Lumatone mapping for 44edo: Difference between revisions

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→Antidiatonic: Insert Bryan Deister's Bidia + Diminished + Charismic + Semitonismic (Flipped Antidiatonic/Superdiatonic) after this
 
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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]].
{{Lumatone mapping intro}}
 
== Antidiatonic ==
You can use the b 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}}
{{Lumatone EDO mapping|n=44|start=28|xstep=6|ystep=1}}


Slicing the perfect 5th or 4th in half are also 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}}
{{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}}
{{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}}
{{Lumatone EDO mapping|n=44|start=0|xstep=8|ystep=-7}}


[[Category:Lumatone mappings]] [[Category:44edo]]
== 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}}
 
{{Navbox Lumatone}}

Latest revision as of 09:49, 11 January 2026

There are many conceivable ways to map 44edo 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.

Antidiatonic

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

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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) ([short clip], [short 2]). 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 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).

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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 44edo improv (Oct 2025)

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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:

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Semiquartal

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

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

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Hemifourths

However, it is the 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.

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2
11
20
29
38
3
12
21
30
39
15
24
33
42
7
16
25
34
2
11
20
29
38
24
33
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