Revision as of 09:29, 3 January 2026 by Lucius Chiaraviglio(talk | contribs)(→Porcupine: Add Bryan Deister's mapping Checkertonic/Flipped Superdiatonic with Porky Generator)
You can use the b val, which can be interpreted as either mavila or undecimation, but is not a particularly great tuning for either.
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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 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. 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 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.
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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.
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 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.
