Lumatone mapping for 34edo: Difference between revisions

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→Hanson: --> Kleismic (Hanson); add headings for the 2 existing mappings; insert Bryan Deister's Kleismic + Würschmidt mapping between these
 
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34edo is an interesting case for [[Lumatone]] mappings, since ([[Lumatone mapping for 24edo|like 24edo]]), it is not generated by fifths and octaves, so the [[Standard Lumatone mapping for Pythagorean]] only reaches [[17edo]] intervals unless you use the b val instead, which generates [[mabila]].
{{Lumatone mapping intro}}
 
== Mabila ==
You can use the b val instead, which generates [[Mabila]], but this puts the perfect fifth in awkward places.
{{Lumatone EDO mapping|n=34|start=14|xstep=4|ystep=3}}
{{Lumatone EDO mapping|n=34|start=14|xstep=4|ystep=3}}


== Tetracot ==
The [[6L 1s]] [[Tetracot]] mapping is probably a better option if you want a heptatonic scale that makes finding intervals relatively easy, since the perfect fifth is in a straight line from the root, the [[7L 6s]] MOS makes 5-limit major and minor chords very easily accessible, and single steps are neatly mapped to the vertical axis. The range is still nearly five octaves, although instead of missing the last note of the highest octave, this layout misses the note two before that. [[Bryan Deister]] has demonstrated this layout in [https://www.youtube.com/shorts/uVZ6tJ1y6ak ''34edo improv''] (2025).
{{Lumatone EDO mapping|n=34|start=31|xstep=5|ystep=-1}}


However, this puts the perfect 5th in awkward places. The [[Tetracot]] mapping is probably a better option if you want a heptatonic scale that makes finding intervals relatively easy, since the perfect 5th is in a straight line from the root, while single steps are neatly mapped to the vertical axis.
== Semiquartal (Immunity) ==
{{Lumatone EDO mapping|n=34|start=25|xstep=5|ystep=-1}}
If you want greater range you can slice the perfect fourth in two and use the [[Immunity]] mapping. However, the resulting [[5L 4s]] MOS has a 6:1 step ratio, making it quite lopsided:
{{Lumatone EDO mapping|n=34|start=19|xstep=7|ystep=-1}}


== Kleismic (Hanson) ==
=== 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.
{{Lumatone EDO mapping|n=34|start=19|xstep=9|ystep=-2}}


If you want greater range you can slice the perfect 4th in two and use the [[immunity]] mapping. However, the resulting [[5L 4s]] MOS has a 6:1 step ratio, making it quite lopsided:
=== Compressed and rotated (3L 1s, adding Würschmidt) ===
{{Lumatone EDO mapping|n=34|start=19|xstep=7|ystep=-1}}
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.)
 
{{Lumatone EDO mapping|n=34|start=21|xstep=11|ystep=-2}}


Or the [[kleismic]] mapping, although the [[3L 1s]] mapping does not quite cover the whole gamut.  
=== Expanded (4L 3s) ===
{{Lumatone EDO mapping|n=34|start=19|xstep=9|ystep=-2}}
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.
{{Lumatone EDO mapping|n=34|start=3|xstep=7|ystep=-5}}


{{Navbox Lumatone}}
{{Navbox Lumatone}}

Latest revision as of 20:02, 5 August 2026

There are many conceivable ways to map 34edo onto the onto the Lumatone keyboard. However, it has 2 mutually-exclusive rings of fifths, so the Standard Lumatone mapping for Pythagorean is not one of them.

Mabila

You can use the b val instead, which generates Mabila, but this puts the perfect fifth in awkward places.

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Tetracot

The 6L 1s Tetracot mapping is probably a better option if you want a heptatonic scale that makes finding intervals relatively easy, since the perfect fifth is in a straight line from the root, the 7L 6s MOS makes 5-limit major and minor chords very easily accessible, and single steps are neatly mapped to the vertical axis. The range is still nearly five octaves, although instead of missing the last note of the highest octave, this layout misses the note two before that. Bryan Deister has demonstrated this layout in 34edo improv (2025).

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Semiquartal (Immunity)

If you want greater range you can slice the perfect fourth in two and use the Immunity mapping. However, the resulting 5L 4s MOS has a 6:1 step ratio, making it quite lopsided:

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Kleismic (Hanson)

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.

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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 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.)

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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.

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