Lumatone mapping for 51edo: Difference between revisions

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~~There are many conceivable ways to map [[51edo]] onto the [[Lumatone]] keyboard. Unfortunately, as it has multiple rings of 5ths, the [[Standard~~ Lumatone mapping ~~for Pythagorean]] is not one of them.~~ You can use the b val, which can be interpreted as either [[mavila]] or [[undecimation]], but is not a particularly great tuning for either.

== Antidiatonic ==

You can use the b val, which can be interpreted as either [[mavila]] or [[undecimation]], but is not a particularly great tuning for either.

[[Bryan Deister]] has used a flipped antidiatonic layout for [[51edo]] in which the generator is a mid major second at 8\51, which maps in between ~[[10/9]] and ~[[9/8]] and is distinct from both, A possible constitution of this interval in 51edo is the septendecimal major second ~[[512/459]] (~|9 -3 0 0 0 0 -1⟩), which maps correctly to 8\51 and is very close by direct approximation. Two of these generators make a fairly flat ~[[5/4]] Ptolemeic major third, and nine of these generators make a slightly sharp ~[[8/3]] perfect eleventh. Octaves alternate between near and far, but the range is just one missing note 47 short of being 5 full octaves, which compares favorably with the standard Antidiatonic ([[Mavila]]/[[Undecimation]]) and [[Porky]] mappings, and is competitive with the [[Slendric]] mapping. (Another possibility would be to move the first note 0 up and left, which would instead put the missing note in the first octave.) The most straightforward scale within an octave is [[2L 5s]] with a step ratio of 8:7, but the octave zigzag could be used to support an [[11L 2s (4/1-equivalent)]] scale, again with a step ratio of 8:7. [https://x31eq.com/temper-pyscript/ Graham Breed's x31eq Temperament Finder] gives no name for this temperament; it is 19 & 51 in the 2.3.5.17 subgroup, but if this layout was actually adapted to [[19edo]], L and s steps would exchange size classes to make this a flipped Diatonic layout. This layout is demonstrated in [https://www.youtube.com/shorts/5pM8OC0fV98 ''51edo improv''] (2025-05-02), with some additional notes outside the 5 (almost) full octaves cut off in and near the upper left and lower right corners due to the use of only 2 MIDI channels.

Instead, it is probably better to use one of the mappings that reaches the perfect 5th in three generator steps. Of these, the [[~~slendric~~]] mapping has the greater range.

== Slendric ==

Instead, it is probably better to use one of the mappings that reaches the perfect 5th in three generator steps. Of these, the [[Slendric]] mapping has the greater range.

== Porcupine ==

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).

== 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.

~~However~~, the [[~~porky~~]] ~~mapping~~ is ~~probably more intuitive to people used~~ to using ~~a heptatonic~~ scale and ~~simple 5~~-~~limit ratios~~ in ~~chords~~.

== 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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-There are many conceivable ways to map [[51edo]] onto the [[Lumatone]] keyboard. Unfortunately, as it has multiple rings of 5ths, the [[Standard Lumatone mapping for Pythagorean]] is not one of them. You can use the b val, which can be interpreted as either [[mavila]] or [[undecimation]], but is not a particularly great tuning for either.
+{{Lumatone mapping intro}}
+== Antidiatonic ==
+You can use the b&nbsp;val, which can be interpreted as either [[mavila]] or [[undecimation]], but is not a particularly great tuning for either.
 {{Lumatone EDO mapping|n=51|start=33|xstep=7|ystep=1}}
+[[Bryan Deister]] has used a flipped antidiatonic layout for [[51edo]] in which the generator is a mid major second at 8\51, which maps in between ~[[10/9]] and ~[[9/8]] and is distinct from both, A possible constitution of this interval in 51edo is the septendecimal major second ~[[512/459]] (~|9 -3 0 0 0 0 -1⟩), which maps correctly to 8\51 and is very close by direct approximation. Two of these generators make a fairly flat ~[[5/4]] Ptolemeic major third, and nine of these generators make a slightly sharp ~[[8/3]] perfect eleventh. Octaves alternate between near and far, but the range is just one missing note 47 short of being 5 full octaves, which compares favorably with the standard Antidiatonic ([[Mavila]]/[[Undecimation]]) and [[Porky]] mappings, and is competitive with the [[Slendric]] mapping. (Another possibility would be to move the first note 0 up and left, which would instead put the missing note in the first octave.) The most straightforward scale within an octave is [[2L&nbsp;5s]] with a step ratio of 8:7, but the octave zigzag could be used to support an [[11L&nbsp;2s (4/1-equivalent)]] scale, again with a step ratio of 8:7. [https://x31eq.com/temper-pyscript/ Graham Breed's x31eq Temperament Finder] gives no name for this temperament; it is 19 & 51 in the 2.3.5.17 subgroup, but if this layout was actually adapted to [[19edo]], L and s steps would exchange size classes to make this a flipped Diatonic layout. This layout is demonstrated in [https://www.youtube.com/shorts/5pM8OC0fV98 ''51edo improv''] (2025-05-02), with some additional notes outside the 5 (almost) full octaves cut off in and near the upper left and lower right corners due to the use of only 2 MIDI channels.
-Instead, it is probably better to use one of the mappings that reaches the perfect 5th in three generator steps. Of these, the [[slendric]] mapping has the greater range.
+{{Lumatone EDO mapping|n=51|start=32|xstep=8|ystep=-1}}
+== Slendric ==
+Instead, it is probably better to use one of the mappings that reaches the perfect 5th in three generator steps. Of these, the [[Slendric]] mapping has the greater range.
 {{Lumatone EDO mapping|n=51|start=24|xstep=10|ystep=-9}}
+== Porcupine ==
+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}}
+== 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}}
-However, the [[porky]] mapping is probably more intuitive to people used to using a heptatonic scale and simple 5-limit ratios in chords.
+== Tritikleismic-related 2.3.25.7 subgroup temperament ==
-{{Lumatone EDO mapping|n=51|start=18|xstep=7|ystep=2}}
+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}}