Lumatone mapping for 44edo: Difference between revisions

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~~There are many conceivable ways to map [[44edo]] onto the [[Lumatone]] keyboard. Unfortunately, as it has multiple rings of 5ths, the [[Standard~~ Lumatone mapping ~~for Pythagorean]] is not one of them.~~ You can use the b val, which can be interpreted as either near equalised [[mavila]], or more accurately but complexly as [[undecimation]].

== Antidiatonic ==

You can use the b val, which can be interpreted as either near equalised [[mavila]], or more accurately but complexly as [[undecimation]].

~~Slicing~~ the ~~perfect 5th or 4th~~ in ~~half~~ are also ~~fairly good options~~, ~~although~~ the ~~semiquartal one does not cover~~ the ~~whole gamut unless expanded from~~ the [[~~4L 1s~~]] mapping to the [[~~5L 4s~~]] ~~one.~~

== Bidia + Diminished + Charismic + Semitonismic (Flipped Antidiatonic/Superdiatonic) ==

[[Bryan Deister]] has demonstrated a [[4L 4s]] mapping (6:5 step ratio) [[44edo]], in ''Buried Treasure - 44edo'' (2026) [https://www.youtube.com/shorts/Oi3v0c7jbjM (''<nowiki>[short clip]</nowiki>''], [https://www.youtube.com/shorts/ZOoiGuUA-9Y ''<nowiki>[short 2]</nowiki>'']). This mapping also functions as a very hard flipped superdiatonic mapping ([[7L 2s]], 6:1 step ratio with the small steps going up instead of down-right), a flipped antidiatonic mapping ([[2L 5s]] with 7:6 step ratio and expanded small step going right + up), and as a [[13L 3s (4/1-equivalent)]] mapping (with 6:5 step ratio, proceeding through the octave zig-zag). Right + down-right divides the octave into slices of 11\56; as an interval in its own right, this is the same as the minor third of [[12edo]], which functions as ~[[19/16]] and ~[[25/21]] (both being near-just). Down-right alone is 4\56, which is the [[Normal forms#Minimal_form|minimal form]] generator for [[Bidia]]; it functions as the classic diatonic semitone ~[[16/15]], the large septendecimal semitone ~[[17/16]], and the small septendecimal semitone ~[[18/17]] (which is inconsistently mapped), meaning that the charisma [[256/255]] and the semitonisma [[289/288]] are both tempered out; two of them make a rather sharp whole tone ~[[9/8]] (which is also inconsistently mapped); three of them (passing the quarter-octave) make a sharp classic minor third ~[[6/5]], while the afore-mentioned quarter-octave (12edo-style) minor third is about equally easy to reach; in contrast, the somewhat flat classic major third ~[[5/4]] requires two moves rightwards plus two moves upwards; four moves right reaches the rather flat fourth ~[[4/3]]; another move right and two moves upreaches the rather sharp fifth ~[[3/2]]. The range is a bit under 4¾ complete octaves (with some extra non-contiguous notes at each end), but unlike the normal antidiatonic mapping, the octaves alternate between near/far and mid or near and far (superimposed upon an overall upwards slope).

== Pseudo-Isomorphic Pseudo-Diatonic ==

To get a quasi-diatonic layout with a reasonable fifth, you can shoehorn the diatonic mapping for [[45edo]] into 44edo, with note 44 being a duplicate note 0, as [[Bryan Deister]] demonstrates in [https://www.youtube.com/shorts/_GoQNEW24fQ ''44edo improv''] (Oct 2025)

== Neutral thirds ==

Another option is to slice the perfect fifth in half, giving this mapping, which is derived from the [[Lumatone mapping for neutral thirds scales]]:

== Semiquartal ==

Slicing the perfect fourth in half also works, but the [[4L 1s]] mapping does not cover the whole gamut:

Expanding this to the [[5L 4s]] mapping solves this problem, but the scale has an 8:1 step ratio, making it very lopsided.

However, it is the [[Diaschismic_family#Hemifourths|Hemifourths]] mapping that combines the widest range that covers the full gamut with the most efficient way of reaching all prime harmonics up to 17.

== Hemifourths ==

However, it is the [[Diaschismic_family#Hemifourths|Hemifourths]] mapping that combines the widest range that covers the full gamut with the most efficient way of reaching all prime harmonics up to 17.

