Meansquared - Revision history

FloraC: Collect non-octave temperaments in one category

2025-04-29T09:25:30Z

Collect non-octave temperaments in one category

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	[[Category:Meansquared\| ]] <!-- main article -->		[[Category:Meansquared\| ]] <!-- main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:~~Subgroup~~ temperaments]]		[[Category:Non-octave temperaments]]
	~~[[Category:Nonoctave]]~~
	~~[[Category:Ed4~~]]

FloraC: - parent category

2025-04-28T14:22:59Z

- parent category

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	<nowiki>*</nowiki> In 4.9.25 subgroup CTE tuning		<nowiki>*</nowiki> In 4.9.25 subgroup CTE tuning

	[[Category:~~Temperaments~~]]		[[Category:Meansquared\| ]] <!-- main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
			[[Category:Subgroup temperaments]]
	[[Category:Nonoctave]]		[[Category:Nonoctave]]
	[[Category:Ed4]]		[[Category:Ed4]]

Lériendil at 23:13, 19 April 2025

2025-04-19T23:13:47Z

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	[[Category:Temperaments]]		[[Category:Temperaments]]
			[[Category:Rank-2 temperaments]]
	[[Category:Nonoctave]]		[[Category:Nonoctave]]
	[[Category:Ed4]]		[[Category:Ed4]]

Bcmills at 18:58, 23 August 2024

2024-08-23T18:58:42Z

← Older revision		Revision as of 18:58, 23 August 2024
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	'''Meansquared''' is a [[nonoctave]] [[regular temperament]] repeating at [[4/1]] based on a chain of tempered [[9/4]] major ninths. It tempers out [[6561/6400]] (or [[81/80]]<sup>2</sup>) in the 4.9.25 subgroup. The name was first coined by [[User:CompactStar\|CompactStar]] in 2023. Meansquared in the 4.9.25 subgroup is an [[sane and insane temperaments\|insane]] restriction of 4.9.5 subgroup meantone, because it includes the interval of [[100/81]]~[[81/64]] which is effectively [[5/4]].		'''Meansquared''' is a [[nonoctave]] [[regular temperament]] repeating at [[4/1]] based on a chain of tempered [[9/4]] major ninths. It tempers out [[6561/6400]] (or [[81/80]]<sup>2</sup>) in the 4.9.25 subgroup. The name was first coined by [[User:CompactStar\|CompactStar]] in 2023. Meansquared in the 4.9.25 subgroup is an [[sane and insane temperaments\|insane]] restriction of 4.9.5 subgroup meantone, because it includes the interval of [[100/81]]~[[81/64]] which is effectively [[5/4]].

	This temperament is [[meantone]] temperament with all intervals (including octaves) squared. It follows that it generates the [[macrodiatonic and microdiatonic scales\|macrodiatonic]] scale [[5L 2s (4/1-equivalent)\|5L 2s&lang;4/1&rang;]] and the macrochromatic scale [[7L 5s (4/1-equivalent)\|7L 5s &lang;4/1&rang;]] (a very xenharmonic variety of [[detempering\|detempered]] whole tone scale). It also follows that the [[Ed4]]s which [[support]] meansquared have the same number of tones as the [[EDO]]s which support [[meantone]]: [[7ed4]], 12ed4 ([[6edo]]), [[19ed4]], 26ed4 ([[13edo]]), [[31ed4]] and so on. Meansquared is supported by both nonoctave odd Ed4s and even Ed4s (EDOs), including ones without conventional meantone temperament (like the previously mentioned 6edo and 13edo). It has [[extension]]s in the 4.9.25.49 subgroup and beyond corresponding to the extensions of meantone, including counterparts of [[septimal meantone]], [[dominant]], [[flattone]] and so on.		This temperament is [[meantone]] temperament with all intervals (including octaves) squared. It follows that it generates the [[macrodiatonic and microdiatonic scales\|macrodiatonic]] scale [[5L 2s (4/1-equivalent)\|5L 2s&lang;4/1&rang;]] and the macrochromatic scale [[7L 5s (4/1-equivalent)\|7L 5s &lang;4/1&rang;]] (a very xenharmonic variety of [[detempering\|detempered]] whole tone scale). It also follows that the [[Ed4]]s which [[support]] meansquared have the same number of tones as the [[EDO]]s which support [[meantone]]: [[7ed4]], 12ed4 ([[6edo]]), [[19ed4]], 26ed4 ([[13edo]]), [[31ed4]] and so on. Meansquared is supported by both nonoctave odd Ed4s and even Ed4s (EDOs), including ones without conventional meantone temperament (like the previously mentioned 6edo and 13edo). It has [[extension]]s in the 4.9.25.49 subgroup and beyond corresponding to the extensions of meantone, including counterparts of [[septimal meantone]], [[dominant (temperament)\|dominant]], [[flattone]] and so on.

