User:Lucius Chiaraviglio/Keyboard Layout Lab/Various other Lumatone mappings: Difference between revisions

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 Moved:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 06:20, 21 June 2025 (UTC)
+== Tritikleismic-related 2.3.25.7 subgroup temperament Lumatone mappings ==
+=== 51edo (demonstrated to work but awaiting approval) ===
+One way of treating [[51edo]] is as three versions of [[17edo]], rearranged so as to divide the fifth and the octave also into three parts each, as demonstrated by [[Bryan Deister]] in [https://www.youtube.com/watch?v=k3NOBYbiqpo ''51edo improv''] (2026-04-22). This is very much like [[landscape]] temperament in equating the octave with a stack of three near-just quasi-tempered major thirds (~[[63/50]], as 17\51), but requires use of the 2.3.25.7 subgroup; division of the fifth (~[[3/2]], as 30\51) into three parts (slightly sharp septimal major seconds ~[[8/7]], as 10\51) also puts this temperament in the [[gamelismic clan]] (thus related to [[tritikleismic]], but again using the 2.3.25.7 subgroup). The obvious scale moving up and right is [[3L&nbsp;3s]] (10:7 step ratio); the obvious scale moving right and down-right is [[9L&nbsp;4s&nbsp;(4/1-equivalent)]] (10:3 step ratio); the upward and downward movements in the latter scale nearly cancel out so that while octaves alternate between far and near, double octaves just barely slope down.  The range is 5¼ octaves with no missed notes and no repeated notes.
+{{Lumatone EDO mapping|n=51|start=4|xstep=10|ystep=-7}}
+Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 05:02, 28 May 2026 (UTC)
 == Sensei Lumatone mappings ==
-=== 84edo (demonstrated to work but awaiting approval) ===
+=== 84edo (demonstrated to work) ===
-It is possible to map [[84edo]] using a supermajor third as a generator, as in [[sensei]] temperament, with a [[3L&nbsp;5s]] scale (13:9 step ratio). 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, this 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. Despite the missing notes [[Bryan Deister]] has used this mapping in [https://www.youtube.com/shorts/Qu6UIA2NmmQ ''84edo groove''] (2026).
+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}}
-Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 04:04, 10 May 2026 (UTC)
+Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 04:04, 10 May 2026 (UTC)<br>
+Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 05:02, 28 May 2026 (UTC)
 == Amity Lumatone mappings ==