Lumatone mapping for 63edo: Difference between revisions

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== ~~Other Mappings~~ ==

== Sevond-related ==

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~~.

Since [[63edo]] is a multiple of 7edo, it can be used with a mapping that divides the octave into seven parts in the manner of [[whitewood]], but with more accuracy due to having a much better fifth; in this case, the actual temperament is related to [[sevond]], but unlike actual sevond, it uses a near-just septimal minor second ~[[7/6]] as its generator, which is 1/7-octave-reduced from 14\63 to 5\63. The 1/7-octave (9\63) is mapped most practically as a slightly flat undevicesimal submajor second ~[[21/19]], resulting in the reduced generator (5\63) being a slightly sharp large undevicesimal semitone ~[[19/18]]. [[Bryan Deister]] has used this mapping in [https://www.youtube.com/shorts/SQsDGSmEVQw ''63edo double improv''] (2026). The range is 4⅓ octaves (with only one repeated note in each octave), which slope upwards with the rows.

=== Sevond ===

== 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.

In the [[7L 1s]] (8:7 step ratio) [[sevond]] mapping, the octave is split into seven equal parts (9\63), as above, but the period is reached by moving one key right plus one key up, and the rightward keyboard mapping generator 8\63 is one seventh part of the octave minus one minimal form Sevond generator (1\63, made by 1/7-octave-reducing the fifth ~[[3/2]]). 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 ===

== 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.

Like [[sensi]], this [[3L 5s]] (11:6 step ratio) 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.

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 ==

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.

[[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.

=== Magic ===

== 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.

The generator for [[Magic_family|Magic]] (with a [[3L 7s]] scale having a 14:3 stepratio) 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.

@@ Line 9: / Line 9: @@
 {{Lumatone EDO mapping|n=64|start=56|xstep=10|ystep=-3}}
-== Other Mappings ==
+== Sevond-related ==
-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.
+Since [[63edo]] is a multiple of 7edo, it can be used with a mapping that divides the octave into seven parts in the manner of [[whitewood]], but with more accuracy due to having a much better fifth; in this case, the actual temperament is related to [[sevond]], but unlike actual sevond, it uses a near-just septimal minor second ~[[7/6]] as its generator, which is 1/7-octave-reduced from 14\63 to 5\63. The 1/7-octave (9\63) is mapped most practically as a slightly flat undevicesimal submajor second ~[[21/19]], resulting in the reduced generator (5\63) being a slightly sharp large undevicesimal semitone ~[[19/18]]. [[Bryan Deister]] has used this mapping in [https://www.youtube.com/shorts/SQsDGSmEVQw ''63edo double improv''] (2026). The range is 4⅓ octaves (with only one repeated note in each octave), which slope upwards with the rows.
+{{Lumatone EDO mapping|n=63|start=59|xstep=9|ystep=-4}}
-=== Sevond ===
+== 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.
+In the [[7L&nbsp;1s]] (8:7 step ratio) [[sevond]] mapping, the octave is split into seven equal parts (9\63), as above, but the period is reached by moving one key right plus one key up, and the rightward keyboard mapping generator 8\63 is one seventh part of the octave minus one minimal form Sevond generator (1\63, made by 1/7-octave-reducing the fifth ~[[3/2]]). 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 ===
+== 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.
+Like [[sensi]], this [[3L&nbsp;5s]] (11:6 step ratio) 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}}
 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 ==
-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.
+[[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.
 {{Lumatone EDO mapping|n=63|start=46|xstep=5|ystep=6}}
-=== Magic ===
+== 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.
+The generator for [[Magic_family|Magic]] (with a [[3L&nbsp;7s]] scale having a 14:3 stepratio) 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}}