User:Lucius Chiaraviglio/Keyboard Layout Lab: Difference between revisions

(34 intermediate revisions by 2 users not shown)

Line 7:

=== 39edo (demonstrated to work) ===

[[Bryan Deister]] has used a [[Porcupine]]-inspired layout for [[39edo]], as demonstrated in [https://www.youtube.com/watch?v=XLRaG_pBN7k&lc=UgwfjZwncsryQjeNUg14AaABAg.AHVkw8aNSEGAHZU_J2qOPM ''39edo jam''] (2025). To take advantage of the fact that 39edo is at the intersection of [[Augmented]] and [[Immunity]], the rightward generator is 5\39, half of a [[6/5]] minor third as [[12/11]] ~ [[11/10]] (but much closer to 12/11). This enables a MODMOS derived from [[1L 6s]] by shrinking the large step from 9\39 to 8\39 and expanding one of the small steps from 5\39 to 6\39, to enable chords such as 12/11 (somewhat sharp, at 5\39) - 6/5 (slightly flat, at 10\39) - [[11/8]] (near-just, at 18\39) - [[3/2]] (mildly sharp, 23\39) - [[18/11]] (moderately sharp, at 28\39) - [[9/5]] (near-just, at 33\39). Playing this chord uses almost the same geometry of depressed keys as that for playing a diatonic scale in a diatonic mapping (but has a very different sound effect), save when proceeding to the next octave. The range is slightly over 6 octaves overall (which slant moderately downwards), but with the first and last octaves missing some notes due to clipping in the upper left and lower right corners of the layout.

[[Bryan Deister]] has used a [[Porcupine]]-inspired layout for [[39edo]], as demonstrated in [https://www.youtube.com/watch?v=XLRaG_pBN7k&lc=UgwfjZwncsryQjeNUg14AaABAg.AHVkw8aNSEGAHZU_J2qOPM ''39edo jam''] (2025). To take advantage of the fact that 39edo is at the intersection of [[Augmented]] and [[Immunity]], the rightward generator is 5\39, half of a [[6/5]] minor third as [[12/11]] ~ [[11/10]] (but much closer to 12/11). This enables a MODMOS derived from [[1L 6s]] by shrinking the large step from 9\39 to 8\39 and expanding one of the small steps from 5\39 to 6\39, to enable chords such as 12/11 (somewhat sharp, at 5\39) - 6/5 (slightly flat, at 10\39) - [[11/8]] (near-just, at 18\39) - [[3/2]] (mildly sharp, 23\39) - [[18/11]] (moderately sharp, at 28\39) - [[9/5]] (near-just, at 33\39). Playing this chord uses almost the same geometry of depressed keys as that for playing a diatonic scale in a diatonic mapping (but has a very different sound effect), save when proceeding to the next octave. The range is slightly over 6 octaves overall (which slant moderately downwards), but with the first and last octaves missing some notes due to clipping in the upper left and lower right corners of the layout. The range is just under four octaves (which slant upwards mildly), with no missed notes and one repeated note in each octave.

Line 14:

Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 06:30, 2 May 2025 (UTC)

== ~~Cantonismic-Werckismic rank-3 temperament~~ Lumatone mappings ==

== Augmented (Triforce) + Bohpier Lumatone mappings ==

~~Due~~ to this ~~page getting too~~ large, ~~moved~~ these to [[User:~~Lucius_Chiaraviglio~~/~~Keyboard_Layout_Lab~~/~~Various rank~~-3 ~~temperament~~ Lumatone mappings|~~Various rank~~-3 ~~temperament~~ Lumatone mappings]].

=== 33edo (demonstrated to work) ===

[[Bryan Deister]] has demonstrated two mappings for [[33edo]] that function for the temperaments [[Augmented]] ([[Augmented family#Triforce|Triforce]], 33d val, [[3L 3s]] scale with 7:4 step ratio) and [[Bohpier]] (33cd val, [[8L 1s]] scale with 4:1 step ratio). The down-right (forward chroma version) or rightward (reverse chroma version) generator is a somewhat flat Alpharabian tendoneutral second ~[[12/11]] which can be stacked to get several consonant intervals; however, some of them map inconsistently. Two of these generators make a near-just neogothic minor third ~[[13/11]], mapped consistently. Three of these generators make a near-just septimal major third ~[[9/7]] by sound, but the mapping only works if 9/7 is constituted as (3♭ × 3♯) ÷ 7 or as 9 ÷ 7♭ (33d val). Four of these generators make a near-just lesser septimal tritone ~[[7/5]], mapped consistently ([[patent val]] or 33cd val). Six of these generators make a flat classic major sixth ~[[5/3]] by sound, but the mapping only works if 5/3 is constituted as 5♭ ÷ 3 (33c val). Seven of these generators make a near-just classic minor seventh ~[[9/5]] by sound, but the mapping only works if 9/5 is constituted as (3♭ × 3♯) ÷ 5 or as 9 ÷ 5♭ (33c val). The range is a bit over six octaves in the forward chroma version or five octaves in the reverse chroma version; in both cases, the octaves slope moderately downwards resulting in a vertical wraparound.

