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

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

=== 33edo (demonstrated to work ~~but awaiting approval~~) ===

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

[[Bryan Deister]] has demonstrated a [[~~3L 3s~~]] ~~(7:4 step ratio)~~ [[Augmented]] ([[Augmented family#Triforce|Triforce]], 33d val~~) +~~ [[8L 1s]] (4:1 step ratio) [[Bohpier]] (33cd val~~) mapping for~~ [[~~33edo~~]] ~~in [https~~:~~//www~~.~~youtube.com/watch?v=GypR6x_Ih1I ''33edo jam'']~~ (~~2025~~)~~. The~~ rightward 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 five octaves, ~~which~~ slope moderately downwards, resulting in a vertical wraparound.

[[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).

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

==== 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 ~~but awaiting approval~~) ===

=== 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.

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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]]) 05:55, 1 August 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 ==

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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.

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 16: / Line 16: @@
 == Augmented (Triforce) + Bohpier Lumatone mappings ==
-=== 33edo (demonstrated to work but awaiting approval) ===
+=== 33edo (demonstrated to work) ===
-[[Bryan Deister]] has demonstrated a [[3L&nbsp;3s]] (7:4 step ratio) [[Augmented]] ([[Augmented family#Triforce|Triforce]], 33d val) + [[8L&nbsp;1s]] (4:1 step ratio) [[Bohpier]] (33cd val) mapping for [[33edo]] in [https://www.youtube.com/watch?v=GypR6x_Ih1I ''33edo jam''] (2025). The rightward 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 five octaves, which slope moderately downwards, resulting in a vertical wraparound.
+[[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.
-{{Lumatone EDO mapping|n=33|start=16|xstep=4|ystep=3}}
+==== Forward chroma ====
+Demonstrated in [https://www.youtube.com/shorts/mkaaAJEyGFU ''33edo riff''] (2025).
+{{Lumatone EDO mapping|n=33|start=0|xstep=7|ystep=-3}}
-Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:09, 2 August 2025 (UTC)
+==== 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 but awaiting approval) ===
+=== 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.
@@ Line 33: / Line 51: @@
 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]]) 05:55, 1 August 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&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 ==
@@ Line 45: / Line 85: @@
 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}}
+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 ==