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 ==

~~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.

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. However, the range is reduced to slightly over four octaves.

== 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:

~~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:~~

== 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]].

~~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 ==
-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.
+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. However, the range is reduced to slightly over four octaves.
 {{Lumatone EDO mapping|n=34|start=25|xstep=5|ystep=-1}}
+== Semiquartal (Immunity) ==
+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}}
-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:
+== Hanson ==
-{{Lumatone EDO mapping|n=34|start=19|xstep=7|ystep=-1}}
+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=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}}