Semaphoresmic family - Revision history

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

2025-11-27T12:28:38Z

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

← Older revision		Revision as of 12:28, 27 November 2025
Line 105:		Line 105:

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

FloraC: Fixes

2025-07-14T10:04:24Z

Fixes

← Older revision		Revision as of 10:04, 14 July 2025
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	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[WE]]: ~2 = 1202.8324{{c}}, ~7/4 = 951.8567{{c}}, ~5/4 = ~~386~~.~~2644~~{{c}}		* [[WE]]: ~2 = 1202.8324{{c}}, ~7/4 = 951.8567{{c}}, ~5/4 = 380.5997{{c}}
	: [[error map]]: {{val\| +2.832 +1.758 -0.049 -11.304 }}		: [[error map]]: {{val\| +2.832 +1.758 -0.049 -11.304 }}
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 950.6890{{c}}, ~5/4 = 382.3522{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 950.6890{{c}}, ~5/4 = 382.3522{{c}}
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	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[WE]]: ~2 = 1200.0412{{c}}, ~7/4 = 951.7616{{c}}, ~5/4 = 390.~~7445~~{{c}}		* [[WE]]: ~2 = 1200.0412{{c}}, ~7/4 = 951.7616{{c}}, ~5/4 = 390.6621{{c}}
	: [[error map]]: {{val\| +0.041 +1.568 +4.431 -16.982 +9.905 }}		: [[error map]]: {{val\| +0.041 +1.568 +4.431 -16.982 +9.905 }}
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 951.7409{{c}}, ~5/4 = 390.6582{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 951.7409{{c}}, ~5/4 = 390.6582{{c}}
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	Optimal tunings:		Optimal tunings:
	* WE: ~2 = 1200.0790{{c}}, ~7/4 = 951.3067{{c}}, ~5/4 = 389.~~7793~~{{c}}		* WE: ~2 = 1200.0790{{c}}, ~7/4 = 951.3067{{c}}, ~5/4 = 389.6213{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 951.2662{{c}}, ~5/4 = 389.6120{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 951.2662{{c}}, ~5/4 = 389.6120{{c}}

FloraC: Units

2025-07-14T10:01:45Z

Units

← Older revision		Revision as of 10:01, 14 July 2025
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	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[WE]]: ~2 = 1202.8324, ~7/4 = 951.8567, ~5/4 = 386.2644		* [[WE]]: ~2 = 1202.8324{{c}}, ~7/4 = 951.8567{{c}}, ~5/4 = 386.2644{{c}}
	: [[error map]]: {{val\| +2.832 +1.758 -0.049 -11.304 }}		: [[error map]]: {{val\| +2.832 +1.758 -0.049 -11.304 }}
	* [[CWE]]: ~2 = 1200.0000, ~7/4 = 950.6890, ~5/4 = 382.3522		* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 950.6890{{c}}, ~5/4 = 382.3522{{c}}
	: error map: {{val\| 0.000 -0.577 -3.962 -18.137 }}		: error map: {{val\| 0.000 -0.577 -3.962 -18.137 }}

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	Optimal tunings:		Optimal tunings:
	* WE: ~2 = 1202.7771, ~7/4 = 951.9629, ~5/4 = 381.0131		* WE: ~2 = 1202.7771{{c}}, ~7/4 = 951.9629{{c}}, ~5/4 = 381.0131{{c}}
	* CWE: ~2 = 1200.0000, ~7/4 = 950.6703, ~5/4 = 382.2972		* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 950.6703{{c}}, ~5/4 = 382.2972{{c}}

	{{Optimal ET sequence\|legend=0\| 5, 9, 10, 14cf, 15, 19, 48df, 53d, 67cddf, 72dd }}		{{Optimal ET sequence\|legend=0\| 5, 9, 10, 14cf, 15, 19, 48df, 53d, 67cddf, 72dd }}
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	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[WE]]: ~2 = 1200.0412, ~7/4 = 951.7616, ~5/4 = 390.7445		* [[WE]]: ~2 = 1200.0412{{c}}, ~7/4 = 951.7616{{c}}, ~5/4 = 390.7445{{c}}
	: [[error map]]: {{val\| +0.041 +1.568 +4.431 -16.982 +9.905 }}		: [[error map]]: {{val\| +0.041 +1.568 +4.431 -16.982 +9.905 }}
	* [[CWE]]: ~2 = 1200.0000, ~7/4 = 951.7409, ~5/4 = 390.6582		* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 951.7409{{c}}, ~5/4 = 390.6582{{c}}
	: error map: {{val\| 0.000 +1.527 +4.344 -17.085 +9.765 }}		: error map: {{val\| 0.000 +1.527 +4.344 -17.085 +9.765 }}

