Lumatone mapping for 58edo: Difference between revisions

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~~There~~ are ~~many conceivable~~ ways to ~~map~~ [[~~58edo~~]] ~~onto~~ the [[~~Lumatone~~]] ~~keyboard~~. ~~Unfortunately, as it has multiple rings~~ of ~~5ths~~, the [[~~Standard Lumatone mapping for Pythagorean~~]] is not ~~one~~ of them, and ~~due to it's size~~, ~~would~~ not ~~cover~~ the ~~whole gamut even if it was~~. ~~Instead~~, the [[~~2L 8s~~]] [~~[diaschismic]~~] mapping ~~is probably~~ the ~~most intuitive way~~ of ~~providing access~~ to ~~all~~ intervals ~~while putting well-tuned ones close together~~.

{{Lumatone mapping intro}} Due to its size, it would not cover the whole gamut even if it was.

== Diaschismic (+ Charismic + Semitonismic) ==

The [[2L 6s]] (14:5 step ratio) and [[2L 8s]] (9:5 step ratio) [[Diaschismic]] mappings are probably the most intuitive ways of covering the whole gamut while putting well-tuned ones close together if you're used to playing 12edo. The rightward generator 5\58 functions as the classic diatonic semitone ~[[16/15]], the large septendecimal semitone ~[[17/16]], and the small septendecimal semitone ~[[18/17]], meaning that the charisma [[256/255]] and the semitonisma [[289/288]] are both tempered out. The rightward generator is also the [[normal forms|minimal form]] of the Diaschismic generator, and indeed the [[diaschisma]] 2048/2045 is also tempered out. This generator makes a slew of intervals of reasonable prime limit that are not far from just: two of them make a near-just whole tone ~[[9/8]]; three of them make a mildly flat classic minor third ~[[6/5]]; four of them make a mildly flat undecimal major third ~[[14/11]]; five of them make a near-just classic acute fourth ~[[27/20]]; six of them pass the [[semioctave]] to make a slightly flat greater septimal tritone ~[[10/7]]; seven of them make a slightly flat septimal superfifth ~[[32/21]]; eight of them make a slightly flat tridecimal supraminor sixth ~[[21/13]]; nine of them make a near-just septimal major sixth ~[[12/7]]; and ten of them make an extremely accurate undecimal supraminor seventh ~[[20/11]]. Other common intervals such as the moderately sharp (although high in relative error) classic major third ~[[5/4]], the near-just perfect fourth ~[[4/3]], and the near-just perfect fifth ~[[3/2]] are in very easy reach of the chain of rightward generators, and not very distant from the root note. This may be sufficient compensation for the reverse chroma and the range of only three full octaves (which slope only slightly upward), with large partial octaves being chopped off by the upper left and lower right corners, which may be compositionally limiting.

=== 2L 6s (14:5 step ratio) ===

[[Bryan Deister]] has demonstrated the 2L 6s mapping in [https://www.youtube.com/shorts/7gkRyld5OU8 ''Waltz in 58edo''] (2025).

=== 2L 8s (9:5 step ratio) ===

This mapping has close to the same full octave range as the 2L 6s mapping, but spreads the range out over more of the Lumatone keyboard to get more repeated notes (and smaller partial octave regions chopped off by the upper left and lower right corners), and the cost of putting common intervals one rightward position further away from the root note.

~~However, this results in a range barely over 3 octaves.~~ The [[6L 2s]] [[Echidna]] mapping has fewer repeated notes while still providing the full gamut, giving you a range almost as large as the standard mapping.

== Echidna ==

The [[6L 2s]] [[Echidna]] mapping has fewer repeated notes while still providing the full gamut, giving you a range almost as large as the standard mapping. (This mapping, like many others, is [https://www.facebook.com/groups/lumatone.keyboard/permalink/5624482024327650 available from the Lumatone Facebook group].) [[Bryan Deister]] demonstrates this mapping in [https://www.youtube.com/shorts/4J4MNno-4PA ''58edo improv''] (2025).

Other good options include [[7L 3s]] [[Hemififths]]

== Hemififths ==

Other good options include the [[7L 3s]] [[Hemififths]]

Or if you don't mind the smaller range and want to more easily exploit narrow intervals, [[2L 12s]] [[Harry]]

== Buzzard ==

The [[5L 3s]] [[Buzzard]] mapping is also another good option, although this occasionally skips a step.

