Sengic family - Revision history

FloraC: Text replacement - "Subgroup-val mapping: {{mapping| " to "{{Mapping|legend=2| "

2026-09-30T17:44:26Z

Text replacement - "Subgroup-val mapping: {{mapping| " to "{{Mapping|legend=2| "

← Older revision		Revision as of 17:44, 30 September 2026
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	Comma list: 91/90, 169/168		Comma list: 91/90, 169/168

	~~Subgroup-val mapping:~~ {{~~mapping~~\| 1 0 2 1 2 \| 0 1 0 1 1 \| 0 0 3 2 1 }}		{{Mapping\|legend=2\| 1 0 2 1 2 \| 0 1 0 1 1 \| 0 0 3 2 1 }}

	Optimal tunings:		Optimal tunings:

FloraC: Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "

2026-09-24T12:32:58Z

Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "

← Older revision		Revision as of 12:32, 24 September 2026
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	Comma list: 91/90, 169/168, 352/351		Comma list: 91/90, 169/168, 352/351

	~~Mapping:~~ {{~~mapping~~\| 1 0 2 1 -3 2 \| 0 1 0 1 4 1 \| 0 0 3 2 1 1 }}		{{Mapping\|legend=0\| 1 0 2 1 -3 2 \| 0 1 0 1 4 1 \| 0 0 3 2 1 1 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 91/90, 136/135, 154/153, 169/168		Comma list: 91/90, 136/135, 154/153, 169/168

	~~Mapping:~~ {{~~mapping~~\| 1 0 2 1 -3 2 -1 \| 0 1 0 1 4 1 3 \| 0 0 3 2 1 1 3 }}		{{Mapping\|legend=0\| 1 0 2 1 -3 2 -1 \| 0 1 0 1 4 1 3 \| 0 0 3 2 1 1 3 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 56/55, 78/77, 91/90		Comma list: 56/55, 78/77, 91/90

	~~Mapping:~~ {{~~mapping~~\| 1 0 2 1 2 2 \| 0 1 0 1 1 1 \| 0 0 3 2 -1 1 }}		{{Mapping\|legend=0\| 1 0 2 1 2 2 \| 0 1 0 1 1 1 \| 0 0 3 2 -1 1 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 91/90, 126/125, 169/168		Comma list: 91/90, 126/125, 169/168

	~~Mapping:~~ {{~~mapping~~\| 1 -1 -1 -2 3 0 \| 0 7 9 13 0 10 \| 0 0 0 0 1 0 }}		{{Mapping\|legend=0\| 1 -1 -1 -2 3 0 \| 0 7 9 13 0 10 \| 0 0 0 0 1 0 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 91/90, 126/125, 154/153, 169/168		Comma list: 91/90, 126/125, 154/153, 169/168

	~~Mapping:~~ {{~~mapping~~\| 1 -1 -1 -2 3 0 4 \| 0 7 9 13 0 10 -1 \| 0 0 0 0 1 0 1 }}		{{Mapping\|legend=0\| 1 -1 -1 -2 3 0 4 \| 0 7 9 13 0 10 -1 \| 0 0 0 0 1 0 1 }}

	Optimal tunings:		Optimal tunings:

FloraC: Recategorize

2026-08-14T12:23:10Z

Recategorize

← Older revision		Revision as of 12:23, 14 August 2026
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	== References ==		== References ==

			[[Category:Sengic family\| ]] <!-- main article -->
	[[Category:Temperament families]]		[[Category:Temperament families]]
	[[Category:~~Sengic family\| ]] <!~~-~~- main article -->~~		[[Category:Catalogs of rank-3 temperaments]]
	~~[[Category:Rank~~ 3]]

FloraC: + overview to extensions

2026-04-11T10:31:34Z

+ overview to extensions

← Older revision		Revision as of 10:31, 11 April 2026
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	{{Technical data page}}		{{Technical data page}}
	The '''sengic family''' of [[rank-3 temperament]]s [[tempering out\|tempers out]] the senga a.k.a. sengic comma, [[686/675]].		The '''sengic family''' of [[rank-3 temperament]]s [[tempering out\|tempers out]] the senga a.k.a. sengic comma, [[686/675]].