	Meansquared has the same structure, MOSes and interval chain as meantone temperament, but with every interval squared, which stretches them out so much that they are in completely different size categories. The perfect fifth becomes a major ninth ([[9/4]]), the major third becomes an augmented fifth ([[25/16]]), and the minor third becomes a diminished fifth ([[36/25]]). The two [[tritone]] intervals are stretched out to compressed and stretched pseudo-octaves, but these are pulled closer to major sevenths and minor ninths in the [[flattone]] equivalents, while in [[6edo]] these two are conflated with each other to produce the pure [[2/1\|octave]], like how in 12edo the tritones are conflated to produce the [[2edo]] tritone. In flatter tunings like [[19ed4]] and [[31ed4]], this system is very xenharmonic with it lacking single octaves, and the stretched versions of the standard 5-limit major and minor chords (1-[[25/16]]-[[9/4]] and 1-[[36/25]]-[[9/4]] respectively) are also exotic and tense-sounding. However, the 12-tone MOS is resemblant in many ways to the familiar 6edo or whole tone scale, being a detempered version of it, and it gets closer and closer to it with a more and more accurate pseudo-octave as L and s become more similar.		Meansquared has the same structure, MOSes and interval chain as meantone temperament, but with every interval squared, which stretches them out so much that they are in completely different size categories. The perfect fifth becomes a major ninth ([[9/4]]), the major third becomes an augmented fifth ([[25/16]]), and the minor third becomes a diminished fifth ([[36/25]]). The two [[tritone]] intervals are stretched out to compressed and stretched pseudo-octaves, but these are pulled closer to major sevenths and minor ninths in the [[flattone]] equivalents, while in [[6edo]] these two are conflated with each other to produce the pure [[2/1\|octave]], like how in 12edo the tritones are conflated to produce the [[2edo]] tritone. In flatter tunings like [[19ed4]] and [[31ed4]], this system is very xenharmonic with it lacking single octaves, and the stretched versions of the standard 5-limit major and minor chords (1-[[25/16]]-[[9/4]] and 1-[[36/25]]-[[9/4]] respectively) are also exotic and tense-sounding. However, the 12-tone MOS is resemblant in many ways to the familiar 6edo or whole tone scale, being a detempered version of it, and it gets closer and closer to it with a more and more accurate pseudo-octave as L and s become more similar.

