Lumatone mapping for 91edo: Difference between revisions

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~~There are many conceivable ways to map [[91edo]] onto the onto the Lumatone keyboard. However, the [[Standard~~ Lumatone mapping ~~for Pythagorean]] is unable to cover the full gamut of every octave, with the flat ([[patent val]]) and sharp (b val) versions having many skipped notes.~~

== Diatonic ==

~~If not for~~ the ~~problem of~~ failing to cover the ~~complete~~ gamut ~~(such as on a hypothetical XL-size Lumatone having at least 485 keys within the span of five octaves)~~, the flat version would be a respectable [[Schismic–Pythagorean_equivalence_continuum#Python|Python]] or [[Meantone]] (91c) mapping, while the sharp version would be a respectable mapping for [[Quasiultra]] (as 91bd).

The large number of notes results in both the flat ([[patent val]]) and sharp (b val) fifths failing to cover the gamut, with both skipping many notes. If not for this problem, the flat version would be a respectable [[Schismic–Pythagorean_equivalence_continuum#Python|Python]] or [[Meantone]] (91c) mapping, while the sharp version would be a respectable mapping for [[Quasiultra]] (as 91bd).

== Quartkeenlig-related rank-3 mappings ==

=== Pseudo-isomorphic ===

[[Bryan Deister]] has demonstrated a pseudo-isomorphic mapping for [[91edo]] in [https://www.youtube.com/shorts/HaYUAg30298 ''microtonal improvisation in 91edo''] (2025). This layout is numbered as for [[92edo]], but note 91 is actually a duplicate of note 0. The range is just one note short of 3 full octaves, with octaves sloping down gently, unlike the fully isomorphic version below, which avoids the interruption from the duplicated note 0 and has slightly greater range, but at the cost of greater (and opposite) octave slope and a vertical wraparound of note 0 with ascending octaves (as well as producing a discontinuity in scales). This mapping has the same generators as the fully isomorphic version, as described below.

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=== Isomorphic ===

[[Bryan Deister]] has demonstrated an isomorphic [[9L 2s]] mapping for [[91edo]] in [https://www.youtube.com/shorts/z6PeEocYMV8 ''improv 91edo''] (2025). The range is just one note beyond 3 full octaves, with octaves sloping up mildly (which results in a wraparound of note 0). The rightward generator 9\91 is the septimal diatonic semitone ~[[15\14]]. The upward generator 4\91 is a quartertone that functions as ~[[32/31]], ~[[33/32]], ~[[34/33]], and ~[[36/35]]; two of them make the minor diatonic semitone ~[[17/16]]; six of them make a near-just minor third ~[[6/5]]. The use of this generator makes this a mapping for [[Quartkeenlig]]; however, since stacking the upward generator quickly leads to wraparounds, and attempting to get the perfect fifth in 91edo with this generator yields 52\91, which is the [[7edo]] (91bb) fifth. Therefore, this mapping really needs to be treated as a rank-3 temperament mapping; for instance, to get the patent fifth 53\92 (a mildly flat ~[[3/2]], almost exactly [[1/7-comma meantone]]), it is easiest to stack five rightward generators and two upward generators.

[[Bryan Deister]] has demonstrated an isomorphic [[9L 2s]] mapping for [[91edo]] in [https://www.youtube.com/shorts/z6PeEocYMV8 ''improv 91edo''] (2025). The range is just one note beyond 3 full octaves, with octaves sloping up mildly (which results in a wraparound of note 0). The rightward generator 9\91 is the septimal diatonic semitone ~[[15/14]]. The upward generator 4\91 is a quartertone that functions as ~[[32/31]], ~[[33/32]], ~[[34/33]], and ~[[36/35]]; two of them make the minor diatonic semitone ~[[17/16]]; six of them make a near-just minor third ~[[6/5]]. The use of this generator makes this a mapping for [[Quartkeenlig]]; however, since stacking the upward generator quickly leads to wraparounds, and attempting to get the perfect fifth in 91edo with this generator yields 52\91, which is the [[7edo]] (91bb) fifth. Therefore, this mapping really needs to be treated as a rank-3 temperament mapping; for instance, to get the patent fifth 53\92 (a mildly flat ~[[3/2]], almost exactly [[1/7-comma meantone]]), it is easiest to stack five rightward generators and two upward generators.

