Lumatone mapping for 34edo: Difference between revisions

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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~~]].

== Mabila ==

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

== 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).

~~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) ==

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:

== Hanson ==

~~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:~~

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]].

~~Or the [[kleismic]] mapping, although the [[3L 1s]] mapping does not quite cover the whole gamut.~~

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-edo 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&nbsp;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}}
+== Tetracot ==
+The [[6L&nbsp;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&nbsp;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&nbsp;4s]] MOS has a 6:1 step ratio, making it quite lopsided:
+{{Lumatone EDO mapping|n=34|start=19|xstep=7|ystep=-1}}
+== Hanson ==
-If you want greater range you can slice the perfect 4th in two and use the [[immunity]] mapping. However, the resulting [[5L&nbsp;4s]] MOS has a 6:1 step ratio, making it quite lopsided:
+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]].
-{{Lumatone EDO mapping|n=34|start=19|xstep=7|ystep=-1}}
+{{Lumatone EDO mapping|n=34|start=19|xstep=9|ystep=-2}}
-Or the [[kleismic]] mapping, although the [[3L 1s]] mapping does not quite cover the whole gamut.
+{{Lumatone EDO mapping|n=34|start=3|xstep=7|ystep=-5}}
-{{Lumatone EDO mapping|n=34|start=19|xstep=9|ystep=-2}}
 {{Navbox Lumatone}}