CompactStar at 03:28, 13 March 2024

2024-03-13T03:28:42Z

← Older revision		Revision as of 03:28, 13 March 2024
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	This temperament is [[meantone]] temperament with all intervals (including octaves) squared. It follows that it generates the [[macrodiatonic and microdiatonic scales\|macrodiatonic]] scale [[5L 2s (4/1-equivalent)\|5L 2s&lang;4/1&rang;]] and the macrochromatic scale [[7L 5s (4/1-equivalent)\|7L 5s &lang;4/1&rang;]] (a very xenharmonic variety of [[detempering\|detempered]] whole tone scale). It also follows that the [[Ed4]]s which [[support]] meansquared have the same number of tones as the [[EDO]]s which support [[meantone]]: [[7ed4]], 12ed4 ([[6edo]]), [[19ed4]], 26ed4 ([[13edo]]), [[31ed4]] and so on. Meansquared is supported by both nonoctave odd Ed4s and even Ed4s (EDOs), including ones without conventional meantone temperament (like the previously mentioned 6edo and 13edo). It has [[extension]]s in the 4.9.25.49 subgroup and beyond corresponding to the extensions of meantone, including counterparts of [[septimal meantone]], [[dominant]], [[flattone]] and so on.		This temperament is [[meantone]] temperament with all intervals (including octaves) squared. It follows that it generates the [[macrodiatonic and microdiatonic scales\|macrodiatonic]] scale [[5L 2s (4/1-equivalent)\|5L 2s&lang;4/1&rang;]] and the macrochromatic scale [[7L 5s (4/1-equivalent)\|7L 5s &lang;4/1&rang;]] (a very xenharmonic variety of [[detempering\|detempered]] whole tone scale). It also follows that the [[Ed4]]s which [[support]] meansquared have the same number of tones as the [[EDO]]s which support [[meantone]]: [[7ed4]], 12ed4 ([[6edo]]), [[19ed4]], 26ed4 ([[13edo]]), [[31ed4]] and so on. Meansquared is supported by both nonoctave odd Ed4s and even Ed4s (EDOs), including ones without conventional meantone temperament (like the previously mentioned 6edo and 13edo). It has [[extension]]s in the 4.9.25.49 subgroup and beyond corresponding to the extensions of meantone, including counterparts of [[septimal meantone]], [[dominant]], [[flattone]] and so on.

	Meansquared has the same structure, MOSes and interval chain as meantone temperament, but with every interval squared, which stretches them out so much that they are in completely different size categories. The perfect fifth becomes a major ninth ([[9/4]]), the major third becomes an augmented fifth ([[25/16]]), and the minor third becomes a diminished fifth ([[36/25]]). The two [[tritone]] intervals are stretched out to compressed and stretched pseudo-octaves, but these are pulled closer to major sevenths and minor ninths in the [[flattone]] equivalents, while in [[6edo]] these two are conflated with each other to produce the pure [[2/1\|octave]], like how in 12edo the tritones are conflated to produce the [[2edo]] tritone. In flatter tunings like [[19ed4]] and [[31ed4]], this system is very xenharmonic with it lacking single octaves, and the stretched versions of the standard 5-limit major and minor chords (1-[[25/16]]-[[9/4]] and 1-[[36/25]]-[[9/4]] respectively) are also exotic and tense-sounding. However, the 12-tone MOS is resemblant in many ways to the familiar 6edo or whole tone scale , being a detempered version of it, and it gets closer and closer to it with a more and more accurate pseudo-octave as L and s become more similar.		Meansquared has the same structure, MOSes and interval chain as meantone temperament, but with every interval squared, which stretches them out so much that they are in completely different size categories. The perfect fifth becomes a major ninth ([[9/4]]), the major third becomes an augmented fifth ([[25/16]]), and the minor third becomes a diminished fifth ([[36/25]]). The two [[tritone]] intervals are stretched out to compressed and stretched pseudo-octaves, but these are pulled closer to major sevenths and minor ninths in the [[flattone]] equivalents, while in [[6edo]] these two are conflated with each other to produce the pure [[2/1\|octave]], like how in 12edo the tritones are conflated to produce the [[2edo]] tritone. In flatter tunings like [[19ed4]] and [[31ed4]], this system is very xenharmonic with it lacking single octaves, and the stretched versions of the standard 5-limit major and minor chords (1-[[25/16]]-[[9/4]] and 1-[[36/25]]-[[9/4]] respectively) are also exotic and tense-sounding. However, the 12-tone MOS is resemblant in many ways to the familiar 6edo or whole tone scale, being a detempered version of it, and it gets closer and closer to it with a more and more accurate pseudo-octave as L and s become more similar.

