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 ~~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.

This temperament is [[meantone]] temperament with all intervals (including octaves) stretched by a stretch factor of exactly 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;]], which constitutes a very xenharmnoic nvariety of [[detempered]] whole tone scale. It also follows that the [[Ed4]]s which [[support]] meanquad have the same number of tones as the [[EDO]]s which support [[meantone]] – [[7ed4]], 12ed4 ([[6edo]]), [[19ed4]], 26ed4 ([[13edo]]), [[31ed4]] and so on. Meanquad is supported by [[EDO]] systems (like the previously mentioned 6edo and 13edo) ilke how meantonecan be used in even EDOs. 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.

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.~~

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.

[[Category:Temperaments]]

[[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. 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.
+This temperament is  [[meantone]] temperament with all intervals (including octaves) stretched by a stretch factor of exactly 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;]], which constitutes a very xenharmnoic nvariety of [[detempered]] whole tone scale. It also follows that the [[Ed4]]s which [[support]] meanquad have the same number of tones as the [[EDO]]s which support [[meantone]] – [[7ed4]], 12ed4 ([[6edo]]), [[19ed4]], 26ed4 ([[13edo]]), [[31ed4]] and so on. Meanquad is supported by [[EDO]] systems (like the previously mentioned 6edo and 13edo) ilke how meantonecan be used in even EDOs. 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.
-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.
+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.
-[[Category:Temperaments]]
+[[Category:Temperaments]
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