5L 2s (3/1-equivalent): Difference between revisions
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{{Infobox MOS}} | {{Infobox MOS}} | ||
{{MOS intro}} | {{MOS intro|Other Names=triatonic}} | ||
== Name == | |||
The name '''triatonic''' was coined by [[User:CompactStar|CompactStar]], and is a back-formation from "diatonic" with di- being interpreted as 2 (the [[2/1|octave]]) and replaced with tri- for 3 (the [[3/1|tritave]]). | |||
== Theory == | == Theory == | ||
=== As a macrodiatonic scale === | === 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| | 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, meaning it contains both a diatonic scale (which approximates 12edo's diatonic scale) and a | 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 triatonic scale. | ||
=== Temperament interpretations === | === 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 (the stretched counterpart of the fifth) is ~[[17/9]] and a stack of 4 generators tritave-reduced (the stretched counterpart of the major third) is ~[[13/9]]. See also the page for [[12edt]]. | 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 (the stretched counterpart of the fifth) is ~[[17/9]] and a stack of 4 generators tritave-reduced (the stretched counterpart of the major third) is ~[[13/9]]. See also the page for [[12edt]]. | ||
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== Scale tree == | == Scale tree == | ||
{{Scale tree| | {{Scale tree|name=triatonic|Comments=3/2:Just [[17/9]] generator (1101.045¢); 2/1:[[CTE tuning]] for the b12 & b5 temperament (1109.689¢)}} | ||