Lumatone mapping for 63edo: Difference between revisions

(3 intermediate revisions by 2 users not shown)

Line 6:

== 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 ===

In the [[Keemic temperaments#Sevond|Sevond]] mapping, the octave is split into seven equal parts (9\63), and the rightward keyboard mapping generator 8\63 is one seventh part of the octave minus one minimal form Sevond generator (1\63). Unfortunately this does not lend itself to producing common intervals conveniently, unless by chance the intervals happen not to cross a vertical wraparound, the position of which shifts considerably when ascending in octaves.

=== Sensi-related (non-Superleap) or Enneaportent ===

Like [[Sensi]], this mapping uses a slightly sharp septimal major third (~[[9/7]], as 23\63), and two of these stack to a classic major sixth (~[[5/3]]); however, unlike actual Sensi, this generator is not equated to the tridecimal semisixth (~[[13/10]] — instead of being tempered out, the superleap comma [[91/90]] is mapped very accurately to 1\63). As an alternative to 23\63, the actual keyboard rightward generator 6\63 (functioning as ~~[[15/14]] and ~[[16/15]]) can be used if the octave is divided into nine equal parts, making it one ninth part of the octave minus one minimal form generator, analogously to the Sevond mapping above, but in this case corresponding to the [[Marvel]] temperament [[Marvel_temperaments#Enneaportent|Enneaportent]]. Unfortunately, the fourth ~[[4/3]] and the fifth ~[[3/2]] are inconveniently situated relative to the root note, and highly subject to the vagaries of vertical wraparound.

~~However~~, neither of these makes consonant chords particularly easy to play. The [[~~fog~~]] and [[~~magic~~]] mappings have smaller ranges, but are more harmonically effective.

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 ===

Fog splits the octave into three parts, 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 gives it an advantage over the above two temperaments, although it shares their disadvantage of many notes in the bottom and top octaves being cut off by the left and right edges.

=== Magic ===

The generator for [[Magic_family|Magic]] is a classic major third ~[[5/4]] as 20\63 (which is somewhat flat), and going down three of them and octave-reducing produces 3\63, the rightward generator of this mapping, whereas going up seven of these generators and octave-reducing yields 14\63, the down-right generator of this layout; stopping at the in-between point of five temperament generators up (octave-reduced) yields the fifth ~[[3/2]] at 37\63; of all of these intervals, the root note, major third, and fifth make a nearly horizontal and just slightly curved line segment, making at least the major triad easy to reach and not likely to be interrupted by a vertical wraparound. Again, this mapping does share the disadvantage with the previous mappings of having many notes of the bottom and top octaves being cut off by the left and right edges.

== 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 — the syntonic comma [[81/80]] is not tempered out, and instead the aureusma [[1445/1444]] equates two quasi-meantones to a classic major third.) 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.

@@ Line 6: / Line 6: @@
 == 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 ===
+In the [[Keemic temperaments#Sevond|Sevond]] mapping, the octave is split into seven equal parts (9\63), and the rightward keyboard mapping generator 8\63 is one seventh part of the octave minus one minimal form Sevond generator (1\63). Unfortunately this does not lend itself to producing common intervals conveniently, unless by chance the intervals happen not to cross a vertical wraparound, the position of which shifts considerably when ascending in octaves.
 {{Lumatone EDO mapping|n=63|start=38|xstep=8|ystep=-1}}
+=== Sensi-related (non-Superleap) or Enneaportent ===
+Like [[Sensi]], this mapping uses a slightly sharp septimal major third (~[[9/7]], as 23\63), and two of these stack to a classic major sixth (~[[5/3]]); however, unlike actual Sensi, this generator is not equated to the tridecimal semisixth (~[[13/10]] &mdash; instead of being tempered out, the superleap comma [[91/90]] is mapped very accurately to 1\63). As an alternative to 23\63, the actual keyboard rightward generator 6\63 (functioning as ~~[[15/14]] and ~[[16/15]]) can be used if the octave is divided into nine equal parts, making it one ninth part of the octave minus one minimal form generator, analogously to the Sevond mapping above, but in this case corresponding to the [[Marvel]] temperament [[Marvel_temperaments#Enneaportent|Enneaportent]]. Unfortunately, the fourth ~[[4/3]] and the fifth ~[[3/2]] are inconveniently situated relative to the root note, and highly subject to the vagaries of vertical wraparound.
 {{Lumatone EDO mapping|n=63|start=47|xstep=6|ystep=5}}
-However, neither of these makes consonant chords particularly easy to play. The [[fog]] and [[magic]] mappings have smaller ranges, but are more harmonically effective.
+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 ===
+Fog splits the octave into three parts, 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 gives it an advantage over the above two temperaments, although it shares their disadvantage of many notes in the bottom and top octaves being cut off by the left and right edges.
 {{Lumatone EDO mapping|n=63|start=46|xstep=5|ystep=6}}
 === Magic ===
+The generator for [[Magic_family|Magic]] is a classic major third ~[[5/4]] as 20\63 (which is somewhat flat), and going down three of them and octave-reducing produces 3\63, the rightward generator of this mapping, whereas going up seven of these generators and octave-reducing yields 14\63, the down-right generator of this layout; stopping at the in-between point of five temperament generators up (octave-reduced) yields the fifth ~[[3/2]] at 37\63; of all of these intervals, the root note, major third, and fifth make a nearly horizontal and just slightly curved line segment, making at least the major triad easy to reach and not likely to be interrupted by a vertical wraparound. Again, this mapping does share the disadvantage with the previous mappings of having many notes of the bottom and top octaves being cut off by the left and right edges.
 {{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 &mdash; the syntonic comma [[81/80]] is not tempered out, and instead the aureusma [[1445/1444]] equates two quasi-meantones to a classic major third.) 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}}