Meansquared: Difference between revisions

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⟨4/1⟩]] and the more melodically usable macrochromatic scale [[7L 5s (4/1-equivalent)|7L 5s ⟨4/1⟩]], which constitutes a very xenharmnoic nvariety of [[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 several [[EDO]] systems including ones without conventional meantone (like the previously mentioned 6edo and 13edo). This is analogous to how meantone can 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.

[[Category:Temperaments]]