Lumatone mapping for 16edo
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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.

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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.

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Other mappings
If you want even greater range, there are the gorgo or magic mappings.
Gorgo

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Magic

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