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

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Revision as of 07:59, 12 July 2025 by Lucius Chiaraviglio (talk | contribs) (→80edo (demonstrated to work but awaiting approval): --> Proposed and untested (Bryan Deister's layout was actually pure Bidia, not this combination))

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 for 91edo and 93edo here from Keyboard Layout Lab/Various other Lumatone mappings: Lucius Chiaraviglio (talk) 06:17, 21 June 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 classic major third ~5/4. 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) 07:59, 12 July 2025 (UTC)

Cantonismic-Werckismic rank-3 temperament Lumatone mappings

74edo (demonstrated to work but awaiting approval)

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 downward moderately, resulting in a vertical wraparound.

 
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Added: Lucius Chiaraviglio (talk) 22:02, 12 June 2025 (UTC)
Last Modified: Lucius Chiaraviglio (talk) 22:17, 12 June 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)

Unnamed rank-3 Lumatone mappings

75edo (demonstrated to work)

Bryan Deister has demonstrated the 7L 3s (step size ratio 9:4) Lumatone mapping for 75edo, in microtonal improvisation in 75edo (2025-06-24). So Right = 9\75 and down-right = 4\75, which means that Up = 5\75. Like 97edo, 75edo has mainly bad harmonics for its size (but with different harmonics being exceptions), so to find useful intervals, it is necessary to try to stick to primes 3, 5, and 23 (those having the least relative error) and/or take advantage of error cancellation as much as possible. Going right (9\75) 1 key is ~25/23 (error canceling, but starting out with some of the least bad harmonics); right 2 keys (18\75) is a subminor third ~625/529 (no simple ratio maps to this interval in the patent val of 75edo, but it merits mention anyway due to extensive use in the video); right 3 keys (27\75) = ~9/7 (errors only partially cancel, so somewhat flat); and right 7 keys (63\75) = ~34/19 (errors nearly cancel). Going down-right (4\75) 1 key functions as both ~27/26 and ~28/27; down-right 2 keys = ~14/13 (errors largely cancel), 3 keys = ~19/17 (errors largely cancel), and 5 keys = ~5/4 (the 5th harmonic has a small relative error). Going up (5\75) 1 key is ~23/22 (errors only partially canceling, so somewhat sharp). The range is just over 3½ octaves, and the octaves are very close to level, with just a slight down slope. This corresponds to the Neutral Thirds mapping on the Lumatone mapping for 75edo page.

 
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Added: Lucius Chiaraviglio (talk) 07:46, 25 June 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 05:48, 29 June 2025 (UTC)

78edo (demonstrated to work)

Bryan Deister] has demonsrated a Lumatone mapping for 78edo that lays out scales 11L 1s (7:1 step ratio) and 6L 6s (7:6 step ratio), in microtonal improvisation in 78edo (2025). The rightward generator 7\78 is slightly sharp large septendecimal semitone ~17/16; two of them make a slightly flat biyatismic whole tone ~17/15; and six of them readh a slightly flat undecimal minor fifth ~16/11. The down-right generator 6\78 is a somewhat sharp small undevicesimal semitone ~20/19; stacking these can yield both a slightly sharp undecimal major fourth ~11/8 (as 36\78, six generators) and slightly flat undecimal minor fifth ~16/11 (as 42\78, seven down-right generators, same as six rightward generators). The range is somewhat under three octaves, with all notes represented; octaves alternate between far and near, with an overall upwards slant.

 
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Added: Lucius Chiaraviglio (talk) 07:52, 3 July 2025 (UTC)

91edo (demonstrated to work)

Bryan Deister has demonstrated an isomorphic 9L 2s mapping for 91edo in improv 91edo (2025). The range is just one note beyond 3 full octaves, with octaves sloping up mildly (which results in a wraparound of note 0). The rightward generator 9\91 is the septimal diatonic semitone ~15/14. The upward generator 4\91 is a quartertone that functions as ~32/31, ~33/32, ~34/33, and ~36/35; two of them make the minor diatonic semitone ~17/16; six of them make a near-just minor third ~6/5. The use of this generator makes this a mapping for Quartkeenlig; however, since stacking the upward generator quickly leads to wraparounds, and attempting to get the perfect fifth in 91edo with this generator yields 52\91, which is the 7edo (91bb) fifth. Therefore, this mapping really needs to be treated as a rank-3 temperament mapping; for instance, to get the patent fifth 53\92 (a mildly flat ~3/2, almost exactly 1/7-comma meantone), it is easiest to stack five rightward generators and two upward generators.

 
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Added: Lucius Chiaraviglio (talk) 16:02, 4 June 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 08:57, 23 June 2025 (UTC)

93edo (demonstrated to work)

(This mapping has been updated with the changes made to the official version by Yourmusic Productions and ArrowHead294.)

Bryan Deister has demonstrated a mapping for 93edo in microtonal improvisation in 93edo (2025). The rightward generator 6\93 represents 21/20, 23/22, and 25/24, producing a 15L 1s scale as in Valentine, although 93edo is contorted with this scale (L = 6 and s = 3) and temperament; choosing the scale 13L 3s avoids contortion, although neither the bright version (64\93) nor the dark version (29\93) of its generator maps to a convenient ratio, so the following discussion instead uses the generators for the mapping itself. Going right 2 keys makes a ~35/32 neutral second (abundantly used in the later part of the video); 3 right = ~8/7; 5 right = ~5/4; and 8 right = ~10/7. To avoid contortion, it is necessary to use a second generator, making this a rank-3 temperament mapping; the upward generator 7\93 is ~20/19; 4 steps up makes ~16/13; 5 steps up makes ~13/10, and 9 steps up (which always involves a vertical wraparound) makes ~8/5. Down-right is −1\93, enabling easy glissandos (demonstrated in the beginning of the video). In order to avoid having notes of the first note 0 to note 0 octave chopped off at the left edge, the first note 5 is placed half way down the left edge, and note 0 is 5 down-right from that. The range is just over an octave and a half, and the octaves slope from near to far.

 
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Added: Lucius Chiaraviglio (talk) 20:43, 31 May 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 08:57, 14 June 2025 (UTC)

98edo (proposed and untested)

(Descriptive text needs to go here for 98edo, starting with rightward generator 9\98 = ~16/15 and 5 of them = ~11/8; and upward generator 5\98 = both ~29/28 ~30/29 and 9 of them = ~11/8; may need to streamline down to rank-2.)

Template:Lumatone EDO mapping

Added: Lucius Chiaraviglio (talk) 07:52, 21 June 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 08:57, 23 June 2025 (UTC)

99edo (proposed and untested)

(Descriptive text needs to go here for 99edo, starting with rightward generator 8\99 = ~135/128, ~18/17, ~19/18, and 3 of them make ~13/11, and 4 of them make ~5/4and 6 of them make ~7/5; and upward generator 1\99 = ~126/125; may need to streamline down to rank-2.)

Template:Lumatone EDO mapping

Added: Lucius Chiaraviglio (talk) 07:52, 21 June 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 08:57, 23 June 2025 (UTC)

100edo (proposed and untested)

(Descriptive text needs to go here for 100edom starting with rightward generator 8\100 = ~37/35, and 2 of them make ~19/17, and 3 of them make ~13/11, and 4 of them make ~5/4; upward generator 1\100 = ?; cannot streamline down to rank-2.)

Template:Lumatone EDO mapping

Added: Lucius Chiaraviglio (talk) 07:52, 21 June 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 08:57, 23 June 2025 (UTC)

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