Meansquared: Difference between revisions

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== Structure ==

Meansquared has the same structure, MOSes and interval chain as meantone temperament, but with every interval squared, which stretches them out so much that they are in completely different size categories. The perfect fifth becomes a major ninth ([[9/4]]), the major third becomes an augmented fifth ([[25/16]]), and the minor third becomes a diminished fifth ([[36/25]]). 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. In flatter tunings like [[19ed4]] and [[31ed4]], this system is very xenharmonic with it lacking single octaves, and the stretched versions of the standard 5-limit major and minor chords (1-[[25/16]]-[[9/4]] and 1-[[36/25]]-[[9/4]] respectively) are also exotic and tense-sounding. However, it is resemblant in many ways to the ~~somewhat-common~~ whole tone scale, and ~~becomes identical~~ to it ~~in the tuning of [[6edo]]~~.

Meansquared has the same structure, MOSes and interval chain as meantone temperament, but with every interval squared, which stretches them out so much that they are in completely different size categories. The perfect fifth becomes a major ninth ([[9/4]]), the major third becomes an augmented fifth ([[25/16]]), and the minor third becomes a diminished fifth ([[36/25]]). 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. In flatter tunings like [[19ed4]] and [[31ed4]], this system is very xenharmonic with it lacking single octaves, and the stretched versions of the standard 5-limit major and minor chords (1-[[25/16]]-[[9/4]] and 1-[[36/25]]-[[9/4]] respectively) are also exotic and tense-sounding. However, the 12-tone MOS is resemblant in many ways to the familiar 6edo or whole tone scale (being a detempered version of it), and it gets closer and closer to it when L and s become more similar.

[[Category:Temperaments]]

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 == Structure ==
-Meansquared has the same structure, MOSes and interval chain as meantone temperament, but with every interval squared, which stretches them out so much that they are in completely different size categories. The perfect fifth becomes a major ninth ([[9/4]]), the major third becomes an augmented fifth ([[25/16]]), and the minor third becomes a diminished fifth ([[36/25]]). 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. In flatter tunings like [[19ed4]] and [[31ed4]], this system is very xenharmonic with it lacking single octaves, and the stretched versions of the standard 5-limit major and minor chords (1-[[25/16]]-[[9/4]] and 1-[[36/25]]-[[9/4]] respectively) are also exotic and tense-sounding. However, it is resemblant in many ways to the somewhat-common whole tone scale, and becomes identical to it in the tuning of [[6edo]].
+Meansquared has the same structure, MOSes and interval chain as meantone temperament, but with every interval squared, which stretches them out so much that they are in completely different size categories. The perfect fifth becomes a major ninth ([[9/4]]), the major third becomes an augmented fifth ([[25/16]]), and the minor third becomes a diminished fifth ([[36/25]]). 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. In flatter tunings like [[19ed4]] and [[31ed4]], this system is very xenharmonic with it lacking single octaves, and the stretched versions of the standard 5-limit major and minor chords (1-[[25/16]]-[[9/4]] and 1-[[36/25]]-[[9/4]] respectively) are also exotic and tense-sounding. However, the 12-tone MOS is resemblant in many ways to the familiar 6edo or whole tone scale (being a detempered version of it), and it gets closer and closer to it when L and s become more similar.
 [[Category:Temperaments]]
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