==== Forward chroma ====

Demonstrated in [https://www.youtube.com/shorts/mkaaAJEyGFU ''33edo riff''] (2025).

==== Reverse chroma ====

Demonstrated in [https://www.youtube.com/watch?v=GypR6x_Ih1I ''33edo jam''] (2025).

Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:09, 2 August 2025 (UTC)

Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 09:24, 6 August 2025 (UTC)

== Bidia + Diminished + Charismic + Semitonismic Lumatone mappings ==

=== 56edo (demonstrated to work) ===

[[Bryan Deister]] has demonstrated a [[4L 4s]] (9:5 step ratio) mapping for [[56edo]], in [https://www.youtube.com/watch?v=xkfao6yGKGE ''Curious Light - DOORS (microtonal cover in 56edo)''] (2025). Right + down-right divides the octave into slices of 14\56; as an interval in its own right, this is the same as the minor third of [[12edo]], which functions as ~[[19/16]] and ~[[25/21]] (both being near-just). Down-right alone is 5\56, which is the [[Normal forms#Minimal_form|minimal form]] generator for [[Bidia]]; it functions as the classic diatonic semitone ~[[16/15]], the large septendecimal semitone ~[[17/16]], and the small septendecimal semitone ~[[18/17]], meaning that the charisma [[256/255]] and the semitonisma [[289/288]] are both tempered out; two of them make a rather sharp whole tone ~[[9/8]]; three of them (passing the quarter-octave) make a mildly sharp classic minor third ~[[6/5]], although the afore-mentioned quarter-octave (12edo-style) minor third is easier to reach; in contrast, the near-just classic major third ~[[5/4]] is very easy to reach with just two moves rightwards, and a down-right move from this reaches the moderately flat fourth ~[[4/3]]; two more down-right moves reaches the rather sharp fifth ~[[3/2]]. The efficiency is almost as good as that of the diatonic mapping, with no missed notes and one repeated note per octave; the overall range is somewhat under five octaves, with no notes chopped off by the left and right edges before reaching the end of overall range. The cost of this is that octaves slant downwards.

Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:38, 21 August 2025 (UTC)

Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 10:00, 21 August 2025 (UTC)

== Biyatismic Lumatone mappings ==

=== 68edo (demonstrated to work) ===

[[Bryan Deister]] has used a [[Biyatismic clan#Zeus|Biyatismic (Zeus)]] layout with a [[7L 1s]] scale (9:5 step ratio) for [[68edo]], as demonstrated in [https://www.youtube.com/shorts/CO1AslAu9E0 ''microtonal improvisation in 68edo''] (2025). The rightward generator 9\68 is a combination of the Alpharabian tendoneutral second ~[[12/11]] and the undecimal submajor second ~[[11/10]], and two of these make a near-just classic minor third ~[[6/5]], with the biyatisma ([[121/120]]) being tempered out. The chroma of the scale (4\68, upwards on this layout) is the near-just diptolemaic chromatic semitone ~[[25/24]], and is convenient to use as a second generator (even though such is not required to avoid [[contorsion]]) to access other consonant intervals quickly, although sometimes with strange preferences built in — for instance, the septimal whole tone ~[[8/7]] is much easier to reach (at 13\68) than the Pythagorean whole tone ~[[9/8]] (which requires a substantial vertical reach at 12\68), while the septimal minor third ~[[7/6]] (at 15\18) is a much longer vertical reach than the classic minor third ~6/5 (at 18\68), and the septimal major third ~[[9/7]] is a much longer vertical reach (at 25\68) than the classic major third ~[[5/4]] (at 22\68). Fortunately the fourth (~[[4/3]], at 28\68), the Axirabian paramajor fourth (~[[11/8]], at 31\68), the Axirabian paraminor fifth (~[[16/11]], at 37\68) and fifth (~[[3/2]], at 40\68) are all easy to reach as long as they do not go through a vertical wraparound (as happens to the fourth in the bass octave). The range is four octaves plus two notes, and octaves slope upwards — not severely, but a vertical wraparound is unavoidable if note 0 is placed to get complete octaves as defined to reach from note 0 to note 0.

Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 06:33, 30 July 2025 (UTC)

Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 12:18, 4 August 2025 (UTC)

== Blackwood + Diminished Lumatone mappings ==

=== 20edo (demonstrated to work) ===

[[Bryan Deister]] has used a [[Diminished]] [[4L 4s]] (4:1 step ratio) mapping for [[20edo]] that also functions as a [[Blackwood]] mapping, as demonstrated in [https://www.youtube.com/shorts/bqYA9flwL_g ''20edo prelude''] (2025). In this mapping, the octave can be interpreted as being divided into five parts (Blackwood temperament) or 4\20 or four parts of 5\20 (Diminished temperament). Octaves slope, as expected for a Blackwood mapping, but with plenty of repeated vertical notes, and the range is a bit over 5½ octaves.

Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 19:34, 11 August 2025 (UTC)

Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 23:18, 11 August 2025 (UTC)

== Compressed Skwares (Fibotonic) Lumatone mappings ==

=== 20edo (demonstrated to work) ===

[[Bryan Deister]] has used a compressed [[Skwares]]) [[2L 1s]] (7:6 step ratio) mapping for [[20edo]], as demonstrated in [https://www.youtube.com/watch?v=BFUTeFs7Ycg ''20edo groove''] (2025). In the version of Skwares used for this, instead of substantially sharpening the undecimal major third ~[[14/11]] (or even a septimal major third ~[[9/7]]) to get a diatonic fourth ~[[4/3]] (by stacking and octave-reducing four generators), the undecimal major third (7\20) is near-just, and the fourth is very flat at 480{{c}} (corresponding to the Blackwood sharp fifth at 720{{c}}). Octaves are nearly level (sloping down very gradually), and the range is a bit over 11 octaves, which suggests dividing the keyboard into zones for different instruments.

Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 23:13, 11 August 2025 (UTC)

Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:00, 13 August 2025 (UTC)

== Cantonismic Lumatone mappings ==

=== 64edo (demonstrated to work) ===

[[Bryan Deister]] has demonstrated a [[Cantonismic]] (flipped and rotated diatonic) mapping of [[64edo]] in [https://www.youtube.com/shorts/ag1FbgAuR6I ''microtonal improvisation in 64edo''] (2025). In this mapping, the rightward generator 7\64 is mapped as a slightly sharp tridecimal supraminor second ~[[14/13]], and the [[cantonisma]] (10985/10976) is tempered out, so that three of them make a fairly sharp classic major third ~[[5/4]], and eight of them make a near-just undecimal neutral seventh ~[[11/6]]; note that apart from ~5/4, these ratios depending upon partial cancellation of errors in the harmonics as represented by 64edo. The rightward generator is actually the short step of the easiest scale to play on this layout (provided that the scale is positioned not to go through a vertical wraparound), with the down-right step being 10\64, which corresponds to the [[Patent val|patent]] (not [[direct approximation]]) whole tone ~[[9/8]], thus enabling a rotated diatonic scale. Octaves alternate between far and near superimposed on an overall slant away over the range of three whole octaves (having no missing notes) plus a fourth octave that has some notes chopped off by the right edge, and some fragmented note sequences in the upper left and lower right corners. A side effect of the alternation of octaves is that accessing the fourth and fifth can be easy or hard depending upon not only the root note, but also the octave — for instance, in the middle and mid-right octaves, 27\64 and 37\64 are both easily reached from 0\64, but in the second full octaves, they same interval requires a long finger stretch if the root note is greater than 0, and the rotated diatonic scale goes through a vertical wraparound (and moving note 0 would simply cause other root notes to have the same problem in some of the octaves).

Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:51, 26 July 2025 (UTC)

Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 10:52, 28 July 2025 (UTC)

== Diaschismic + Charismic + Semitonismic Lumatone mappings ==

=== 58edo (demonstrated to work) ===

[[Bryan Deister]] has demonstrated a [[2L 6s]] (14:5 step ratio) mapping for [[58edo]] in [https://www.youtube.com/shorts/7gkRyld5OU8 ''Waltz in 58edo''] (2025). The rightward generator 5\58 functions as the classic diatonic semitone ~[[16/15]], the large septendecimal semitone ~[[17/16]], and the small septendecimal semitone ~[[18/17]], meaning that the charisma [[256/255]] and the semitonisma [[289/288]] are both tempered out. The rightward generator is also the [[normal forms|minimal form]] of the [[Diaschismic]] generator, and indeed the [[diaschisma]] 2048/2045 is also tempered out. This generator makes a slew of intervals of reasonable prime limit that are not far from just: two of them make a near-just whole tone ~[[9/8]]; three of them make a mildly flat classic minor third ~[[6/5]]; four of them make a mildly flat undecimal major third ~[[14/11]]; five of them make a near-just classic acute fourth ~[[27/20]]; six of them pass the [[semioctave]] to make a slightly flat greater septimal tritone ~[[10/7]]; seven of them make a slightly flat septimal superfifth ~[[32/21]]; eight of them make a slightly flat tridecimal supraminor sixth ~[[21/13]]; nine of them make a near-just septimal major sixth ~[[12/7]]; and ten of them make an extremely accurate undecimal supraminor seventh ~[[20/11]]. Other common intervals such as the moderately sharp (although high in relative error) classic major third ~[[5/4]], the near-just perfect fourth ~[[4/3]], and the near-just perfect fifth ~[[3/2]] are in very easy reach of the chain of rightward generators, and not very distant from the root note. This may be sufficient compensation for the reverse chroma and the range of only three full octaves (which slope only slightly upward), with large partial octaves being chopped off by the upper left and lower right corners.

