Alphaxenic rank-3 clan - Revision history

FloraC: - duplicate data

2026-05-15T11:12:21Z

- duplicate data

@@ Line 4: / Line 4: @@
 Temperaments discussed elsewhere include:
 * ''[[Uniwiz]]'' (+385/384) → [[Keenanismic temperaments #Uniwiz|Keenanismic temperaments]]
+* ''[[Rabic]]'' (+243/242) → [[Rastmic rank-3 clan #Rabic|Rastmic rank-3 clan]]
 [[Category:Temperament clans]]
 [[Category:Alphaxenic rank-3 clan| ]] <!-- main article -->
 [[Category:Rank 3]]

FloraC: Switch to Sintel's badness, WE & CWE tunings. - redundant category

2026-05-15T11:00:33Z

Switch to Sintel's badness, WE & CWE tunings. - redundant category

← Older revision		Revision as of 11:00, 15 May 2026
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	{{Technical data page}}		{{Technical data page}}
	The '''alphaxenic rank-3 clan''' of [[temperament]]s [[tempering out\|tempers out]] the [[Alpharabian comma]], {{monzo\| -17 2 0 0 4 }} = 131769/131072. Both no-5 alphaxenic and no-7 alphaxenic can be the head of this clan~~, but we can begin with the rank-4 temperament~~.		The '''alphaxenic rank-3 clan''' of [[temperament]]s [[tempering out\|tempers out]] the [[Alpharabian comma]] ({{monzo\|legend=1\| -17 2 0 0 4 }}, [[ratio]]: 131769/131072). Both no-5 alphaxenic and no-7 alphaxenic can be the head of this clan.

	Temperaments discussed elsewhere include:		Temperaments discussed elsewhere include:
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	{{Mapping\|legend=1\| 2 1 0 0 8 \| 0 2 0 0 -1 \| 0 0 1 0 0 \| 0 0 0 1 0 }}		{{Mapping\|legend=1\| 2 1 0 0 8 \| 0 2 0 0 -1 \| 0 0 1 0 0 \| 0 0 0 1 0 }}

	: mapping generators: ~363/256, ~16/11, ~5, ~7		: mapping generators: ~363/256, ~16/11, ~5, ~7

	[[Optimal tuning]] ([[~~POTE~~]]): ~363/256 = ~~1\2~~, ~16/11 = 650.~~6784~~, ~5/4 = 385.~~5751~~, ~7/4 = ~~967~~.~~9328~~		[[Optimal tuning]]s:
			* [[WE]]: ~363/256 = 600.1590{{c}}, ~16/11 = 650.8508{{c}}, ~5/4 = 385.6773{{c}}, ~7/4 = 968.1894{{c}}
			: [[error map]]: {{val\| +0.318 -0.094 -0.000 -0.000 -0.897 }}
			* [[CWE]]: ~363/256 = 600.0000{{c}}, ~16/11 = 650.7321{{c}}, ~5/4 = 385.7900{{c}}, ~7/4 = 968.1927{{c}}
			: error map: {{val\| 0.000 -0.491 -0.524 -0.633 -2.050 }}

	{{Optimal ET sequence\|legend=1\| 22, 46, 68, 72, 118, 190, 212, 284, 330e, 402de, 498e, 544e, 616ee, 806dee, 828cee, 946cdeee, 1018cdeee }}		{{Optimal ET sequence\|legend=1\| 22, 46, 68, 72, 118, 190, 212, 284, 330e, 402de, 498e, 544e, 616ee, 806dee, 828cee, 946cdeee, 1018cdeee }}

	[[Badness]]: 1.~~26 × 10<sup>-6</sup>~~		[[Badness]] (Sintel): 23.0

	== Rabic ==		== Rabic ==
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	{{Mapping\|legend=1\| 24 38 0 0 83 \| 0 0 1 0 0 \| 0 0 0 1 0 }}		{{Mapping\|legend=1\| 24 38 0 0 83 \| 0 0 1 0 0 \| 0 0 0 1 0 }}