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	Optimal tunings:		Optimal tunings:
	* WE: ~2 = 1200.0790, ~7/4 = 951.3067, ~5/4 = 389.7793		* WE: ~2 = 1200.0790{{c}}, ~7/4 = 951.3067{{c}}, ~5/4 = 389.7793{{c}}
	* CWE: ~2 = 1200.0000, ~7/4 = 951.2662, ~5/4 = 389.6120		* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 951.2662{{c}}, ~5/4 = 389.6120{{c}}

	{{Optimal ET sequence\|legend=0\| 5, 9, 10, 15, 19, 24, 34 }}		{{Optimal ET sequence\|legend=0\| 5, 9, 10, 15, 19, 24, 34 }}
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	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[WE]]: ~2 = 1203.4810, ~15/14 = 125.9724, ~11/8 = 540.7985		* [[WE]]: ~2 = 1203.4810{{c}}, ~15/14 = 125.9724{{c}}, ~11/8 = 540.7985{{c}}
	: [[error map]]: {{val\| +3.481 +1.118 -1.435 -10.328 -0.076 }}		: [[error map]]: {{val\| +3.481 +1.118 -1.435 -10.328 -0.076 }}
	* [[CWE]]: ~2 = 1200.0000, ~15/14 = 125.4347, ~11/8 = 541.8688		* [[CWE]]: ~2 = 1200.0000{{c}}, ~15/14 = 125.4347{{c}}, ~11/8 = 541.8688{{c}}
	: error map: {{val\| 0.000 -3.694 -10.009 -19.695 -9.449 }}		: error map: {{val\| 0.000 -3.694 -10.009 -19.695 -9.449 }}

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	Optimal tunings:		Optimal tunings:
	* WE: ~2 = 1203.6981, ~14/13 = 125.9545, ~11/8 = 540.1440		* WE: ~2 = 1203.6981{{c}}, ~14/13 = 125.9545{{c}}, ~11/8 = 540.1440{{c}}
	* CWE: ~2 = 1200.0000, ~14/13 = 125.3543, ~11/8 = 540.9490		* CWE: ~2 = 1200.0000{{c}}, ~14/13 = 125.3543{{c}}, ~11/8 = 540.9490{{c}}

	{{Optimal ET sequence\|legend=0\| 9, 10, 19, 29, 38df, 67cddef, 105cdddeefff }}		{{Optimal ET sequence\|legend=0\| 9, 10, 19, 29, 38df, 67cddef, 105cdddeefff }}

FloraC: + obvious no-11 13-limit extension

2025-07-14T09:45:09Z

+ obvious no-11 13-limit extension

← Older revision		Revision as of 09:45, 14 July 2025
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	The '''semaphoresmic family''' of [[rank-3 temperament\|rank-3]] [[regular temperament\|temperaments]] [[tempering out\|tempers out]] [[49/48]] in the full [[7-limit]], and thereby identifies the septimal minor third, [[7/6]], and the septimal whole tone, [[8/7]]. It also splits the fourth into two of these intervals; hence the name, which sounds like "semi-fourth". Related to this is the 2.3.7-subgroup {49/48} temperament [[Semaphoresmic clan #Semaphore\|semaphore]], and the 7-limit {49/48, 81/80} temperament [[Semaphoresmic clan #Godzilla\|godzilla]].		The '''semaphoresmic family''' of [[rank-3 temperament\|rank-3]] [[regular temperament\|temperaments]] [[tempering out\|tempers out]] [[49/48]] in the full [[7-limit]], and thereby identifies the septimal minor third, [[7/6]], and the septimal whole tone, [[8/7]]. It also splits the fourth into two of these intervals; hence the name, which sounds like "semi-fourth". Related to this is the 2.3.7-subgroup {49/48} temperament [[Semaphoresmic clan #Semaphore\|semaphore]], and the 7-limit {49/48, 81/80} temperament [[Semaphoresmic clan #Godzilla\|godzilla]].

