There are many conceivable ways to map 16edo onto the onto the Lumatone keyboard. Only one, however, agrees with the Standard Lumatone mapping for Pythagorean.
Antidiatonic
Since 16edo is a mavila temperament, its best fifths are quite dissonant and the chromatic semitone goes in the opposite direction than it usually does. Though, its major third and harmonic seventh are somewhat better. Bryan Deister demonstrates this layout in 16edo waltz (2025).
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Lemba
As the Lemba mapping reaches both these intervals with a single generator step, it is probably easier to find consonant chords using it. Bryan Deister demonstrates this layout in 16edo jam (2025).
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Gorgo + Semaja
You can get range of over six octaves (with a gentle upwards slope) with the 1L 4s (4:3 step ratio) mapping of Gorgo and Semaja.
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Magic (Muggles/Sephiroth)
You can get range of over eight octaves (with a very gentle upwards slope) with the 3L 1s (5:1 step ratio) mapping of Magic (Muggles/Sephiroth).
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Diminished + Gorgo + Magic (Muggles/Sephiroth) + Semaja
One of the temperaments 16edo lends itself to most obviously is Diminished, with a 4L 4s scale having a 3:1 step ratio, as demonstrated to accompany a vocal work by Bryan Deister, in Doubt by Bryan Deister (microtonal 16edo snippet) (2025). This yields all of the temperaments and scales of the previous two mappings, with range nearly as great as that of the Magic (Muggles/Sephiroth) mapping at eight octaves, although the octaves slope up with the rightward key progression.
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