Shibboleth family - Revision history

Lériendil: dissolved the family

2025-05-06T17:21:56Z

dissolved the family

← Older revision		Revision as of 17:21, 6 May 2025
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	~~{{Technical data page}}~~		#redirect [[Miscellaneous 5-limit temperaments#Shibboleth]]
	~~The '''shibboleth family''' tempers out the [[shibboleth comma]], 1953125/1889568.~~

	~~Temperaments discussed elsewhere include:~~
	* [[superthird]], {245/243, 78125/76832} → [[Sensamagic clan #~~Superthird]]~~

	~~== Shibboleth ==~~
	~~[[Subgroup]]: 2.3.5~~

	[[~~Comma list]]: 1953125/1889568~~

	~~{{Mapping\|legend=1\| 1 4~~ 5 ~~\| 0~~ -~~9 -10 }}~~

	~~[[Optimal tuning]]s:~~
	* [[CTE]]: ~2 = 1\1, ~6/5 = 321.773
	* [[POTE]]: ~2 = 1\1, ~6/5 = 321.852

	~~{{Optimal ET sequence\|legend=1\| 15, 26, 41, 179c, 220c, 261cc, 302cc }}~~

	~~[[Badness]]: 0.227553~~

	~~== Gilead ==~~
	~~[[Subgroup]]: 2.3.5.7~~

	~~[[Comma list]]: 126/125, 343/324~~

	~~{{Mapping\|legend=1\| 1 4 5 6 \| 0 -9 -10 -12 }}~~

	~~{{Multival\|legend=1\| 9 10 12 -5 -6 0 }}~~

	~~[[Optimal tuning]]s:~~
	* [[CTE]]: ~2 = 1\1, ~6/5 = 321.109
	* [[POTE]]: ~2 = 1\1, ~6/5 = 321.423

	~~{{Optimal ET sequence\|legend=1\| 11cd, 15, 41dd, 56dd }}~~

	~~[[Badness]]: 0.115292~~

	~~[[Category:Temperament families]]~~
	~~[[Category:~~Shibboleth ~~family\| ]] <!-- main article -->~~
	~~[[Category:Rank 2~~]]

Lériendil: dissolving the family pursuant to fumica's suggestion

2025-05-06T17:17:57Z

dissolving the family pursuant to fumica's suggestion

← Older revision		Revision as of 17:17, 6 May 2025
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	[[Badness]]: 0.227553		[[Badness]]: 0.227553

	~~== Superkleismic ==~~
	~~{{Main\| Superkleismic }}~~

	The [[S-expression]]-based comma list of superkleismic is {[[875/864\|S5/S6]], [[1029/1024\|S7/S8]], [[100/99\|S10]], [[144/143\|S12]](, [[441/440\|S21]])}. Through careful observation of the equivalences therein one can derive that a sharpened ~6/5 is the generator as well as the mapping of the full 13-limit.

	~~[[Subgroup]]: 2.3.5.7~~

	~~[[Comma list]]: 875/864, 1029/1024~~

	~~{{Mapping\|legend=1\| 1 4 5 2 \| 0 -9 -10 3 }}~~

	~~{{Multival\|legend=1\| 9 10 -3 -5 -30 -35 }}~~

	~~[[Optimal tuning]]s:~~
	* [[CTE]]: ~2 = 1\1, ~6/5 = 321.798
	* [[POTE]]: ~2 = 1\1, ~6/5 = 321.930

	~~{{Optimal ET sequence\|legend=1\| 11c, 15, 26, 41 }}~~

	~~[[Badness]]: 0.047932~~

	~~=== 11-limit ===~~
	~~Subgroup: 2.3.5.7.11~~

	~~Comma list: 100/99, 245/242, 385/384~~

	~~Mapping: {{mapping\| 1 4 5 2 4 \| 0 -9 -10 3 -2 }}~~

	~~Optimal tunings:~~
	* CTE: ~2 = 1\1, ~6/5 = 321.815
	* POTE: ~2 = 1\1, ~6/5 = 321.847

