Lumatone mapping for 51edo: Difference between revisions

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However, the [[Porky]] mapping is probably more intuitive to people used to using a heptatonic scale and simple 5-limit ratios in chords. [[Bryan Deister]] demonstrates this mapping in [https://www.youtube.com/shorts/Fymg9vYO6iQ ''Northernlight - Deltarune (microtonal cover in 51edo)''] (2025).

=== Flipped version ===

The flipped [[porcupine]] ([[porky]]) mapping demonstrated in [[Bryan Deister]]'s [https://www.youtube.com/shorts/-ZFMDsE8jy4 ''51edo groove''] (2026) increases the octave slope and decreases the range (to just over four octaves) relative to the normal mapping for this temperament, but might be needed for easy reach to certain chords.

== Checkertonic/Flipped Superdiatonic with Porky Generator ==

[[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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 However, the [[Porky]] mapping is probably more intuitive to people used to using a heptatonic scale and simple 5-limit ratios in chords. [[Bryan Deister]] demonstrates this mapping in [https://www.youtube.com/shorts/Fymg9vYO6iQ ''Northernlight - Deltarune (microtonal cover in 51edo)''] (2025).
 {{Lumatone EDO mapping|n=51|start=11|xstep=7|ystep=2}}
+=== Flipped version ===
+The flipped [[porcupine]] ([[porky]]) mapping demonstrated in [[Bryan Deister]]'s [https://www.youtube.com/shorts/-ZFMDsE8jy4 ''51edo groove''] (2026) increases the octave slope and decreases the range (to just over four octaves) relative to the normal mapping for this temperament, but might be needed for easy reach to certain chords.
+{{Lumatone EDO mapping|n=51|start=22|xstep=7|ystep=-9}}
 == Checkertonic/Flipped Superdiatonic with Porky Generator ==
 [[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}}