Bryan Deister invented the Devichromic Octacot(*) Lumatone mapping for 69edo shown below, and I got curious about how Devichromic temperament would work for other sizes. Devichromic temperament currently has no article (the link just given will change from red to blue if it gets one), but Devichromic chords does, and gives a brief description of the temperament, along with its defining comma 400/399.
(*)This is a placeholder name for the extension of Devichromic temperament that divides the fifth into eight parts, and is actually a weak extension of meantone.
(In principle, this should work somewhat similarly to the layout for 69edo below, but this needs to be checked for accuracy, and some differences are necessary to avoid mapping contortion even though the temperament is not contorted.)
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.)
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.
(In principle, right in this mapping works like down-right in the 69edo mapping, except that the fifth obtained this way is the very flat b val fifth.)