	: mapping generators: ~33/32, ~5, ~7		: mapping generators: ~33/32, ~5, ~7

	[[Optimal tuning]] ([[~~POTE~~]]): ~33/32 = 1~~\24~~, ~5/4 = 385.0647, ~7/4 = 967.3158		[[Optimal tuning]]s:
			* [[WE]]: ~33/32 = 50.0220{{c}}, ~5/4 = 385.0647{{c}}, ~7/4 = 967.3158{{c}}
			: [[error map]]: {{val\| +0.538 -1.104 -0.002 -0.002 +0.541 }}
			* [[CWE]]: ~33/32 = 50.0000{{c}}, ~5/4 = 385.0647{{c}}, ~7/4 = 967.3158{{c}}
			: error map: {{val\| 0.000 -1.955 -0.937 -1.133 -1.318 }}

	{{Optimal ET sequence\|legend=1\| 24, 48, 72, 264, 336b, 408b, 480bcde }}		{{Optimal ET sequence\|legend=1\| 24, 48(d), 72, 264, 336b, 408b, 480bcde }}

	[[Badness]]: 6.~~07 × 10<sup>-3</sup>~~		[[Badness]] (Sintel): 7.30

	[[Category:Temperament clans]]		[[Category:Temperament clans]]
	[[Category:Alphaxenic rank-3 clan\| ]] <!-- main article -->		[[Category:Alphaxenic rank-3 clan\| ]] <!-- main article -->
	~~[[Category:Alphaxenic\| ]] <!-- key article -->~~
	[[Category:Rank 3]]		[[Category:Rank 3]]

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

2025-11-27T12:31:03Z

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

← Older revision		Revision as of 12:31, 27 November 2025
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	[[Category:Temperament clans]]		[[Category:Temperament clans]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Alphaxenic rank-3 clan\| ]] <!-- main article -->		[[Category:Alphaxenic rank-3 clan\| ]] <!-- main article -->
	[[Category:Alphaxenic\| ]] <!-- key article -->		[[Category:Alphaxenic\| ]] <!-- key article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

FloraC: FloraC moved page Alphaxenic rank three clan to Alphaxenic rank-3 clan: For obvious reasons

2025-08-27T12:50:07Z

FloraC moved page Alphaxenic rank three clan to Alphaxenic rank-3 clan: For obvious reasons

← Older revision	Revision as of 12:50, 27 August 2025
(No difference)

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

2025-06-24T00:31:42Z

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

← Older revision		Revision as of 00:31, 24 June 2025
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	[[Category:Temperament clans]]		[[Category:Temperament clans]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Alphaxenic rank-3 clan\| ]] <!-- main article -->		[[Category:Alphaxenic rank-3 clan\| ]] <!-- main article -->
	[[Category:Alphaxenic\| ]] <!-- key article -->		[[Category:Alphaxenic\| ]] <!-- key article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

VectorGraphics at 04:50, 12 June 2025

2025-06-12T04:50:44Z

← Older revision		Revision as of 04:50, 12 June 2025
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	: mapping generators: ~33/32, ~5, ~7		: mapping generators: ~33/32, ~5, ~7

	~~{{Multival\|legend=1\|rank=3\| 0 0 0 24 0 0 38 0 0 83 }}~~

	[[Optimal tuning]] ([[POTE]]): ~33/32 = 1\24, ~5/4 = 385.0647, ~7/4 = 967.3158		[[Optimal tuning]] ([[POTE]]): ~33/32 = 1\24, ~5/4 = 385.0647, ~7/4 = 967.3158

BudjarnLambeth: {{Technical data page}}

2025-04-13T14:24:25Z

← Older revision		Revision as of 14:24, 13 April 2025
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			{{Technical data page}}
	The '''alphaxenic rank-3 clan''' of [[temperament]]s [[tempering out\|tempers out]] the [[Alpharabian comma]], {{monzo\| -17 2 0 0 4 }} = 131769/131072. Both no-5 alphaxenic and no-7 alphaxenic can be the head of this clan, but we can begin with the rank-4 temperament.		The '''alphaxenic rank-3 clan''' of [[temperament]]s [[tempering out\|tempers out]] the [[Alpharabian comma]], {{monzo\| -17 2 0 0 4 }} = 131769/131072. Both no-5 alphaxenic and no-7 alphaxenic can be the head of this clan, but we can begin with the rank-4 temperament.