== Harry ==

Or if you don't mind the smaller range and want to more easily exploit narrow intervals, there is the [[2L 12s]] [[Harry]] mapping (as in [[Lumatone mapping for harry]])

~~[[Category:~~Lumatone ~~mappings]] [[Category:58edo]]~~

@@ Line 1: / Line 1: @@
-There are many conceivable ways to map [[58edo]] onto the [[Lumatone]] keyboard. Unfortunately, as it has multiple rings of 5ths, the [[Standard Lumatone mapping for Pythagorean]] is not one of them, and due to it's size, would not cover the whole gamut even if it was. Instead, the [[2L 8s]] [[diaschismic]] mapping is probably the most intuitive way of providing access to all intervals while putting well-tuned ones close together.
+{{Lumatone mapping intro}} Due to its size, it would not cover the whole gamut even if it was.
+== Diaschismic (+ Charismic + Semitonismic) ==
+The [[2L&nbsp;6s]] (14:5 step ratio) and [[2L&nbsp;8s]] (9:5 step ratio) [[Diaschismic]] mappings are probably the most intuitive ways of covering the whole gamut while putting well-tuned ones close together if you're used to playing 12edo. The rightward generator 5\58 functions as the classic diatonic semitone ~[[16/15]], the large septendecimal semitone ~[[17/16]], and the small septendecimal semitone ~[[18/17]], meaning that the charisma [[256/255]] and the semitonisma [[289/288]] are both tempered out. The rightward generator is also the [[normal forms|minimal form]] of the Diaschismic generator, and indeed the [[diaschisma]] 2048/2045 is also tempered out. This generator makes a slew of intervals of reasonable prime limit that are not far from just: two of them make a near-just whole tone ~[[9/8]]; three of them make a mildly flat classic minor third ~[[6/5]]; four of them make a mildly flat undecimal major third ~[[14/11]]; five of them make a near-just classic acute fourth ~[[27/20]]; six of them pass the [[semioctave]] to make a slightly flat greater septimal tritone ~[[10/7]]; seven of them make a slightly flat septimal superfifth ~[[32/21]]; eight of them make a slightly flat tridecimal supraminor sixth ~[[21/13]]; nine of them make a near-just septimal major sixth ~[[12/7]]; and ten of them make an extremely accurate undecimal supraminor seventh ~[[20/11]]. Other common intervals such as the moderately sharp (although high in relative error) classic major third ~[[5/4]], the near-just perfect fourth ~[[4/3]], and the near-just perfect fifth ~[[3/2]] are in very easy reach of the chain of rightward generators, and not very distant from the root note. This may be sufficient compensation for the reverse chroma and the range of only three full octaves (which slope only slightly upward), with large partial octaves being chopped off by the upper left and lower right corners, which may be compositionally limiting.
+=== 2L&nbsp;6s (14:5 step ratio) ===
+[[Bryan Deister]] has demonstrated the 2L&nbsp;6s mapping in [https://www.youtube.com/shorts/7gkRyld5OU8 ''Waltz in 58edo''] (2025).
+{{Lumatone EDO mapping|n=58|start=27|xstep=5|ystep=9}}
+=== 2L&nbsp;8s (9:5 step ratio) ===
+This mapping has close to the same full octave range as the 2L&nbsp;6s mapping, but spreads the range out over more of the Lumatone keyboard to get more repeated notes (and smaller partial octave regions chopped off by the upper left and lower right corners), and the cost of putting common intervals one rightward position further away from the root note.
 {{Lumatone EDO mapping|n=58|start=19|xstep=5|ystep=4}}
-However, this results in a range barely over 3 octaves. The [[6L 2s]] [[Echidna]] mapping has fewer repeated notes while still providing the full gamut, giving you a range almost as large as the standard mapping.
+== Echidna ==
+The [[6L&nbsp;2s]] [[Echidna]] mapping has fewer repeated notes while still providing the full gamut, giving you a range almost as large as the standard mapping. (This mapping, like many others, is [https://www.facebook.com/groups/lumatone.keyboard/permalink/5624482024327650 available from the Lumatone Facebook group].) [[Bryan Deister]] demonstrates this mapping in [https://www.youtube.com/shorts/4J4MNno-4PA ''58edo improv''] (2025).
 {{Lumatone EDO mapping|n=58|start=54|xstep=8|ystep=-3}}
-Other good options include [[7L 3s]] [[Hemififths]]
+== Hemififths ==
+Other good options include the [[7L&nbsp;3s]] [[Hemififths]]
 {{Lumatone EDO mapping|n=58|start=2|xstep=7|ystep=-4}}
-Or if you don't mind the smaller range and want to more easily exploit narrow intervals, [[2L 12s]] [[Harry]]
+== Buzzard ==
+The [[5L&nbsp;3s]] [[Buzzard]] mapping is also another good option, although this occasionally skips a step.
+{{Lumatone EDO mapping|n=58|start=9|xstep=11|ystep=-10}}
+== Harry ==
+Or if you don't mind the smaller range and want to more easily exploit narrow intervals, there is the [[2L&nbsp;12s]] [[Harry]] mapping (as in [[Lumatone mapping for harry]])
 {{Lumatone EDO mapping|n=58|start=40|xstep=4|ystep=1}}
-[[Category:Lumatone mappings]] [[Category:58edo]]
+{{Navbox Lumatone}}