Xenharmonic Wiki

User:Lucius Chiaraviglio/Keyboard Layout Lab/Various rank-3 temperament Lumatone mappings

< User:Lucius Chiaraviglio | Keyboard Layout Lab

Due to the Lumatone wizardry of Bryan Deister, including at the larger EDO sizes, rank-3 temperament lumatone mappings are going here to avoid having other Keyboard Layout Lab pages getting too many Lumatone mappings (which causes the dreaded "template include too large" error).

Moved named rank-3 temperament Lumatone mappings here from Keyboard Layout Lab: Lucius Chiaraviglio (talk) 05:52, 21 June 2025 (UTC)
Moved unnamed rank-3 temperament Lumatone mappings to Unnamed rank-3 temperament Lumatone mappings: Lucius Chiaraviglio (talk) 08:51, 14 December 2025 (UTC)

Biyatismic family rank-3 variant with Magic (Witchcraft) generator Lumatone mappings

60edo (demonstrated to work)

Bryan Deister has demonstrated a 4L 2s (11:8 step ratio) mapping for 60edo, in 60edo improv (2025-11-22). The rightward generator 8\60e functions as both a sharp undecimal neutral second ~12/11 and a somewhat flat undecimal submajor second ~11/10 — the biyatisma 121/120 is tempered out. However, 8 is not co-prime with 60, so an additional generator is needed; for this, the right + down-right generator 9\60e works nicely as a somewhat flat classic major third ~5/4, as in Magic, specifically Witchcraft due to use of the 60e val. Indeed, the 60e version of the undecimal major fourth ~11/8 is easily accessible as two keys right and one key down-right, while the accessing the patent val version requires moving four keys left from the next root note one octave up. This classic major third second generator even stands fine on its own for rank-2 temperament purposes, but it is hard to pass up the convenience of the single key rightward generator 8\60e. This mapping misses some notes in each octave (due to trying to get over five octaves of range on a standard-sized Lumatone), with the octaves sloping severely downwards, and has a reverse chroma; but on the other hand, common consonant intervals are easily accessible from the root note as long as not cut by a vertical wraparound. (Note that in the demo video, the MIDI note numbers are offset by +1 relative to the layout chosen here to maximize note 0 to note 0 octaves.)

 
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Added: Lucius Chiaraviglio (talk) 00:13, 23 November 2025 (UTC)
Last modified, and moved here from Unnamed Temperament Lumatone mappings: Lucius Chiaraviglio (talk) 08:57, 25 November 2025 (UTC)

Canou family rank-3 variant temperament with Bidia + Superlimmal generators Lumatone mappings

80edo (proposed and untested)

Here is an as-yet untested Bidia + [[|Canousmic_temperaments#Superlimmal|Superlimmal]] 8L 4s (9:2 step ratio) mapping for 80edo. The rightward generator 9\80 is the Superlimmal generator ~27/25, which also functions as ~14/13 and ~13/12;; three of these make a sharp major third that maps as ~19/15 and ~24/19. The upward generator 7\80 is the Bidia generator which functions as ~16/15, ~17/16, and ~18/17; two of these make a somewhat sharp ~9/8; if allowed to pass the quarter-octave, three of these make a near-just classic minor third ~6/5; and four of them make a slightly sharp undecimal major third ~14/11. The temperament of this mapping might best be thought of as a variant of the Canou family rank-3 temperaments, but with Bidia and Superlimmal generators instead of the normal Canou family generators. The range is over 2¾ octaves with no missing notes and just a few repeated notes, and the octaves slope downwards very gently.

 
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Added: Lucius Chiaraviglio (talk) 08:14, 11 July 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 09:12, 19 July 2025 (UTC)

Cantonismic-Werckismic rank-3 temperament Lumatone mappings

74edo (demonstrated to work)

Bryan Deister has demonstrated the 7L 6s mapping of 74edo in microtonal improvisation in 74edo (2025). The rightward generator (8\74) functions as ~14/13; three of them make a classic major third ~5/4 (the cantonisma 10985/10976 is tempered out); five of them make an essentially-just undecimal subfifth ~16/11; and eight of them make a highly accurate undecimal supraminor seventh ~20/11. The upward generator (5\74) functions as ~21/20 and ~22/21 (the Werckisma (441/440 is tempered out); two of these make ~11/10; five of these make ~24/19 (which is distinguished from ~5/4); and eight of these make ~16/11. The range is about just over 3 octaves with no missing notes, and the octaves slope down and wrap around vertically.