~~Contents of this section moved to separate page~~: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 05:57, 21 ~~June~~ 2025 (UTC)

Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 23:11, 17 August 2025 (UTC)

Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:40, 21 August 2025 (UTC)

== Compton-related rank 3 temperament Lumatone mappings ==

Line 42:

Line 119:

Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 10:55, 22 May 2025 (UTC)

Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:00, 24 May 2025 (UTC)

=== 90edo (demonstrated to work) ===

[[Bryan Deister]] has demonstrated the [[Diaschismic]]-[[256/255|Charismic]] [[10L 2s]] mapping for [[90edo]] (with 8:5 step ratio), in [https://www.youtube.com/shorts/0j33e4F-4jY ''microtonal improvisation in 90edo''] (20025). The rightward generator 8\90 is a semitone that functions as both ~[[16/15]] and ~[[17/16]] (the charisma [[256/255]] is tempered out). Splitting the octave in half (the [[diaschisma]] 2048/2025 is tempered out) enables this generator to produce the mapping without [[contorsion]]. The range is about 2⅔ octaves with no missed notes, with a mild upward slope.

Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 22:10, 26 July 2025 (UTC)

Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 11:25, 28 July 2025 (UTC)

== Diatonicized Chromaticism + Kleischismic + Cassandra (Garibaldi) Lumatone mappings ==

Line 66:

Line 152:

Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 18:30, 9 July 2025 (UTC)

== ~~Hemiwürschmidt~~/~~Hemithir~~/~~HemiwurLumatone mappings~~ ==

== Godzilla-related rank-3 Lumatone mappings ==

=== 62edo (demonstrated to work) ===

[[Bryan Deister]] has demonstrated a [[Godzilla]] Lumatone mapping for [[62edo]] in [https://www.youtube.com/shorts/UerD0NqBbng ''microtonal improvisation in 62edo''] (2025), with scale [[5L 4s]] with 10:3 step ratio, which also has easy provision for dividing the near-just septimal minor seventh ~[[7/4]] (50\62) into five equal parts each functioning as a meantone whole tone (~[[9/8]], ~[[10/9]], and ~[[19/17]]) (10\62 is right by one key), which is naturally useful in its own right for mixing the common practice sound in with the xenharmonic sounds. A logical implication of splitting the ~7/4 into five meantone whole tones is that the near-just classic major third ~[[5/4]] is very easily accessible as two of these divided generators, and the only slightly flat lesser septimal tritone ~[[7/5]] is easily accessible as three of them. As convenient as this rightward generator is, it would produce a contorted mapping if not for a second generator; the upwards generator 7\62 is convenient for this as a a tridecimal neutral second that functions as both ~[[12/13]] and ~[[13/14]] (the buzurgisma/dhanvantarisma [[169/168]] is tempered out); backing off from ~7/4 by two of these generators gives the fifth (the flat ~[[3/2]] shared with [[31edo]]), while backing off from ~7/5 by two of these generators gives a moderately flat classic minor third ~[[6/5]]. Octaves slant down moderately, and the range is just under 4⅓ octaves with no missed notes and no repeated notes.

Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 21:00, 22 July 2025 (UTC)

Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:18, 24 July 2025 (UTC)

==~~= 99edo~~ (~~demonstrated to work but awaiting approval~~) ===

== Magic (Divination/Soothsaying) related Lumatone mappings ==

~~[[Bryan Deister]]'s [https://www.youtube.com/shorts/p9OUaFuTUek ''99edo waltz'']~~ (~~2025). (Temperament text goes here.~~)

=== 82edo (demonstrated to work) ===

[[Bryan Deister]] has demonstrated a [[8L 6s]] mapping of [[82edo]]. Being even 82edo supports a [[semioctave]] period, with the diagassormisma ([[3042/3025]]) being tempered out in the [[patent val]] or the kalisma ([[9801/9800]]) being tempered out in the 82e val; this enables it to use the (somewhat sharp) septimal major third ~[[9/7]] (as 30\82) as a generator (which would be [[contorted]] down to [[41edo]] with a whole octave period), in a temperament like [[Magic family#Soothsaying|Soothsaying]] or [[Magic family#Divination|Divination]], but using the septimal major third as a generator instead of the classic major third ~[[5/4]]. (Since 82edo also supports actual Soothsaying in its patent val and actual Divination in its 82e val, it is also possible to use generator 26\82, the somewhat flat ~[[5/4]], although the resulting [[6L 4s]] scale is a bit more tricky to play using this layout.) The range is about 2¾ octaves with no missed notes, and the octaves slant down.

Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 12:55, 6 July 2025 (UTC)

Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 11:45, 15 July 2025 (UTC)

Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 05:24, 16 July 2025 (UTC)

