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

Hyperkleismic Lumatone mappings: Move this section down to proper place; 11edo: Fix section heading
m 46edo (demonstrated to work): Add more specific date to demo video because now another ''46edo improv'' is out
 
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Moved here from [[User:Lucius Chiaraviglio/Musical Mad Science|Musical Mad Science]]:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 06:54, 28 March 2025 (UTC)
Moved here from [[User:Lucius Chiaraviglio/Musical Mad Science|Musical Mad Science]]:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 06:54, 28 March 2025 (UTC)
== Mavila (Superdiatonic) + Baldy (Amsochromic) Lumatone mappings ==
=== 23edo (demonstrated to work) ===
Still using the [[23edo]] flat fifth ~[[3/2]] for [[mavila]] temperament, an alternative to the antidiatonic mapping is the superdiatonic mapping, having a [[7L 2s]] scale (3:1 step ratio), with the generator 13\23 being reached by moving four keys right plus one key down-right. This reduces the range from just under five octaves to about 3½ octaves, although it keeps them nearly level — rising gently enough to support division into multiple manuals. It also supports a [[6L 5s]] scale (3:1 step ratio) if the mildly sharp directly-approximated Pythagorean whole tone ~[[9/8]] is used as a generator instead, although this causes the octaves to slope down enough to prevent vertical division into two contiguous manuals; this generator (4\23) is reached by moving one key right plus one key down-right, which is easier than reaching the mavila generator. This mapping is demonstrated on the left Lumatone in {{W|David Wise}}'s [https://www.youtube.com/watch?v=joi8vyChSy4&list=WL&index=266 ''Aquatic Ambience''] (1993 via {{W|Donkey Kong Country}} (1994) – microtonal cover in 23edo by [[Stephen Weigel]] (right) and [[Vito Sicurella]] (left) on Lumatones (2026, from UnTwelve 2025); the color scheme is for the superdiatonic scale, but different between the left and right halves of the layout to represent division into two horizontal zones for different soft synthesizers. This layout is used on the left Lumatone; for the right Lumatone layout, see Oolong (Smitonic) below.
{{Lumatone EDO mapping|n=23|start=0|xstep=3|ystep=-2}}
Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 16:49, 24 July 2026 (UTC)<br>
Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 03:12, 25 July 2026 (UTC)
== Oolong (Smitonic) Lumatone mappings ==
=== 23edo (demonstrated to work) ===
An alternative for [[23edo]] to using either (highly inaccurate) fifth as a generator is stacking the much more accurate (only slightly flat) classic minor third ~[[6/5]], as in [[oolong]] temperament, having a [[4L&nbsp;3s]] scale (5:1 step ratio); the generator 6\23 is reached by moving one key right plus one key down-right. This results in a moderate downwards slope of the octaves, but the range is 5¾ octaves, still with a generous allocation of repeated notes to mitigate vertical wraparounds. This mapping is demonstrated on the right Lumatone in {{W|David Wise}}'s [https://www.youtube.com/watch?v=joi8vyChSy4&list=WL&index=266 ''Aquatic Ambience''] (1993 via {{W|Donkey Kong Country}} (1994) – microtonal cover in 23edo by [[Stephen Weigel]] (right) and [[Vito Sicurella]] (left) on Lumatones (2026, from UnTwelve 2025). This layout is used on the right Lumatone; for the left Lumatone layout, see Mavila (Superdiatonic) + Baldy (Amsochromic) above.
{{Lumatone EDO mapping|n=23|start=0|xstep=5|ystep=-4}}
Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 16:49, 24 July 2026 (UTC)<br>
Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 03:12, 25 July 2026 (UTC)
== Amavil Lumatone mappings ==
=== 43edo (demonstrated to work) ===
It is possible to use a [[7L&nbsp;2s]] (5:4 step ratio) superdiatonic mapping with [[43edo]], as in [[mavila]]. Mavila itself is not a high-accuracy tuning, but it has some relatives that are high-accuracy &mdash; in this case, [[amavil]], of the [[mabila family]]. As with mavila, it uses a sub-fifth as its generator, in this case 24\43; however, unlike actual mavila, the generator is explicitly defined as something other than the fifth, which is instead left at the most accurate mapping 43edo has to offer for ~[[3/2]] (at 25\43). Instead, the sub-fifth is mapped as a mildly flat undecimal diminished fifth ~[[22/15]]. After octave-reduction, three of them make a somewhat flat classic minor sixth ~[[8/5]]; four of them make a subminor third that functions as ~[[7/6]] (sharp), ~[[13/11]] (flat), and ~[[20/17]] (diatismic minor third, close to just, only slightly sharp); six of them make a near-just pentacircle major third ~[[14/11]]; seven of them make a near-just classic major seventh ~[[15/8]]; eight of them make a moderately flat undecimal major fourth ~[[11/8]]; and ten of them make the moderately flat perfect fifth ~[[3/2]]. The range is about 3¾ octaves, which slope mildly upwards, with a generous allotment of repeated notes to mitigate vertical wraparounds.
{{Lumatone EDO mapping|n=43|start=34|xstep=5|ystep=-1}}
Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 04:03, 27 May 2026 (UTC)<br>
Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 01:45, 30 May 2026 (UTC)


