Meansquared
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 81/802) in the 4.9.25 subgroup. The name was first coined by CompactStar in 2023. Meansquared in the 4.9.25 subgroup is an 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 stretch factor of exactly 2, and it follows that it is assosicated with the macrodiatonic scale 5L 2s⟨4/1⟩ and the more melodically usable macrochromatic scale 7L 5s ⟨4/1⟩, which constitutes a very xenharmnoic nvariety of detempered whole tone scale. It also follows that the Ed4s which support meanquad have the same number of tones as the EDOs 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 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.
[[Category:Temperaments]