Lumatone mapping for 52edo: Difference between revisions

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~~[[52edo]] is an interesting case for [[Lumatone]] mappings, since ([[Lumatone mapping for 24edo|like 24edo]]), it is not generated by fifths and octaves, so the [[Standard~~ Lumatone mapping ~~for Pythagorean]] only reaches [[26edo]] intervals.~~ You can use the b val, but it is ~~very~~ 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.

The neutral thirds mapping is probably easier to navigate.

== Neutral thirds ==

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

== 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.

~~[[Category:~~Lumatone ~~mappings]] [[Category:52edo]]~~

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-[[52edo]] is an interesting case for [[Lumatone]] mappings, since ([[Lumatone mapping for 24edo|like 24edo]]), it is not generated by fifths and octaves, so the [[Standard Lumatone mapping for Pythagorean]] only reaches [[26edo]] intervals. You can use the b val, but it is very sharp, to the point where major seconds become 8/7 instead of 9/8.
+{{Lumatone mapping intro}}
+== 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.
 {{Lumatone EDO mapping|n=52|start=16|xstep=10|ystep=-9}}
-The neutral thirds mapping is probably easier to navigate.
+== 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}}
+== 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.
+{{Lumatone EDO mapping|n=52|start=4|xstep=9|ystep=-5}}
-[[Category:Lumatone mappings]] [[Category:52edo]]
+{{Navbox Lumatone}}