User:Lucius Chiaraviglio/Keyboard Layout Lab/Unnamed temperament Lumatone mappings: Difference between revisions

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 These Lumatone mappings were not created for a particular temperament, but as experiments in modifying the Lumatone mapping of one EDO to work for a nearby size without regard to whether they have any temperaments in common. This is a placeholder section in case more of these are created.
-Moved 28edo to new Machine Lumatone mappings section on [[User:Lucius_Chiaraviglio/Keyboard_Layout_Lab/Various_other_Lumatone mappings|Various Other Lumatone mappings]]; moved 30edo to Rank-3 Lumatone mappings page:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 19:35, 23 July 2025 (UTC)
+Moved 28edo to new Machine Lumatone mappings section on [[User:Lucius_Chiaraviglio/Keyboard_Layout_Lab/Various_other_Lumatone mappings|Various Other Lumatone mappings]]; moved 30edo to Rank-3 Lumatone mappings page:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 19:35, 23 July 2025 (UTC)<br>
 Moved this section here:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:36, 11 October 2025 (UTC)
+== Various Described but Unnamed Temperament Lumatone mappings ==
+Various Lumatone mappings that do not match the mapping for another size of EDO, and seem to have been designed for a temperament for which the name is currently not defined or not set, with the temperament described beyond identification of the generator.
+=== 51edo: 19 & 51 flipped antidiatonic (demonstrated to work) ===
+[[Bryan Deister]] has used a flipped antidiatonic layout for [[51edo]] in which the generator is a mid major second at 8\51, which maps in between ~[[10/9]] and ~[[9/8]] and is distinct from both, A possible constitution of this interval in 51edo is the septendecimal major second ~[[512/459]] (~|9 -3 0 0 0 0 -1⟩), which maps correctly to 8\51 and is very close by direct approximation. Two of these generators make a fairly flat ~[[5/4]] Ptolemeic major third, and nine of these generators make a slightly sharp ~[[8/3]] perfect eleventh. Octaves alternate between near and far, but the range is just one missing note 47 short of being 5 full octaves, which compares favorably with the standard Antidiatonic ([[Mavila]]/[[Undecimation]]) and [[Porky]] mappings, and is competitive with the [[Slendric]] mapping. (Another possibility would be to move the first note 0 up and left, which would instead put the missing note in the first octave.) The most straightforward scale within an octave is [[2L&nbsp;5s]] with a step ratio of 8:7, but the octave zigzag could be used to support an [[11L&nbsp;2s (4/1-equivalent)]] scale, again with a step ratio of 8:7. [https://x31eq.com/temper-pyscript/ Graham Breed's x31eq Temperament Finder] gives no name for this temperament; it is 19 & 51 in the 2.3.5.17 subgroup, but if this layout was actually adapted to [[19edo]], L and s steps would exchange size classes to make this a flipped Diatonic layout. This layout is demonstrated in [https://www.youtube.com/shorts/5pM8OC0fV98 ''51edo improv''] (202505-02), with some additional notes outside the 5 (almost) full octaves cut off in and near the upper left and lower right corners due to the use of only 2 MIDI channels.
+{{Lumatone EDO mapping|n=51|start=32|xstep=8|ystep=-1}}
+Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:21, 5 May 2025 (UTC)<br>
+Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 04:35, 28 May 2026 (UTC)
 == Various Unnamed Temperament Lumatone mappings ==
-Various Lumatone mappings that do not match the mapping for another size of EDO, and were not designed for a particular temperament.
+Various Lumatone mappings that do not match the mapping for another size of EDO, and do not seem to have been designed for a particular temperament, for which temperament description beyond identification of the generator is not available.
