5L 2s (3/1-equivalent): Difference between revisions

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=== As a macrodiatonic scale ===

It is the [[macrodiatonic and microdiatonic scales|macrodiatonic scale]] with the period of a [[3/1|tritave]]. This means it is a [[5L 2s|

diatonic scale]], but has [[2/1|octave]]s stretched out to the size of a [[3/1|tritave]]. Other intervals are also stretched in a way that makes the unrecognizable–the diatonic fifth is now the size of a major seventh. Interestingly [[19edt]], an approximation of [[12edo]], has a tuning of this scale ~~(being a stretched version of 19edo's diatonic scale)~~, meaning it contains both ~~the~~ diatonic scale (~~identical to~~ 12edo's) and ~~the~~ macrodiatonic scale.

diatonic scale]], but has [[2/1|octave]]s stretched out to the size of a [[3/1|tritave]]. Other intervals are also stretched in a way that makes the unrecognizable–the diatonic fifth is now the size of a major seventh. Interestingly, [[19edt]], an approximation of [[12edo]], has a tuning of this scale, meaning it contains both a diatonic scale (which approximates 12edo's diatonic scale) and a macrodiatonic scale.

=== Temperament interpretations ===

Although they have not been studied in detail, it is possible to construct no-twos [[rank-2 temperament]] interpretations of this scale, such as the as-of-yet unnamed b12 & b5 temperament in the 3.13.17 [[subgroup]], in which the generator is ~[[17/9]] and a stack of 4 generators tritave-reduced is ~[[13/9]]. See also the page for [[12edt]].

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 === As a macrodiatonic scale ===
 It is the [[macrodiatonic and microdiatonic scales|macrodiatonic scale]] with the period of a [[3/1|tritave]]. This means it is a [[5L 2s|
-diatonic scale]], but has [[2/1|octave]]s stretched out to the size of a [[3/1|tritave]]. Other intervals are also stretched in a way that makes the unrecognizable–the diatonic fifth is now the size of a major seventh. Interestingly [[19edt]], an approximation of [[12edo]], has a tuning of this scale (being a stretched version of 19edo's diatonic scale), meaning it contains both the diatonic scale (identical to 12edo's) and the macrodiatonic scale.
+diatonic scale]], but has [[2/1|octave]]s stretched out to the size of a [[3/1|tritave]]. Other intervals are also stretched in a way that makes the unrecognizable–the diatonic fifth is now the size of a major seventh. Interestingly, [[19edt]], an approximation of [[12edo]], has a tuning of this scale, meaning it contains both a diatonic scale (which approximates 12edo's diatonic scale) and a macrodiatonic scale.
 === Temperament interpretations ===
 Although they have not been studied in detail, it is possible to construct no-twos [[rank-2 temperament]] interpretations of this scale, such as the as-of-yet unnamed b12 & b5 temperament in the 3.13.17 [[subgroup]], in which the generator is ~[[17/9]] and a stack of 4 generators tritave-reduced is ~[[13/9]]. See also the page for [[12edt]].