Lumatone mapping for 34edo: Difference between revisions

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== Hanson ==

== Kleismic (Hanson) ==

The [[Hanson]] mapping also puts 5-limit consonances within easy reach of each other, but does not cover the full gamut ~~unless expanded from the [[3L 1s]] mapping to [[4L 3s]]~~.

=== Compressed (3L 1s) ===

The kleismic [[Hanson]] mapping also puts 5-limit consonances within easy reach of each other, but does not cover the full gamut.

=== Compressed and rotated (3L 1s, adding Würschmidt) ===

It is possible to accommodate both [[kleismic]] (stacking classic minor thirds) and [[würschmidt]] (stacking classic major thirds) temperaments in a [[34edo]] mapping by using a rotated [[3L 1s]] scale (9:7 step ratio), as demonstrated in [https://www.youtube.com/watch?v=JKblQe375pw ''34edo bossa''] (2026). This mapping puts both the classic minor third ~[[6/5]] and the classic major third ~[[5/4]] (both just slightly sharp) right next to both the root note and to the fifth ~[[3/2]], as 9\34 (one key down-right) and 11\34 (one key right), respectively. This comes at the cost of missing some notes (including some instances of note 0) due to trying to get too much range (close to ten octaves) to fit them all on a standard-sized Lumatone, as well as causing the octaves to alternate between near and far. (Note that in the demo video, the range appears far less due to mapping of only a single MIDI channel.)

=== Expanded (4L 3s) ===

To achieve the full gamut, it is necessary to expand the mapping to [[4L 3s]], which adds space between the root note, the major and minor thirds, and the fifth.

@@ Line 13: / Line 13: @@
 {{Lumatone EDO mapping|n=34|start=19|xstep=7|ystep=-1}}
-== Hanson ==
+== Kleismic (Hanson) ==
-The [[Hanson]] mapping also puts 5-limit consonances within easy reach of each other, but does not cover the full gamut unless expanded from the [[3L&nbsp;1s]] mapping to [[4L&nbsp;3s]].
+=== Compressed (3L&nbsp;1s) ===
+The kleismic [[Hanson]] mapping also puts 5-limit consonances within easy reach of each other, but does not cover the full gamut.
 {{Lumatone EDO mapping|n=34|start=19|xstep=9|ystep=-2}}
+=== Compressed and rotated (3L&nbsp;1s, adding Würschmidt) ===
+It is possible to accommodate both [[kleismic]] (stacking classic minor thirds) and [[würschmidt]] (stacking classic major thirds) temperaments in a [[34edo]] mapping by using a rotated [[3L&nbsp;1s]] scale (9:7 step ratio), as demonstrated in [https://www.youtube.com/watch?v=JKblQe375pw ''34edo bossa''] (2026). This mapping puts both the classic minor third ~[[6/5]] and the classic major third ~[[5/4]] (both just slightly sharp) right next to both the root note and to the fifth ~[[3/2]], as 9\34 (one key down-right) and 11\34 (one key right), respectively. This comes at the cost of missing some notes (including some instances of note 0) due to trying to get too much range (close to ten octaves) to fit them all on a standard-sized Lumatone, as well as causing the octaves to alternate between near and far. (Note that in the demo video, the range appears far less due to mapping of only a single MIDI channel.)
+{{Lumatone EDO mapping|n=34|start=21|xstep=11|ystep=-2}}
+=== Expanded (4L&nbsp;3s) ===
+To achieve the full gamut, it is necessary to expand the mapping to [[4L&nbsp;3s]], which adds space between the root note, the major and minor thirds, and the fifth.
 {{Lumatone EDO mapping|n=34|start=3|xstep=7|ystep=-5}}
 {{Navbox Lumatone}}