 Moved here from [[User:Lucius_Chiaraviglio/Keyboard_Layout_Lab/Various_other_Lumatone mappings|Various Other Lumatone mappings]]:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:36, 11 October 2025 (UTC)
@@ Line 20: / Line 33: @@
 Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 20:01, 27 October 2025 (UTC)<br>
 Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 12:51, 28 October 2025 (UTC)
+=== 44edo (demonstrated to work, and found Bidia + Diminished + Charismic + Semitonismic temperament) ===
+Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:55, 4 January 2026 (UTC)<br>
+Found Bidia + Diminished + Charismic + Semitonismic temperament, and moved to [[User:Lucius_Chiaraviglio/Keyboard_Layout_Lab|Keyboard Layout Lab]]:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 09:46, 11 January 2026 (UTC)
 === 46edo (demonstrated to work and found Bison temperament) ===
@@ Line 28: / Line 46: @@
 === 51edo (demonstrated to work) ===
-[[Bryan Deister]] has used a flipped antidiatonic layout for [[51edo]] in which the generator is a mid major second at 8\51, which maps in between ~[[10/9]] and ~[[9/8]] and is distinct from both, A possible constitution of this interval in 51edo is the septendecimal major second ~[[512/459]] (~|9 -3 0 0 0 0 -1⟩), which maps correctly to 8\51 and is very close by direct approximation. Two of these generators make a slightly flat ~[[5/4]] Ptolmeic major third, and nine of these generators make a slightly sharp ~[[8/3]] perfect eleventh. Octaves alternate between near and far, but the range is just one missing note #47 short of being 5 full octaves, which compares favorably with the standard Antidiatonic ([[Mavila]]/[[Undecimation]]) and [[Porky]] mappings, and is competitive with the [[Slendric]] mapping. (Another possibility would be to move the first note 0 up and left, which would instead put the missing note in the first octave.) The most straightforward scale within an octave is [[2L&nbsp;5s]] with a step ratio of 8:7, but the octave zigzag could be used to support an [[11L&nbsp;2s (4/1-equivalent)]] scale, again with a step ratio of 8:7. [https://x31eq.com/temper-pyscript/ Graham Breed's x31eq Temperament Finder] gives no name for this temperament; it is 19 & 51 in the 2.3.5.17 subgroup, but if this layout was actually adapted to [[19edo]], L and s steps would exchange size classes to make this a flipped Diatonic layout. This layout is demonstrated in [https://www.youtube.com/shorts/5pM8OC0fV98 ''51edo improv''] (2025), with some additional notes outside the 5 (almost) full octaves cut off in and near the upper left and lower right corners due to the use of only 2 MIDI channels.
+[[Bryan Deister]] has demonstrated a mapping of [[51edo]] for a [[3L&nbsp;5s]] scale rotated (checkertonic, with 7:6 step ratio), that also lends itself to a [[7L&nbsp;2s]] scale (flipped superdiatonic, with 7:1 step ratio) and a [[12L&nbsp;3s (4/1-equivalent)]] scale (7:6 step ratio, passing right through the octave zigzag), in [https://www.youtube.com/shorts/sTPJtuHUwkg ''51edo improv''] (2025-02-03). The rightward generator is 7\51, which is a near-just large undecimal neutral second ~[[11/10]], as in [[Porky]], but this mapping is sufficiently different from the Porky layout as to warrant a different name. The range is a bit over 4¼ octaves, and the octaves alternate between near/far and mid.
-{{Lumatone EDO mapping|n=51|start=32|xstep=8|ystep=-1}}
+{{Lumatone EDO mapping|n=51|start=31|xstep=7|ystep=-1}}
-Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:21, 5 May 2025 (UTC)<br>
+Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 11:21, 1 January 2026 (UTC)<br>
-Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 06:23, 6 May 2025 (UTC)
+Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 09:27, 3 January 2026 (UTC)
 === 52edo (demonstrated to work) ===
-[[Bryan Deister]] has used a layout for [[52edo]] in which the generator is 9\52, as ~[[9/8]] but mapped by direct approximation rather than as the version mapped by the patent val or by the 52b val, which means that it has to be constituted as (3♭&nbsp;×&nbsp;3♯)&nbsp;/&nbsp;8 to make use of the dual-fifth feature of 52edo. Two of these map to a ~[[14/11]] major third, as in [[Pentacircle clan|Pentacircle]] but for the direct approximation mapping of ~9/8. The upward generator is ~[[16/15]]. Octaves slant down and then wrap around, but the compass is 5 full octaves, with no missed notes, which is competitive with the Diatonic and Neutral Thirds layouts. This layout is demonstrated in [https://www.youtube.com/shorts/lNJCZz7EjL0 ''microtonal improvisation in 52edo''] (2025); in the video, some notes are cut off at the right edge due to the use of only 2 MIDI channels.
