 0 0 1 1 }}		{{Mapping\|legend=1\| 1 2 3 0 0 \| 0 -3 -5 0 5 \| 0 0 0 1 1 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~10/9 = 161.5193, ~7/4 = 971.0457		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1195.9857{{c}}, ~11/10 = 160.9790{{c}}, ~7/4 = 967.7973{{c}}
			: [[error map]]: {{val\| -4.014 +7.079 -3.252 -9.057 +13.346 }}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/10 = 162.1977{{c}}, ~7/4 = 964.6202{{c}}
			: error map: {{val\| 0.000 +11.452 +2.698 -4.206 +24.291 }}
			<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~10/9 = 161.5193{{c}}, ~7/4 = 971.0457{{c}} -->

	{{Optimal ET sequence\|legend=1\| 7d, 8d, 15, 30dee, 37ee, 52bee }}		{{Optimal ET sequence\|legend=1\| 7d, 8d, 15, 30dee, 37ee, 52bee }}

	[[Badness]]: 1.~~973 × 10<sup>-3</sup>~~		[[Badness]] (Sintel): 2.37

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

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

2025-08-27T13:06:11Z

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

← Older revision	Revision as of 13:06, 27 August 2025
(No difference)

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

2025-06-24T00:32:26Z

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

FloraC: Text replacement - "{{Technical data page}}

" to "{{Technical data page}}"

2025-04-13T13:40:59Z

Text replacement - "{{Technical data page}}<br><br>" to "{{Technical data page}}"

← Older revision		Revision as of 13:40, 13 April 2025
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	{{Technical data page}}~~<br><br>~~		{{Technical data page}}
	The '''porcupine rank-3 family''' of [[temperament]]s [[tempering out\|tempers out]] the porcupine comma or maximal diesis, [[250/243]]. 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 '''porcupine rank-3 family''' of [[temperament]]s [[tempering out\|tempers out]] the porcupine comma or maximal diesis, [[250/243]]. 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.

BudjarnLambeth: {{Technical data page}}

2025-04-13T07:11:35Z

{{Technical data page}}<br><br>

← Older revision		Revision as of 07:11, 13 April 2025
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			{{Technical data page}}<br><br>
	The '''porcupine rank-3 family''' of [[temperament]]s [[tempering out\|tempers out]] the porcupine comma or maximal diesis, [[250/243]]. 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 '''porcupine rank-3 family''' of [[temperament]]s [[tempering out\|tempers out]] the porcupine comma or maximal diesis, [[250/243]]. 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.

FloraC: Update keys

2023-09-11T12:17:09Z

Update keys

← Older revision		Revision as of 12:17, 11 September 2023
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	~~These are the~~ rank-3 ~~temperaments~~ tempering out the porcupine comma or maximal diesis, [[250/243]]. 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 '''porcupine rank-3 family''' of [[temperament]]s [[tempering out\|tempers out]] the porcupine comma or maximal diesis, [[250/243]]. 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.

	== Rank-3 porcupine ==		== Rank-3 porcupine ==
	Subgroup: 2.3.5.7		[[Subgroup]]: 2.3.5.7

	[[Comma list]]: [[250/243]]		[[Comma list]]: [[250/243]]

	~~[[Mapping]]: [~~{{~~val~~\| 1 2 3 0 ~~}}, {{val~~\| 0 -3 -5 0 ~~}}, {{val~~\| 0 0 0 1 }}]		{{Mapping\|legend=1\| 1 2 3 0 \| 0 -3 -5 0 \| 0 0 0 1 }}

	~~Mapping~~ generators: ~2, ~10/9, ~7		: mapping generators: ~2, ~10/9, ~7

	[[POTE ~~generator~~]]s: ~10/9 = 163.9504, ~7/4 = 970.0552		[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~10/9 = 163.9504, ~7/4 = 970.0552

	{{Optimal ET sequence\|legend=1\| 7d, 8d, 14c, 15, 22, 37, 51, 73c }}		{{Optimal ET sequence\|legend=1\| 7d, 8d, 14c, 15, 22, 37, 51, 73c }}
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	== Sonic ==		== Sonic ==
	Subgroup: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

