Lumatone mapping for 52edo: Difference between revisions

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{{Lumatone mapping intro}} You can use the b val, but it is extremely sharp, to the point where major seconds become 8/7 instead of 9/8.

== Diatonic ==

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.

== Neutral thirds ==

The [[Lumatone mapping for neutral thirds scales|neutral thirds mapping]] is probably easier to navigate.

== 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.

== 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]]. 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.

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).

== 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.

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-{{Lumatone mapping intro}} 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.
+{{Lumatone mapping intro}}
+== Diatonic ==
+You can use the b&nbsp;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}}
+== Neutral thirds ==
 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}}
+== Porcupine ==
+[[52edo]] is a valid [[porcupine]] tuning (with scale [[1L&nbsp;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 ==
+[[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]]. In addition, this mapping makes a [[4L&nbsp;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}}
+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}}
+== 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&nbsp;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}}