+Found Diminished temperament, and moved to [[User:Lucius_Chiaraviglio/Keyboard_Layout_Lab/Various_other_Lumatone_mappings|Various other Lumatone mappings]]:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 12:05, 28 March 2026 (UTC)
-{{Lumatone EDO mapping|n=52|start=4|xstep=9|ystep=-5}}
-Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 09:22, 5 May 2025 (UTC)<br>
-Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 06:03, 6 May 2025 (UTC)
 === 57edo (demonstrated to work) ===
@@ Line 53: / Line 66: @@
 Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 19:07, 12 May 2025 (UTC)
-Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 17:43, 31 July 2025 (UTC)
+=== 60edo (demonstrated to work) ===
+Found Biyatismic family rank-3 variant with Magic (Witchcraft) generator, and moved to [[User:Lucius_Chiaraviglio/Keyboard_Layout_Lab/Various_rank-3_temperament_Lumatone_mappings|Various rank-3 temperament Lumatone mappings]]:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 09:01, 25 November 2025 (UTC)
 === 62edo (demonstrated to work) ===
 Accidental duplicate of official semi-Mohajira mapping, removed:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:36, 11 October 2025 (UTC)
+=== 67edo (demonstrated to work) ===
+Moved to [[User:Lucius_Chiaraviglio/Keyboard_Layout_Lab/Various_other_Lumatone_mappings#Infraorwell_Lumatone_mappings|Various other Lumatone mappings]]:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:51, 6 November 2025 (UTC)
+=== 81edo (demonstrated to work) ===
+[[Bryan Deister]] has demonstrated a [[5L&nbsp;9s]] (9:4 step ratio) layout for [[81edo]], in [https://www.youtube.com/shorts/yY0TzTiNeB8 ''81edo improv''] (2025). Both the rightward generator (4\81) and the down-right generator (9\81) map to high-limit intervals: 4\81 maps to ~[[29/28]], ~[[30/29]], and ~[[31/30]]; while 9\81 maps to ~[[40/37]]. The down-right generator is [[Saturation, torsion, and contorsion|contorted]] by itself; in principle, the first generator could be used by itself for an unnamed rank-2 temperament, but it is so small that the second generator is needed for convenience. Alternatively, one could make a rank-2 temperament using the combination of these generators, which is 13\81, which maps to the quasi-meantone ~[[19/17]] and to both sizes of classic whole tone ~[[9/8]] and ~[[10/9]], as befits 81edo being a [[meantone]] tuning; the last step in arriving at meantone is to add an octave to this generator and split it in half to get 47\81, which is the closest approximation to the perfect fifth in 81edo. This produces a interleaved and rotated diatonic layout yielding a range close to 2½ octaves (with some repeated notes to mitigate vertical wraparounds) having a slight downward slant.
+{{Lumatone EDO mapping|n=81|start=44|xstep=4|ystep=5}}
+Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 23:01, 3 December 2025 (UTC)<br>
+Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 11:06, 6 December 2025 (UTC)
 === 91edo pseudo-isomorphic (demonstrated to work) ===
@@ Line 71: / Line 99: @@
 Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 01:51, 2 June 2025 (UTC)<br>
 Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 15:28, 4 June 2025 (UTC)
+=== 95edo (demonstrated to work) ===
+==== Quasi-Diatonic ====
+A quasi-diatonic layout is also possible, which functions similarly to a diatonic mapping, but with the octaves shifting pitch class up by 2\95 with each higher octave. Thus, despite the missed notes, all notes are accessible in some octaves. [[Bryan Deister]] has demonstrated this in [https://www.youtube.com/shorts/aQapbuGFnhk ''Impostor Syndrome - Sidney Gish (microtonal cover in 95edo)''] (2025) with the MIDI mapping set to octave 1 | octave 2 | octave 2 | octave 3 | octave 3 | octave 4, to get the greater portion of the notes within each octave other than the bass (which is missing note 0 among other notes, whilethe last octave only has 3 notes represented), at the cost of less range.
+{{Lumatone EDO mapping|n=95|start=75|xstep=15|ystep=-4}}
+Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 21:52, 20 November 2025 (UTC)
+Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 19:28, 24 November 2025 (UTC)
 === 97edo (demonstrated to work) ===
-[[Bryan Deister]] has used the [[16L&nbsp;1s]]/[[15L&nbsp;7s]] layout for [[97edo]], as demonstrated in [https://www.youtube.com/watch?v=hXDdKO3-RL4 ''microtonal improvisation in 97edo''] (2025). Although 97edo is at the intersection of [[Immunity]] and [[Orson]], this layout does not closely match either temperament, instead using a rightward generator 6\97 which is very close to [[24/23]], and an upward generator 5\97 which is very close to [[29/28]]. The range is less than 2 octaves, and the octaves slant upwards if following the 16L&nbsp;1s scale but are nearly level if following the 15L&nbsp;7s scale; all notes are represented at least once (although getting this within a full 0 to 0 octave requires shifting the 0 point 1 key right from Bryan Deister's usual placement in the lower left corner, to avoid cutting off some notes on the left end).