 
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Added: Lucius Chiaraviglio (talk) 22:02, 12 June 2025 (UTC)
Last Modified: Lucius Chiaraviglio (talk) 06:37, 26 July 2025 (UTC)

Char-based Diatonic + Erato + Injera + Diatonicized Chromaticism (divided 11/8) + Passion/Freivald Lumatone mappings

98edo (demonstrated to work)

It is possible to produce a Lumatone mapping for 98edo that supports scales 12L 2s (Injera mega-chromatic, 8:1 step ratio), 5L 2s (standard diatonic, 16:9 step ratio), and 11L 2s (Ivan Wyschnegradsky's Diatonicized Chromaticism, 8:5 step ratio). By itself, the rightward step is 8\98, which maps to the classic diatonic semitone ~16/15 if the 98b val is used as in Passion/Freivald temperament, in which five of these steps make the flat fourth ~4/3, with ~11/8 being used as a second generator as described above (elevating the temperament to rank-3). This gives inspiration for what to do with the patent val, which tempers the classic diatonic semitone ~16/15 together with the minor diatonic semitone ~17/16 (the charisma 256/255 is tempered out) as 9\98. Used as a generator, this combines the rightward and down-right steps on the keyboard. Five of these right-down-right generators make 45\98, which maps as the near-just undecimal major fourth ~11/8, which itself serves as the dark generator for Ivan Wyschnegradsky's Diatonicized Chromaticism, for which the steps line up in neat rows. The flat (patent) fifth ~3/2 (57\98) functions as the generator for Meantone (also supporting Injera), with the diatonic scale laid out intuitively although stretched, with each two rightward steps corresponding to one whole step (16\98) of the diatonic scale. Although the patent fifth avoids contorsion on its own, use of both generators in combination makes for a convenient rank-3 temperament (as an off-beat tuning of Erato). With no missed notes and some repeated notes to alleviate vertical wraparounds, the range is just over two octaves, which alternate between middle and near/far, superimposed upon an overall downward slope. Bryan Deister has demonstrated this mapping (not much over a day after its proposal) in 98edo prelude (2025).

 
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Added: Lucius Chiaraviglio (talk) 19:05, 3 August 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 08:51, 6 August 2025 (UTC)

Char-based + Sesquart rank-3 Lumatone mappings

89edo (demonstrated to work)

Bryan Deister has demonstrated a 10L 3s (8:3 step ratio) mapping for 89edo in microtonal improvisation in 89edo (2025). The rightward generator 8\89 functions as both the 16/15 (the classical diatonic semitone) and 17/16 (the large septendecimal semitone), meaning that the charisma 256/255 is tempered out, although 89edo is not listed as a tuning of any of the temperaments on the page for 256/255. Eight of these generators make a near-just Axirabian paraminor fifth ~16/11. Although being prime, 89edo technically needs no second generator, a second generator helps with reaching consonant intervals other than ~16/11; one obvious choice is the scale chroma (upwards generator) 5\89 which functions as a somewhat sharp small tridecimal third tone ~27/26; three of these make a near-just Pythagorean whole tone ~9/8; four of them make a near-just septimal minor third ~7/6. It is also possible to combine both generators to get 13\89, a slightly sharp undevicesimal supraneutral second ~21/19; four of these generator combinations make a near-just fifth ~3/2, as in Sesquiquartififths temperament and its higher-limit Sesquart extension. The range is slightly over 2⅓ octaves with no missed notes and a few repeated notes, and the octaves slope up mildly.

 
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Added: Lucius Chiaraviglio (talk) 17:43, 31 July 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 19:05, 3 August 2025 (UTC)

Compton-related rank 3 temperament Lumatone mappings

96edo (demonstrated to work)

Bryan Deister has demonstrated a mapping for 96edo in which the rightward generator is 8\96 (~18/17) as in 12edo, while the upward generator is 7\96 (~20/19), in microtonal improvisation in 96edo (2025). The range is just over two octaves, with octaves sloping away and then wrapping around; on the other hand, it is easy to play eight 12edo subsets of 96edo that are displaced slightly from each other, as if one had eight pianos (even if of rather short compass) somehow all in reach at once. (Here, note 0 is in the middle of the left edge instead of Bryan Deister's usual lower left corner, to avoid skipping some of the bottom notes in the lowest note 0 to note 0 octave.) Although not shown in the video, this mapping also enables easy glissandos diagonally up-left or down-right.

