5L 2s (3/1-equivalent): Difference between revisions
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{{MOS intro|Other Names=triatonic}} | {{MOS intro|Other Names=triatonic}} | ||
== Name == | == Name == | ||
The name '''triatonic''' was coined by [[User:CompactStar|CompactStar]], | The name '''triatonic''' was coined by [[User:CompactStar|CompactStar]], as a back-formation from "diatonic" with di- being interpreted as 2 (the [[2/1|octave]]) and tri- being interpreted as 3 (the [[3/1|tritave]]), though it is not an official name in [[TAMNAMS]]. | ||
== Scale properties == | == Scale properties == | ||
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=== Modes === | === Modes === | ||
The modes of | The modes of {{MOS scalesig|5L 2s <3/1>}} have step patterns which are the same as the modes of the diatonic scale. | ||
{{MOS mode degrees}} | {{MOS mode degrees}} | ||
== Theory == | == Theory == | ||
=== As a macrodiatonic scale === | === As a macrodiatonic scale === | ||
{{MOS scalesig|5L 2s <3/1>}} is a [[macrodiatonic and microdiatonic scales|macrodiatonic scale]] with the period of a [[3/1|tritave]]. This means it is a [[5L 2s|diatonic scale]], but its intervals are all stretched to the point of being unrecognizable—the diatonic fifth is now the size of a major seventh, and octaves are stretched out to tritaves. 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 === | ||
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== Notation == | == Notation == | ||
Being a macrodiatonic scale, it can notated using the traditional diatonic notation, if all intervals are reinterpreted as their stretched versions (like octaves as tritaves). However, this approach involves 1-based indexing for a non-diatonic MOS which is generally discouraged. Alternatively, a generic MOS notation may be used like [[diamond-mos notation]], which enables 0-based indexing at the cost of obscuring the connection to the standard diatonic scale. | Being a macrodiatonic scale, it can notated using the traditional diatonic notation, if all intervals are reinterpreted as their stretched versions (like octaves as tritaves). However, this approach involves 1-based indexing for a non-diatonic MOS which is generally discouraged. Alternatively, a generic MOS notation may be used like [[diamond-mos notation]], which enables 0-based indexing at the cost of obscuring the connection to the standard diatonic scale. | ||
== Scale tree == | == Scale tree == | ||
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| 4/1 = [[Mintaka]] is around here | | 4/1 = [[Mintaka]] is around here | ||
| 5/1 = [[No-twos subgroup temperaments#Minalzidar|Minalzidar]] | | 5/1 = [[No-twos subgroup temperaments#Minalzidar|Minalzidar]] | ||
}} | }} | ||