+[[Bryan Deister]] has used a layout for [[97edo]] that provides both [[16L&nbsp;1s]] and [[15L&nbsp;7s]] scales (in both cases with 6:1 step ratio), as demonstrated in [https://www.youtube.com/watch?v=hXDdKO3-RL4 ''microtonal improvisation in 97edo''] (2025). Although 97edo is at the intersection of [[Immunity]] and [[Orson]], this layout does not closely match either temperament, instead using a rightward generator 6\97 which is very close to [[24/23]], and an upward generator 5\97 which is very close to [[29/28]]. The range is less than 2 octaves, and the octaves slant upwards if following the 16L&nbsp;1s scale but are nearly level if following the 15L&nbsp;7s scale; all notes are represented at least once (although getting this within a full 0 to 0 octave requires shifting the 0 point 1 key right from Bryan Deister's usual placement in the lower left corner, to avoid cutting off some notes on the left end).
 {{Lumatone EDO mapping|n=97|start=10|xstep=6|ystep=-5}}
 Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 09:09, 16 April 2025 (UTC)<br>
-Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 20:51, 26 May 2025 (UTC)<br>
+Restored:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 13:24, 28 May 2025 (UTC)<br>
-Restored:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 13:24, 28 May 2025 (UTC)
+Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:04, 12 November 2025 (UTC)
+==== Quasi-diatonic (demonstrated to work) ====
+A quasi-diatonic layout is also possible, which functions similarly to a diatonic mapping, but with the octaves shifting pitch class up by 1\97 with each higher octave. Thus, despite the missed notes, all notes are accessible in some octaves. [[Bryan Deister]] has demonstrated this in [https://www.youtube.com/shorts/6iXy1D9RZ-U ''Charlie's Inferno - That Handsome Devil (microtonal cover in 97edo)''] (2025), with the MIDI mapping set to octave 1 | octave 2 | octave 2 | octave 3 | octave 3 to get all of the notes within each octave other than the bass, at the cost of less range. (In the demonstration video, note 0 is also shifted to appear where note 2 appears here.)
+{{Lumatone EDO mapping|n=97|start=93|xstep=16|ystep=-7}}
+Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:05, 12 November 2025 (UTC)
+=== 240edo (demonstrated to work) ===
+Approaching the limits of the number of keys to a Lumatone and the pitch resolution of most people, is [[240edo]]. [[Bryan Deister]] has demonstrated a mapping for this in [https://www.youtube.com/shorts/Nu-xBrsd8_o ''microtonal improvisation in 240edo''] (2025). Following in the footsteps of [[Julián Carrillo]], whose highest EDO ([[96edo]]) piano had just one octave, this layout achieves 1.14 octaves with no missing notes and just four repeated notes in the first octave and one more repeated note in the fractional octave at the end. In the demonstration video, the purple/pink notes are octave-reduced harmonics, except for 73/64 accidentally being left green.
+{{Lumatone EDO mapping|n=240|start=0|xstep=9|ystep=-4}}
+Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:25, 15 November 2025 (UTC)<br>
+Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 09:19, 22 November 2025 (UTC)
+=== 336edo (demonstrated to work) ===
+By a large margin, the entire gamut of [[336edo]] will not fit on a Lumatone. Nevertheless, a Lumatone can be used to play a musically useful subset of it. One of these subsets is 7ed(575{{c}}), of which each increment corresponds to 23 increments of 336edo. For practical purposes, this is a non-octave tuning, although technically it repeats at the octave at 23 octaves, which would require a hypothetical XXXXL-sized Lumatone to implement and some kind of Shepard tone pattern to be all audible within the range of human hearing. [[Bryan Deister]] has demonstrated a mapping of this in [https://www.youtube.com/shorts/kPqYmCzZ8uY ''7ed(575 cents) improv''] (2025). In this, 7ed(575{{c}}) is doubled to 14ed(1150{{c}}), and then a compressed (non-octave) 4L&nbsp;1s (3:2 step ratio) scale laid out on it if proceeding right and down, or a compressed 4L&nbsp;2s (3:1 step ratio) scale if proceeding right and up. The range is over 6¼ instances of 1150{{c}}, which slope gently upwards.
+{{Lumatone EDO mapping|n=336|start=0|xstep=69|ystep=-23}}
+Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 02:48, 3 November 2025 (UTC)<br>
+Last Modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 23:23, 3 November 2025 (UTC)