FloraC: Update keys

2023-09-14T08:16:12Z

Update keys

← Older revision		Revision as of 08:16, 14 September 2023
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	The '''alphaxenic rank-3 clan''' of ~~temperaments~~ tempers out the [[Alpharabian comma]], {{monzo\| -17 2 0 0 4 }} = 131769/131072. Both no-5 alphaxenic and no-7 alphaxenic can be the head of this clan, but we can begin with the rank-4 temperament.		The '''alphaxenic rank-3 clan''' of [[temperament]]s [[tempering out\|tempers out]] the [[Alpharabian comma]], {{monzo\| -17 2 0 0 4 }} = 131769/131072. Both no-5 alphaxenic and no-7 alphaxenic can be the head of this clan, but we can begin with the rank-4 temperament.

	Temperaments discussed elsewhere include:		Temperaments discussed elsewhere include:
	* [[Uniwiz]] (+385/384) → [[Keenanismic temperaments #Uniwiz\|Keenanismic temperaments]]		* ''[[Uniwiz]]'' (+385/384) → [[Keenanismic temperaments #Uniwiz\|Keenanismic temperaments]]

	== Alphaxenic ==		== Alphaxenic ==
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	[[Comma list]]: 131769/131072		[[Comma list]]: 131769/131072

	~~[[Mapping]]: [~~{{~~val~~\| 2 1 0 0 8 ~~}}, {{val~~\| 0 2 0 0 -1 ~~}}, {{val~~\| 0 0 1 0 0 ~~}}, {{val~~\| 0 0 0 1 0 }}]		{{Mapping\|legend=1\| 2 1 0 0 8 \| 0 2 0 0 -1 \| 0 0 1 0 0 \| 0 0 0 1 0 }}

	: mapping generators: ~363/256, ~16/11, ~5, ~7		: mapping generators: ~363/256, ~16/11, ~5, ~7
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	[[Comma list]]: 243/242, 131769/131072		[[Comma list]]: 243/242, 131769/131072

	~~[[Mapping]]: [~~{{~~val~~\| 24 38 0 0 83 ~~}}, {{val~~\| 0 0 1 0 0 ~~}}, {{val~~\| 0 0 0 1 0 }}]		{{Mapping\|legend=1\| 24 38 0 0 83 \| 0 0 1 0 0 \| 0 0 0 1 0 }}

	: mapping generators: ~33/32, ~5, ~7		: mapping generators: ~33/32, ~5, ~7
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	[[Category:Temperament clans]]		[[Category:Temperament clans]]
	[[Category:Alphaxenic rank-3 clan\| ]] <!-- main article -->		[[Category:Alphaxenic rank-3 clan\| ]] <!-- main article -->
			[[Category:Alphaxenic\| ]] <!-- key article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

FloraC: Update

2023-06-17T06:43:43Z

Update

← Older revision		Revision as of 06:43, 17 June 2023
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	The '''~~alpharabian~~ rank-3 clan''' of temperaments tempers out the [[Alpharabian comma]], {{monzo\| -17 2 0 0 4 }} = 131769/131072. Both no-5 ~~alpharabian~~ and no-7 ~~alpharabian~~ can be the head of this clan, but we can begin with the rank-4 temperament.		The '''alphaxenic rank-3 clan''' of temperaments tempers out the [[Alpharabian comma]], {{monzo\| -17 2 0 0 4 }} = 131769/131072. Both no-5 alphaxenic and no-7 alphaxenic can be the head of this clan, but we can begin with the rank-4 temperament.