~~[[Category:~~Lumatone ~~mappings]] [[Category:44edo]]~~

@@ Line 1: / Line 1: @@
-There are many conceivable ways to map [[44edo]] onto the [[Lumatone]] keyboard. Unfortunately, as it has multiple rings of 5ths, the [[Standard Lumatone mapping for Pythagorean]] is not one of them. You can use the b val, which can be interpreted as either near equalised [[mavila]], or more accurately but complexly as [[undecimation]].
+{{Lumatone mapping intro}}
+== Antidiatonic ==
+You can use the b&nbsp;val, which can be interpreted as either near equalised [[mavila]], or more accurately but complexly as [[undecimation]].
 {{Lumatone EDO mapping|n=44|start=28|xstep=6|ystep=1}}
-Slicing the perfect 5th or 4th in half are also fairly good options, although the semiquartal one does not cover the whole gamut unless expanded from the [[4L 1s]] mapping to the [[5L 4s]] one.
+== Bidia + Diminished + Charismic + Semitonismic (Flipped Antidiatonic/Superdiatonic) ==
+[[Bryan Deister]] has demonstrated a [[4L&nbsp;4s]] mapping (6:5 step ratio) [[44edo]], in ''Buried Treasure - 44edo'' (2026) [https://www.youtube.com/shorts/Oi3v0c7jbjM (''<nowiki>[short clip]</nowiki>''], [https://www.youtube.com/shorts/ZOoiGuUA-9Y ''<nowiki>[short 2]</nowiki>'']). This mapping also functions as a very hard flipped superdiatonic mapping ([[7L&nbsp;2s]], 6:1 step ratio with the small steps going up instead of down-right), a flipped antidiatonic mapping ([[2L&nbsp;5s]] with 7:6 step ratio and expanded small step going right + up), and as a [[13L&nbsp;3s (4/1-equivalent)]] mapping (with 6:5 step ratio, proceeding through the octave zig-zag). Right + down-right divides the octave into slices of 11\56; as an interval in its own right, this is the same as the minor third of [[12edo]], which functions as ~[[19/16]] and ~[[25/21]] (both being near-just). Down-right alone is 4\56, which is the [[Normal forms#Minimal_form|minimal form]] generator for [[Bidia]]; it functions as the classic diatonic semitone ~[[16/15]], the large septendecimal semitone ~[[17/16]], and the small septendecimal semitone ~[[18/17]] (which is inconsistently mapped), meaning that the charisma [[256/255]] and the semitonisma [[289/288]] are both tempered out; two of them make a rather sharp whole tone ~[[9/8]] (which is also inconsistently mapped); three of them (passing the quarter-octave) make a sharp classic minor third ~[[6/5]], while the afore-mentioned quarter-octave (12edo-style) minor third is about equally easy to reach; in contrast, the somewhat flat classic major third ~[[5/4]] requires two moves rightwards plus two moves upwards; four moves right reaches the rather flat fourth ~[[4/3]]; another move right and two moves upreaches the rather sharp fifth ~[[3/2]]. The range is a bit under 4¾ complete octaves (with some extra non-contiguous notes at each end), but unlike the normal antidiatonic mapping, the octaves alternate between near/far and mid or near and far (superimposed upon an overall upwards slope).
+{{Lumatone EDO mapping|n=44|start=28|xstep=6|ystep=-1}}
+== Pseudo-Isomorphic Pseudo-Diatonic ==
+To get a quasi-diatonic layout with a reasonable fifth, you can shoehorn the diatonic mapping for [[45edo]] into 44edo, with note 44 being a duplicate note 0, as [[Bryan Deister]] demonstrates in [https://www.youtube.com/shorts/_GoQNEW24fQ ''44edo improv''] (Oct 2025)
+{{Lumatone EDO mapping|n=45|start=39|xstep=7|ystep=-2}}
+== Neutral thirds ==
+Another option is to slice the perfect fifth in half, giving this mapping, which is derived from the [[Lumatone mapping for neutral thirds scales]]:
 {{Lumatone EDO mapping|n=44|start=33|xstep=5|ystep=3}}
+== Semiquartal ==
+Slicing the perfect fourth in half also works, but the [[4L&nbsp;1s]] mapping does not cover the whole gamut:
 {{Lumatone EDO mapping|n=44|start=23|xstep=9|ystep=-1}}
+Expanding this to the [[5L&nbsp;4s]] mapping solves this problem, but the scale has an 8:1 step ratio, making it very lopsided.
 {{Lumatone EDO mapping|n=44|start=0|xstep=8|ystep=-7}}
-However, it is the [[Diaschismic_family#Hemifourths|Hemifourths]] mapping that combines the widest range that covers the full gamut with the most efficient way of reaching all prime harmonics up to 17.
+== Hemifourths ==
+However, it is the [[Diaschismic_family#Hemifourths|Hemifourths]] mapping that combines the widest range that covers the full gamut with the most efficient way of reaching all prime harmonics up to 17.
 {{Lumatone EDO mapping|n=44|start=1|xstep=9|ystep=-5}}
-[[Category:Lumatone mappings]] [[Category:44edo]]
+{{Navbox Lumatone}}