	~~Temperaments considered below are demeter, krypton, and sensigh.~~

	== Sengic ==		== Sengic ==
	Sengic is generated by a perfect fifth and a wide semitone of ~[[15/14]], two of which make ~[[7/6]] and three make ~[[5/4]]. It is naturally a [[2.3.5.7.13 subgroup\|2.3.5.7.13-subgroup]] temperament due to the identity 686/675 ({{S\|13⋅S14<sup>2</sup>}}) = ([[91/90]])⋅([[196/195]]) and 91/90 (S13⋅S14) = ([[169/168]])⋅(196/195). This identifies the last generator as 13/12~14/13~15/14. The 7-limit parent was discovered and named in 2005, whereas the extension was noted by [[Keenan Pepper]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_19390.html Yahoo! Tuning Group \| ''It's the "thirds", stupid!'']</ref>.		Sengic is generated by a perfect fifth and a wide semitone of ~[[15/14]], two of which make ~[[7/6]] and three make ~[[5/4]]. It was discovered and named in 2005.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	[[Projection pair]]s: ~5 = 3375/686, ~7 = 675/98 to 2.3.7/5		[[Projection pair]]s: ~5 = 3375/686, ~7 = 675/98 to 2.3.7/5

			=== Overview to extensions ===
			First noted by [[Keenan Pepper]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_19390.html Yahoo! Tuning Group \| ''It's the "thirds", stupid!'']</ref>, sengic is naturally a [[2.3.5.7.13 subgroup\|2.3.5.7.13-subgroup]] temperament due to the identity 686/675 = ([[169/168]])⋅([[196/195]])<sup>2</sup>, as we can see from its [[S-expression]], S13⋅S14<sup>2</sup>. This identifies the last generator as [[13/12]]~[[14/13]]~15/14. This extension is considered immediately below.

			11-limit temperaments considered below are demeter, krypton, and sensigh.

	=== 2.3.5.7.13 subgroup ===		=== 2.3.5.7.13 subgroup ===

FloraC: Move sensigh here

2026-04-11T10:05:36Z

Move sensigh here

@@ Line 2: / Line 2: @@
 The '''sengic family''' of [[rank-3 temperament]]s [[tempering out|tempers out]] the senga a.k.a. sengic comma, [[686/675]].
-Temperament discussed elsewhere include [[sensigh]] (→ [[Sensamagic family #Sensigh|Sensamagic family]]). Considered below are demeter and krypton.
+Temperaments considered below are demeter, krypton, and sensigh.
 == Sengic ==
-Sengic is generated by a perfect fifth and a wide semitone of ~[[15/14]], two of which make ~[[7/6]] and three make ~[[5/4]]. It is naturally a 2.3.5.7.13-subgroup temperament due to the identity 686/675 ({{S|13⋅S14<sup>2</sup>}}) = ([[91/90]])⋅([[196/195]]) and 91/90 (S13⋅S14) = ([[169/168]])⋅(196/195). This identifies the last generator as 13/12~14/13~15/14. The 7-limit parent was discovered and named in 2005, whereas the extension was noted by [[Keenan Pepper]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_19390.html Yahoo! Tuning Group | ''It's the "thirds", stupid!'']</ref>.
+Sengic is generated by a perfect fifth and a wide semitone of ~[[15/14]], two of which make ~[[7/6]] and three make ~[[5/4]]. It is naturally a [[2.3.5.7.13 subgroup|2.3.5.7.13-subgroup]] temperament due to the identity 686/675 ({{S|13⋅S14<sup>2</sup>}}) = ([[91/90]])⋅([[196/195]]) and 91/90 (S13⋅S14) = ([[169/168]])⋅(196/195). This identifies the last generator as 13/12~14/13~15/14. The 7-limit parent was discovered and named in 2005, whereas the extension was noted by [[Keenan Pepper]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_19390.html Yahoo! Tuning Group | ''It's the "thirds", stupid!'']</ref>.
 [[Subgroup]]: 2.3.5.7
@@ Line 135: / Line 135: @@
 Projection pairs: ~5 = 6912/1331, ~7 = 854/121, ~13 = 144/11 to 2.3.11
 == References ==