== Ammonite + Gariberttet + Porcupinefish Lumatone mappings ==
== Ammonite + Gariberttet + Porcupinefish Lumatone mappings ==
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== Augmented (August) Lumatone mappings ==
=== 21edo (demonstrated to work) ===
It is possible to use [[21edo]] for some types of blues music, taking advantage of its highly accurate [[7/1|7th harmonic]], as demonstrated by [[Bryan Deister]] in [https://www.youtube.com/watch?v=1S4C-m_Dcno ''21edo improv''] (2026). The mapping for this uses a sharp septimal minor third ~[[7/6]] as a generator with the octave divided in to three parts as a sharp classic major third ~[[5/4]], making this an [[augmented_(temperament)|augmented temperament]] mapping of the flat fifth ([[august]]) variety, with scales [[3L&nbsp;3s]] proceeding right and down-right and [[8L&nbsp;1s&nbsp;(4/1-equivalent)]] proceeding right, with both scales having a 5:2 step ratio. (The ⅓-octave complement of ~[[7/6]] is a mildly-flat septimal diatonic semitone ~[[15/14]], which is one key down-right, a convenient mapping for a diatonic semitone.) The range is about 6¾ octaves, and the octaves slope down considerably (incurring vertical wraparounds mitigated by repeated notes), while the double octaves slope upwards mildly.
{{Lumatone EDO mapping|n=21|start=2|xstep=5|ystep=-3}}
Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 03:32, 2 June 2026 (UTC)


== Augmented (Triforce) + Bohpier Lumatone mappings ==
== Augmented (Triforce) + Bohpier Lumatone mappings ==
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=== 46edo (demonstrated to work) ===
=== 46edo (demonstrated to work) ===


[[Bryan Deister]] has demonstrated a [[6L&nbsp;2s]] (6:5 step ratio) [[Sensipent_family#Bison|Bison]] mapping for [[46edo]] in [https://www.youtube.com/shorts/K-Gu_YkjYS4 ''46edo improv''] (2025), with Bison being the intersection of [[Porwell temperaments|Porwell]] with [[Sensi]]. The (rightward) generator for this is 6\46, which is a near-just septimal neutral second ~[[35/32]], and two of them yield a near-just (barely flat) classic major third ~[[6/5]] (the Porwell comma [[6144/6125]] is tempered out). The range is just over four octaves with no missing notes and some repeats to mitigate vertical wraparounds, and the octaves are almost level.
[[Bryan Deister]] has demonstrated a [[6L&nbsp;2s]] (6:5 step ratio) [[Sensipent_family#Bison|Bison]] mapping for [[46edo]] in [https://www.youtube.com/shorts/K-Gu_YkjYS4 ''46edo improv''] (2025-10-25), with Bison being the intersection of [[Porwell temperaments|Porwell]] with [[Sensi]]. The (rightward) generator for this is 6\46, which is a near-just septimal neutral second ~[[35/32]], and two of them yield a near-just (barely flat) classic major third ~[[6/5]] (the Porwell comma [[6144/6125]] is tempered out). The range is just over four octaves with no missing notes and some repeats to mitigate vertical wraparounds, and the octaves are almost level.


{{Lumatone EDO mapping|n=46|start=38|xstep=6|ystep=-1}}
{{Lumatone EDO mapping|n=46|start=38|xstep=6|ystep=-1}}


Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 09:11, 20 October 2025 (UTC)<br>
Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 09:11, 20 October 2025 (UTC)<br>
Last modified, and moved here from [[User:Lucius Chiaraviglio/Keyboard Layout Lab/Unnamed Temperament Lumatone mappings|Unnamed Temperaments Lumatone mappings]]:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:11, 23 October 2025 (UTC)
Moved here from [[User:Lucius Chiaraviglio/Keyboard Layout Lab/Unnamed Temperament Lumatone mappings|Unnamed Temperaments Lumatone mappings]]:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:11, 23 October 2025 (UTC)<br>
Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 18:30, 31 July 2026 (UTC)