	== ~~Semiphore~~ ==		== Semaphoresmic a.k.a. semiphore ==
	~~This temperament is also known as '''semaphoresmic'''.~~

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

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	: error map: {{val\| 0.000 -0.577 -3.962 -18.137 }}		: error map: {{val\| 0.000 -0.577 -3.962 -18.137 }}

	{{Optimal ET sequence\|legend=1\| 4, 5, 9, 10, 14c, 15, 19 }}		{{Optimal ET sequence\|legend=1\| 4, 5, 9, 10, 14c, 15, 19, 48d, 53d, 67cdd, 86cdd }}

	[[Badness]] (Sintel): 0.510		[[Badness]] (Sintel): 0.510

			=== 2.3.5.7.13 subgroup ===
			Subgroup: 2.3.5.7.13

			Comma list: 49/48, 91/90

			Sval mapping: {{mapping\| 1 0 0 2 -1 \| 0 2 0 1 3 \| 0 0 1 0 1 }}

			Optimal tunings:
			* WE: ~2 = 1202.7771, ~7/4 = 951.9629, ~5/4 = 381.0131
			* CWE: ~2 = 1200.0000, ~7/4 = 950.6703, ~5/4 = 382.2972

			{{Optimal ET sequence\|legend=0\| 5, 9, 10, 14cf, 15, 19, 48df, 53d, 67cddf, 72dd }}

			Badness (Sintel): 0.380

	== Selenium ==		== Selenium ==

FloraC: - CTE & POTE tunings

2025-07-14T09:36:14Z

- CTE & POTE tunings

← Older revision		Revision as of 09:36, 14 July 2025
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	* [[CWE]]: ~2 = 1200.0000, ~7/4 = 950.6890, ~5/4 = 382.3522		* [[CWE]]: ~2 = 1200.0000, ~7/4 = 950.6890, ~5/4 = 382.3522
	: error map: {{val\| 0.000 -0.577 -3.962 -18.137 }}		: error map: {{val\| 0.000 -0.577 -3.962 -18.137 }}
	~~<!-- * [[CTE]]: ~2 = 1200.0000, ~7/4 = 952.2948, ~5/4 = 386.3137~~
	~~: [[error map]]: {{val\| 0.000 +2.635 0.000 -16.531 }} -->~~
	~~<!-- * [[POTE]]: ~2 = 1200.0000, ~7/4 = 949.6154, ~5/4 = 379.7035~~
	~~: error map: {{val\| 0.000 -2.724 -6.610 -19.211 }} -->~~

	{{Optimal ET sequence\|legend=1\| 4, 5, 9, 10, 14c, 15, 19 }}		{{Optimal ET sequence\|legend=1\| 4, 5, 9, 10, 14c, 15, 19 }}
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	* [[CWE]]: ~2 = 1200.0000, ~7/4 = 951.7409, ~5/4 = 390.6582		* [[CWE]]: ~2 = 1200.0000, ~7/4 = 951.7409, ~5/4 = 390.6582
	: error map: {{val\| 0.000 +1.527 +4.344 -17.085 +9.765 }}		: error map: {{val\| 0.000 +1.527 +4.344 -17.085 +9.765 }}
	~~<!-- * [[CTE]]: ~2 = 1200.0000, ~7/4 = 951.8194, ~5/4 = 390.7202~~
	~~: [[error map]]: {{val\| 0.000 +1.684 +4.407 -17.007 +9.781 }} -->~~
	~~<!-- * [[POTE]]: ~2 = 1200.0000, ~7/4 = 951.7290, ~5/4 = 390.6487~~
	~~: error map: {{val\| 0.000 +1.503 +4.335 -17.097 +9.762 }} -->~~

	{{Optimal ET sequence\|legend=1\| 4, 5, 9, 10, 15, 19, 24, 34 }}		{{Optimal ET sequence\|legend=1\| 4, 5, 9, 10, 15, 19, 24, 34 }}
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	* WE: ~2 = 1200.0790, ~7/4 = 951.3067, ~5/4 = 389.7793		* WE: ~2 = 1200.0790, ~7/4 = 951.3067, ~5/4 = 389.7793
	* CWE: ~2 = 1200.0000, ~7/4 = 951.2662, ~5/4 = 389.6120		* CWE: ~2 = 1200.0000, ~7/4 = 951.2662, ~5/4 = 389.6120
	~~<!-- * CTE: ~2 = 1200.0000, ~7/4 = 951.3729, ~5/4 = 389.6907 -->~~
	~~<!-- * POTE: ~2 = 1200.0000, ~7/4 = 951.2441, ~5/4 = 389.5957 -->~~

