Lumatone mapping for 84edo: Difference between revisions

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== Sensei ==

Instead, the most efficient layout that allows access to all notes is ~~the~~ [[Sensei]] mapping, ~~although~~ this ~~does reduce~~ the range to a little over three octaves.

=== 3L 5s ===

It is possible to map [[84edo]] using a supermajor third as a generator, as in [[sensei]] temperament. The generator 31\84 is two keys right plus one key down-right, and it functions as a flat ~[[162/125]] in the 5-limit, as a near-just ~[[84/65]] in the 13-limit, as a somewhat flat septendecimal ultramajor third ~[[22/17]] in the 17-limit (requires use of the 84e val to map correctly), and as a slightly sharp ~[[49/38]] in the 19-limit. Two of these generators make a near-just classic major sixth ~[[5/3]]; five of them make a somewhat flat classic minor seventh ~[[9/5]]; seven of them make a near-just (slightly flat) fifth ~[[3/2]]; and nine of them make a near-just classic major third ~[[5/4]]. Unfortunately, the [[3L 5s]] scale (13:9 step ratio) mapping tries to get too many octaves (four) for mapping a tuning system this large on the currently available version of the Lumatone, so it misses some notes in each octave; furthermore, the octaves slope down mildly. Despite the missing notes [[Bryan Deister]] has used this mapping in [https://www.youtube.com/shorts/Qu6UIA2NmmQ ''84edo groove''] (2026).

=== 8L 3s ===

Instead, the most efficient layout that allows access to all notes is an expanded [[Sensei]] mapping, using an [[8L 3s]] scale with a 9:4 step ratio, this reduces the range to a little over three octaves, but they are nearly level.

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 == Sensei ==
-Instead, the most efficient layout that allows access to all notes is the [[Sensei]] mapping, although this does reduce the range to a little over three octaves.
+=== 3L&nbsp;5s ===
+It is possible to map [[84edo]] using a supermajor third as a generator, as in [[sensei]] temperament. The generator 31\84 is two keys right plus one key down-right, and it functions as a flat ~[[162/125]] in the 5-limit, as a near-just ~[[84/65]] in the 13-limit, as a somewhat flat septendecimal ultramajor third ~[[22/17]] in the 17-limit (requires use of the 84e val to map correctly), and as a slightly sharp ~[[49/38]] in the 19-limit. Two of these generators make a near-just classic major sixth ~[[5/3]]; five of them make a somewhat flat classic minor seventh ~[[9/5]]; seven of them make a near-just (slightly flat) fifth ~[[3/2]]; and nine of them make a near-just classic major third ~[[5/4]]. Unfortunately, the [[3L&nbsp;5s]] scale (13:9 step ratio) mapping tries to get too many octaves (four) for mapping a tuning system this large on the currently available version of the Lumatone, so it misses some notes in each octave; furthermore, the octaves slope down mildly. Despite the missing notes [[Bryan Deister]] has used this mapping in [https://www.youtube.com/shorts/Qu6UIA2NmmQ ''84edo groove''] (2026).
+{{Lumatone EDO mapping|n=84|start=67|xstep=9|ystep=4}}
+=== 8L&nbsp;3s ===
+Instead, the most efficient layout that allows access to all notes is an expanded [[Sensei]] mapping, using an [[8L&nbsp;3s]] scale with a 9:4 step ratio, this reduces the range to a little over three octaves, but they are nearly level.
 {{Lumatone EDO mapping|n=84|start=2|xstep=9|ystep=-5}}