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. This temperament is the precise logarithmic stretching of [[meantone]] temperament by a factor of 2, and it follows that it is assosicated with the [[macrodiatonic and microdiatonic scales|macrodiatonic]] scale [[5L 2s (4/1-equivalent)|5L 2s<4/1>]]~~. The name was first coined by~~ [[~~User:CompactStar~~|~~CompactStar~~]]. ~~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 the precise logarithmic stretching of [[meantone]] temperament by a factor of 2, and it follows that it is assosicated with the [[macrodiatonic and microdiatonic scales|macrodiatonic]] scale [[5L 2s (4/1-equivalent)|5L 2s&lang;4/1&rang;]] and the more melodically usable macrochromatic scale [[7L 5s (4/1-equivalent)|7L 5s &lang;4/1&rang;]]. It also follows that the [[Ed4]]s which [[support]] meansquad have the same number of tones as the [[EDO]]s which support [[meantone]] – [[7ed4]], 12ed4 ([[6edo]]), [[19ed4]], 26ed4 ([[13edo]]), [[31ed4]] and so on.

Meansquared has a nearly identical structure to meantone temperament, but it sounds very much unrecognizable and xenharmonic, due to the extreme stretching involved and the lack of octaves. The 5-limit major and minor triads are stretched out into the macro-major triad (16:25:36) and macro-minor triad (100:144:225). Both of these have a somewhat minor-like sound, with the [[25/16]] coming off as a subminor sixth.

[[Category:Temperaments]]

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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. This temperament is the precise logarithmic stretching of [[meantone]] temperament by a factor of 2, and it follows that it is assosicated with the [[macrodiatonic and microdiatonic scales|macrodiatonic]] scale [[5L 2s (4/1-equivalent)|5L 2s<4/1>]]. The name was first coined by [[User:CompactStar|CompactStar]].  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 the precise logarithmic stretching of [[meantone]] temperament by a factor of 2, and it follows that it is assosicated with the [[macrodiatonic and microdiatonic scales|macrodiatonic]] scale [[5L 2s (4/1-equivalent)|5L 2s&lang;4/1&rang;]] and the more melodically usable macrochromatic scale [[7L 5s (4/1-equivalent)|7L 5s &lang;4/1&rang;]]. It also follows that the [[Ed4]]s which [[support]] meansquad have the same number of tones as the [[EDO]]s which support [[meantone]] – [[7ed4]], 12ed4 ([[6edo]]), [[19ed4]], 26ed4 ([[13edo]]), [[31ed4]] and so on.
+Meansquared has a nearly identical structure to meantone temperament, but it sounds very much unrecognizable and xenharmonic, due to the extreme stretching involved and the lack of octaves. The 5-limit major and minor triads are stretched out into the macro-major triad (16:25:36) and macro-minor triad (100:144:225). Both of these have a somewhat minor-like sound, with the [[25/16]] coming off as a subminor sixth.
 [[Category:Temperaments]]