	~~Optimal ET sequence: {{Optimal ET sequence\| 11c, 15, 26, 41, 179cde, 220cde, 261ccdee }}~~

	~~Badness: 0.025659~~

	~~=== 13-limit ===~~
	~~Subgroup: 2.3.5.7.11.13~~

	~~Comma list: 100/99, 105/104, 144/143, 245/242~~

	~~Mapping: {{mapping\| 1 4 5 2 4 8 \| 0 -9 -10 3 -2 -16 }}~~

	~~Optimal tunings:~~
	* CTE: ~2 = 1\1, ~6/5 = 321.986
	* POTE: ~2 = 1\1, ~6/5 = 321.994

	~~Optimal ET sequence: {{Optimal ET sequence\| 11cf, 15, 26, 41 }}~~

	~~Badness: 0.021478~~

	== Gilead ==		== Gilead ==

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

" to "{{Technical data page}}"

2025-04-13T13:45:55Z

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

← Older revision		Revision as of 13:45, 13 April 2025
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	{{Technical data page}}~~<br><br>~~		{{Technical data page}}
	The '''shibboleth family''' tempers out the [[shibboleth comma]], 1953125/1889568.		The '''shibboleth family''' tempers out the [[shibboleth comma]], 1953125/1889568.

BudjarnLambeth: {{Technical data page}}

2025-04-13T11:52:24Z

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

← Older revision		Revision as of 11:52, 13 April 2025
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			{{Technical data page}}<br><br>
	The '''shibboleth family''' tempers out the [[shibboleth comma]], 1953125/1889568.		The '''shibboleth family''' tempers out the [[shibboleth comma]], 1953125/1889568.

Godtone: /* Superkleismic */ link

2025-01-25T18:04:54Z

Superkleismic: link

← Older revision		Revision as of 18:04, 25 January 2025
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	{{Main\| Superkleismic }}		{{Main\| Superkleismic }}

	The S-expression-based comma list of superkleismic is {[[875/864\|S5/S6]], [[1029/1024\|S7/S8]], [[100/99\|S10]], [[144/143\|S12]](, [[441/440\|S21]])}. Through careful observation of the equivalences therein one can derive that a sharpened ~6/5 is the generator as well as the mapping of the full 13-limit.		The [[S-expression]]-based comma list of superkleismic is {[[875/864\|S5/S6]], [[1029/1024\|S7/S8]], [[100/99\|S10]], [[144/143\|S12]](, [[441/440\|S21]])}. Through careful observation of the equivalences therein one can derive that a sharpened ~6/5 is the generator as well as the mapping of the full 13-limit.

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

FloraC: +CTE tunings

2024-09-29T13:23:05Z

+CTE tunings

← Older revision		Revision as of 13:23, 29 September 2024
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	{{Mapping\|legend=1\| 1 4 5 \| 0 -9 -10 }}		{{Mapping\|legend=1\| 1 4 5 \| 0 -9 -10 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 321.852		[[Optimal tuning]]s:
			* [[CTE]]: ~2 = 1\1, ~6/5 = 321.773
			* [[POTE]]: ~2 = 1\1, ~6/5 = 321.852

	{{Optimal ET sequence\|legend=1\| 15, 26, 41, 179c, 220c, 261cc, 302cc }}		{{Optimal ET sequence\|legend=1\| 15, 26, 41, 179c, 220c, 261cc, 302cc }}
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	== Superkleismic ==		== Superkleismic ==
	{{Main\| Superkleismic }}		{{Main\| Superkleismic }}
	~~{{See also\| Gamelismic clan #Superkleismic }}~~
	The S-expression-based comma list of superkleismic is {[[875/864\|S5/S6]], [[1029/1024\|S7/S8]], [[100/99\|S10]], [[144/143\|S12]](, [[441/440\|S21]])}. Through careful observation of the equivalences therein one can derive that a sharpened ~6/5 is the generator as well as the mapping of the full 13-limit.		The S-expression-based comma list of superkleismic is {[[875/864\|S5/S6]], [[1029/1024\|S7/S8]], [[100/99\|S10]], [[144/143\|S12]](, [[441/440\|S21]])}. Through careful observation of the equivalences therein one can derive that a sharpened ~6/5 is the generator as well as the mapping of the full 13-limit.