 
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Added: Lucius Chiaraviglio (talk) 07:40, 24 May 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 06:33, 26 May 2025 (UTC)

Diminished-related rank-3 temperament mappings

76edo (2 mappings demonstrated to work)

Using the 8L 4s scale of Diminished temperament, Bryan Deister has tested two 8L 4s mappings for 76edo. Both give access to both fifths of 76edo, but the version with the 8:3 step ratio favors the flat fifth, while the version with the 7:5 step ratio favors the sharp fifth.

Version with 8:3 step ratio (flat fifth favored)

The version with the 8:3 step ratio is demonstrated in microtonal improvisation in 76edo (2025). Although this is technically a Diminished layout (rank-2, with the quarter-octave at 19\76), it is probably more conveniently thought of as a rank-3 temperament layout. The rightward generator 8\76 is a near-just tridecimal 2/3-tone or trienthird, ~[[14/13]; three of these make a somewhat flat ~5/4 classic major third (the cantonisma 10985/10976 is tempered out); four of them (32\56) make the sharp (patent) version of the fourth ~4/3 (corresponding to the flat patent fifth ~3/2); seven of them (56\76) make a near-just classic major sixth ~5/3. Of the two single-key-step generators other than rightward, the upward generator 5\76 has a more convenient mapping than down-rightward (3\76); 5\76 is a slightly sharp greater vicesimotertial semitone ~[[23/22]; four of them make a near-just classic minor third ~[[6/5]. Eight rightward generators minus four upward generators reach the flat version of the fifth at 44\76 (the corresponding sharp fourth being reached with rightward generators alone, as noted above); five rightward generators plus one upward generator reach the sharp fifth, and two rightward generators plus three upward generators reach the corresponding flat fourth. The range is a bit under 3 octaves, and the octaves slope down mildly.

 
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Version with 7:5 step ratio (sharp fifth favored)

Bryan Deister has also tested the version that has a 7:5 step ratio, but no demonstration video is available at this time. As with the 8:3 step ratio version, this is probably more conveniently thought of as a rank-3 temperament layout than a Diminished temperament layout. The rightward generator 7\76 is a flat septimal major semitone ~15/14; it also functions as a near-just classic diatonic semitone ~16/15, but only if the sharp fifth (76b val) is used (which tempers out the marvel comma 225/224); five of these make a near-just undecimal major fourth ~11/8; eight of them make a near-just classic major sixth ~5/3. Of the two single-key-step generators other than rightward, the down-right generator 5\76 has the attraction (for anyone trying out both versions of the 8L 4s mapping) of being the same as the upward generator for the 8:3 step ratio mapping; further, when used with the 7:5 step ratio mapping, its alignment with the small step scale provides added convenience, since one does not have to count chromas separately from small steps. Five (large) steps right plus two (small) steps down-right yields the sharp version of the fifth (45\76); three (large) steps right plus two (small) steps down-right yields the corresponding flat version of the fourth, putting it in the same row as the sharp fifth and the classic major third, which is one (large) step left of the flat fourth. Seven (large) steps right minus one (small) step down-right (thus plus one step up-left) yields the flat version of the fifth (44\76), while six (large) steps right minus two (small) steps down-right (thus plus two steps up-left) yields the corresponding sharp version of the fourth (32\76). The range is a bit under 3 octaves, and the octaves slope down mildly.

