Lumatone mapping for 94edo: Difference between revisions

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~~There are many conceivable ways to map [[94edo]] onto the [[Lumatone]] keyboard. Only one, however, agrees with the [[Standard~~ Lumatone mapping ~~for Pythagorean]].~~ Note that due to the size of the edo, this only covers slightly over half of its notes.

== Diatonic ==

Note that due to the size of the edo, this only covers slightly over half of its notes.

Since 94edo is a [[schismatic]] tuning, the best approximation to ~~the 5th harmonic~~ is the diminished ~~4th~~. There is an alternate diatonic scale based on [[Carlos Beta]] that makes [[5-limit]] chords easy to play, but it has a slight octave stretch and misses out even more notes.

Since 94edo is a [[schismatic]] tuning, the best approximation to [[5/4]] is the diminished fourth. There is an alternate diatonic scale based on [[Carlos Beta]] that makes [[5-limit]] chords easy to play, but it has a slight octave stretch and misses out even more notes.

== Bischismic ==

If you want to be able to access the full gamut, the [[10L 2s]] [[bischismic]] mapping is the most efficient layout, although it only covers a little under three octaves and the best ratios are not as easy to play together as in a true [[diaschismic]] system.

== Diatonicized Chromaticism + Kleischismic + Cassandra (Garibaldi) ==

[[Bryan Deister]] has demonstrated the [[11L 2s]] mapping of [[94edo]] in [https://www.youtube.com/shorts/Zx4xbJhXmgc ''microtonal improvisation in 94edo''] (2025). In the application of this temperament to this mapping, the rightward step corresponds to a stack of two quite accurate ~[[16/11]] generators (51\94, and the [[octave complement]] is ~[[11/8]], at 43\94) after octave-reduction, making this a mapping closely related to the Diatonicized Chromaticism used extensively by [[Ivan Wyschnegradsky]] in his [[24edo]] compositions. The rightward step can also be made by going down by the octave-complemented generator (39\94, ~11/8) and [[semioctave]]-reducing. This makes it a mapping for 11-limit (or higher) [[Schismatic_family#Kleischismic|Kleischismic]] (substituting the normal generator ~[[35/24]] with the simpler ~11/8, which 94edo represents more accurately), although this yields an extremely soft [[10L 2s]] scale (step ratio 8:7, currently off the right edge of the scale tree) instead of 11L 2s. Similarly, if one uses the highly accurate ~[[4/3]] (39\94, octave complement ~[[3/2]] as 55\94) and stacks two of these, the result is a rightward double step, making this mapping also work for [[Garibaldi]] and its 11-limit (or higher) extension [[Schismatic_family#Cassandra|Cassandra]] (although with some vertical wraparound challenges as noted following). A diatonic scale, or better yet a Ptolemy's intense diatonic (Zarlino) scale appears possible to do using both hands, although the octave slope causes the wraparound point to change with octave. The range is a bit under three octaves, and the octaves slope up, which puts the third note 0 at the far edge (although it does repeat at the near edge). A possibility for addressing this (not shown here) is to set note 0 is set to a point on the left edge half way between its current location and the lower left corner (to get note 0 two octaves higher to be 3/4 of the way up); this results in a skipped note 1 in the lowest note 0 to note 0 octave, but if one is willing to assign one key to a non-isomorphic position, the note 92 in the lower left corner (from the octave below the lowest note 0) could be reassigned to the missing note 1.

~~If you want to be able to access the full gamut, the~~ [[~~10L 2s~~]] mapping is the ~~most efficient~~ layout~~, although it only covers a little under three octaves~~ and ~~the best ratios are not as easy to play together~~ as ~~in a true~~ [[~~diaschismic~~]] ~~system~~.

== 19 Note MODMOS Subset ==

[[Bryan Deister]] has demonstrated a pseudo-isomorphic pseudo-diatonic mapping for [[94edo]] in [https://www.youtube.com/shorts/KJ5dbF4aH2A ''Twinleaf Town - Pokémon Diamond and Pearl (microtonal cover in 94edo)''] (2026) that takes a 19 note subset supporting an almost-diatonic scale with a 15:10 step ratio overall, but with one of the steps (which one depends upon choice of root note) always being shortened by 1\94. This layout is numbered as for [[95edo]] and laid out as for [[19edo]], with the potential for two complete manuals and one incomplete manual, with note 94 (which is one of the missing notes) actually being a duplicate of note 0.