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

2025-11-27T12:27:10Z

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

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

FloraC: - redundant category

2025-11-26T17:02:57Z

- redundant category

← Older revision		Revision as of 17:02, 26 November 2025
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	[[Category:Pages with mostly numerical content]]		[[Category:Pages with mostly numerical content]]
	[[Category:Sengic family\| ]] <!-- main article -->		[[Category:Sengic family\| ]] <!-- main article -->
	~~[[Category:Sengic\| ]] <!-- key article -->~~
	[[Category:Rank 3]]		[[Category:Rank 3]]

Lériendil: /* Sengic */

2025-10-10T14:16:32Z

Sengic

← Older revision		Revision as of 14:16, 10 October 2025
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	== Sengic ==		== Sengic ==
	Sengic is generated by a perfect fifth and a wide semitone of ~15/14, two of which make ~7/6 and three make ~5/4. It is naturally a 2.3.5.7.13-subgroup temperament due to the identity 686/675 = (91/90)⋅(196/195) and 91/90 = (169/168)⋅(196/195). This identifies the last generator as 13/12~14/13~15/14. The 7-limit parent was discovered and named in 2005, whereas the extension was noted by [[Keenan Pepper]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_19390.html Yahoo! Tuning Group \| ''It's the "thirds", stupid!'']</ref>.		Sengic is generated by a perfect fifth and a wide semitone of ~[[15/14]], two of which make ~[[7/6]] and three make ~[[5/4]]. It is naturally a 2.3.5.7.13-subgroup temperament due to the identity 686/675 ({{S\|13⋅S14<sup>2</sup>}}) = ([[91/90]])⋅([[196/195]]) and 91/90 (S13⋅S14) = ([[169/168]])⋅(196/195). This identifies the last generator as 13/12~14/13~15/14. The 7-limit parent was discovered and named in 2005, whereas the extension was noted by [[Keenan Pepper]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_19390.html Yahoo! Tuning Group \| ''It's the "thirds", stupid!'']</ref>.

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

FloraC: /* Sengic */ intro to the 7-limit temp

2025-10-10T12:38:47Z

Sengic: intro to the 7-limit temp

← Older revision		Revision as of 12:38, 10 October 2025
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	== Sengic ==		== Sengic ==
	Sengic is naturally a 2.3.5.7.13-subgroup temperament due to the identity 686/675 = (91/90)(196/195) and 91/90 = (169/168)(196/195). This identifies the last generator as 13/12~14/13~15/14. The 7-limit parent was discovered and named in 2005, whereas the extension was noted by [[Keenan Pepper]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_19390.html Yahoo! Tuning Group \| ''It's the "thirds", stupid!'']</ref>.		Sengic is generated by a perfect fifth and a wide semitone of ~15/14, two of which make ~7/6 and three make ~5/4. It is naturally a 2.3.5.7.13-subgroup temperament due to the identity 686/675 = (91/90)⋅(196/195) and 91/90 = (169/168)⋅(196/195). This identifies the last generator as 13/12~14/13~15/14. The 7-limit parent was discovered and named in 2005, whereas the extension was noted by [[Keenan Pepper]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_19390.html Yahoo! Tuning Group \| ''It's the "thirds", stupid!'']</ref>.

