Lumatone mapping for 63edo: Difference between revisions

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As noted above, neither of these makes consonant chords particularly easy to play. The [[Misty_family#Fog|Fog]] and [[Magic]] mappings have smaller ranges, but are more harmonically effective.

== Fog-Related Neutral Seconds ==

In [[63edo]], it is possible to divide the octave into three parts, each 21\63 being a mildly sharp fwiwismic major third ~[[44/35]] (or more accurately but less practically, a near-just undetricesimal major third ~[[29/23]]), with a [[3L 3s]] scale (13:8 step ratio), similar to [[Misty_family#Fog|fog]]. Unlike actual fog, the generator is a slightly flat undecimal neutral second ~[[12/11]], with the layout being designed for easy access to intervals that are close to common consonant intervals, but different (including the generator itself). The range is over five octaves, which is too much to include all of the notes in a standard-sized Lumatone. Despite the missing notes, [[Bryan Deister]] has used this mapping in [https://www.youtube.com/shorts/NwcS36rurOI ''63edo improv''] (2026-08-03), with the xenharmonic intervals forming a sound flavor that seems both Gaelic and Middle-Eastern.

== Fog ==

[[Misty_family#Fog|~~Fog~~]] splits the octave into three parts with a [[3L 6s]] scale (11:5 step ratio), and uses a rightward generator 5\63, which functions as as sharp (and inconsistently mapped) septimal minor semitone ~[[21/20]] and a flat undecimal semitone ~[[35/33]]~~; two~~ of these make a near-just Quasi-meantone ~[[19/17]]; three of them make a somewhat flat classic major third ~[[5/4]], from which the fifth ~[[3/2]] is easily reachable by moving down-right. This mapping has the disadvantage of many notes in the bottom and top octaves being cut off by the left and right edges.

Actual [[Misty_family#Fog|fog]] splits the octave into three parts with a [[3L 6s]] scale (11:5 step ratio), and uses a rightward generator 5\63, which functions as as sharp (and inconsistently mapped) septimal minor semitone ~[[21/20]] and a flat undecimal semitone ~[[35/33]], derived by 1/3-octave reduction of the fourth ~[[4/3]]. Two of these make a near-just Quasi-meantone ~[[19/17]]; three of them make a somewhat flat classic major third ~[[5/4]], from which the fifth ~[[3/2]] is easily reachable by moving down-right. This mapping has the disadvantage of many notes in the bottom and top octaves being cut off by the left and right edges, but at least no notes are missing out of the middle octaves (although this mapping offers only two of these).

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 As noted above, neither of these makes consonant chords particularly easy to play. The [[Misty_family#Fog|Fog]] and [[Magic]] mappings have smaller ranges, but are more harmonically effective.
+== Fog-Related Neutral Seconds ==
+In [[63edo]], it is possible to divide the octave into three parts, each 21\63 being a mildly sharp fwiwismic major third ~[[44/35]] (or more accurately but less practically, a near-just undetricesimal major third ~[[29/23]]), with a [[3L&nbsp;3s]] scale (13:8 step ratio), similar to [[Misty_family#Fog|fog]]. Unlike actual fog, the generator is a slightly flat undecimal neutral second ~[[12/11]], with the layout being designed for easy access to intervals that are close to common consonant intervals, but different (including the generator itself). The range is over five octaves, which is too much to include all of the notes in a standard-sized Lumatone. Despite the missing notes, [[Bryan Deister]] has used this mapping in [https://www.youtube.com/shorts/NwcS36rurOI ''63edo improv''] (2026-08-03), with the xenharmonic intervals forming a sound flavor that seems both Gaelic and Middle-Eastern.
+{{Lumatone EDO mapping|n=63|start=42|xstep=8|ystep=5}}
 == Fog ==
-[[Misty_family#Fog|Fog]] splits the octave into three parts with a [[3L&nbsp;6s]] scale (11:5 step ratio), and uses a rightward generator 5\63, which functions as as sharp (and inconsistently mapped) septimal minor semitone ~[[21/20]] and a flat undecimal semitone ~[[35/33]]; two of these make a near-just Quasi-meantone ~[[19/17]]; three of them make a somewhat flat classic major third ~[[5/4]], from which the fifth ~[[3/2]] is easily reachable by moving down-right. This mapping has the disadvantage of many notes in the bottom and top octaves being cut off by the left and right edges.
+Actual [[Misty_family#Fog|fog]] splits the octave into three parts with a [[3L&nbsp;6s]] scale (11:5 step ratio), and uses a rightward generator 5\63, which functions as as sharp (and inconsistently mapped) septimal minor semitone ~[[21/20]] and a flat undecimal semitone ~[[35/33]], derived by 1/3-octave reduction of the fourth ~[[4/3]]. Two of these make a near-just Quasi-meantone ~[[19/17]]; three of them make a somewhat flat classic major third ~[[5/4]], from which the fifth ~[[3/2]] is easily reachable by moving down-right. This mapping has the disadvantage of many notes in the bottom and top octaves being cut off by the left and right edges, but at least no notes are missing out of the middle octaves (although this mapping offers only two of these).
 {{Lumatone EDO mapping|n=63|start=46|xstep=5|ystep=6}}