	Temperaments discussed elsewhere include:		Temperaments discussed elsewhere include:
	* [[Uniwiz]]~~, {~~385/384~~, 9801/9800}~~ → [[Keenanismic temperaments #Uniwiz\|Keenanismic temperaments]]		* [[Uniwiz]] (+385/384) → [[Keenanismic temperaments #Uniwiz\|Keenanismic temperaments]]

	== ~~Alpharabian~~ ==		== Alphaxenic ==
	~~: ''Not to be confused with~~ [[~~Alpharabian tuning~~]]~~.''~~		[[Subgroup]]: 2.3.5.7.11

	~~Subgroup~~: 2.3.5.7.11

	[[Comma list]]: 131769/131072		[[Comma list]]: 131769/131072
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	[[Mapping]]: [{{val\| 2 1 0 0 8 }}, {{val\| 0 2 0 0 -1 }}, {{val\| 0 0 1 0 0 }}, {{val\| 0 0 0 1 0 }}]		[[Mapping]]: [{{val\| 2 1 0 0 8 }}, {{val\| 0 2 0 0 -1 }}, {{val\| 0 0 1 0 0 }}, {{val\| 0 0 0 1 0 }}]

	~~Mapping~~ generators: ~363/256, ~16/11, ~5, ~7		: mapping generators: ~363/256, ~16/11, ~5, ~7

	[[POTE ~~generator~~]]s: ~16/11 = 650.6784, ~5/4 = 385.5751, ~7/4 = 967.9328		[[Optimal tuning]] ([[POTE]]): ~363/256 = 1\2, ~16/11 = 650.6784, ~5/4 = 385.5751, ~7/4 = 967.9328

	{{Optimal ET sequence\|legend=1\| 22, 46, 68, 72, 118, 190, 212, 284, 330e, 402de, 498e, 544e, 616ee, 806dee, 828cee, 946cdeee, 1018cdeee }}		{{Optimal ET sequence\|legend=1\| 22, 46, 68, 72, 118, 190, 212, 284, 330e, 402de, 498e, 544e, 616ee, 806dee, 828cee, 946cdeee, 1018cdeee }}
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	== Rabic ==		== Rabic ==
	Whenever the [[rastma]] is added to the list of commas tempered out among ~~Alpharabian~~ temperaments, you end up with ~~Rabic~~, which splits the octave into 24 equal parts. This temperament is named as such because tempering out both the Alpharabian comma and the rastma automatically tempers out the [[Betarabian comma]].		Whenever the [[rastma]] is added to the list of commas tempered out among alphaxenic temperaments, you end up with rabic, which splits the octave into 24 equal parts. This temperament is named as such because tempering out both the Alpharabian comma and the rastma automatically tempers out the [[Betarabian comma]].

	Subgroup: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

	[[Comma list]]: 243/242, 131769/131072		[[Comma list]]: 243/242, 131769/131072
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	[[Mapping]]: [{{val\| 24 38 0 0 83 }}, {{val\| 0 0 1 0 0 }}, {{val\| 0 0 0 1 0 }}]		[[Mapping]]: [{{val\| 24 38 0 0 83 }}, {{val\| 0 0 1 0 0 }}, {{val\| 0 0 0 1 0 }}]

	~~Mapping~~ generators: ~33/32, ~5, ~7		: mapping generators: ~33/32, ~5, ~7

	{{Multival\|legend=1\|rank=3\| 0 0 0 24 0 0 38 0 0 83 }}		{{Multival\|legend=1\|rank=3\| 0 0 0 24 0 0 38 0 0 83 }}

	[[POTE ~~generator~~]]s: ~5/4 = 385.0647, ~7/4 = 967.3158		[[Optimal tuning]] ([[POTE]]): ~33/32 = 1\24, ~5/4 = 385.0647, ~7/4 = 967.3158

	{{Optimal ET sequence\|legend=1\| 24, 48, 72, 264, 336b, 408b, 480bcde }}		{{Optimal ET sequence\|legend=1\| 24, 48, 72, 264, 336b, 408b, 480bcde }}
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	[[Category:Temperament clans]]		[[Category:Temperament clans]]
	[[Category:~~Alpharabian~~ rank-3 clan\| ]] <!-- main article -->		[[Category:Alphaxenic rank-3 clan\| ]] <!-- main article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

FloraC: FloraC moved page Alpharabian rank three clan to Alphaxenic rank three clan: We agreed the corresponding temperament of the Alpharabian comma shouldn't be "alpharabian"

2023-06-17T06:40:13Z

FloraC moved page Alpharabian rank three clan to Alphaxenic rank three clan: We agreed the corresponding temperament of the Alpharabian comma shouldn't be "alpharabian"

← Older revision	Revision as of 06:40, 17 June 2023
(No difference)