Lumatone mapping for 94edo: Difference between revisions

{{Lumatone EDO mapping|n=94|start=76|xstep=8|ystep=-1}}

[[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.