Lumatone mapping for 63edo: Difference between revisions

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== Other Mappings ==

Of the mappings that cover all the notes, the [[7L 1s]] scale generated by 8/63 and the [[3L 5s]] one generated by 23/63 are ~~the most~~ efficient, with the second of those keeping octaves closer to horizontal.

Of the mappings that cover all the notes, the [[7L 1s]] scale (of [[Sevond]] temperament) generated by 8/63 and the [[3L 5s]] one generated by 23/63 are highly efficient, with the second of those keeping octaves closer to horizontal.

=== Sevond ===

=== Unidentified temperament ===

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=== Magic ===

== Pseudo-Meantone ==

[[Bryan Deister]] has demonstrated a [[6L 1s]] (10:3 step ratio) mapping for [[63edo]] in [https://www.youtube.com/shorts/IYLzF4ogl_w ''microtonal improvisation in 63edo''] (2025). The generator 10\93 is the quasi-meantone ~[[19/17]], which is composed of highly inaccurate harmonics whose errors nearly cancel out, rendering it just slightly flat; two of them make a somewhat flat classic major third ~[[5/4]]. (In contrast to actual [[meantone]] temperament, 63edo represents ~19/17, ~[[10/9]], and ~[[9/8]] as distinct intervals.) Although 10\63 can reach all of the notes of 63edo without the need for a second generator, a second generator 7\63 (upward, as a tridecimal supraminor/neutral second that functions as both ~[[13/12]] and ~[[14/13]]) is convenient for quick access to additional common intervals — for instance, three rightward generators plus one upward generator reach the just slightly sharp fifth ~[[3/2]]; while five rightward generators minus one upwards generator reach a mildly sharp minor sixth ~[[8/5]]. The range is somewhat over four octaves (which slant up mildly) with no missed notes and no repeated notes.

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 == Other Mappings ==
-Of the mappings that cover all the notes, the [[7L 1s]] scale generated by 8/63 and the [[3L 5s]] one generated by 23/63 are the most efficient, with the second of those keeping octaves closer to horizontal.
+Of the mappings that cover all the notes, the [[7L&nbsp;1s]] scale (of [[Sevond]] temperament) generated by 8/63 and the [[3L&nbsp;5s]] one generated by 23/63 are highly efficient, with the second of those keeping octaves closer to horizontal.
+=== Sevond ===
 {{Lumatone EDO mapping|n=63|start=38|xstep=8|ystep=-1}}
+=== Unidentified temperament ===
 {{Lumatone EDO mapping|n=63|start=47|xstep=6|ystep=5}}
@@ Line 18: / Line 21: @@
 === Magic ===
 {{Lumatone EDO mapping|n=63|start=13|xstep=3|ystep=11}}
+== Pseudo-Meantone ==
+[[Bryan Deister]] has demonstrated a [[6L&nbsp;1s]] (10:3 step ratio) mapping for [[63edo]] in [https://www.youtube.com/shorts/IYLzF4ogl_w ''microtonal improvisation in 63edo''] (2025). The generator 10\93 is the quasi-meantone ~[[19/17]], which is composed of highly inaccurate harmonics whose errors nearly cancel out, rendering it just slightly flat; two of them make a somewhat flat classic major third ~[[5/4]]. (In contrast to actual [[meantone]] temperament, 63edo represents ~19/17, ~[[10/9]], and ~[[9/8]] as distinct intervals.) Although 10\63 can reach all of the notes of 63edo without the need for a second generator, a second generator 7\63 (upward, as a tridecimal supraminor/neutral second that functions as both ~[[13/12]] and ~[[14/13]]) is convenient for quick access to additional common intervals &mdash; for instance, three rightward generators plus one upward generator reach the just slightly sharp fifth ~[[3/2]]; while five rightward generators minus one upwards generator reach a mildly sharp minor sixth ~[[8/5]]. The range is somewhat over four octaves (which slant up mildly) with no missed notes and no repeated notes.
+{{Lumatone EDO mapping|n=63|start=6|xstep=10|ystep=-7}}
 {{Navbox Lumatone}}