@@ Line 1: / Line 1: @@
-There are many conceivable ways to map [[91edo]] onto the onto the Lumatone keyboard. However, the [[Standard Lumatone mapping for Pythagorean]] is unable to cover the full gamut of every octave, with the flat ([[patent val]]) and sharp (b val) versions having many skipped notes.
+{{Lumatone mapping intro}}
 == Diatonic ==
-If not for the problem of failing to cover the complete gamut (such as on a hypothetical XL-size Lumatone having at least 485 keys within the span of five octaves), the flat version would be a respectable [[Schismic–Pythagorean_equivalence_continuum#Python|Python]] or [[Meantone]] (91c) mapping, while the sharp version would be a respectable mapping for [[Quasiultra]] (as 91bd).
+The large number of notes results in both the flat ([[patent val]]) and sharp (b&nbsp;val) fifths failing to cover the gamut, with both skipping many notes. If not for this problem, the flat version would be a respectable [[Schismic–Pythagorean_equivalence_continuum#Python|Python]] or [[Meantone]] (91c) mapping, while the sharp version would be a respectable mapping for [[Quasiultra]] (as 91bd).
 {{Lumatone EDO mapping|n=91|start=89|xstep=15|ystep=-7}}
 {{Lumatone EDO mapping|n=91|start=22|xstep=17|ystep=-14}}
 == Quartkeenlig-related rank-3 mappings ==
 === Pseudo-isomorphic ===
 [[Bryan Deister]] has demonstrated a pseudo-isomorphic mapping for [[91edo]] in [https://www.youtube.com/shorts/HaYUAg30298 ''microtonal improvisation in 91edo''] (2025). This layout is numbered as for [[92edo]], but note 91 is actually a duplicate of note 0. The range is just one note short of 3 full octaves, with octaves sloping down gently, unlike the fully isomorphic version below, which avoids the interruption from the duplicated note 0 and has slightly greater range, but at the cost of greater (and opposite) octave slope and a vertical wraparound of note 0 with ascending octaves (as well as producing a discontinuity in scales). This mapping has the same generators as the fully isomorphic version, as described below.
@@ Line 14: / Line 14: @@
 === Isomorphic ===
-[[Bryan Deister]] has demonstrated an isomorphic [[9L&nbsp;2s]] mapping for [[91edo]] in [https://www.youtube.com/shorts/z6PeEocYMV8 ''improv 91edo''] (2025). The range is just one note beyond 3 full octaves, with octaves sloping up mildly (which results in a wraparound of note 0). The rightward generator 9\91 is the septimal diatonic semitone ~[[15\14]]. The upward generator 4\91 is a quartertone that functions as ~[[32/31]], ~[[33/32]], ~[[34/33]], and ~[[36/35]]; two of them make the minor diatonic semitone ~[[17/16]]; six of them make a near-just minor third ~[[6/5]]. The use of this generator makes this a mapping for [[Quartkeenlig]]; however, since stacking the upward generator quickly leads to wraparounds, and attempting to get the perfect fifth in 91edo with this generator yields 52\91, which is the [[7edo]] (91bb) fifth. Therefore, this mapping really needs to be treated as a rank-3 temperament mapping; for instance, to get the patent fifth 53\92 (a mildly flat ~[[3/2]], almost exactly [[1/7-comma meantone]]), it is easiest to stack five rightward generators and two upward generators.
+[[Bryan Deister]] has demonstrated an isomorphic [[9L&nbsp;2s]] mapping for [[91edo]] in [https://www.youtube.com/shorts/z6PeEocYMV8 ''improv 91edo''] (2025). The range is just one note beyond 3 full octaves, with octaves sloping up mildly (which results in a wraparound of note 0). The rightward generator 9\91 is the septimal diatonic semitone ~[[15/14]]. The upward generator 4\91 is a quartertone that functions as ~[[32/31]], ~[[33/32]], ~[[34/33]], and ~[[36/35]]; two of them make the minor diatonic semitone ~[[17/16]]; six of them make a near-just minor third ~[[6/5]]. The use of this generator makes this a mapping for [[Quartkeenlig]]; however, since stacking the upward generator quickly leads to wraparounds, and attempting to get the perfect fifth in 91edo with this generator yields 52\91, which is the [[7edo]] (91bb) fifth. Therefore, this mapping really needs to be treated as a rank-3 temperament mapping; for instance, to get the patent fifth 53\92 (a mildly flat ~[[3/2]], almost exactly [[1/7-comma meantone]]), it is easiest to stack five rightward generators and two upward generators.
 {{Lumatone EDO mapping|n=91|start=0|xstep=9|ystep=-4}}
 {{Navbox Lumatone}}