Sensamagic family - Revision history

FloraC: Expand

2026-04-11T10:14:04Z

Expand

← Older revision		Revision as of 10:14, 11 April 2026
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	=== Overview to extensions ===		=== Overview to extensions ===
	Temperaments discussed elsewhere include [[supernatural]] (→ [[Keemic family #Supernatural\|Keemic family]]) and [[sensigh]] (→ [[Sengic family #Sensigh\|Sengic family]]). ~~Considered~~ below ~~are undecimal sensamagic, sensawer, octarod, shrusus, and bisector~~.		The second comma in the comma list defines which [[11-limit]] family member we are looking at. Undecimal sensamagic adds [[385/384]], sensawer adds [[441/440]], octarod adds [[100/99]], shrusus adds [[176/175]]. These temperaments use the same generators as sensamagic. Bisector adds [[121/120]] with a half-octave period.

			Temperaments discussed elsewhere include [[supernatural]] (→ [[Keemic family #Supernatural\|Keemic family]]) and [[sensigh]] (→ [[Sengic family #Sensigh\|Sengic family]]). The rest are considered below.

	== Undecimal sensamagic ==		== Undecimal sensamagic ==

FloraC: Move sensigh to sengic family

2026-04-11T10:05:53Z

Move sensigh to sengic family

@@ Line 54: / Line 54: @@
 === Overview to extensions ===
-Temperaments discussed elsewhere include [[supernatural]] (→ [[Keemic family #Supernatural|Keemic family]]). Considered below are undecimal sensamagic, sensawer, octarod, shrusus, bisector and sensigh.
+Temperaments discussed elsewhere include [[supernatural]] (→ [[Keemic family #Supernatural|Keemic family]]) and [[sensigh]] (→ [[Sengic family #Sensigh|Sengic family]]). Considered below are undecimal sensamagic, sensawer, octarod, shrusus, and bisector.
 == Undecimal sensamagic ==
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 [[Badness]] (Sintel): 1.31
 [[Category:Temperament families]]
 [[Category:Sensamagic family| ]] <!-- main article -->
 [[Category:Rank 3]]

Overthink: /* Octarod */ asterisk, caps

2026-02-14T04:50:59Z

Octarod: asterisk, caps

← Older revision		Revision as of 04:50, 14 February 2026
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	: error map: {{val\| 0.000 +2.570 -3.230 +0.944 +5.801 }}		: error map: {{val\| 0.000 +2.570 -3.230 +0.944 +5.801 }}

	{{Optimal ET sequence\|legend=1\| 14c, 19, 22, 27e, 41, 90e, 131e }} *		{{Optimal ET sequence\|legend=1\| 14c, 19, 22, 27e, 41, 90e, 131e}}*

	<nowiki/>[[~~optimal~~ patent val]]: [[104edo\|104]]		<nowiki/>*[[Optimal patent val]]: [[104edo\|104]]

	[[Badness]] (Sintel): 0.698		[[Badness]] (Sintel): 0.698

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

2025-11-27T12:22:58Z

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

← Older revision		Revision as of 12:22, 27 November 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Sensamagic family\| ]] <!-- main article -->		[[Category:Sensamagic family\| ]] <!-- main article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

FloraC: - redundant category

2025-11-26T17:02:00Z

- 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:Sensamagic family\| ]] <!-- main article -->		[[Category:Sensamagic family\| ]] <!-- main article -->
	~~[[Category:Sensamagic\| ]] <!-- key article -->~~
	[[Category:Rank 3]]		[[Category:Rank 3]]

FloraC: Note some good tunings

2025-11-09T11:52:06Z

Note some good tunings

← Older revision		Revision as of 11:52, 9 November 2025
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	{{Main\| Sensamagic }}		{{Main\| Sensamagic }}

	Sensamagic is generated by a perfect fifth and a wide supermajor third of ~[[9/7]], two of which make ~[[5/3]].		Sensamagic is generated by a perfect fifth and a wide supermajor third of ~[[9/7]], two of which make ~[[5/3]]. Among the good edo tunings are [[87edo]] and [[128edo]], as well as the [[optimal patent val]] [[283edo]].

	A notable tuning ~~of sensamagic~~ is given by [[TE]], [[CTE]] and [[POTE]], all coinciding at 703.7424{{c}}, 440.9020{{c}} with pure octaves since prime 2 is not involved in the comma to begin with.		Another notable tuning is given by [[TE]], [[CTE]] and [[POTE]], all coinciding at 703.7424{{c}}, 440.9020{{c}} with pure octaves since prime 2 is not involved in the comma to begin with, though its difference from [[CWE]] is practically unnoticeable.

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

Lériendil: /* Octarod */

2025-10-11T18:36:22Z

Octarod

← Older revision		Revision as of 18:36, 11 October 2025
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	== Octarod ==		== Octarod ==
	Octarod tempers out 100/99 and the interval class of [[11/1\|11]] is found as a stack of four ~9/7's. The name ''octarod'' was the former name of the sensamagic comma before being ~~used~~ for this 11-limit extension, and comes from [[octacot]] and [[rodan]]; it should be noted however that rodan does not temper out 100/99 and therefore does not support this temperament.		Octarod tempers out [[100/99]] and the interval class of [[11/1\|11]] is found as a stack of four ~9/7's. The name ''octarod'' was the former name of the sensamagic comma before being reused for this 11-limit extension, and comes from [[octacot]] and [[rodan]]; it should be noted however that rodan does not temper out 100/99 and therefore does not support this temperament.