	{{Optimal ET sequence\|legend=0\| 5, 9, 10, 15, 19, 24, 34 }}		{{Optimal ET sequence\|legend=0\| 5, 9, 10, 15, 19, 24, 34 }}
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	* [[CWE]]: ~2 = 1200.0000, ~15/14 = 125.4347, ~11/8 = 541.8688		* [[CWE]]: ~2 = 1200.0000, ~15/14 = 125.4347, ~11/8 = 541.8688
	: error map: {{val\| 0.000 -3.694 -10.009 -19.695 -9.449 }}		: error map: {{val\| 0.000 -3.694 -10.009 -19.695 -9.449 }}
	~~<!-- * [[CTE]]: ~2 = 1200.0000, ~15/14 = 124.8134, ~11/8 = 551.3179~~
	~~: [[error map]]: {{val\| 0.000 -1.209 -11.874 -18.453 0.000 }} -->~~
	~~<!-- * [[POTE]]: ~2 = 1200.0000, ~15/14 = 125.6080, ~11/8 = 539.2342~~
	~~: error map: {{val\| 0.000 -4.387 -9.490 -20.042 -12.084 }} -->~~

	{{Optimal ET sequence\|legend=1\| 9, 10, 19, 29, 38d, 67cdde, 105cdddee }}		{{Optimal ET sequence\|legend=1\| 9, 10, 19, 29, 38d, 67cdde, 105cdddee }}
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	* WE: ~2 = 1203.6981, ~14/13 = 125.9545, ~11/8 = 540.1440		* WE: ~2 = 1203.6981, ~14/13 = 125.9545, ~11/8 = 540.1440
	* CWE: ~2 = 1200.0000, ~14/13 = 125.3543, ~11/8 = 540.9490		* CWE: ~2 = 1200.0000, ~14/13 = 125.3543, ~11/8 = 540.9490
	~~<!-- * CTE: ~2 = 1200.0000, ~14/13 = 124.4571, ~11/8 = 551.3179 -->~~
	~~<!-- * POTE: ~2 = 1200.0000, ~14/13 = 125.5675, ~11/8 = 538.4845 -->~~

	{{Optimal ET sequence\|legend=0\| 9, 10, 19, 29, 38df, 67cddef, 105cdddeefff }}		{{Optimal ET sequence\|legend=0\| 9, 10, 19, 29, 38df, 67cddef, 105cdddeefff }}

FloraC: + WE tunings

2025-07-14T09:35:47Z

+ WE tunings

← Older revision		Revision as of 09:35, 14 July 2025
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	{{Technical data page}}		{{Technical data page}}
	The '''semaphoresmic family''' of [[rank-3 temperament\|rank-3]] [[regular temperament\|temperaments]] [[tempering out\|tempers out]] [[49/48]] in the full [[7-limit]], and thereby identifies the septimal minor third, [[7/6]], and the septimal whole tone, [[8/7]]. It also splits the fourth into two of these intervals; hence the name, which sounds like "semi-fourth". Related to this is the 2.3.7-~~limit~~ 49/48 temperament [[Semaphoresmic clan #Semaphore\|semaphore]], and the ~~2.3.5.~~7 49/48 ~~and~~ 81/80 temperament [[Semaphoresmic clan #Godzilla\|godzilla]].		The '''semaphoresmic family''' of [[rank-3 temperament\|rank-3]] [[regular temperament\|temperaments]] [[tempering out\|tempers out]] [[49/48]] in the full [[7-limit]], and thereby identifies the septimal minor third, [[7/6]], and the septimal whole tone, [[8/7]]. It also splits the fourth into two of these intervals; hence the name, which sounds like "semi-fourth". Related to this is the 2.3.7-subgroup {49/48} temperament [[Semaphoresmic clan #Semaphore\|semaphore]], and the 7-limit {49/48, 81/80} temperament [[Semaphoresmic clan #Godzilla\|godzilla]].

