Meansquared: Difference between revisions

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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]].

This temperament is [[meantone]] temperament with all intervals (including octaves) stretched by a factor of exactly ] 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 ([[EDO]]s), including ones without conventional meantone temperament (like the previously mentioned 6edo and 13edo). It has 4.9.25.49 subgroup extensions 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) stretched by a factor of exactly ] 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 ([[EDO]]s), including ones without conventional meantone temperament (like the previously mentioned 6edo and 13edo). It has 4.9.25.49 subgroup extensions corresponding to the extensions of meantone, including counterparts of [[septimal meantone]], [[dominant]], [[flattone]] and so on.

== Structure ==

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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]].
-This temperament is  [[meantone]] temperament with all intervals (including octaves) stretched by a factor of exactly ] 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 ([[EDO]]s), including ones without conventional meantone temperament (like the previously mentioned 6edo and 13edo). It has 4.9.25.49 subgroup extensions 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) stretched by a factor of exactly ] 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 ([[EDO]]s), including ones without conventional meantone temperament (like the previously mentioned 6edo and 13edo). It has 4.9.25.49 subgroup extensions corresponding to the extensions of meantone, including counterparts of [[septimal meantone]], [[dominant]], [[flattone]] and so on.
 == Structure ==