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	{{Multival\|legend=1\| 9 10 -3 -5 -30 -35 }}		{{Multival\|legend=1\| 9 10 -3 -5 -30 -35 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 321.930		[[Optimal tuning]]s:
			* [[CTE]]: ~2 = 1\1, ~6/5 = 321.798
			* [[POTE]]: ~2 = 1\1, ~6/5 = 321.930

	{{Optimal ET sequence\|legend=1\| 11c, 15, 26, 41 }}		{{Optimal ET sequence\|legend=1\| 11c, 15, 26, 41 }}
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	Mapping: {{mapping\| 1 4 5 2 4 \| 0 -9 -10 3 -2 }}		Mapping: {{mapping\| 1 4 5 2 4 \| 0 -9 -10 3 -2 }}

	Optimal ~~tuning (~~POTE): ~2 = 1\1, ~6/5 = 321.847		Optimal tunings:
			* CTE: ~2 = 1\1, ~6/5 = 321.815
			* POTE: ~2 = 1\1, ~6/5 = 321.847

	{{Optimal ET sequence~~\|legend=1~~\| 11c, 15, 26, 41, 179cde, 220cde, 261ccdee }}		Optimal ET sequence: {{Optimal ET sequence\| 11c, 15, 26, 41, 179cde, 220cde, 261ccdee }}

	Badness: 0.025659		Badness: 0.025659
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	Mapping: {{mapping\| 1 4 5 2 4 8 \| 0 -9 -10 3 -2 -16 }}		Mapping: {{mapping\| 1 4 5 2 4 8 \| 0 -9 -10 3 -2 -16 }}

	Optimal ~~tuning (~~POTE): ~2 = 1\1, ~6/5 = 321.994		Optimal tunings:
			* CTE: ~2 = 1\1, ~6/5 = 321.986
			* POTE: ~2 = 1\1, ~6/5 = 321.994

	{{Optimal ET sequence~~\|legend=1~~\| 11cf, 15, 26, 41 }}		Optimal ET sequence: {{Optimal ET sequence\| 11cf, 15, 26, 41 }}

	Badness: 0.021478		Badness: 0.021478
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	{{Multival\|legend=1\| 9 10 12 -5 -6 0 }}		{{Multival\|legend=1\| 9 10 12 -5 -6 0 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 321.423		[[Optimal tuning]]s:
			* [[CTE]]: ~2 = 1\1, ~6/5 = 321.109
			* [[POTE]]: ~2 = 1\1, ~6/5 = 321.423

	{{Optimal ET sequence\|legend=1\| 11cd, 15, 41dd, 56dd }}		{{Optimal ET sequence\|legend=1\| 11cd, 15, 41dd, 56dd }}

FloraC: /* Superkleismic */ copyedit and correct a comma

2024-09-29T13:14:23Z

Superkleismic: copyedit and correct a comma

← Older revision		Revision as of 13:14, 29 September 2024
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	{{Main\| Superkleismic }}		{{Main\| Superkleismic }}
	{{See also\| Gamelismic clan #Superkleismic }}		{{See also\| Gamelismic clan #Superkleismic }}
	The S-expression-based comma list of superkleismic is {[[875/864\|S5/S6]], [[1029/1024\|S7/S8]], [[100/99\|S10]], [[144/143\|S12]](, [[441/440\|S21]])}~~, from which (through~~ careful observation of the equivalences therein) one can derive that a sharpened ~6/5 is the generator as well as the mapping of the full 13-limit.		The S-expression-based comma list of superkleismic is {[[875/864\|S5/S6]], [[1029/1024\|S7/S8]], [[100/99\|S10]], [[144/143\|S12]](, [[441/440\|S21]])}. Through careful observation of the equivalences therein one can derive that a sharpened ~6/5 is the generator as well as the mapping of the full 13-limit.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

