User:Lucius Chiaraviglio/Keyboard Layout Lab/Various other Lumatone mappings: Difference between revisions

=== 65edo (demonstrated to work but awaiting approval) ===

[[Bryan Deister]] has used the [[9L 2s]] (7:1 step ratio) mapping for [[65edo]] in [https://www.youtube.com/shorts/W5PXWFduPco ''microtonal improvisation in 65edo''] (2025). The rightward generator 9\65 is a slightly flat acute minor second ~[[27/25]], and three of these make a near-just classic major third ~[[5/4]]; in turn eight classic major thirds (21\65) make a near-just 6th harmonic ~[[6/1]], qualifying this for [[Würschmidt]] temperament, or an extension thereof that divides the Würschmidt generator into three equal parts, but using ~27/25 instead of the tridecimal supraminor second ~[[14/13]], which technically maps to the same interval in 65edo, but is composed of a very flat 7th harmonic and a very sharp 13th harmonic and is thus subject to wart adjustment to another interval for consistency improvement. The range is somewhat under three octaves, and the octaves slant up mildly, with some repeated notes to ease vertical wraparounds.

Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 06:47, 22 July 2025 (UTC)

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

The Würschmidt generator, which is the classic major third ~[[5/4]] (near-just), is 32\99 in [[99edo]], so it is divisible by 2 or 4 but not by 3 (seen with [[65edo]]. Division by 2 to get 16\99 yields [[Hemimean_clan#Hemiwürschmidt|Hemiwürschmidt/Würschmidt/Hemiwur]] with a slightly flat septimal) middle whole ton ~[[28/25]] for the divided generator, with a scale [[6L 1s]] (16:3 step ratio). Division by 2 again (for 4 overall) yields a further extension that uses this mapping's rightward generator 8\99 as a slightly sharp ptolemaic chromatic semitone (major limma) ~[[135/128]]. This mapping only splits the [[Würschmidt]] in half to get greater range (over four octaves) than when splitting it in quarters, but at the cost of missing many notes in each octave. Despite the missing notes, [[Bryan Deister]] has demonstrated this mapping in [https://www.youtube.com/shorts/p9OUaFuTUek ''99edo waltz''] (2025).

{{Lumatone EDO mapping|n=99|start=40|xstep=16|ystep=-3}}

 

 

The Würschmidt generator, which is the classic major third ~[[5/4]] (near-just), is 32\99, so it is divisible by 2 or 4 but not by 3. Division by 2 to get 16\99 yields [[Hemimean_clan#Hemiwürschmidt|Hemiwürschmidt/Würschmidt/Hemiwur]] with a slightly flat septimal) middle whole ton ~[[28/25]] for the divided generator, but tries to get too much range for 99edo, and thereby misses notes. Division by 2 again (for 4 overall) yields a further extension that uses this mapping's rightward generator 8\99 as a slightly sharp ptolemaic chromatic semitone (major limma) ~[[135/128]], with a scale [[12L 3s]] (8:1 step ratio). As befits Würschmidt, eight classic major thirds (32\65) make a near-just 6th harmonic ~[[6/1]]. The range is just over two octaves, and the octaves slant up mildly, with some repeated notes to ease vertical wraparound.

Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:32, 22 July 2025 (UTC)<br>

Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 20:39, 22 July 2025 (UTC)

=== 28edo (demonstrated to work) ===

 

[[Bryan Deister]] has used a layout for [[28edo]] that was inspired by the layout for [[29edo]] (rather than being made for any specific temperament), as demonstrated in [https://www.youtube.com/shorts/--BIQKJ9uvI ''minuet in 28edo''] (2025). The right-moving generator is a somewhat sharp Pythagorean whole tone (~[[9/8]], or near-just [[17/15]], 5\28). The up-moving generator is an almost-just tridecimal supraminor second (~[[14/13]], 3\28).  The range is a bit over five octaves, with octaves alternating near/far and middle with an overall small upwards slant. Although this layout was not designed for any particular temperament, it so happens that the right-moving generator matches [[Machine]].

{{Lumatone EDO mapping|n=28|start=4|xstep=5|ystep=-3}}

 

 

 

[[Bryan Deister]] has used a layout for [[30edo]] that was also inspired by the layout for [[29edo]] (rather than being made for any specific temperament), as demonstrated in [https://www.youtube.com/watch?v=NP3HGr3ZD70&lc=UgxFBmbxZa5dF4ZPj0F4AaABAg.AFzcn1LkVZNAG4JYIvXZvZ ''minuet in 30edo''] (2025). The right-moving generator is a somewhat flat Pythagorean whole tone (~[[9/8]], 5\30; and in the video, the row segments that include note 0 are colored solid red).  The up-moving generator is a somewhat flat tridecimal supraminor second (~[[14/13]], 3\30); neither would be able access the full gamut on its own, but together they cover the full gamut with a generous allotment of repeated notes (indicating that if this layout was to represent a particular temperament, that would have to be a rank-3 temperament if having an octave period, or a rank-2 temperament dividing the octave into multiple periods). The range is a bit under five octaves, with octaves slanting up (while wrapping around) at the same angle as the right-moving generator.

{{Lumatone EDO mapping|n=30|start=4|xstep=5|ystep=-3}}

 

Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 21:39, 29 March 2025 (UTC)