== Meantone Lumatone mappings ==

@@ Line 7: / Line 7: @@
 === 39edo (demonstrated to work) ===
-[[Bryan Deister]] has used a [[Porcupine]]-inspired layout for [[39edo]], as demonstrated in [https://www.youtube.com/watch?v=XLRaG_pBN7k&lc=UgwfjZwncsryQjeNUg14AaABAg.AHVkw8aNSEGAHZU_J2qOPM ''39edo jam''] (2025). To take advantage of the fact that 39edo is at the intersection of [[Augmented]] and [[Immunity]], the rightward generator is 5\39, half of a [[6/5]] minor third as [[12/11]] ~ [[11/10]] (but much closer to 12/11).  This enables a MODMOS derived from [[1L&nbsp;6s]] by shrinking the large step from 9\39 to 8\39 and expanding one of the small steps from 5\39 to 6\39, to enable chords such as 12/11 (somewhat sharp, at 5\39) - 6/5 (slightly flat, at 10\39) - [[11/8]] (near-just, at 18\39) - [[3/2]] (mildly sharp, 23\39) - [[18/11]] (moderately sharp, at 28\39) - [[9/5]] (near-just, at 33\39). Playing this chord uses almost the same geometry of depressed keys as that for playing a diatonic scale in a diatonic mapping (but has a very different sound effect), save when proceeding to the next octave. The range is slightly over 6 octaves overall (which slant moderately downwards), but with the first and last octaves missing some notes due to clipping in the upper left and lower right corners of the layout.
+[[Bryan Deister]] has used a [[Porcupine]]-inspired layout for [[39edo]], as demonstrated in [https://www.youtube.com/watch?v=XLRaG_pBN7k&lc=UgwfjZwncsryQjeNUg14AaABAg.AHVkw8aNSEGAHZU_J2qOPM ''39edo jam''] (2025). To take advantage of the fact that 39edo is at the intersection of [[Augmented]] and [[Immunity]], the rightward generator is 5\39, half of a [[6/5]] minor third as [[12/11]] ~ [[11/10]] (but much closer to 12/11).  This enables a MODMOS derived from [[1L&nbsp;6s]] by shrinking the large step from 9\39 to 8\39 and expanding one of the small steps from 5\39 to 6\39, to enable chords such as 12/11 (somewhat sharp, at 5\39) - 6/5 (slightly flat, at 10\39) - [[11/8]] (near-just, at 18\39) - [[3/2]] (mildly sharp, 23\39) - [[18/11]] (moderately sharp, at 28\39) - [[9/5]] (near-just, at 33\39). Playing this chord uses almost the same geometry of depressed keys as that for playing a diatonic scale in a diatonic mapping (but has a very different sound effect), save when proceeding to the next octave. The range is slightly over 6 octaves overall (which slant moderately downwards), but with the first and last octaves missing some notes due to clipping in the upper left and lower right corners of the layout. The range is just under four octaves (which slant upwards mildly), with no missed notes and one repeated note in each octave.
 {{Lumatone EDO mapping|n=39|start=34|xstep=5|ystep=3}}
@@ Line 14: / Line 14: @@
 Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 06:30, 2 May 2025 (UTC)
-== Cantonismic-Werckismic rank-3 temperament Lumatone mappings ==
+== Augmented (Triforce) + Bohpier Lumatone mappings ==
-Due to this page getting too large, moved these to [[User:Lucius_Chiaraviglio/Keyboard_Layout_Lab/Various rank-3 temperament Lumatone mappings|Various rank-3 temperament Lumatone mappings]].
+=== 33edo (demonstrated to work) ===
+[[Bryan Deister]] has demonstrated two mappings for [[33edo]] that function for the temperaments [[Augmented]] ([[Augmented family#Triforce|Triforce]], 33d val, [[3L&nbsp;3s]] scale with 7:4 step ratio) and [[Bohpier]] (33cd val, [[8L&nbsp;1s]] scale with 4:1 step ratio). The down-right (forward chroma version) or rightward (reverse chroma version) generator is a somewhat flat Alpharabian tendoneutral second ~[[12/11]] which can be stacked to get several consonant intervals; however, some of them map inconsistently. Two of these generators make a near-just neogothic minor third ~[[13/11]], mapped consistently. Three of these generators make a near-just septimal major third ~[[9/7]] by sound, but the mapping only works if 9/7 is constituted as (3♭ × 3♯) ÷ 7 or as 9 ÷ 7♭ (33d val). Four of these generators make a near-just lesser septimal tritone ~[[7/5]], mapped consistently ([[patent val]] or 33cd val). Six of these generators make a flat classic major sixth ~[[5/3]] by sound, but the mapping only works if 5/3 is constituted as 5♭ ÷ 3 (33c val). Seven of these generators make a near-just classic minor seventh ~[[9/5]] by sound, but the mapping only works if 9/5 is constituted as (3♭ × 3♯) ÷ 5 or as 9 ÷ 5♭ (33c val). The range is a bit over six octaves in the forward chroma version or five octaves in the reverse chroma version; in both cases, the octaves slope moderately downwards resulting in a vertical wraparound.
+==== Forward chroma ====
+Demonstrated in [https://www.youtube.com/shorts/mkaaAJEyGFU ''33edo riff''] (2025).
+{{Lumatone EDO mapping|n=33|start=0|xstep=7|ystep=-3}}
+==== Reverse chroma ====
+Demonstrated in [https://www.youtube.com/watch?v=GypR6x_Ih1I ''33edo jam''] (2025).
+{{Lumatone EDO mapping|n=33|start=15|xstep=4|ystep=3}}
+Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:09, 2 August 2025 (UTC)<br>
+Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 09:24, 6 August 2025 (UTC)
+== Bidia + Diminished + Charismic + Semitonismic Lumatone mappings ==
+=== 56edo (demonstrated to work) ===
+[[Bryan Deister]] has demonstrated a [[4L&nbsp;4s]] (9:5 step ratio) mapping for [[56edo]], in [https://www.youtube.com/watch?v=xkfao6yGKGE ''Curious Light - DOORS (microtonal cover in 56edo)''] (2025). Right + down-right divides the octave into slices of 14\56; as an interval in its own right, this is the same as the minor third of [[12edo]], which functions as ~[[19/16]] and ~[[25/21]] (both being near-just). Down-right alone is 5\56, which is the [[Normal forms#Minimal_form|minimal form]] generator for [[Bidia]]; it functions as the classic diatonic semitone ~[[16/15]], the large septendecimal semitone ~[[17/16]], and the small septendecimal semitone ~[[18/17]], meaning that the charisma [[256/255]] and the semitonisma [[289/288]] are both tempered out; two of them make a rather sharp whole tone ~[[9/8]]; three of them (passing the quarter-octave) make a mildly sharp classic minor third ~[[6/5]], although the afore-mentioned quarter-octave (12edo-style) minor third is easier to reach; in contrast, the near-just classic major third ~[[5/4]] is very easy to reach with just two moves rightwards, and a down-right move from this reaches the moderately flat fourth ~[[4/3]]; two more down-right moves reaches the rather sharp fifth ~[[3/2]]. The efficiency is almost as good as that of the diatonic mapping, with no missed notes and one repeated note per octave; the overall range is somewhat under five octaves, with no notes chopped off by the left and right edges before reaching the end of overall range. The cost of this is that octaves slant downwards.
+{{Lumatone EDO mapping|n=56|start=0|xstep=9|ystep=-4}}
+Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:38, 21 August 2025 (UTC)<br>
+Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 10:00, 21 August 2025 (UTC)
+== Biyatismic Lumatone mappings ==
+=== 68edo (demonstrated to work) ===
+[[Bryan Deister]] has used a [[Biyatismic clan#Zeus|Biyatismic (Zeus)]] layout with a [[7L&nbsp;1s]] scale (9:5 step ratio) for [[68edo]], as demonstrated in [https://www.youtube.com/shorts/CO1AslAu9E0 ''microtonal improvisation in 68edo''] (2025). The rightward generator 9\68 is a combination of the Alpharabian tendoneutral second ~[[12/11]] and the undecimal submajor second ~[[11/10]], and two of these make a near-just classic minor third ~[[6/5]], with the biyatisma ([[121/120]]) being tempered out. The chroma of the scale (4\68, upwards on this layout) is the near-just diptolemaic chromatic semitone ~[[25/24]], and is convenient to use as a second generator (even though such is not required to avoid [[contorsion]]) to access other consonant intervals quickly, although sometimes with strange preferences built in &mdash; for instance, the septimal whole tone ~[[8/7]] is much easier to reach (at 13\68) than the Pythagorean whole tone ~[[9/8]] (which requires a substantial vertical reach at 12\68), while the septimal minor third ~[[7/6]] (at 15\18) is a much longer vertical reach than the classic minor third ~6/5 (at 18\68), and the septimal major third ~[[9/7]] is a much longer vertical reach (at 25\68) than the classic major third ~[[5/4]] (at 22\68). Fortunately the fourth (~[[4/3]], at 28\68), the Axirabian paramajor fourth (~[[11/8]], at 31\68), the Axirabian paraminor fifth (~[[16/11]], at 37\68) and fifth (~[[3/2]], at 40\68) are all easy to reach as long as they do not go through a vertical wraparound (as happens to the fourth in the bass octave). The range is four octaves plus two notes, and octaves slope upwards &mdash; not severely, but a vertical wraparound is unavoidable if note 0 is placed to get complete octaves as defined to reach from note 0 to note 0.
+{{Lumatone EDO mapping|n=68|start=0|xstep=9|ystep=-4}}
+Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 06:33, 30 July 2025 (UTC)<br>
+Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 12:18, 4 August 2025 (UTC)
+== Blackwood + Diminished Lumatone mappings ==
+=== 20edo (demonstrated to work) ===
+[[Bryan Deister]] has used a [[Diminished]] [[4L&nbsp;4s]] (4:1 step ratio) mapping for [[20edo]] that also functions as a [[Blackwood]] mapping, as demonstrated in [https://www.youtube.com/shorts/bqYA9flwL_g ''20edo prelude''] (2025). In this mapping, the octave can be interpreted as being divided into five parts (Blackwood temperament) or 4\20 or four parts of 5\20 (Diminished temperament). Octaves slope, as expected for a Blackwood mapping, but with plenty of repeated vertical notes, and the range is a bit over 5½ octaves.
+{{Lumatone EDO mapping|n=20|start=6|xstep=4|ystep=-3}}
+Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 19:34, 11 August 2025 (UTC)<br>
+Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 23:18, 11 August 2025 (UTC)
+== Compressed Skwares (Fibotonic) Lumatone mappings ==
+=== 20edo (demonstrated to work) ===
