Lumatone mapping for 79edo

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There are many conceivable ways to map 79edo onto the onto the Lumatone keyboard. Only one, however, agrees with the Standard Lumatone mapping for Pythagorean.

Diatonic

Note that 79edo is a Python tuning rather than meantone in the patent val, so while there is a decent approximation to 5/4 as a major third, there's an even better one to be found as a doubly-augmented second. However, due to the size of this edo, the diatonic mapping does not cover all the notes (to do so would require a hypothetical XL-size Lumatone to have 395 keys in the span of five octaves).

77
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5
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78
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66
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13
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68

Neutral seconds/thirds

The 7L 3s neutral thirds mapping uses the Alpharabian tendoneutral second ~12/11 as its generator (mapped as 10\79). It covers the whole gamut as efficiently as possible (no missed notes and no repeated notes in a range a bit under 3½ octaves) and keeps octaves close to horizontal. Bryan Deister has demonstrated this mapping in microtonal improvisation in 79edo (2025).

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15
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75
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16
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36
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77
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18
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78
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19
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10
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40
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11
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71
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12
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34
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54
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77
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11
21

Magic

The 3L 7s magic mapping is similarly efficient, but favors different intervals.

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