	== Interval chain ==		== Interval chain ==

CompactStar at 03:28, 13 March 2024

2024-03-13T03:28:34Z

← Older revision		Revision as of 03:28, 13 March 2024
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	This temperament is [[meantone]] temperament with all intervals (including octaves) squared. It follows that it generates the [[macrodiatonic and microdiatonic scales\|macrodiatonic]] scale [[5L 2s (4/1-equivalent)\|5L 2s&lang;4/1&rang;]] and the macrochromatic scale [[7L 5s (4/1-equivalent)\|7L 5s &lang;4/1&rang;]] (a very xenharmonic variety of [[detempering\|detempered]] whole tone scale). It also follows that the [[Ed4]]s which [[support]] meansquared have the same number of tones as the [[EDO]]s which support [[meantone]]: [[7ed4]], 12ed4 ([[6edo]]), [[19ed4]], 26ed4 ([[13edo]]), [[31ed4]] and so on. Meansquared is supported by both nonoctave odd Ed4s and even Ed4s (EDOs), including ones without conventional meantone temperament (like the previously mentioned 6edo and 13edo). It has [[extension]]s in the 4.9.25.49 subgroup and beyond corresponding to the extensions of meantone, including counterparts of [[septimal meantone]], [[dominant]], [[flattone]] and so on.		This temperament is [[meantone]] temperament with all intervals (including octaves) squared. It follows that it generates the [[macrodiatonic and microdiatonic scales\|macrodiatonic]] scale [[5L 2s (4/1-equivalent)\|5L 2s&lang;4/1&rang;]] and the macrochromatic scale [[7L 5s (4/1-equivalent)\|7L 5s &lang;4/1&rang;]] (a very xenharmonic variety of [[detempering\|detempered]] whole tone scale). It also follows that the [[Ed4]]s which [[support]] meansquared have the same number of tones as the [[EDO]]s which support [[meantone]]: [[7ed4]], 12ed4 ([[6edo]]), [[19ed4]], 26ed4 ([[13edo]]), [[31ed4]] and so on. Meansquared is supported by both nonoctave odd Ed4s and even Ed4s (EDOs), including ones without conventional meantone temperament (like the previously mentioned 6edo and 13edo). It has [[extension]]s in the 4.9.25.49 subgroup and beyond corresponding to the extensions of meantone, including counterparts of [[septimal meantone]], [[dominant]], [[flattone]] and so on.

	Meansquared has the same structure, MOSes and interval chain as meantone temperament, but with every interval squared, which stretches them out so much that they are in completely different size categories. The perfect fifth becomes a major ninth ([[9/4]]), the major third becomes an augmented fifth ([[25/16]]), and the minor third becomes a diminished fifth ([[36/25]]). The two [[tritone]] intervals are stretched out to compressed and stretched pseudo-octaves, but these are pulled closer to major sevenths and minor ninths in the [[flattone]] equivalents, while in [[6edo]] these two are conflated with each other to produce the pure [[2/1\|octave]], like how in 12edo the tritones are conflated to produce the [[2edo]] tritone. In flatter tunings like [[19ed4]] and [[31ed4]], this system is very xenharmonic with it lacking single octaves, and the stretched versions of the standard 5-limit major and minor chords (1-[[25/16]]-[[9/4]] and 1-[[36/25]]-[[9/4]] respectively) are also exotic and tense-sounding. However, the 12-tone MOS is resemblant in many ways to the familiar 6edo or whole tone scale (being a detempered version of it), and it gets closer and closer to it with a more and more accurate pseudo-octave as L and s become more similar.		Meansquared has the same structure, MOSes and interval chain as meantone temperament, but with every interval squared, which stretches them out so much that they are in completely different size categories. The perfect fifth becomes a major ninth ([[9/4]]), the major third becomes an augmented fifth ([[25/16]]), and the minor third becomes a diminished fifth ([[36/25]]). The two [[tritone]] intervals are stretched out to compressed and stretched pseudo-octaves, but these are pulled closer to major sevenths and minor ninths in the [[flattone]] equivalents, while in [[6edo]] these two are conflated with each other to produce the pure [[2/1\|octave]], like how in 12edo the tritones are conflated to produce the [[2edo]] tritone. In flatter tunings like [[19ed4]] and [[31ed4]], this system is very xenharmonic with it lacking single octaves, and the stretched versions of the standard 5-limit major and minor chords (1-[[25/16]]-[[9/4]] and 1-[[36/25]]-[[9/4]] respectively) are also exotic and tense-sounding. However, the 12-tone MOS is resemblant in many ways to the familiar 6edo or whole tone scale , being a detempered version of it, and it gets closer and closer to it with a more and more accurate pseudo-octave as L and s become more similar.

