Lumatone mapping for 69edo

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There are many conceivable ways to map 69edo onto the onto the Lumatone keyboard. However, the Standard Lumatone mapping for Pythagorean is unable to cover the full gamut of every octave, with both the flat (patent val) and sharp (b val) versions having many skipped notes.

Diatonic

If not for the problem of failing to cove the complete gamut (such as on a hypothetical XL-size Lumatone having at least 345 keys within the span of five octaves), the sharp version would be a respectable mapping for UltraPyth; while the flat version would be a respectable Meantone mapping.

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Despite the missing notes, Bryan Deister has demonstrated the flat fifth (patent val) diatonic mapping in Compass - Mili (microtonal cover in 69edo) (2025).

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Devichromic Octacot + off-beat Ogene + Nessafof (Porwell)

The 6L 3s mapping was originally meant to get as many notes of 69edo as possible onto the space available on existing Lumatones, while enabling easy access to slightly flat classic major and minor thirds (~5/4 and ~6/5, respectively). However, moving down and right yields 5\69, which maps as 20/19 ~ 21/20 (69edo tempers out 400/399) and can be interpreted as Ogene with the 69bceef val; however, that is a val with an awful lot of warts, so perhaps the better temperament interpretation would be to take advantage of eight of this generator mapping to the fifth (40\69, all in the patent val), making the temperament a devichromic octacot (NOT the octacot of the tetracot family); no article about devichromic octacot temperament is currently available (and even if one was, as a weak extension of meantone, the temperament would likely get a different permanent name), but an article about devichromic chords exists. In addition to easy access to the patent fifth as noted above, three generators yield a somewhat flat ~7/6; four of them yield a near-just ~11/9; five of them yield a near-just ~9/7; seven of them yield a mildly flat ~10/7; and nine of them yield a near-just ~11/7. Alternatively, the rightward generator 9\69 serves for nessafof (which has a ⅓-octave period); this generator is a near-just septimal neutral second ~35/32; two of these make a slightly flat classic minor third ~6/5 (the porwell comma 6144/6125 is tempered out). This mapping gets just short of four full octaves, with no missed notes and a very slight slope. Bryan Deister has demonstrated this mapping for 69edo in microtonal improvisation in 69edo (2025). (For maximally efficient fitting of note 0 to note 0 octaves, note 0 is in the upper left corner instead of Bryan Deister's usual placement in the lower left corner.)

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Reverse chroma

Bryan Deister has also demonstrated a reverse-chroma version of this in 69edo groove (2026). The devichromic octacot and ogene generator 5\69 (20/19 ~ 21/20) is now one key right plus one key up, while the nessafof generator 9\63 is still one key right (and for ogene and nessafof, the ⅓-octave is three keys right plus one key up). The range is somewhat over five octaves, which alternate between far and near with the double octave having a gentle upwards slope, but misses some of the notes in each octave, especially the bass octave.

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