Lumatone mapping for 51edo: Difference between revisions

(One intermediate revision by one other user not shown)

Line 1:

{{Lumatone mapping intro}} 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 slightly flat ~[[5/4]] Ptolmeic 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), 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.

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

@@ Line 1: / Line 1: @@
-{{Lumatone mapping intro}} 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 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 slightly flat ~[[5/4]] Ptolmeic 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), 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.
+However, the [[Porky]] mapping is probably more intuitive to people used to using a heptatonic scale and simple 5-limit ratios in chords.
 {{Lumatone EDO mapping|n=51|start=18|xstep=7|ystep=2}}
 {{Navbox Lumatone}}