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

Lériendil: /* Octarod */

2025-10-11T18:28:13Z

Octarod

← Older revision		Revision as of 18:28, 11 October 2025
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	== Octarod ==		== Octarod ==
	Octarod tempers out 100/99 and the interval class of [[11/1\|11]] is found as a stack of four ~9/7's. The name ''octarod'' ~~presumably~~ comes from [[octacot]] and [[rodan]]; it should be noted however that rodan does not temper out 100/99 and therefore does not support this temperament.		Octarod tempers out 100/99 and the interval class of [[11/1\|11]] is found as a stack of four ~9/7's. The name ''octarod'' was the former name of the sensamagic comma before being used for this 11-limit extension, and comes from [[octacot]] and [[rodan]]; it should be noted however that rodan does not temper out 100/99 and therefore does not support this temperament.

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

FloraC: /* Sensigh */ exists in the 11-limit too

2025-10-11T16:11:35Z

Sensigh: exists in the 11-limit too

← Older revision		Revision as of 16:11, 11 October 2025
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	== Sensigh ==		== Sensigh ==
			Sensigh uses the same mapping as 7-limit [[sensi]] with an independent generator for prime 11.

			[[Subgroup]]: 2.3.5.7.11

			[[Comma list]]: 126/125, 245/243

			{{Mapping\|legend=1\| 1 -1 -1 -2 3 \| 0 7 9 13 0 \| 0 0 0 0 1 }}
			: mapping generators: ~2, ~9/7, ~11

			[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1199.7081{{c}}, ~9/7 = 443.2748{{c}}, ~11/8 = 552.1736{{c}}
			: [[error map]]: {{val\| -0.2919 +1.2608 +3.4518 -5.6691 -0.0202 }}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~9/7 = 443.3493{{c}}, ~11/8 = 551.8069{{c}}
			: error map: {{val\| 0.0000 +1.4899 +3.8297 -5.2854 +0.4890 }}

			{{Optimal ET sequence\|legend=1\| 27e, 38df, 46, 111d }}

			[[Badness]] (Sintel): 1.48

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

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

	Mapping: {{mapping\| 1 ~~6 8 11~~ 0 10 \| 0 -7 -9 -13 0 -10 \| 0 0 0 0 1 0 }}		Mapping: {{mapping\| 1 -1 -1 -2 3 0 \| 0 7 9 13 0 10 \| 0 0 0 0 1 0 }}
	~~: mapping generators: ~2, ~9/7, ~11~~

	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 ~~6 8 11 0 10~~ 0 \| 0 -7 -9 -13 0 -10 1 \| 0 0 0 0 1 0 1 }}		Mapping: {{mapping\| 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: + intro to certain entries

2025-10-11T16:04:50Z

+ intro to certain entries

← Older revision		Revision as of 16:04, 11 October 2025
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	== Sensamagic ==		== Sensamagic ==
	{{Main\| Sensamagic }}		{{Main\| Sensamagic }}

			Sensamagic is generated by a perfect fifth and a wide supermajor third of ~[[9/7]], two of which make ~[[5/3]].

			A notable tuning of sensamagic is given by [[TE]], [[CTE]] and [[POTE]], all coinciding at 703.7424{{c}}, 440.9020{{c}} with pure octaves since prime 2 is not involved in the comma to begin with.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	* [[7-odd-limit]]		* [[7-odd-limit]]
	: {{monzo list\| 1 0 0 0 \| 0 0 1/5 2/5 \| 0 0 1 0 \| 0 0 0 1 }}		: {{monzo list\| 1 0 0 0 \| 0 0 1/5 2/5 \| 0 0 1 0 \| 0 0 0 1 }}
	: [[~~Eigenmonzo~~ basis\|unchanged-interval (eigenmonzo) basis]]: 2.5.7		: [[eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.5.7
	* [[9-odd-limit]]		* [[9-odd-limit]]
	: {{monzo list\| 1 0 0 0 \| 0 1 0 0 \| 0 5/3 2/3 -2/3 \| 0 5/3 -1/3 1/3 }}		: {{monzo list\| 1 0 0 0 \| 0 1 0 0 \| 0 5/3 2/3 -2/3 \| 0 5/3 -1/3 1/3 }}
	: [[~~Eigenmonzo~~ basis\|unchanged-interval (eigenmonzo) basis]]: 2.3.7/5		: [[eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.3.7/5

	{{Optimal ET sequence\|legend=1\| 5, 8d, 14c, 17, 19, 27, 41, 68, 87, 128, 196, 283 }}		{{Optimal ET sequence\|legend=1\| 5, 8d, 14c, 17, 19, 27, 41, 68, 87, 128, 196, 283 }}
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	== Undecimal sensamagic ==		== Undecimal sensamagic ==
	{{Main\| Sensamagic }}		{{Main\| Sensamagic }}

			Undecimal sensamagic tempers out not only [[385/384]], but [[896/891]], making itself a [[strong extension]] of [[parapyth]].

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11
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	: [[error map]]: {{val\| -0.033 +1.793 -0.755 -2.236 +0.048 }}		: [[error map]]: {{val\| -0.033 +1.793 -0.755 -2.236 +0.048 }}
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.7948{{c}}, ~9/7 = 440.9180{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.7948{{c}}, ~9/7 = 440.9180{{c}}
	: error map: {{val\| 0.000 +1.840 -0.683 -2.~~1554~~ +0.175 }}		: error map: {{val\| 0.000 +1.840 -0.683 -2.154 +0.175 }}

	[[Minimax tuning]]:		[[Minimax tuning]]:
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	== Octarod ==		== Octarod ==
			Octarod tempers out 100/99 and the interval class of [[11/1\|11]] is found as a stack of four ~9/7's. The name ''octarod'' presumably comes from [[octacot]] and [[rodan]]; it should be noted however that rodan does not temper out 100/99 and therefore does not support this temperament.

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11