	Comma list: 100/99, 105/104, 144/143, 245/~~243~~		Comma list: 100/99, 105/104, 144/143, 245/242

	Mapping: {{mapping\| 1 4 5 2 4 8 \| 0 -9 -10 3 -2 -16 }}		Mapping: {{mapping\| 1 4 5 2 4 8 \| 0 -9 -10 3 -2 -16 }}

Godtone: /* Superkleismic */ add S-expression-based comma list

2024-07-11T18:53:07Z

Superkleismic: add S-expression-based comma list

← Older revision		Revision as of 18:53, 11 July 2024
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	{{Main\| Superkleismic }}		{{Main\| Superkleismic }}
	{{See also\| Gamelismic clan #Superkleismic }}		{{See also\| Gamelismic clan #Superkleismic }}
			The S-expression-based comma list of superkleismic is {[[875/864\|S5/S6]], [[1029/1024\|S7/S8]], [[100/99\|S10]], [[144/143\|S12]](, [[441/440\|S21]])}, from which (through careful observation of the equivalences therein) one can derive that a sharpened ~6/5 is the generator as well as the mapping of the full 13-limit.

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

FloraC: Update keys

2023-08-26T12:28:41Z

Update keys

← Older revision		Revision as of 12:28, 26 August 2023
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	== Shibboleth ==		== Shibboleth ==
	Subgroup: 2.3.5		[[Subgroup]]: 2.3.5

	[[Comma list]]: 1953125/1889568		[[Comma list]]: 1953125/1889568

	~~[[Mapping]]: [~~{{~~val~~\| 1 4 5 ~~}}, {{val~~\| 0 -9 -10 }}]		{{Mapping\|legend=1\| 1 4 5 \| 0 -9 -10 }}

	[[POTE ~~generator~~]]: ~6/5 = 321.852		[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 321.852

	{{Optimal ET sequence\|legend=1\| 15, 26, 41, 179c, 220c, 261cc, 302cc }}		{{Optimal ET sequence\|legend=1\| 15, 26, 41, 179c, 220c, 261cc, 302cc }}
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	== Superkleismic ==		== Superkleismic ==
	{{~~main~~\| Superkleismic }}		{{Main\| Superkleismic }}
	{{~~see~~ also\| Gamelismic clan #Superkleismic }}		{{See also\| Gamelismic clan #Superkleismic }}

	Subgroup: 2.3.5.7		[[Subgroup]]: 2.3.5.7

	[[Comma list]]: 875/864, 1029/1024		[[Comma list]]: 875/864, 1029/1024

	~~[[Mapping]]: [~~{{~~val~~\| 1 4 5 2 ~~}}, {{val~~\| 0 -9 -10 3 }}]		{{Mapping\|legend=1\| 1 4 5 2 \| 0 -9 -10 3 }}

	{{Multival\|legend=1\| 9 10 -3 -5 -30 -35 }}		{{Multival\|legend=1\| 9 10 -3 -5 -30 -35 }}

	[[POTE ~~generator~~]]: ~6/5 = 321.930		[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 321.930

	{{Optimal ET sequence\|legend=1\| 11c, 15, 26, 41 }}		{{Optimal ET sequence\|legend=1\| 11c, 15, 26, 41 }}
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	Comma list: 100/99, 245/242, 385/384		Comma list: 100/99, 245/242, 385/384

	Mapping: [{{~~val~~\| 1 4 5 2 4 ~~}}, {{val~~\| 0 -9 -10 3 -2 }}]		Mapping: {{mapping\| 1 4 5 2 4 \| 0 -9 -10 3 -2 }}

	POTE ~~generator~~: ~6/5 = 321.847		Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 321.847