	== Interval chain ==		== Interval chain ==

CompactStar: /* Interval chain */

2024-03-13T03:27:23Z

Interval chain

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	\| 1		\| 1
	\| 1394.429		\| 1394.429
	\| [[9/4]]		\| [[9/4]], ([[20/9]])
	\|-		\|-
	\| 2		\| 2

CompactStar at 03:27, 13 March 2024

2024-03-13T03:27:03Z

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	\| 2		\| 2
	\| 388.858		\| 388.858
	\| [[81/64]], [[100/81]]		\| ([[5/4]]), [[81/64]], [[100/81]]
	\|-		\|-
	\| 3		\| 3

CompactStar at 03:26, 13 March 2024

2024-03-13T03:26:04Z

← Older revision		Revision as of 03:26, 13 March 2024
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	\|}		\|}

	* In 4.9.25 subgroup CTE tuning		<nowiki>*</nowiki> In 4.9.25 subgroup CTE tuning

	[[Category:Temperaments]]		[[Category:Temperaments]]
			[[Category:Nonoctave]]
			[[Category:Ed4]]

CompactStar at 03:25, 13 March 2024

2024-03-13T03:25:45Z

@@ Line 3: / Line 3: @@
 This temperament is  [[meantone]] temperament with all intervals (including octaves) squared. It follows that it generates the [[macrodiatonic and microdiatonic scales|macrodiatonic]] scale [[5L 2s (4/1-equivalent)|5L 2s&lang;4/1&rang;]] and the macrochromatic scale [[7L 5s (4/1-equivalent)|7L 5s &lang;4/1&rang;]] (a very xenharmonic variety of [[detempering|detempered]] whole tone scale). It also follows that the [[Ed4]]s which [[support]] meansquared have the same number of tones as the [[EDO]]s which support [[meantone]]: [[7ed4]], 12ed4 ([[6edo]]), [[19ed4]], 26ed4 ([[13edo]]), [[31ed4]] and so on. Meansquared is supported by both nonoctave odd Ed4s and even Ed4s (EDOs), including ones without conventional meantone temperament (like the previously mentioned 6edo and 13edo). It has [[extension]]s in the 4.9.25.49 subgroup and beyond corresponding to the extensions of meantone, including counterparts of [[septimal meantone]], [[dominant]], [[flattone]] and so on.
 Meansquared has the same structure, MOSes and interval chain as meantone temperament, but with every interval squared, which stretches them out so much that they are in completely different size categories. The perfect fifth becomes a major ninth ([[9/4]]), the major third becomes an augmented fifth ([[25/16]]), and the minor third becomes a diminished fifth ([[36/25]]). The two [[tritone]] intervals are stretched out to compressed and stretched pseudo-octaves, but these are pulled closer to major sevenths and minor ninths in the [[flattone]] equivalents, while in [[6edo]] these two are conflated with each other to produce the pure [[2/1|octave]], like how in 12edo the tritones are conflated to produce the [[2edo]] tritone. In flatter tunings like [[19ed4]] and [[31ed4]], this system is very xenharmonic with it lacking single octaves, and the stretched versions of the standard 5-limit major and minor chords (1-[[25/16]]-[[9/4]] and 1-[[36/25]]-[[9/4]] respectively) are also exotic and tense-sounding. However, the 12-tone MOS is resemblant in many ways to the familiar 6edo or whole tone scale (being a detempered version of it), and it gets closer and closer to it with a more and more accurate pseudo-octave as L and s become more similar.
 [[Category:Temperaments]]