 
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Added: Lucius Chiaraviglio (talk) 07:19, 27 June 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 08:27, 2 July 2025 (UTC)

Gothic-related rank-3 Lumatone mappings

85edo (demonstrated to work)

Bryan Deister has demonstrated a 7L 5s (step ratio 10:3) Lumatone mapping for 85edo in microtonal improvisation in 85edo (2025). The rightward generator 10\85 is a slightly sharp lesser tridecimal neutral second ~13/12; as in 17edo, which 85edo quintuples (thereby making it a tuning of Gothic temperament), two of them make the moderately flat minor third ~20/17, while three of them make the moderately sharp major third ~23/18; likewise, five of them make the slightly sharp perfect fifth ~3/2. Without a second generator, this would contort under 17edo; the down-right generator 3\85 itself does not have a very convenient ratio (the nearest simple ratio being ~41/40, although this is near-just). But three of them make a near-just tridecimal supraminor second ~14/13; and seven of them make the near-just octave-reduced 19th harmonic ~19/16. The range is just over three octaves, with no missed notes and no duplicated notes; the octaves slant down moderately

 
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Added: Lucius Chiaraviglio (talk) 06:44, 9 July 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 17:01, 10 July 2025 (UTC)

Meantone-related rank-3 Lumatone mappings

74edo (proposed but judged unsuitable)

An alternate 9L 4s mapping of 74edo is worthy of consideration. The rightward generator (6\74) functions as ~17/16 and ~18/17 (the semitonisma 289/288 is tempered out); two of them make a meantone whole tone (which functions as ~10/9, ~9/8, and ~19/17 — the syntonic comma 81/80, the ganassisma 153/152, and the malcolmisma 171/170 are all tempered out); three of them make the neogothic minor third ~13/11; four of them make the classic major third ~5/4; and six of them make the lesser septimal tritone ~7/5. The down-right generator (5\74) functions as ~21/20 and ~22/21 (the Werckisma (441/440 is tempered out); two of these make ~11/10; five of these make ~24/19 (which is distinguished from ~5/4); and eight of these make ~16/11. The stacking of two or four instances of ~3/2 (43\74) and octave-reducing also yields the same results as two or four instances (respectively) of the rightward generator, making this a meantone mapping as expected for the patent val of 74edo; yet the usefulness of the down-right generator for reaching higher-limit intervals is undeniable, making this a mapping for a Meantone-related rank-3 temperament in the 19-limit that is different from Didymus. The range is about 2⅔ octaves with no missing notes, less than Bryan Deister's Cantonismic-Werckismic detailed above, but the octaves slope downward only very gently, and include a few more duplicate notes which partially alleviate vertical wraparounds (in addition to the useful temperament properties detailed above). On the other hand, Bryan Deister has tried this mapping and reported that it is too spread out (challenging finger stretches).

 
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Added: Lucius Chiaraviglio (talk) 07:00, 12 June 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 06:50, 26 June 2025 (UTC)

Moved 81edo to m-Chromatic Lumatone mappings inn Keyboard Layout Lab: Lucius Chiaraviglio (talk) 05:54, 15 July 2025 (UTC)

Tesseract + Negri Lumatone mappings

86edo (demonstrated to work)

Bryan Deister has demonstrated a 9L 1s mapping for 86edo in microtonal improvisation in 86edo (2025). The rightwards generator 9\86 is a slightly flat tridecimal supraminor second (~14\13), which is a quarter of the somewhat sharp perfect fourth (~4/3), as befits Tesseract temperament (28812/28561 is tempered out); unfortunately, the infill extension of Tesseract to include the 5th harmonic (as three of these generators) reaches the second-best approximation of it for 86 (86c val); this also puts this mapping on the spectrum for Negri temperament in the 5-limit, although not in the 7-limit, since 86edo does not temper ~8/7, ~7/6, and ~15/13 to the same interval (instead, it represents them all as distinct intervals). It is possible to reach all of the notes in each octave with sufficient stacking of only the rightward generator; but for convenience, it may be preferable to add as a second generator the upwards generator 4\86, a chromatic quarter-tone that functions primarily as the al-Farabi quarter tone ~33/32, but also ~30/29, ~31/30, and ~32/31. The range is just a bit over three octaves with no missed notes, and the octaves slope up substantially, hence the placement of the first note 0 in the lower left corner.

 
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Added: Lucius Chiaraviglio (talk) 09:03, 19 July 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 09:05, 21 July 2025 (UTC)

Unnamed rank-3 Lumatone mappings

Moved unnamed rank-3 temperament Lumatone mappings to Unnamed rank-3 temperament Lumatone mappings: Lucius Chiaraviglio (talk) 08:51, 14 December 2025 (UTC)

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