Lumatone mapping for 52edo: Difference between revisions

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== Diatonic ==

You can use the b~~ ~~val, but it is extremely sharp, to the point where major seconds become 8/7 instead of 9/8~~. This gives~~ [[~~ultrapyth~~]].

You can use the b val, which produces [[Syntonic–diatonic_equivalence_continuum#Dirt|Dirt]], but the fifth is extremely sharp, to the point where major seconds become [[8/7]] instead of [[9/8]] and the best approximation to [[5/4]] is a doubly augmented 7th.

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== Pseudo-Pentacircle ==

[[Bryan Deister]] has used a layout for [[52edo]] in which the generator is 9\52, as ~[[9/8]] but mapped by direct approximation rather than as the version mapped by the patent val or by the 52b val, which means that it has to be constituted as {{nowrap|(3♭ × 3♯) / 8}} to make use of the dual-fifth feature of 52edo. Two of these map to a ~[[14/11]] major third, as in [[Pentacircle clan|Pentacircle]] but for the direct approximation mapping of ~9/8. The upward generator is ~[[16/15]]. Octaves slant down and then wrap around, but the compass is 5 full octaves, with no missed notes, which is competitive with the Diatonic and Neutral Thirds layouts. This layout is demonstrated in [https://www.youtube.com/shorts/lNJCZz7EjL0 ''microtonal improvisation in 52edo''] (2025); in the video, some notes are cut off at the right edge due to the use of only 2 MIDI channels.

[[Bryan Deister]] has used a layout for [[52edo]] in which the generator is 9\52, as ~[[9/8]] but mapped by direct approximation rather than as the version mapped by the patent val or by the 52b val, which means that it has to be constituted as (3♭~~ ~~×~~ ~~3♯)~~ ~~/~~ ~~8 to make use of the dual-fifth feature of 52edo. Two of these map to a ~[[14/11]] major third, as in [[Pentacircle clan|Pentacircle]] but for the direct approximation mapping of ~9/8. The upward generator is ~[[16/15]]. Octaves slant down and then wrap around, but the compass is 5 full octaves, with no missed notes, which is competitive with the Diatonic and Neutral Thirds layouts. This layout is demonstrated in [https://www.youtube.com/shorts/lNJCZz7EjL0 ''microtonal improvisation in 52edo''] (2025); in the video, some notes are cut off at the right edge due to the use of only 2 MIDI channels.

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 == Diatonic ==
-You can use the b&nbsp;val, but it is extremely sharp, to the point where major seconds become 8/7 instead of 9/8. This gives [[ultrapyth]].
+You can use the b val, which produces [[Syntonic–diatonic_equivalence_continuum#Dirt|Dirt]], but the fifth is extremely sharp, to the point where major seconds become [[8/7]] instead of [[9/8]] and the best approximation to [[5/4]] is a doubly augmented 7th.
 {{Lumatone EDO mapping|n=52|start=16|xstep=10|ystep=-9}}
@@ Line 10: / Line 10: @@
 == Pseudo-Pentacircle ==
+[[Bryan Deister]] has used a layout for [[52edo]] in which the generator is 9\52, as ~[[9/8]] but mapped by direct approximation rather than as the version mapped by the patent val or by the 52b&nbsp;val, which means that it  has to be constituted as {{nowrap|(3♭ × 3♯) / 8}} to make use of the dual-fifth feature of 52edo. Two of these map to a ~[[14/11]] major third, as in [[Pentacircle clan|Pentacircle]] but for the direct approximation mapping of ~9/8. The upward generator is ~[[16/15]]. Octaves slant down and then wrap around, but the compass is 5 full octaves, with no missed notes, which is competitive with the Diatonic and Neutral Thirds layouts. This layout is demonstrated in [https://www.youtube.com/shorts/lNJCZz7EjL0 ''microtonal improvisation in 52edo''] (2025); in the video, some notes are cut off at the right edge due to the use of only 2 MIDI channels.
-[[Bryan Deister]] has used a layout for [[52edo]] in which the generator is 9\52, as ~[[9/8]] but mapped by direct approximation rather than as the version mapped by the patent val or by the 52b val, which means that it  has to be constituted as (3♭&nbsp;×&nbsp;3♯)&nbsp;/&nbsp;8 to make use of the dual-fifth feature of 52edo. Two of these map to a ~[[14/11]] major third, as in [[Pentacircle clan|Pentacircle]] but for the direct approximation mapping of ~9/8. The upward generator is ~[[16/15]]. Octaves slant down and then wrap around, but the compass is 5 full octaves, with no missed notes, which is competitive with the Diatonic and Neutral Thirds layouts. This layout is demonstrated in [https://www.youtube.com/shorts/lNJCZz7EjL0 ''microtonal improvisation in 52edo''] (2025); in the video, some notes are cut off at the right edge due to the use of only 2 MIDI channels.
 {{Lumatone EDO mapping|n=52|start=4|xstep=9|ystep=-5}}
 {{Navbox Lumatone}}