== Bison + Hemikleismic + Divination + Hocus Lumatone mappings ==
== Bison + Hemikleismic + Divination + Hocus Lumatone mappings ==
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== Blackwood + Decimal/Lemba Lumatone mappings ==
=== 10edo (demonstrated to work) ===
Since [[10edo]] is a tuning of [[blackwood]], a blackwood mapping can work (although it is not the most efficient in terms of note usage), as demonstrated in [https://bee-swarm-simulator.fandom.com/wiki/Onett_(Developer) Onett]'s [https://www.youtube.com/shorts/EZCCjsjgCss ''Stick Bug''] (2019?) – microtonal cover in 10edo by [[Bryan Deister]] (2026). The scale is [[4L&nbsp;2s]] with a 2:1 step ratio, as in [[decimal]] and [[lemba]] temperaments. The octaves slope up with the rows (as expected for Blackwood) or slightly downwards with the scale, and the range is just under 6 octaves, with the potential for division into multiple manuals (although the upper and lower ones will necessarily be partial or wedge-shaped, depending upon details of the division).
{{Lumatone EDO mapping|n=10|start=0|xstep=2|ystep=-1}}
Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 04:39, 10 July 2026 (UTC)<br>
Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 03:32, 16 July 2026 (UTC)


== Blackwood + Diminished Lumatone mappings ==
== Blackwood + Diminished Lumatone mappings ==
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== Compressed Skwares (Fibotonic) Lumatone mappings ==
== Blackwood + Whitewood Lumatone mappings ==


=== 20edo (demonstrated to work) ===
=== 35edo (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.
A flipped version of the [[5L&nbsp;5s]] (5:2 step ratio) [[blackwood]] + [[whitewood]] mapping is possible. The octaves slope upwards with the rows (as expected for blackwood mappings), and the range is a bit under 5½ octaves with no missed notes and some repeated notes to mitigate vertical wraparounds. [[Bryan Deister]] has used this mapping in [https://www.youtube.com/watch?v=x8doWEgXMCY ''35edo improv''] (2026).


{{Lumatone EDO mapping|n=20|start=3|xstep=7|ystep=-1}}
{{Lumatone EDO mapping|n=35|start=3|xstep=7|ystep=-5}}


Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 23:13, 11 August 2025 (UTC)<br>
Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 04:04, 9 June 2026 (UTC)<br>
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== Cantonismic Lumatone mappings ==
== Cantonismic Lumatone mappings ==
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== Compton-related rank 3 temperament 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]].
Contents of this section moved to separate page:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 05:57, 21 June 2025 (UTC)


== Diaschismic + Charismic + Semitonismic Lumatone mappings ==
== Diaschismic + Charismic + Semitonismic Lumatone mappings ==
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== Compton-related rank 3 temperament 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]].
Contents of this section moved to separate page:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 05:57, 21 June 2025 (UTC)


== Devichromic Lumatone mappings ==
== Devichromic Lumatone mappings ==
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Moved here from [[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]]) 05:49, 15 July 2025 (UTC)
Moved here from [[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]]) 05:49, 15 July 2025 (UTC)
=== Rotated Meantone Lumatone mappings ===
==== 74edo (demonstrated to work) ====
One option for dealing with the large gamut of [[74edo]] on a standard-sized Lumatone is to flip and rotate the diatonic mapping, as demonstrated by [[Bryan Deister]] in [https://www.youtube.com/shorts/vi-KljzPkGs ''74edo improv''] (2026). The scale is still [[5L&nbsp;2s]] with a 12:7 step ratio, but now the whole tones proceed down-right while the diatonic semitones proceed right. Each octave is still missing some notes, but due to the octave slope, they are different missing notes in each octave (other than the octaves chopped off by the upper left and lower right corners); the range is three mostly-complete octaves plus a bass octave of full compass but severely truncated gamut, plus a partial treble octave.
{{Lumatone EDO mapping|n=74|start=0|xstep=7|ystep=5}}
Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 01:12, 30 June 2026 (UTC)<br>
Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 03:00, 2 July 2026 (UTC)
==== 88edo (demonstrated to work) ====
Since [[88edo]] is too large for the normal Standard Lumatone Mapping for Pythagorean to get all the notes, while the [[7L&nbsp;2s]] mapping may cause excessive stretching of the fingers for some people, another possibility is to rotate the Lumatone to make the [[5L&nbsp;2s]] scale (14:9 step ratio) run down-right and down, as demonstrated in {{W|Nobuo Uematsu}}'s [https://www.youtube.com/shorts/d3v6ji8EqQ8 ''The Extreme''] from ''{{W|Final Fantasy VIII}}'' (1999) – microtonal cover in 88edo by [[Bryan Deister]] (2026). This layout yields just under 2⅛ complete octaves with no missing notes and very few repeated note, although the upper left and lower right corners both have a large number of notes in partial octaves below and above these, due to the lopsidedness of the mapping; if the Lumatone is not rotated, the octaves slope down, but if the Lumatone is rotated 90° left as shown in the video, then the octaves proceed upward with a rightward slant.
{{Lumatone EDO mapping|n=88|start=9|xstep=5|ystep=9}}
Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 03:21, 11 July 2026 (UTC)<br>
Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 06:11, 14 July 2026 (UTC)