	== Semiphore ==		== Semiphore ==
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	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[~~CTE~~]]: ~2 = ~~1200~~.~~0000~~, ~7/4 = ~~952~~.~~2948~~, ~5/4 = 386.~~3137~~		* [[WE]]: ~2 = 1202.8324, ~7/4 = 951.8567, ~5/4 = 386.2644
	: [[error map]]: {{val\| 0.~~000~~ +2.~~635~~ 0.~~000~~ -16.~~531~~ }}		: [[error map]]: {{val\| +2.832 +1.758 -0.049 -11.304 }}
	* [[CWE]]: ~2 = 1200.0000, ~7/4 = 950.6890, ~5/4 = 382.3522		* [[CWE]]: ~2 = 1200.0000, ~7/4 = 950.6890, ~5/4 = 382.3522
	: error map: {{val\| 0.000 -0.577 -3.962 -18.137 }}		: error map: {{val\| 0.000 -0.577 -3.962 -18.137 }}
			<!-- * [[CTE]]: ~2 = 1200.0000, ~7/4 = 952.2948, ~5/4 = 386.3137
			: [[error map]]: {{val\| 0.000 +2.635 0.000 -16.531 }} -->
	<!-- * [[POTE]]: ~2 = 1200.0000, ~7/4 = 949.6154, ~5/4 = 379.7035		<!-- * [[POTE]]: ~2 = 1200.0000, ~7/4 = 949.6154, ~5/4 = 379.7035
	: error map: {{val\| 0.000 -2.724 -6.610 -19.211 }} -->		: error map: {{val\| 0.000 -2.724 -6.610 -19.211 }} -->
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	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[~~CTE~~]]: ~2 = 1200.~~0000~~, ~7/4 = 951.~~8194~~, ~5/4 = 390.~~7202~~		* [[WE]]: ~2 = 1200.0412, ~7/4 = 951.7616, ~5/4 = 390.7445
	: [[error map]]: {{val\| 0.~~000~~ +1.~~684~~ +4.~~407~~ -17.~~007~~ +9.~~781~~ }}		: [[error map]]: {{val\| +0.041 +1.568 +4.431 -16.982 +9.905 }}
	* [[CWE]]: ~2 = 1200.0000, ~7/4 = 951.7409, ~5/4 = 390.6582		* [[CWE]]: ~2 = 1200.0000, ~7/4 = 951.7409, ~5/4 = 390.6582
	: error map: {{val\| 0.000 +1.527 +4.344 -17.085 +9.765 }}		: error map: {{val\| 0.000 +1.527 +4.344 -17.085 +9.765 }}
			<!-- * [[CTE]]: ~2 = 1200.0000, ~7/4 = 951.8194, ~5/4 = 390.7202
			: [[error map]]: {{val\| 0.000 +1.684 +4.407 -17.007 +9.781 }} -->
	<!-- * [[POTE]]: ~2 = 1200.0000, ~7/4 = 951.7290, ~5/4 = 390.6487		<!-- * [[POTE]]: ~2 = 1200.0000, ~7/4 = 951.7290, ~5/4 = 390.6487
	: error map: {{val\| 0.000 +1.503 +4.335 -17.097 +9.762 }} -->		: error map: {{val\| 0.000 +1.503 +4.335 -17.097 +9.762 }} -->
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	Optimal tunings:		Optimal tunings:
	* ~~CTE~~: ~2 = 1200.~~0000~~, ~7/4 = 951.~~3729~~, ~5/4 = 389.~~6907~~		* WE: ~2 = 1200.0790, ~7/4 = 951.3067, ~5/4 = 389.7793
	* CWE: ~2 = 1200.0000, ~7/4 = 951.2662, ~5/4 = 389.6120		* CWE: ~2 = 1200.0000, ~7/4 = 951.2662, ~5/4 = 389.6120
			<!-- * CTE: ~2 = 1200.0000, ~7/4 = 951.3729, ~5/4 = 389.6907 -->
	<!-- * POTE: ~2 = 1200.0000, ~7/4 = 951.2441, ~5/4 = 389.5957 -->		<!-- * POTE: ~2 = 1200.0000, ~7/4 = 951.2441, ~5/4 = 389.5957 -->

