Lumatone mapping for 42edo: Difference between revisions

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→Whitewood + Qeema/Tritikleismic: Reorganize and add another version from Bryan Deister; also fix mistake in the mapping (42edo is a minefield)
 
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There are many conceivable ways to map [[42edo]] onto the [[Lumatone]] keyboard. Only one, however, agrees with the [[Standard Lumatone mapping for Pythagorean]].
{{Lumatone mapping intro}}
 
== Diatonic ==
The flat fifth is the same as that of [[7edo]], which if used would result in six mutually-exclusive rings of fifths, so to cycle through all notes using the [[circle of fifths]] you need to use the sharp fifth instead, which gives [[ultrapyth]].
{{Lumatone EDO mapping|n=42|start=12|xstep=8|ystep=-7}}
{{Lumatone EDO mapping|n=42|start=12|xstep=8|ystep=-7}}


The [[Lemba]] mapping is also of particular interest despite using a non patent val.
== Pseudo-Isomorphic Pseudo-Diatonic ==
A pseudo-isomorphic pseudo-diatonic mapping for [[42edo]] that duplicates note 0 (as note 18) enables diatonic playing while keeping octaves level — it is the [[43edo]] diatonic layout, but with only 42 unique notes per octave. [[Bryan Deister]] has demonstrated this mapping in [https://www.youtube.com/watch?v=cL6CY3U9mHM ''42edo groove''] (2025).
{{Lumatone EDO mapping|n=43|start=41|xstep=7|ystep=-3}}
 
== Whitewood + Qeema/Tritikleismic ==
Since [[42edo]] is a multiple of [[7edo]], and not far beyond the last diatonic-incapable tuning [[35edo]], [[whitewood]] is still a legitimate mapping for it; since the 5th harmonic is also close to maximally far from just, this suggests [[qeema]]/[[tritikleismic]] temperament, using the 42bc [[val]] (42bcd if using the 7-limit), for which the generator 11\42 is a near-just classic minor third ~[[6/5]] (with the very large errors in the 3rd and 5th harmonics canceling each other almost perfectly), and corresponds to one key right plus one key down-right, although the two mappings below differ in how the generator is constituted.
 
==== 2L 6s + 2L 4s version ====
On one version of the mapping, one key right 6\42 corresponds to the very flatly approximated ptolemaic whole tone ~[[10/9]]), and one key down-right 5\42 is a neutral second close to ~[[25/23]] by direct approximation (which, however, does not map to this interval by [[patent val]] [[mapping]]). Combining these to form the generator plus some extra down-right key movements as needed gives rise to the scales [[2L&nbsp;6s]] (6:5 step ratio) and [[2L&nbsp;4s]] (11:5 step ratio). [[Bryan Deister]] has demonstrated this in [https://www.youtube.com/shorts/B90JT_SxSSE ''<nowiki>A Hunger Awakes - 42edo [short]</nowiki>''] (2026), although with different placement of MIDI note 0. The range is about 4¾ octaves, which slant up with the rows (as normal for whitewood mappings).
{{Lumatone EDO mapping|n=42|start=34|xstep=6|ystep=-1}}
 
==== 2L&nbsp;7s + 2L&nbsp;5s version ====
In an alternate version of the above mapping, one key right 7\42 corresponds to the werckismic tone ~[[55/49]] (since the similar ~[[9/8]] maps inconsistently to another interval), and one key down-right 4\42 corresponds to a sharp large septendecimal semitone ~[[17/16]]. Combining these to form the generator generator plus some extra down-right key movements as needed gives rise to the scales [[2L&nbsp;7s]] (7:4 step ratio) and [[2L&nbsp;5s]] (11:4 step ratio). [[Bryan Deister]] has demonstrated this in [https://www.youtube.com/shorts/D_YgzRJFg8I ''<nowiki>Waltz in 42edo [short]</nowiki>''] (2026). The range is a bit over five octaves, which slant up with the rows (as normal for whitewood mappings).
{{Lumatone EDO mapping|n=42|start=0|xstep=7|ystep=-3}}
 
