Lumatone mapping for 64edo: Difference between revisions

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== Diatonic ==

The cd val tunes lower limit [[flattone]] about as well as it can be tuned, falling neatly between the 7 & 9-odd limit minimax tunings. The b val is shared with [[32edo]] and only covers half the notes.

===Standard Flattone ===

The cd val tunes lower limit [[flattone]] about as well as it can be tuned, falling neatly between the 7 & 9-odd limit minimax tunings, but missing some notes. The b val is shared with [[32edo]] and only covers half the notes.

=== Cantonismic (flipped and rotated diatonic) ===

[[Bryan Deister]] has demonstrated a [[Cantonismic]] (flipped and rotated diatonic) mapping of [[64edo]] in [https://www.youtube.com/shorts/ag1FbgAuR6I ''microtonal improvisation in 64edo''] (2025). In this mapping, the rightward generator 7\64 is mapped as a slightly sharp tridecimal supraminor second ~[[14/13]], and the [[cantonisma]] (10985/10976) is tempered out, so that three of them make a fairly sharp classic major third ~[[5/4]], and eight of them make a near-just undecimal neutral seventh ~[[11/6]]; note that apart from ~5/4, these ratios depending upon partial cancellation of errors in the harmonics as represented by 64edo. The rightward generator is actually the short step of the easiest scale to play on this layout (provided that the scale is positioned not to go through a vertical wraparound), with the down-right step being 10\64, which corresponds to the [[Patent val|patent]] (not [[direct approximation]]) whole tone ~[[9/8]], thus enabling a rotated diatonic scale. Octaves alternate between far and near superimposed on an overall slant away over the range of three whole octaves (having no missing notes) plus a fourth octave that has some notes chopped off by the right edge, and some fragmented note sequences in the upper left and lower right corners. A side effect of the alternation of octaves is that accessing the fourth and fifth can be easy or hard depending upon not only the root note, but also the octave — for instance, in the middle and mid-right octaves, 27\64 and 37\64 are both easily reached from 0\64, but in the second full octaves, they same interval requires a long finger stretch if the root note is greater than 0, and the rotated diatonic scale goes through a vertical wraparound (and moving note 0 would simply cause other root notes to have the same problem in some of the octaves).

== Nadir ==

@@ Line 2: / Line 2: @@
 == Diatonic ==
-The cd val tunes lower limit [[flattone]] about as well as it can be tuned, falling neatly between the 7 & 9-odd limit minimax tunings. The b val is shared with [[32edo]] and only covers half the notes.
+===Standard Flattone ===
+The cd val tunes lower limit [[flattone]] about as well as it can be tuned, falling neatly between the 7 & 9-odd limit minimax tunings, but missing some notes. The b val is shared with [[32edo]] and only covers half the notes.
 {{Lumatone EDO mapping|n=64|start=56|xstep=10|ystep=-3}}
+=== Cantonismic (flipped and rotated diatonic) ===
+[[Bryan Deister]] has demonstrated a [[Cantonismic]] (flipped and rotated diatonic) mapping of [[64edo]] in [https://www.youtube.com/shorts/ag1FbgAuR6I ''microtonal improvisation in 64edo''] (2025). In this mapping, the rightward generator 7\64 is mapped as a slightly sharp tridecimal supraminor second ~[[14/13]], and the [[cantonisma]] (10985/10976) is tempered out, so that three of them make a fairly sharp classic major third ~[[5/4]], and eight of them make a near-just undecimal neutral seventh ~[[11/6]]; note that apart from ~5/4, these ratios depending upon partial cancellation of errors in the harmonics as represented by 64edo. The rightward generator is actually the short step of the easiest scale to play on this layout (provided that the scale is positioned not to go through a vertical wraparound), with the down-right step being 10\64, which corresponds to the [[Patent val|patent]] (not [[direct approximation]]) whole tone ~[[9/8]], thus enabling a rotated diatonic scale. Octaves alternate between far and near superimposed on an overall slant away over the range of three whole octaves (having no missing notes) plus a fourth octave that has some notes chopped off by the right edge, and some fragmented note sequences in the upper left and lower right corners. A side effect of the alternation of octaves is that accessing the fourth and fifth can be easy or hard depending upon not only the root note, but also the octave &mdash; for instance, in the middle and mid-right octaves, 27\64 and 37\64 are both easily reached from 0\64, but in the second full octaves, they same interval requires a long finger stretch if the root note is greater than 0, and the rotated diatonic scale goes through a vertical wraparound (and moving note 0 would simply cause other root notes to have the same problem in some of the octaves).
+{{Lumatone EDO mapping|n=64|start=17|xstep=7|ystep=3}}
 == Nadir ==