+[[Bryan Deister]] has used a compressed [[Skwares]]) [[2L&nbsp;1s]] (7:6 step ratio) mapping for [[20edo]], as demonstrated in [https://www.youtube.com/watch?v=BFUTeFs7Ycg ''20edo groove''] (2025). In the version of Skwares used for this, instead of substantially sharpening the undecimal major third ~[[14/11]] (or even a septimal major third ~[[9/7]]) to get a diatonic fourth ~[[4/3]] (by stacking and octave-reducing four generators), the undecimal major third (7\20) is near-just, and the fourth is very flat at 480{{c}} (corresponding to the Blackwood sharp fifth at 720{{c}}). Octaves are nearly level (sloping down very gradually), and the range is a bit over 11 octaves, which suggests dividing the keyboard into zones for different instruments.
+{{Lumatone EDO mapping|n=20|start=3|xstep=7|ystep=-1}}
+Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 23:13, 11 August 2025 (UTC)<br>
+Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:00, 13 August 2025 (UTC)
+== Cantonismic Lumatone mappings ==
+=== 64edo (demonstrated to work) ===
+[[Bryan Deister]] has demonstrated a [[Cantonismic]] (flipped and rotated diatonic) mapping of [[64edo]] in [https://www.youtube.com/shorts/ag1FbgAuR6I ''microtonal improvisation in 64edo''] (2025). In this mapping, the rightward generator 7\64 is mapped as a slightly sharp tridecimal supraminor second ~[[14/13]], and the [[cantonisma]] (10985/10976) is tempered out, so that three of them make a fairly sharp classic major third ~[[5/4]], and eight of them make a near-just undecimal neutral seventh ~[[11/6]]; note that apart from ~5/4, these ratios depending upon partial cancellation of errors in the harmonics as represented by 64edo. The rightward generator is actually the short step of the easiest scale to play on this layout (provided that the scale is positioned not to go through a vertical wraparound), with the down-right step being 10\64, which corresponds to the [[Patent val|patent]] (not [[direct approximation]]) whole tone ~[[9/8]], thus enabling a rotated diatonic scale. Octaves alternate between far and near superimposed on an overall slant away over the range of three whole octaves (having no missing notes) plus a fourth octave that has some notes chopped off by the right edge, and some fragmented note sequences in the upper left and lower right corners. A side effect of the alternation of octaves is that accessing the fourth and fifth can be easy or hard depending upon not only the root note, but also the octave &mdash; for instance, in the middle and mid-right octaves, 27\64 and 37\64 are both easily reached from 0\64, but in the second full octaves, they same interval requires a long finger stretch if the root note is greater than 0, and the rotated diatonic scale goes through a vertical wraparound (and moving note 0 would simply cause other root notes to have the same problem in some of the octaves).
+{{Lumatone EDO mapping|n=64|start=17|xstep=7|ystep=3}}
+Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:51, 26 July 2025 (UTC)<br>
+Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 10:52, 28 July 2025 (UTC)
+== Diaschismic + Charismic + Semitonismic Lumatone mappings ==
+=== 58edo (demonstrated to work) ===
+[[Bryan Deister]] has demonstrated a [[2L&nbsp;6s]] (14:5 step ratio) mapping for [[58edo]] in [https://www.youtube.com/shorts/7gkRyld5OU8 ''Waltz in 58edo''] (2025). The rightward generator 5\58 functions as the classic diatonic semitone ~[[16/15]], the large septendecimal semitone ~[[17/16]], and the small septendecimal semitone ~[[18/17]], meaning that the charisma [[256/255]] and the semitonisma [[289/288]] are both tempered out. The rightward generator is also the [[normal forms|minimal form]] of the [[Diaschismic]] generator, and indeed the [[diaschisma]] 2048/2045 is also tempered out. This generator makes a slew of intervals of reasonable prime limit that are not far from just: two of them make a near-just whole tone ~[[9/8]]; three of them make a mildly flat classic minor third ~[[6/5]]; four of them make a mildly flat undecimal major third ~[[14/11]]; five of them make a near-just classic acute fourth ~[[27/20]]; six of them pass the [[semioctave]] to make a slightly flat greater septimal tritone ~[[10/7]]; seven of them make a slightly flat septimal superfifth ~[[32/21]]; eight of them make a slightly flat tridecimal supraminor sixth ~[[21/13]]; nine of them make a near-just septimal major sixth ~[[12/7]]; and ten of them make an extremely accurate undecimal supraminor seventh ~[[20/11]]. Other common intervals such as the moderately sharp (although high in relative error) classic major third ~[[5/4]], the near-just perfect fourth ~[[4/3]], and the near-just perfect fifth ~[[3/2]] are in very easy reach of the chain of rightward generators, and not very distant from the root note. This may be sufficient compensation for the reverse chroma and the range of only three full octaves (which slope only slightly upward), with large partial octaves being chopped off by the upper left and lower right corners.
+{{Lumatone EDO mapping|n=58|start=27|xstep=5|ystep=9}}