	[[Comma list]]: 55/54, 100/99		[[Comma list]]: 55/54, 100/99

	~~[[Mapping]]: [~~{{~~val~~\| 1 2 3 0 4 ~~}}, {{val~~\| 0 -3 -5 0 -4 ~~}}, {{val~~\| 0 0 0 1 0 }}]		{{Mapping\|legend=1\| 1 2 3 0 4 \| 0 -3 -5 0 -4 \| 0 0 0 1 0 }}

	[[POTE ~~generator~~]]s: ~11/10 = 164.0777, ~7/4 = 967.8413		[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/10 = 164.0777, ~7/4 = 967.8413

	{{Optimal ET sequence\|legend=1\| 7d, 8d, 14c, 15, 22, 37, 51, 88b }}		{{Optimal ET sequence\|legend=1\| 7d, 8d, 14c, 15, 22, 37, 51, 88b }}
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	== Tikal ==		== Tikal ==
	Subgroup: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

	[[Comma list]]: 56/55, 250/243		[[Comma list]]: 56/55, 250/243

	~~[[Mapping]]: [~~{{~~val~~\| 1 2 3 0 0 ~~}}, {{val~~\| 0 -3 -5 0 5 ~~}}, {{val~~\| 0 0 0 1 1 }}]		{{Mapping\|legend=1\| 1 2 3 0 0 \| 0 -3 -5 0 5 \| 0 0 0 1 1 }}

	[[POTE ~~generator~~]]s: ~10/9 = 161.5193, ~7/4 = 971.0457		[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~10/9 = 161.5193, ~7/4 = 971.0457

	{{Optimal ET sequence\|legend=1\| 7d, 8d, 15, 30dee, 37ee, 52bee }}		{{Optimal ET sequence\|legend=1\| 7d, 8d, 15, 30dee, 37ee, 52bee }}
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	[[Category:Porcupine rank-3 family\| ]] <!-- main article -->		[[Category:Porcupine rank-3 family\| ]] <!-- main article -->
			[[Category:Porcupine\| ]] <!-- key article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

Cmloegcmluin: "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

2023-05-07T18:12:55Z

"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

← Older revision		Revision as of 18:12, 7 May 2023
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	[[POTE generator]]s: ~10/9 = 163.9504, ~7/4 = 970.0552		[[POTE generator]]s: ~10/9 = 163.9504, ~7/4 = 970.0552

	{{~~Val list~~\|legend=1\| 7d, 8d, 14c, 15, 22, 37, 51, 73c }}		{{Optimal ET sequence\|legend=1\| 7d, 8d, 14c, 15, 22, 37, 51, 73c }}

	[[Badness]]: 0.535 × 10<sup>-3</sup>		[[Badness]]: 0.535 × 10<sup>-3</sup>
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	[[POTE generator]]s: ~11/10 = 164.0777, ~7/4 = 967.8413		[[POTE generator]]s: ~11/10 = 164.0777, ~7/4 = 967.8413

	{{~~Val list~~\|legend=1\| 7d, 8d, 14c, 15, 22, 37, 51, 88b }}		{{Optimal ET sequence\|legend=1\| 7d, 8d, 14c, 15, 22, 37, 51, 88b }}

	[[Badness]]: 0.523 × 10<sup>-3</sup>		[[Badness]]: 0.523 × 10<sup>-3</sup>
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	[[POTE generator]]s: ~10/9 = 161.5193, ~7/4 = 971.0457		[[POTE generator]]s: ~10/9 = 161.5193, ~7/4 = 971.0457

	{{~~Val list~~\|legend=1\| 7d, 8d, 15, 30dee, 37ee, 52bee }}		{{Optimal ET sequence\|legend=1\| 7d, 8d, 15, 30dee, 37ee, 52bee }}

	[[Badness]]: 1.973 × 10<sup>-3</sup>		[[Badness]]: 1.973 × 10<sup>-3</sup>

Fredg999 category edits: Removing from Category:Regular temperament theory using Cat-a-lot

2022-03-02T22:04:29Z

Removing from Category:Regular temperament theory using Cat-a-lot

← Older revision		Revision as of 22:04, 2 March 2022
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	[[Badness]]: 1.973 × 10<sup>-3</sup>		[[Badness]]: 1.973 × 10<sup>-3</sup>

	~~[[Category:Regular temperament theory]]~~
	[[Category:Temperament families]]		[[Category:Temperament families]]
	[[Category:Porcupine rank-3 family\| ]] <!-- main article -->		[[Category:Porcupine rank-3 family\| ]] <!-- main article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]