Lumatone mapping for 51edo: Difference between revisions

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[[Bryan Deister]] has demonstrated a mapping of [[51edo]] for a [[3L 5s]] scale rotated (checkertonic, with 7:6 step ratio), that also lends itself to a [[7L 2s]] scale (flipped superdiatonic, with 7:1 step ratio) and a [[12L 3s (4/1-equivalent)]] scale (7:6 step ratio, passing right through the octave zigzag), in [https://www.youtube.com/shorts/sTPJtuHUwkg ''51edo improv''] (2025-02-03). The rightward generator is 7\51, which is a near-just large undecimal neutral second ~[[11/10]], as in [[Porky]], but this mapping is sufficiently different from the Porky layout as to warrant a different name. The range is a bit over 4¼ octaves, and the octaves alternate between near/far and mid.

== Tritikleismic-related 2.3.25.7 subgroup temperament ==

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 3s]] (10:7 step ratio); the obvious scale moving right and down-right is [[9L 4s (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.

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 [[Bryan Deister]] has demonstrated a mapping of [[51edo]] for a [[3L&nbsp;5s]] scale rotated (checkertonic, with 7:6 step ratio), that also lends itself to a [[7L&nbsp;2s]] scale (flipped superdiatonic, with 7:1 step ratio) and a [[12L&nbsp;3s (4/1-equivalent)]] scale (7:6 step ratio, passing right through the octave zigzag), in [https://www.youtube.com/shorts/sTPJtuHUwkg ''51edo improv''] (2025-02-03). The rightward generator is 7\51, which is a near-just large undecimal neutral second ~[[11/10]], as in [[Porky]], but this mapping is sufficiently different from the Porky layout as to warrant a different name. The range is a bit over 4¼ octaves, and the octaves alternate between near/far and mid.
 {{Lumatone EDO mapping|n=51|start=31|xstep=7|ystep=-1}}
+== Tritikleismic-related 2.3.25.7 subgroup temperament ==
+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}}
 {{Navbox Lumatone}}