There are many conceivable ways to map 87edo onto the onto the Lumatone keyboard. However, it has 3 mutually-exclusive rings of fifths, so the Standard Lumatone mapping for Pythagorean is not one of them. Due to the edos size, it would not cover the whole gamut even if it was.
Diatonic
You can use the b val, which is at least a near perfect tuning for deeptone.
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5
There is an alternate diatonic scale that makes 5-limit chords easy to play, but it has a slight octave stretch. Since every note is available in at least some of the octaves, this may actually be advantageous.
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86
Pseudo-Isomorphic Quasi-Diatonic
For those who do not want the octave stretch, Bryan Deister has demonstrated a pseudo-isomorphic mapping for 87edo in 87edo waltz (2025). This mapping retains a diatonic-style layout for ease of access to common consonant intervals, although it does not include all the notes of the tuning system. Each note 87 is actually another note 0, so as to reset octave pitch down by half of the near-just ~64/63 (half of the moderately inflated ~81/80).
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Aureus Pseudo-Meantone
It is possible to lay out 87edo using the generator 14\87, which is the quasi-meantone ~19/17, which is composed of highly inaccurate harmonics whose errors nearly cancel out, rendering it near-just; two of them make an essentially just classic major third ~5/4. (In contrast to actual meantone temperament, 87edo represents ~19/17, ~10/9, and ~9/8 as distinct intervals — the syntonic comma 81/80 is not tempered out, and instead the aureusma 1445/1444 equates two quasi-meantones to a classic major third.)
Flipped and Rotated
In the flipped and rotated verions with a 3L 5s scale (14:9 step ratio) the above-mentioned 14\87 generator is one key down-right, while key right is 9\87, which functions as a flat tridecimal 2/3-tone ~14/13 and a sharp septimal diatonic semitone ~15/14. This mapping makes it easy to play melodies that sound very diatonic despite the scale being non-diatonic, with octaves sloping moderately down, and a range of over three octaves (although with large partial octaves chopped off by the upper left and lower right corners), which is a bit too much for 87edo, resulting in some missed notes even in the middle octaves. Despite the missing notes, Bryan Deister has used this mapping in 87edo improv (2026-07-11).
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Split Generator
A split generator version of the above mapping returns to mostly horizontal progression with a 11L 5s scale (7:2 step ratio). As in the previous mapping, the generator 14\87 is the quasi-meantone ~19/17, but in this case, it is two keys right, making this a split generator version of the mapping, in which each ~19/17 is split into two equal intervals that function as both a small septendecimal semitone ~18/17 and a large undevicesimal semitone ~19/18, both being close to just (and the photisma 324/323 is tempered out). Although no second generator is needed to reach all of the notes, for convenience, down-right by one key (2\87) can be used for convenience as a second generator that functions as ~49/48 (inconsistently mapped), ~55/54, ~64/63, ~65/64, and ~81/80, of which the septimal chroma ~64/63 is near-just, and four of these make a near-just classic diatonic semitone ~16/15 (the currently unnamed unnoticeable comma 5250987/5242880 is tempered out). The range is somewhat over two octaves (which slant very slightly downwards) with no missed notes and some repeated notes to mitigate vertical wraparounds. Bryan Deister has demonstrated this mapping in Circuit Bent - Stomach Book (microtonal cover in 87edo) (2025).
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Rodan
The rodan mapping is quite efficient and 87edo is an essentially perfect tuning for the temperament, which would make it an excellent option if not for the missing notes problem. Rodan splits the near-just (only slightly sharp) fifth ~3/2 into three mildly sharp septimal whole tones ~8/7, as 17\87 (the gamelisma 1029/1024 is tempered out); furthermore, it splits the slightly flat classic major sixth ~5/3 into a two sharp septimal major thirds ~9/7, as 32\87 (the sensamagic comma 245/243 is tempered out). Finally, it defines a fine-adjustment interval known as the "quark" (a type of aberrisma) which may or may not corresond to the MOS chroma; at 2\87, this functions as several intervals including a near-just ~64/63 and a sharp ~81/80 (the aberschisma 5120/5103, formerly known as the hemifamity comma, is tempered out). Thus, even though it is rank-2 because the generators are not independent, from the user's point of view it works like a rank-3 temperament, which is good for a large tuning system like 87edo. However, the 1L 4s and 5L 1s mappings only cover about half the notes and the 5L 6s one has heavily sloped octaves whichever direction you put the chroma. The reverse chroma one is the only one of these that covers the full gamut in the central octave.
1L 4s reverse chroma
In the 1L 4s (19:17 step ratio) reverse chroma version of the rodan mapping, the septimal major second ~8/7 is one key right, and the quark is the MOS chroma; the septimal major third ~9/7 is one key right plus one key up. The range is over six octaves gently sloping up, but many notes are missing.
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5L 1s forward chroma
In the 5L 1s (19:2 step ratio) forward chroma version of the rodan mapping, the septimal major second ~8/7 is still one key right, and the quark is the small step of the scale (which is still proper since it only occurs once per octave); the septimal major third ~9/7 is two keys right plus one key up. The range is over five octaves gently sloping up, but many notes are missing. Despite the missing notes, Bryan Deister has used this mapping in 87edo improv (2026-09-28).
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5L 6s forward chroma
In the 5L 6s (19:2 step ratio) forward chroma version of the rodan mapping, the septimal major second ~8/7 is now one key right plus one key down-right, and the quark is still the small step of the scale (now no longer proper); the septimal major third ~9/7 is two keys right plus one key down-right. The range is over three octaves severely sloping down, but many notes still are missing.
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75
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78
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77
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80
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23
79
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37
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67
82
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39
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71
86
5L 6s reverse chroma
In the 5L 6s (19:2 step ratio) forward chroma version of the rodan mapping, the septimal major second ~8/7 is still one key right plus one key down-right, and the quark is still the small step of the scale; the septimal major third ~9/7 is one key right plus two keys down-right. The range is over two octaves moderately sloping down; although the middle octave is complete (and even has a fair number of repeated notes), in practice many notes are still missing due to the lopsided nature of the layout causing many notes to be lost at the left and right edges (as well as likely stretching fingers to the limits) even though not cut off vertically.
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Kleismic
The 4L 7s mapping covers the full gamut and keeps octaves fairly horizontal when the small step goes rightward.
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Misty
The 3L 9s Misty mapping is quite efficient at making harmonics easy to play together, gives you a relatively 12edo-like experience and keeps octaves near horizontal, but has a slightly smaller range. Bryan Deister has demonstrated this mapping in microtonal improvisation in 87edo (2025).
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