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	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[~~CTE~~]]: ~2 = ~~1200~~.~~0000~~, ~15/14 = ~~124~~.~~8134~~, ~11/8 = ~~551~~.~~3179~~		* [[WE]]: ~2 = 1203.4810, ~15/14 = 125.9724, ~11/8 = 540.7985
	: [[error map]]: {{val\| 0.~~000~~ -1.~~209~~ -11.~~874~~ -~~18.453~~ 0.~~000~~ }}		: [[error map]]: {{val\| +3.481 +1.118 -1.435 -10.328 -0.076 }}
	* [[CWE]]: ~2 = 1200.0000, ~15/14 = 125.4347, ~11/8 = 541.8688		* [[CWE]]: ~2 = 1200.0000, ~15/14 = 125.4347, ~11/8 = 541.8688
	: error map: {{val\| 0.000 -3.694 -10.009 -19.695 -9.449 }}		: error map: {{val\| 0.000 -3.694 -10.009 -19.695 -9.449 }}
			<!-- * [[CTE]]: ~2 = 1200.0000, ~15/14 = 124.8134, ~11/8 = 551.3179
			: [[error map]]: {{val\| 0.000 -1.209 -11.874 -18.453 0.000 }} -->
	<!-- * [[POTE]]: ~2 = 1200.0000, ~15/14 = 125.6080, ~11/8 = 539.2342		<!-- * [[POTE]]: ~2 = 1200.0000, ~15/14 = 125.6080, ~11/8 = 539.2342
	: error map: {{val\| 0.000 -4.387 -9.490 -20.042 -12.084 }} -->		: error map: {{val\| 0.000 -4.387 -9.490 -20.042 -12.084 }} -->
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	Optimal tunings:		Optimal tunings:
	* ~~CTE~~: ~2 = ~~1200~~.~~0000~~, ~14/13 = ~~124~~.~~4571~~, ~11/8 = ~~551~~.~~3179~~		* WE: ~2 = 1203.6981, ~14/13 = 125.9545, ~11/8 = 540.1440
	* CWE: ~2 = 1200.0000, ~14/13 = 125.3543, ~11/8 = 540.9490		* CWE: ~2 = 1200.0000, ~14/13 = 125.3543, ~11/8 = 540.9490
			<!-- * CTE: ~2 = 1200.0000, ~14/13 = 124.4571, ~11/8 = 551.3179 -->
	<!-- * POTE: ~2 = 1200.0000, ~14/13 = 125.5675, ~11/8 = 538.4845 -->		<!-- * POTE: ~2 = 1200.0000, ~14/13 = 125.5675, ~11/8 = 538.4845 -->

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

2025-06-24T00:36:25Z

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

← Older revision		Revision as of 00:36, 24 June 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Semaphoresmic family\| ]] <!-- main article -->		[[Category:Semaphoresmic family\| ]] <!-- main article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

FloraC: Tunings and badnesses

2025-06-17T13:32:17Z

Tunings and badnesses

← Older revision		Revision as of 13:32, 17 June 2025
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	: Angle (7/6, 5/4) = 90 degrees		: Angle (7/6, 5/4) = 90 degrees

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~7/4 = 949.6154, ~5/4 = 379.7035		[[Optimal tuning]]s:
			* [[CTE]]: ~2 = 1200.0000, ~7/4 = 952.2948, ~5/4 = 386.3137
			: [[error map]]: {{val\| 0.000 +2.635 0.000 -16.531 }}
			* [[CWE]]: ~2 = 1200.0000, ~7/4 = 950.6890, ~5/4 = 382.3522
			: error map: {{val\| 0.000 -0.577 -3.962 -18.137 }}
			<!-- * [[POTE]]: ~2 = 1200.0000, ~7/4 = 949.6154, ~5/4 = 379.7035
			: error map: {{val\| 0.000 -2.724 -6.610 -19.211 }} -->

	{{Optimal ET sequence\|legend=1\| 4, 5, 9, 10, 14c, 15, 19 }}		{{Optimal ET sequence\|legend=1\| 4, 5, 9, 10, 14c, 15, 19 }}

	[[Badness]]: 0.~~116 × 10<sup>-3</sup>~~		[[Badness]] (Sintel): 0.510

	== Selenium ==		== Selenium ==
	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