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-There are many conceivable ways to map [[94edo]] onto the [[Lumatone]] keyboard. Only one, however, agrees with the [[Standard Lumatone mapping for Pythagorean]]. Note that due to the size of the edo, this only covers slightly over half of its notes.
+{{Lumatone mapping intro}}
+== Diatonic ==
+Note that due to the size of the edo, this only covers slightly over half of its notes.
 {{Lumatone EDO mapping|n=94|start=4|xstep=16|ystep=-9}}
-Since 94edo is a [[schismatic]] tuning, the best approximation to the 5th harmonic is the diminished 4th. There is an alternate diatonic scale based on [[Carlos Beta]] that makes [[5-limit]] chords easy to play, but it has a slight octave stretch and misses out even more notes.
+Since 94edo is a [[schismatic]] tuning, the best approximation to [[5/4]] is the diminished fourth. There is an alternate diatonic scale based on [[Carlos Beta]] that makes [[5-limit]] chords easy to play, but it has a slight octave stretch and misses out even more notes.
 {{Lumatone EDO mapping|n=94|start=84|xstep=15|ystep=-5}}
+== Bischismic ==
+If you want to be able to access the full gamut, the [[10L&nbsp;2s]] [[bischismic]] mapping is the most efficient layout, although it only covers a little under three octaves and the best ratios are not as easy to play together as in a true [[diaschismic]] system.
+{{Lumatone EDO mapping|n=94|start=76|xstep=8|ystep=-1}}
+== Diatonicized Chromaticism + Kleischismic + Cassandra (Garibaldi) ==
+[[Bryan Deister]] has demonstrated the [[11L&nbsp;2s]] mapping of [[94edo]] in [https://www.youtube.com/shorts/Zx4xbJhXmgc ''microtonal improvisation in 94edo''] (2025). In the application of this temperament to this mapping, the rightward step corresponds to a stack of two quite accurate ~[[16/11]] generators (51\94, and the [[octave complement]] is ~[[11/8]], at 43\94) after octave-reduction, making this a mapping closely related to the Diatonicized Chromaticism used extensively by [[Ivan Wyschnegradsky]] in his [[24edo]] compositions. The rightward step can also be made by going down by the octave-complemented generator (39\94, ~11/8) and [[semioctave]]-reducing. This makes it a mapping for 11-limit (or higher) [[Schismatic_family#Kleischismic|Kleischismic]] (substituting the normal generator ~[[35/24]] with the simpler ~11/8, which 94edo represents more accurately), although this yields an extremely soft [[10L&nbsp;2s]] scale (step ratio 8:7, currently off the right edge of the scale tree) instead of 11L&nbsp;2s. Similarly, if one uses the highly accurate ~[[4/3]] (39\94, octave complement ~[[3/2]] as 55\94) and stacks two of these, the result is a rightward double step, making this mapping also work for [[Garibaldi]] and its 11-limit (or higher) extension [[Schismatic_family#Cassandra|Cassandra]] (although with some vertical wraparound challenges as noted following). A diatonic scale, or better yet a Ptolemy's intense diatonic (Zarlino) scale appears possible to do using both hands, although the octave slope causes the wraparound point to change with octave. The range is a bit under three octaves, and the octaves slope up, which puts the third note 0 at the far edge (although it does repeat at the near edge). A possibility for addressing this (not shown here) is to set note 0 is set to a point on the left edge half way between its current location and the lower left corner (to get note 0 two octaves higher to be 3/4 of the way up); this results in a skipped note 1 in the lowest note 0 to note 0 octave, but if one is willing to assign one key to a non-isomorphic position, the note 92 in the lower left corner (from the octave below the lowest note 0) could be reassigned to the missing note 1.
-If you want to be able to access the full gamut, the [[10L 2s]] mapping is the most efficient layout, although it only covers a little under three octaves and the best ratios are not as easy to play together as in a true [[diaschismic]] system.
+{{Lumatone EDO mapping|n=94|start=4|xstep=8|ystep=-5}}
-{{Lumatone EDO mapping|n=94|start=76|xstep=8|ystep=-1}}
+== 19 Note MODMOS Subset ==
+[[Bryan Deister]] has demonstrated a pseudo-isomorphic pseudo-diatonic mapping for [[94edo]] in [https://www.youtube.com/shorts/KJ5dbF4aH2A ''Twinleaf Town - Pokémon Diamond and Pearl (microtonal cover in 94edo)''] (2026) that takes a 19 note subset supporting an almost-diatonic scale with a 15:10 step ratio overall, but with one of the steps (which one depends upon choice of root note) always being shortened by 1\94. This layout is numbered as for [[95edo]] and laid out as for [[19edo]], with the potential for two complete manuals and one incomplete manual, with note 94 (which is one of the missing notes) actually being a duplicate of note 0.
+{{Lumatone EDO mapping|n=95|start=85|xstep=15|ystep=-5}}
 {{Navbox Lumatone}}