== Lemba ==
The [[Lemba]] mapping is also of particular interest despite using a non-patent val. It achieves a range of almost six octaves, with only a slight downwards slope.
{{Lumatone EDO mapping|n=42|start=40|xstep=8|ystep=-3}}
{{Lumatone EDO mapping|n=42|start=40|xstep=8|ystep=-3}}


[[Category:Lumatone mappings]] [[Category:42edo]]
{{Navbox Lumatone}}

Latest revision as of 10:03, 4 March 2026

There are many conceivable ways to map 42edo onto the onto the Lumatone keyboard. However, as both of its fifths are about as far away from just as possible, neither the sharp or the flat versions of the Standard Lumatone mapping for Pythagorean work particularly well.

Diatonic

The flat fifth is the same as that of 7edo, which if used would result in six mutually-exclusive rings of fifths, so to cycle through all notes using the circle of fifths you need to use the sharp fifth instead, which gives ultrapyth.

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22
30
38
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39
5
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21
29
14
22

Pseudo-Isomorphic Pseudo-Diatonic

A pseudo-isomorphic pseudo-diatonic mapping for 42edo that duplicates note 0 (as note 18) enables diatonic playing while keeping octaves level — it is the 43edo diatonic layout, but with only 42 unique notes per octave. Bryan Deister has demonstrated this mapping in 42edo groove (2025).

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0
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42
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0
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42
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31
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0
7
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35
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30
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27
34
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31
38

Whitewood + Qeema/Tritikleismic

Since 42edo is a multiple of 7edo, and not far beyond the last diatonic-incapable tuning 35edo, whitewood is still a legitimate mapping for it; since the 5th harmonic is also close to maximally far from just, this suggests qeema/tritikleismic temperament, using the 42bc val (42bcd if using the 7-limit), for which the generator 11\42 is a near-just classic minor third ~6/5 (with the very large errors in the 3rd and 5th harmonics canceling each other almost perfectly), and corresponds to one key right plus one key down-right, although the two mappings below differ in how the generator is constituted.

2L 6s + 2L 4s version

On one version of the mapping, one key right 6\42 corresponds to the very flatly approximated ptolemaic whole tone ~10/9), and one key down-right 5\42 is a neutral second close to ~25/23 by direct approximation (which, however, does not map to this interval by patent val mapping). Combining these to form the generator plus some extra down-right key movements as needed gives rise to the scales 2L 6s (6:5 step ratio) and 2L 4s (11:5 step ratio). Bryan Deister has demonstrated this in A Hunger Awakes - 42edo [short] (2026), although with different placement of MIDI note 0. The range is about 4¾ octaves, which slant up with the rows (as normal for whitewood mappings).

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32
38
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31
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36
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30
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28
34

2L 7s + 2L 5s version

In an alternate version of the above mapping, one key right 7\42 corresponds to the werckismic tone ~55/49 (since the similar ~9/8 maps inconsistently to another interval), and one key down-right 4\42 corresponds to a sharp large septendecimal semitone ~17/16. Combining these to form the generator generator plus some extra down-right key movements as needed gives rise to the scales 2L 7s (7:4 step ratio) and 2L 5s (11:4 step ratio). Bryan Deister has demonstrated this in Waltz in 42edo [short] (2026). The range is a bit over five octaves, which slant up with the rows (as normal for whitewood mappings).

0
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18
25
32
1
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22
29
36
1
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19
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33
40
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26
33
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30
37
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29
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19
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33
40
5
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2

Lemba

The Lemba mapping is also of particular interest despite using a non-patent val. It achieves a range of almost six octaves, with only a slight downwards slope.

40
6
3
11
19
27
35
0
8
16
24
32
40
6
14
5
13
21
29
37
3
11
19
27
35
1
2
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18
26
34
0
8
16
24
32
40
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14
22
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31
39
5
13
21
29
37
3
11
19
27
35
1
9
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12
20
28
36
2
10
18
26
34
0
8
16
24
32
40
6
14
22
30
9
17
25
33
41
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15
23
31
39
5
13
21
29
37
3
11
19
27
35
1
9
17
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14
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30
38
4
12
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28
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2
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0
8
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27
35
1
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11
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9
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14
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2
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0
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35
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9
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