Line 30:		Line 36:
	{{Mapping\|legend=1\| 1 0 2 2 5 \| 0 2 0 1 1 \| 0 0 1 0 -1 }}		{{Mapping\|legend=1\| 1 0 2 2 5 \| 0 2 0 1 1 \| 0 0 1 0 -1 }}

	[[Optimal tuning]] ([[~~POTE~~]]): ~2 = 1\1, ~7/4 = 951.7290, ~5/4 = 390.6487		[[Optimal tuning]]s:
			* [[CTE]]: ~2 = 1200.0000, ~7/4 = 951.8194, ~5/4 = 390.7202
			: [[error map]]: {{val\| 0.000 +1.684 +4.407 -17.007 +9.781 }}
			* [[CWE]]: ~2 = 1200.0000, ~7/4 = 951.7409, ~5/4 = 390.6582
			: error map: {{val\| 0.000 +1.527 +4.344 -17.085 +9.765 }}
			<!-- * [[POTE]]: ~2 = 1200.0000, ~7/4 = 951.7290, ~5/4 = 390.6487
			: error map: {{val\| 0.000 +1.503 +4.335 -17.097 +9.762 }} -->

	{{Optimal ET sequence\|legend=1\| 4, 5, 9, 10, 15, 19, 24, 34 }}		{{Optimal ET sequence\|legend=1\| 4, 5, 9, 10, 15, 19, 24, 34 }}

	[[Badness]]: 0.~~665 × 10<sup>-3</sup>~~		[[Badness]] (Sintel): 0.800

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

Line 43:		Line 55:
	Mapping: {{mapping\| 1 0 2 2 5 -1 \| 0 2 0 1 1 3 \| 0 0 1 0 -1 1 }}		Mapping: {{mapping\| 1 0 2 2 5 -1 \| 0 2 0 1 1 3 \| 0 0 1 0 -1 1 }}

	Optimal ~~tuning (~~POTE): ~2 = ~~1\1~~, ~7/4 = 951.2441, ~5/4 = 389.5957		Optimal tunings:
			* CTE: ~2 = 1200.0000, ~7/4 = 951.3729, ~5/4 = 389.6907
			* CWE: ~2 = 1200.0000, ~7/4 = 951.2662, ~5/4 = 389.6120
			<!-- * POTE: ~2 = 1200.0000, ~7/4 = 951.2441, ~5/4 = 389.5957 -->

	{{Optimal ET sequence\|legend=1\| 5, 9, 10, 15, 19, 24, 34 }}		{{Optimal ET sequence\|legend=0\| 5, 9, 10, 15, 19, 24, 34 }}

	Badness: 0.~~787 × 10<sup>-3</sup>~~		Badness (Sintel): 0.736

	== Negric ==		== Negric ==
	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

Line 56:		Line 71:
	{{Mapping\|legend=1\| 1 2 2 3 0 \| 0 -4 3 -2 0 \| 0 0 0 0 1 }}		{{Mapping\|legend=1\| 1 2 2 3 0 \| 0 -4 3 -2 0 \| 0 0 0 0 1 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~15/14 = 125.6080, ~11/8 = 539.2342		[[Optimal tuning]]s:
			* [[CTE]]: ~2 = 1200.0000, ~15/14 = 124.8134, ~11/8 = 551.3179
			: [[error map]]: {{val\| 0.000 -1.209 -11.874 -18.453 0.000 }}
			* [[CWE]]: ~2 = 1200.0000, ~15/14 = 125.4347, ~11/8 = 541.8688
			: error map: {{val\| 0.000 -3.694 -10.009 -19.695 -9.449 }}
			<!-- * [[POTE]]: ~2 = 1200.0000, ~15/14 = 125.6080, ~11/8 = 539.2342
			: error map: {{val\| 0.000 -4.387 -9.490 -20.042 -12.084 }} -->

	{{Optimal ET sequence\|legend=1\| 9, 10, 19, 29, 38d, ~~67cde~~ }}		{{Optimal ET sequence\|legend=1\| 9, 10, 19, 29, 38d, 67cdde, 105cdddee }}

	[[Badness]]: 1.~~087 × 10<sup>-3</sup>~~		[[Badness]] (Sintel): 1.31

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

Line 69:		Line 90:
	Mapping: {{mapping\| 1 2 2 3 0 4 \| 0 -4 3 -2 0 -3 \| 0 0 0 0 1 0 }}		Mapping: {{mapping\| 1 2 2 3 0 4 \| 0 -4 3 -2 0 -3 \| 0 0 0 0 1 0 }}

