Lumatone mapping for 52edo: Difference between revisions

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{{Lumatone EDO mapping|n=52|start=43|xstep=7|ystep=1}}
{{Lumatone EDO mapping|n=52|start=43|xstep=7|ystep=1}}


== Pseudo-Pentacircle ==
== Diminished + 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 {{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]]. In addition, this mapping makes a [[4L 4s]] scale with 9:4 step ratio easily accessible (barring a vertical wraparound), and 52edo tempers out the greater diesis [[648/625]], making this also a [[Diminished_(temperament)|diminished]] mapping. 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}}
{{Lumatone EDO mapping|n=52|start=4|xstep=9|ystep=-5}}


Revision as of 12:11, 28 March 2026

There are many conceivable ways to map 52edo onto the onto the Lumatone keyboard. However, it has 2 mutually-exclusive rings of fifths, so the Standard Lumatone mapping for Pythagorean is not one of them.

Diatonic

You can use the b val, which produces 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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Neutral thirds

The neutral thirds mapping is probably easier to navigate.

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Diminished + 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 (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 but for the direct approximation mapping of ~9/8. The upward generator is ~16/15. In addition, this mapping makes a 4L 4s scale with 9:4 step ratio easily accessible (barring a vertical wraparound), and 52edo tempers out the greater diesis 648/625, making this also a diminished mapping. 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 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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A version of the above that duplicates note 0 (as note 52, as if making a layout for 53edo) keeps the octaves level. This is demonstrated in Bryan Deister's 52edo improv (2025).

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