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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-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.