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

FloraC: - CTE & POTE tunings

2025-10-10T12:32:34Z

- CTE & POTE tunings

← Older revision		Revision as of 12:32, 10 October 2025
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.9671{{c}}, ~15/14 = 129.7330{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.9671{{c}}, ~15/14 = 129.7330{{c}}
	: error map: {{val\| 0.000 +2.012 +2.885 -5.393 }}		: error map: {{val\| 0.000 +2.012 +2.885 -5.393 }}
	~~<!-- * [[CTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.7873{{c}}, ~15/14 = 129.6451{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 8d, 9, 10, 17c, 19, 27, 46 }}		{{Optimal ET sequence\|legend=1\| 8d, 9, 10, 17c, 19, 27, 46 }}
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	* WE: ~2 = 1200.3448{{c}}, ~3/2 = 704.1998{{c}}, ~14/13 = 129.5253{{c}}		* WE: ~2 = 1200.3448{{c}}, ~3/2 = 704.1998{{c}}, ~14/13 = 129.5253{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.2688{{c}}, ~14/13 = 129.6115{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.2688{{c}}, ~14/13 = 129.6115{{c}}
	~~<!-- * CTE: ~2 = 1200.0000{{c}}, ~3/2 = 704.5918{{c}}, ~14/13 = 129.7585{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 8d, 9, 10, 17c, 19, 27, 46, 111df, 121df }}		{{Optimal ET sequence\|legend=0\| 8d, 9, 10, 17c, 19, 27, 46, 111df, 121df }}
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 705.2789{{c}}, ~15/14 = 129.8330{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 705.2789{{c}}, ~15/14 = 129.8330{{c}}
	: error map: {{val\| 0.000 +3.324 +3.185 -3.881 -0.369 }}		: error map: {{val\| 0.000 +3.324 +3.185 -3.881 -0.369 }}
	~~<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 705.518{{c}}, ~15/14 = 130.039{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 10, 17c, 19e, 27e, 46, 102, 148 }}		{{Optimal ET sequence\|legend=1\| 10, 17c, 19e, 27e, 46, 102, 148 }}
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	* WE: ~2 = 1200.0393{{c}}, ~3/2 = 705.1360{{c}}, ~14/13 = 129.6770{{c}}		* WE: ~2 = 1200.0393{{c}}, ~3/2 = 705.1360{{c}}, ~14/13 = 129.6770{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 705.1277{{c}}, ~14/13 = 129.6854{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 705.1277{{c}}, ~14/13 = 129.6854{{c}}
	~~<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 705.113{{c}}, ~14/13 = 129.673{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 10, 17c, 19e, 27e, 29, 46, 102, 148f }}		{{Optimal ET sequence\|legend=0\| 10, 17c, 19e, 27e, 29, 46, 102, 148f }}
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	* WE: ~2 = 1200.0255{{c}}, ~3/2 = 705.1616{{c}}, ~14/13 = 129.7024{{c}}		* WE: ~2 = 1200.0255{{c}}, ~3/2 = 705.1616{{c}}, ~14/13 = 129.7024{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 705.1553{{c}}, ~14/13 = 129.7071{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 705.1553{{c}}, ~14/13 = 129.7071{{c}}
	~~<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 705.147{{c}}, ~14/13 = 129.700{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 10, 17cg, 19eg, 27eg, 29g, 46, 102, 148f }}		{{Optimal ET sequence\|legend=0\| 10, 17cg, 19eg, 27eg, 29g, 46, 102, 148f }}
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.6964{{c}}, ~15/14 = 131.8166{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.6964{{c}}, ~15/14 = 131.8166{{c}}
	: error map: {{val\| 0.000 +1.741 +9.136 -1.496 +20.562 }}		: error map: {{val\| 0.000 +1.741 +9.136 -1.496 +20.562 }}
	~~<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 705.978{{c}}, ~12/11 = 132.544{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 8d, 9, 10, 17c, 19, 27e, 63cee }} *		{{Optimal ET sequence\|legend=1\| 8d, 9, 10, 17c, 19, 27e, 63cee }} *
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	* WE: ~2 = 1197.6484{{c}}, ~3/2 = 704.6450{{c}}, ~14/13 = 132.1686{{c}}		* WE: ~2 = 1197.6484{{c}}, ~3/2 = 704.6450{{c}}, ~14/13 = 132.1686{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.1616{{c}}, ~14/13 = 131.8445{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.1616{{c}}, ~14/13 = 131.8445{{c}}
	~~<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 706.029{{c}}, ~14/13 = 132.428{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 8d, 9, 10, 17c, 19, 27e }} *		{{Optimal ET sequence\|legend=0\| 8d, 9, 10, 17c, 19, 27e }} *