=== Meantone-related rank-3 Lumatone mappings ===
=== Meantone-related rank-3 Lumatone mappings ===
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== Niner + Diminished Lumatone mappings ==
=== 36edo (demonstrated to work) ===
It is possible to use the [[blackwood]] + [[whitewood]] mappings of [[35edo]] as inspiration for mapping [[36edo]] as a lattice, using its factors of closest size to those of 35edo, which are 4 and 9, as in [[niner]] + [[Diminished_(temperament)|diminished]] temperaments, with a [[4L&nbsp;4s]] scale of step ratio 5:4 running right and down. Similarly to blackwood and whitewood, the octaves slope upwards with the rows, but even so the mapping works to give 5 octaves with some repeated notes to mitigate vertical wraparounds, with no missed notes except for one missed note 35 in the top otherwise contiguous octave. [[Bryan Deister]] has used this mapping in [https://www.youtube.com/shorts/KCtEYSkEK8U ''36edo improv''] (2026).
{{Lumatone EDO mapping|n=36|start=2|xstep=4|ystep=5}}
Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 05:10, 9 June 2026 (UTC)<br>
Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 18:51, 26 June 2026 (UTC)


== Orwell mappings ==
== Orwell mappings ==
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== Reversed-Chroma Compressed Tetracot Lumatone mappings ==
== Skwares (Compressed, Fibotonic) Lumatone mappings ==


=== 75edo (demonstrated to work) ===
=== 20edo (demonstrated to work) ===


[[Bryan Deister]] has demonstrated a compressed [[1L&nbsp;5s mapping of [[75edo]] in [https://www.youtube.com/watch?v=5-G2KkYfKLs&list=WL&index=343&pp=gAQBiAQB8AUB ''microtonal improvisation in 75edo''] (2025-06-22). This combines the temperament of [[Tetracot]] with the idea of the compressed [[Lumatone mapping for Porcupine]], by reversing the chroma. (This also contains the Tetracot [[6L&nbsp;1s]] scale, but playing that scale in this layout requires backtracking.) This expands the overall range to more than five octaves, but too much so for anything so large as 75edo, thereby causing missed notes (although it demonstrates how such a mapping could shine for a smaller EDO or a hypothetical XL-sized Lumatone that has room for all of the notes).
[[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=75|start=17|xstep=11|ystep=9}}
{{Lumatone EDO mapping|n=20|start=3|xstep=7|ystep=-1}}


Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 06:23, 29 June 2025 (UTC)<br>
Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 23:13, 11 August 2025 (UTC)<br>
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== Squirrel Lumatone mappings ==
== Squirrel Lumatone mappings ==
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Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:03, 11 July 2025 (UTC)
== Tetracot (Compressed, Reverse-Chroma) Lumatone mappings ==
=== 75edo (demonstrated to work) ===
[[Bryan Deister]] has demonstrated a compressed [[1L&nbsp;5s mapping of [[75edo]] in [https://www.youtube.com/watch?v=5-G2KkYfKLs&list=WL&index=343&pp=gAQBiAQB8AUB ''microtonal improvisation in 75edo''] (2025-06-22). This combines the temperament of [[Tetracot]] with the idea of the compressed [[Lumatone mapping for Porcupine]], by reversing the chroma. (This also contains the Tetracot [[6L&nbsp;1s]] scale, but playing that scale in this layout requires backtracking.) This expands the overall range to more than five octaves, but too much so for anything so large as 75edo, thereby causing missed notes (although it demonstrates how such a mapping could shine for a smaller EDO or a hypothetical XL-sized Lumatone that has room for all of the notes).
{{Lumatone EDO mapping|n=75|start=17|xstep=11|ystep=9}}
Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 06:23, 29 June 2025 (UTC)<br>
Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 00:16, 30 June 2025 (UTC)


== Tsaharuk (Schismatic) Lumatone mappings ==
== Tsaharuk (Schismatic) Lumatone mappings ==