Lumatone mapping for 43edo: Difference between revisions

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~~There are many conceivable ways to map [[43edo]] onto the [[Lumatone]] keyboard. Only one, however, agrees with the [[Standard~~ Lumatone mapping ~~for Pythagorean]].~~

== Diatonic ==

== Amavil (superdiatonic) ==

It is possible to use a [[7L 2s]] (5:4 step ratio) superdiatonic mapping with [[43edo]], as in [[mavila]]. Mavila itself is not a high-accuracy tuning, but it has some relatives that are high-accuracy — in this case, [[amavil]], of the [[mabila family]]. As with mavila, it uses a sub-fifth as its generator, in this case 24\43; however, unlike actual mavila, the generator is explicitly defined as something other than the fifth, which is instead left at the most accurate mapping 43edo has to offer for ~[[3/2]] (at 25\43). Instead, the sub-fifth is mapped as a mildly flat undecimal diminished fifth ~[[22/15]]. After octave-reduction, three of them make a somewhat flat classic minor sixth ~[[8/5]]; four of them make a subminor third that functions as ~[[7/6]] (sharp), ~[[13/11]] (flat), and ~[[20/17]] (diatismic minor third, close to just, only slightly sharp); six of them make a near-just pentacircle major third ~[[14/11]]; seven of them make a near-just classic major seventh ~[[15/8]]; eight of them make a moderately flat undecimal major fourth ~[[11/8]]; and ten of them make the moderately flat perfect fifth ~[[3/2]]. The range is about 3¾ octaves, which slope mildly upwards, with a generous allotment of repeated notes to mitigate vertical wraparounds.

The [[~~semiquartal~~]] layout is also particularly notable for putting the best tuned intervals within easy reach of one-another, as also demonstrated in [[Skip fretting system 43 2 9]], although it doesn't quite cover the whole gamut.

== Semiquartal ==

The [[4L 1s]] layout is also particularly notable for putting the best tuned intervals within easy reach of one-another, as also demonstrated in [[Skip fretting system 43 2 9]], although it doesn't quite cover the whole gamut.

If you want easily accessible single step movements, the [[Meantone_family#Trimean|~~trimean~~]] mapping is probably the best option.

== Trimean ==

If you want easily accessible single-step movements, the [[Meantone_family#Trimean|Trimean]] mapping is probably the best option.

@@ Line 1: / Line 1: @@
-There are many conceivable ways to map [[43edo]] onto the [[Lumatone]] keyboard. Only one, however, agrees with the [[Standard Lumatone mapping for Pythagorean]].
+{{Lumatone mapping intro}}
+== Diatonic ==
 {{Lumatone EDO mapping|n=43|start=41|xstep=7|ystep=-3}}
+== Amavil (superdiatonic) ==
+It is possible to use a [[7L&nbsp;2s]] (5:4 step ratio) superdiatonic mapping with [[43edo]], as in [[mavila]]. Mavila itself is not a high-accuracy tuning, but it has some relatives that are high-accuracy &mdash; in this case, [[amavil]], of the [[mabila family]]. As with mavila, it uses a sub-fifth as its generator, in this case 24\43; however, unlike actual mavila, the generator is explicitly defined as something other than the fifth, which is instead left at the most accurate mapping 43edo has to offer for ~[[3/2]] (at 25\43). Instead, the sub-fifth is mapped as a mildly flat undecimal diminished fifth ~[[22/15]]. After octave-reduction, three of them make a somewhat flat classic minor sixth ~[[8/5]]; four of them make a subminor third that functions as ~[[7/6]] (sharp), ~[[13/11]] (flat), and ~[[20/17]] (diatismic minor third, close to just, only slightly sharp); six of them make a near-just pentacircle major third ~[[14/11]]; seven of them make a near-just classic major seventh ~[[15/8]]; eight of them make a moderately flat undecimal major fourth ~[[11/8]]; and ten of them make the moderately flat perfect fifth ~[[3/2]]. The range is about 3¾ octaves, which slope mildly upwards, with a generous allotment of repeated notes to mitigate vertical wraparounds.
+{{Lumatone EDO mapping|n=43|start=34|xstep=5|ystep=-1}}
-The [[semiquartal]] layout is also particularly notable for putting the best tuned intervals within easy reach of one-another, as also demonstrated in [[Skip fretting system 43 2 9]], although it doesn't quite cover the whole gamut.
+== Semiquartal ==
+The [[4L&nbsp;1s]] layout is also particularly notable for putting the best tuned intervals within easy reach of one-another, as also demonstrated in [[Skip fretting system 43 2 9]], although it doesn't quite cover the whole gamut.
 {{Lumatone EDO mapping|n=43|start=28|xstep=9|ystep=-2}}
-If you want easily accessible single step movements, the [[Meantone_family#Trimean|trimean]] mapping is probably the best option.
+== Trimean ==
+If you want easily accessible single-step movements, the [[Meantone_family#Trimean|Trimean]] mapping is probably the best option.
 {{Lumatone EDO mapping|n=43|start=19|xstep=6|ystep=1}}
 {{Navbox Lumatone}}