Lumatone mapping for 57edo: Difference between revisions

Line 4:

The 57b val has a fifth so sharp that using it to play a pentatonic scale would sound more like a circulating temperament of [[5edo]] than a pentatonic scale of [[Meantone]], [[Superpyth]], or any of their relatives. The sharp fifth does have the feature that six of them add up to 12/1, which octave-reduces to the [[Patent val|patent]] fifth, and the diatonic mapping does provide easy access to the patent fifth (just up and left of the sharp fifth, which is also three keys right of the root note), so on a hypothetical XL-sized Lumatone having enough keys to avoid skipping notes, it would be a reasonable mapping despite giving an extremely hard [[5L 2s]] scale and nearly equalized [[2L 3s]] scale. The division of the patent fifth into three intervals all in a row, each of which is an essentially just septimal whole tone (~[[8/7]]), makes this a good [[Gamelismic_clan#Mothra|Mothra]] mapping. Despite the missing notes, [[Bryan Deister]] has demonstrated this mapping in [https://www.youtube.com/shorts/FylRB5MGBz4 ''<nowiki>Prelude in 57edo (Part 1) [short clip]</nowiki>''] (2025).

== Lithium ==

[[Bryan Deister]] has demonstrated a [[3L 3s]] (12:7 step ratio) [[Lithium]] mapping for [[57edo]], in [https://www.youtube.com/shorts/yVv0s8t--pg ''<nowiki>Prelude in 57edo (Part 2) [short clip]</nowiki>''] (2025). Lithium divides the octave into 3 parts, each of which is 19\57, defined by inconsistently-mapped ~[[56/45]], and corresponding to one key right + one key down-right. It uses the ⅓-octave-reduced fourth ~[[4/3]] (24\57, reduced to 5\57) to get the downwards generator. This mapping exceeds the amount of range (over six octaves) supported an EDO of this size on a standard-sized Lumatone, and so it misses several notes in each octave (especially at the left and right edges), and the octaves slant down.

== Unnamed temperament ==

@@ Line 4: / Line 4: @@
 The 57b val has a fifth so sharp that using it to play a pentatonic scale would sound more like a circulating temperament of [[5edo]] than a pentatonic scale of [[Meantone]], [[Superpyth]], or any of their relatives. The sharp fifth does have the feature that six of them add up to 12/1, which octave-reduces to the [[Patent val|patent]] fifth, and the diatonic mapping does provide easy access to the patent fifth (just up and left of the sharp fifth, which is also three keys right of the root note), so on a hypothetical XL-sized Lumatone having enough keys to avoid skipping notes, it would be a reasonable mapping despite giving an extremely hard [[5L&nbsp;2s]] scale and nearly equalized [[2L&nbsp;3s]] scale. The division of the patent fifth into three intervals all in a row, each of which is an essentially just septimal whole tone (~[[8/7]]), makes this a good [[Gamelismic_clan#Mothra|Mothra]] mapping. Despite the missing notes, [[Bryan Deister]] has demonstrated this mapping in [https://www.youtube.com/shorts/FylRB5MGBz4 ''<nowiki>Prelude in 57edo (Part 1) [short clip]</nowiki>''] (2025).
 {{Lumatone EDO mapping|n=57|start=18|xstep=11|ystep=-10}}
+== Lithium ==
+[[Bryan Deister]] has demonstrated a [[3L&nbsp;3s]] (12:7 step ratio) [[Lithium]] mapping for [[57edo]], in [https://www.youtube.com/shorts/yVv0s8t--pg ''<nowiki>Prelude in 57edo (Part 2) [short clip]</nowiki>''] (2025). Lithium divides the octave into 3 parts, each of which is 19\57, defined by inconsistently-mapped ~[[56/45]], and corresponding to one key right + one key down-right. It uses the ⅓-octave-reduced fourth ~[[4/3]] (24\57, reduced to 5\57) to get the downwards generator. This mapping exceeds the amount of range (over six octaves) supported an EDO of this size on a standard-sized Lumatone, and so it misses several notes in each octave (especially at the left and right edges), and the octaves slant down.
+{{Lumatone EDO mapping|n=57|start=45|xstep=7|ystep=5}}
 == Unnamed temperament ==