	{{Optimal ET sequence\|legend=1\| 11c, 15, 26, 41, 179cde, 220cde, 261ccdee }}		{{Optimal ET sequence\|legend=1\| 11c, 15, 26, 41, 179cde, 220cde, 261ccdee }}
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	Comma list: 100/99, 105/104, 144/143, 245/243		Comma list: 100/99, 105/104, 144/143, 245/243

	Mapping: [{{~~val~~\| 1 4 5 2 4 8 ~~}}, {{val~~\| 0 -9 -10 3 -2 -16 }}]		Mapping: {{mapping\| 1 4 5 2 4 8 \| 0 -9 -10 3 -2 -16 }}

	POTE ~~generator~~: ~6/5 = 321.994		Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 321.994

	{{Optimal ET sequence\|legend=1\| 11cf, 15, 26, 41 }}		{{Optimal ET sequence\|legend=1\| 11cf, 15, 26, 41 }}
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	== Gilead ==		== Gilead ==
	Subgroup: 2.3.5.7		[[Subgroup]]: 2.3.5.7

	[[Comma list]]: 126/125, 343/324		[[Comma list]]: 126/125, 343/324

	~~[[Mapping]]: [~~{{~~val~~\| 1 4 5 6 ~~}}, {{val~~\| 0 -9 -10 -12 }}]		{{Mapping\|legend=1\| 1 4 5 6 \| 0 -9 -10 -12 }}

	{{Multival\|legend=1\| 9 10 12 -5 -6 0 }}		{{Multival\|legend=1\| 9 10 12 -5 -6 0 }}

	[[POTE ~~generator~~]]: ~6/5 = 321.423		[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 321.423

	{{Optimal ET sequence\|legend=1\| 11cd, 15, 41dd, 56dd }}		{{Optimal ET sequence\|legend=1\| 11cd, 15, 41dd, 56dd }}

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

2023-05-07T16:31:43Z

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

← Older revision		Revision as of 16:31, 7 May 2023
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	[[POTE generator]]: ~6/5 = 321.852		[[POTE generator]]: ~6/5 = 321.852

	{{~~Val list~~\|legend=1\| 15, 26, 41, 179c, 220c, 261cc, 302cc }}		{{Optimal ET sequence\|legend=1\| 15, 26, 41, 179c, 220c, 261cc, 302cc }}

	[[Badness]]: 0.227553		[[Badness]]: 0.227553
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	[[POTE generator]]: ~6/5 = 321.930		[[POTE generator]]: ~6/5 = 321.930

	{{~~Val list~~\|legend=1\| 11c, 15, 26, 41 }}		{{Optimal ET sequence\|legend=1\| 11c, 15, 26, 41 }}

	[[Badness]]: 0.047932		[[Badness]]: 0.047932
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	POTE generator: ~6/5 = 321.847		POTE generator: ~6/5 = 321.847

	Optimal ~~GPV~~ sequence~~: {{Val list~~\| 11c, 15, 26, 41, 179cde, 220cde, 261ccdee }}		{{Optimal ET sequence\|legend=1\| 11c, 15, 26, 41, 179cde, 220cde, 261ccdee }}

	Badness: 0.025659		Badness: 0.025659
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	POTE generator: ~6/5 = 321.994		POTE generator: ~6/5 = 321.994

	Optimal ~~GPV~~ sequence~~: {{Val list~~\| 11cf, 15, 26, 41 }}		{{Optimal ET sequence\|legend=1\| 11cf, 15, 26, 41 }}

	Badness: 0.021478		Badness: 0.021478
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	[[POTE generator]]: ~6/5 = 321.423		[[POTE generator]]: ~6/5 = 321.423

	{{~~Val list~~\|legend=1\| 11cd, 15, 41dd, 56dd }}		{{Optimal ET sequence\|legend=1\| 11cd, 15, 41dd, 56dd }}

	[[Badness]]: 0.115292		[[Badness]]: 0.115292