	Optimal ~~tuning (~~POTE): ~2 = ~~1\1~~, ~14/13 = 125.5675, ~11/8 = 538.4845		Optimal tunings:
			* CTE: ~2 = 1200.0000, ~14/13 = 124.4571, ~11/8 = 551.3179
			* CWE: ~2 = 1200.0000, ~14/13 = 125.3543, ~11/8 = 540.9490
			<!-- * POTE: ~2 = 1200.0000, ~14/13 = 125.5675, ~11/8 = 538.4845 -->

	{{Optimal ET sequence\|legend=1\| 9, 10, 19, 29, 38df, ~~67cdef~~ }}		{{Optimal ET sequence\|legend=0\| 9, 10, 19, 29, 38df, 67cddef, 105cdddeefff }}

	Badness: 0.~~8076 × 10<sup>-3</sup>~~		Badness (Sintel): 0.755

	[[Category:Temperament families]]		[[Category:Temperament families]]
	[[Category:Semaphoresmic family\| ]] <!-- main article -->		[[Category:Semaphoresmic family\| ]] <!-- main article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

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

" to "{{Technical data page}}"

2025-04-13T13:47:58Z

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

← Older revision		Revision as of 13:47, 13 April 2025
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	{{Technical data page}}~~<br><br>~~		{{Technical data page}}
	The '''semaphoresmic family''' of [[rank-3 temperament\|rank-3]] [[regular temperament\|temperaments]] [[tempering out\|tempers out]] [[49/48]] in the full [[7-limit]], and thereby identifies the septimal minor third, [[7/6]], and the septimal whole tone, [[8/7]]. It also splits the fourth into two of these intervals; hence the name, which sounds like "semi-fourth". Related to this is the 2.3.7-limit 49/48 temperament [[Semaphoresmic clan #Semaphore\|semaphore]], and the 2.3.5.7 49/48 and 81/80 temperament [[Semaphoresmic clan #Godzilla\|godzilla]].		The '''semaphoresmic family''' of [[rank-3 temperament\|rank-3]] [[regular temperament\|temperaments]] [[tempering out\|tempers out]] [[49/48]] in the full [[7-limit]], and thereby identifies the septimal minor third, [[7/6]], and the septimal whole tone, [[8/7]]. It also splits the fourth into two of these intervals; hence the name, which sounds like "semi-fourth". Related to this is the 2.3.7-limit 49/48 temperament [[Semaphoresmic clan #Semaphore\|semaphore]], and the 2.3.5.7 49/48 and 81/80 temperament [[Semaphoresmic clan #Godzilla\|godzilla]].

BudjarnLambeth: {{Technical data page}}

2025-04-13T11:51:57Z

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

← Older revision		Revision as of 11:51, 13 April 2025
Line 1:		Line 1:
			{{Technical data page}}<br><br>
	The '''semaphoresmic family''' of [[rank-3 temperament\|rank-3]] [[regular temperament\|temperaments]] [[tempering out\|tempers out]] [[49/48]] in the full [[7-limit]], and thereby identifies the septimal minor third, [[7/6]], and the septimal whole tone, [[8/7]]. It also splits the fourth into two of these intervals; hence the name, which sounds like "semi-fourth". Related to this is the 2.3.7-limit 49/48 temperament [[Semaphoresmic clan #Semaphore\|semaphore]], and the 2.3.5.7 49/48 and 81/80 temperament [[Semaphoresmic clan #Godzilla\|godzilla]].		The '''semaphoresmic family''' of [[rank-3 temperament\|rank-3]] [[regular temperament\|temperaments]] [[tempering out\|tempers out]] [[49/48]] in the full [[7-limit]], and thereby identifies the septimal minor third, [[7/6]], and the septimal whole tone, [[8/7]]. It also splits the fourth into two of these intervals; hence the name, which sounds like "semi-fourth". Related to this is the 2.3.7-limit 49/48 temperament [[Semaphoresmic clan #Semaphore\|semaphore]], and the 2.3.5.7 49/48 and 81/80 temperament [[Semaphoresmic clan #Godzilla\|godzilla]].