Lumatone mapping for 52edo: Difference between revisions

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→Pseudo-Pentacircle: Add Diminished temperament
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The [[Lumatone mapping for neutral thirds scales|neutral thirds mapping]] is probably easier to navigate.
The [[Lumatone mapping for neutral thirds scales|neutral thirds mapping]] is probably easier to navigate.
{{Lumatone EDO mapping|n=52|start=43|xstep=7|ystep=1}}
{{Lumatone EDO mapping|n=52|start=43|xstep=7|ystep=1}}
== Porcupine ==
[[52edo]] is a valid [[porcupine]] tuning (with scale [[1L 6s]] having a 10:7 step ratio), as [[Bryan Deister]] demonstrates in [https://www.youtube.com/shorts/YMjz4thpjxQ ''52edo jam''] (2026). The range with no missed notes is 4½ octaves, which slope upwards moderately.
{{Lumatone EDO mapping|n=52|start=13|xstep=7|ystep=3}}


== Diminished + Pseudo-Pentacircle ==
== Diminished + Pseudo-Pentacircle ==
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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 [https://www.youtube.com/shorts/PgSsSM5pJcM ''52edo improv''] (2025).
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 [https://www.youtube.com/shorts/PgSsSM5pJcM ''52edo improv''] (2025).
{{Lumatone EDO mapping|n=53|start=4|xstep=9|ystep=-5}}
{{Lumatone EDO mapping|n=53|start=4|xstep=9|ystep=-5}}
== Diminished + Pseudo-Mothra ==
[[Bryan Deister]] has used a layout for [[52edo]] in which the generator is 10\52, as the near-just septimal major second ~[[8/7]] (and three of these yielding the fifth ~[[3/2]]), making this a [[gamelismic clan]] mapping similar to [[Gamelismic_clan#mothra|mothra]], but much simpler in obtaining the classic major third ~[[5/4]] at 4 generators instead of 12 (which would be the case in real mothra), and with the [[4L 4s]] scale (10:3 step ratio) and the fact that 52edo tempers out the greater diesis [[648/625]], thereby using a quarter-octave period as in [[Diminished_(temperament)|diminished]] temperament, without which the temperament would otherwise be [[Saturation, torsion, and contorsion|contorted]] (the quarter-octave period is required to wrap the generator stack properly). Octaves slant downwards (incurring a vertical wraparound), and the compass is 5⅛ octaves, with no missed notes and no repeated notes. This layout is demonstrated in [https://www.youtube.com/shorts/ovA5-YkjxWk ''52edo groove''] (2026); in the video, some notes are cut off at the left and right edges due to the use of only 2 MIDI channels.
{{Lumatone EDO mapping|n=52|start=4|xstep=10|ystep=-7}}


{{Navbox Lumatone}}
{{Navbox Lumatone}}

Latest revision as of 15:47, 3 May 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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Porcupine

52edo is a valid porcupine tuning (with scale 1L 6s having a 10:7 step ratio), as Bryan Deister demonstrates in 52edo jam (2026). The range with no missed notes is 4½ octaves, which slope upwards moderately.

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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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Diminished + Pseudo-Mothra

Bryan Deister has used a layout for 52edo in which the generator is 10\52, as the near-just septimal major second ~8/7 (and three of these yielding the fifth ~3/2), making this a gamelismic clan mapping similar to mothra, but much simpler in obtaining the classic major third ~5/4 at 4 generators instead of 12 (which would be the case in real mothra), and with the 4L 4s scale (10:3 step ratio) and the fact that 52edo tempers out the greater diesis 648/625, thereby using a quarter-octave period as in diminished temperament, without which the temperament would otherwise be contorted (the quarter-octave period is required to wrap the generator stack properly). Octaves slant downwards (incurring a vertical wraparound), and the compass is 5⅛ octaves, with no missed notes and no repeated notes. This layout is demonstrated in 52edo groove (2026); in the video, some notes are cut off at the left and right edges due to the use of only 2 MIDI channels.

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