-Contents of this section moved to separate page:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 05:57, 21 June 2025 (UTC)
+Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 23:11, 17 August 2025 (UTC)<br>
+Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:40, 21 August 2025 (UTC)
 == Compton-related rank 3 temperament Lumatone mappings ==
@@ Line 42: / Line 119: @@
 Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 10:55, 22 May 2025 (UTC)<br>
 Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:00, 24 May 2025 (UTC)
+=== 90edo (demonstrated to work) ===
+[[Bryan Deister]] has demonstrated the [[Diaschismic]]-[[256/255|Charismic]] [[10L&nbsp;2s]] mapping for [[90edo]] (with 8:5 step ratio), in [https://www.youtube.com/shorts/0j33e4F-4jY ''microtonal improvisation in 90edo''] (20025). The rightward generator 8\90 is a semitone that functions as both ~[[16/15]] and ~[[17/16]] (the charisma [[256/255]] is tempered out). Splitting the octave in half (the [[diaschisma]] 2048/2025 is tempered out) enables this generator to produce the mapping without [[contorsion]]. The range is about 2⅔ octaves with no missed notes, with a mild upward slope.
+{{Lumatone EDO mapping|n=90|start=84|xstep=8|ystep=-3}}
+Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 22:10, 26 July 2025 (UTC)<br>
+Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 11:25, 28 July 2025 (UTC)
 == Diatonicized Chromaticism + Kleischismic + Cassandra (Garibaldi) Lumatone mappings ==
@@ Line 66: / Line 152: @@
 Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 18:30, 9 July 2025 (UTC)
-== Hemiwürschmidt/Hemithir/HemiwurLumatone mappings ==
+== Godzilla-related rank-3 Lumatone mappings ==
+=== 62edo (demonstrated to work) ===
+[[Bryan Deister]] has demonstrated a [[Godzilla]] Lumatone mapping for [[62edo]] in [https://www.youtube.com/shorts/UerD0NqBbng ''microtonal improvisation in 62edo''] (2025), with scale [[5L&nbsp;4s]] with 10:3 step ratio, which also has easy provision for dividing the near-just septimal minor seventh ~[[7/4]] (50\62) into five equal parts each functioning as a meantone whole tone (~[[9/8]], ~[[10/9]], and ~[[19/17]]) (10\62 is right by one key), which is naturally useful in its own right for mixing the common practice sound in with the xenharmonic sounds. A logical implication of splitting the ~7/4 into five meantone whole tones is that the near-just classic major third ~[[5/4]] is very easily accessible as two of these divided generators, and the only slightly flat lesser septimal tritone ~[[7/5]] is easily accessible as three of them. As convenient as this rightward generator is, it would produce a contorted mapping if not for a second generator; the upwards generator 7\62 is convenient for this as a a tridecimal neutral second that functions as both ~[[12/13]] and ~[[13/14]] (the buzurgisma/dhanvantarisma [[169/168]] is tempered out); backing off from ~7/4 by two of these generators gives the fifth (the flat ~[[3/2]] shared with [[31edo]]), while backing off from ~7/5 by two of these generators gives a moderately flat classic minor third ~[[6/5]]. Octaves slant down moderately, and the range is just under 4⅓ octaves with no missed notes and no repeated notes.
+{{Lumatone EDO mapping|n=62|start=4|xstep=10|ystep=-7}}
+Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 21:00, 22 July 2025 (UTC)<br>
+Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:18, 24 July 2025 (UTC)
-=== 99edo (demonstrated to work but awaiting approval) ===
+== Magic (Divination/Soothsaying) related Lumatone mappings ==
-[[Bryan Deister]]'s [https://www.youtube.com/shorts/p9OUaFuTUek ''99edo waltz''] (2025).  (Temperament text goes here.)
+=== 82edo (demonstrated to work) ===
-{{Lumatone EDO mapping|n=99|start=40|xstep=16|ystep=-3}}
+[[Bryan Deister]] has demonstrated a [[8L&nbsp;6s]] mapping of [[82edo]]. Being even 82edo supports a [[semioctave]] period, with the diagassormisma ([[3042/3025]]) being tempered out in the [[patent val]] or the kalisma ([[9801/9800]]) being tempered out in the 82e val; this enables it to use the (somewhat sharp) septimal major third ~[[9/7]] (as 30\82) as a generator (which would be [[contorted]] down to [[41edo]] with a whole octave period), in a temperament like [[Magic family#Soothsaying|Soothsaying]] or [[Magic family#Divination|Divination]], but using the septimal major third as a generator instead of the classic major third ~[[5/4]].  (Since 82edo also supports actual Soothsaying in its patent val and actual Divination in its 82e val, it is also possible to use generator 26\82, the somewhat flat ~[[5/4]], although the resulting [[6L&nbsp;4s]] scale is a bit more tricky to play using this layout.) The range is about 2¾ octaves with no missed notes, and the octaves slant down.
+{{Lumatone EDO mapping|n=82|start=4|xstep=8|ystep=-5}}
-Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 12:55, 6 July 2025 (UTC)
+Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 11:45, 15 July 2025 (UTC)<br>
+Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 05:24, 16 July 2025 (UTC)
 == Meantone Lumatone mappings ==