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.
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.
12
20
13
21
29
37
3
6
14
22
30
38
4
12
20
7
15
23
31
39
5
13
21
29
37
3
0
8
16
24
32
40
6
14
22
30
38
4
12
20
1
9
17
25
33
41
7
15
23
31
39
5
13
21
29
37
3
36
2
10
18
26
34
0
8
16
24
32
40
6
14
22
30
38
4
12
20
37
3
11
19
27
35
1
9
17
25
33
41
7
15
23
31
39
5
13
21
29
37
3
30
38
4
12
20
28
36
2
10
18
26
34
0
8
16
24
32
40
6
14
22
30
38
4
12
20
39
5
13
21
29
37
3
11
19
27
35
1
9
17
25
33
41
7
15
23
31
39
5
13
21
29
37
3
14
22
30
38
4
12
20
28
36
2
10
18
26
34
0
8
16
24
32
40
6
14
22
30
38
4
39
5
13
21
29
37
3
11
19
27
35
1
9
17
25
33
41
7
15
23
31
39
5
14
22
30
38
4
12
20
28
36
2
10
18
26
34
0
8
16
24
32
40
39
5
13
21
29
37
3
11
19
27
35
1
9
17
25
33
41
14
22
30
38
4
12
20
28
36
2
10
18
26
34
39
5
13
21
29
37
3
11
19
27
35
14
22
30
38
4
12
20
28
39
5
13
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).
41
5
2
9
16
23
30
42
6
13
20
27
34
41
5
3
10
17
24
31
38
2
9
16
23
30
0
7
14
21
28
35
42
6
13
20
27
34
41
5
4
11
18
25
32
39
3
10
17
24
31
38
2
9
16
23
30
1
8
15
22
29
36
0
7
14
21
28
35
42
6
13
20
27
34
41
5
5
12
19
26
33
40
4
11
18
25
32
39
3
10
17
24
31
38
2
9
16
23
30
2
9
16
23
30
37
1
8
15
22
29
36
0
7
14
21
28
35
42
6
13
20
27
34
41
5
13
20
27
34
41
5
12
19
26
33
40
4
11
18
25
32
39
3
10
17
24
31
38
2
9
16
23
30
31
38
2
9
16
23
30
37
1
8
15
22
29
36
0
7
14
21
28
35
42
6
13
20
27
34
13
20
27
34
41
5
12
19
26
33
40
4
11
18
25
32
39
3
10
17
24
31
38
31
38
2
9
16
23
30
37
1
8
15
22
29
36
0
7
14
21
28
35
13
20
27
34
41
5
12
19
26
33
40
4
11
18
25
32
39
31
38
2
9
16
23
30
37
1
8
15
22
29
36
13
20
27
34
41
5
12
19
26
33
40
31
38
2
9
16
23
30
37
13
20
27
34
41
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 valmapping). 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).
34
40
39
3
9
15
21
38
2
8
14
20
26
32
38
1
7
13
19
25
31
37
1
7
13
19
0
6
12
18
24
30
36
0
6
12
18
24
30
36
5
11
17
23
29
35
41
5
11
17
23
29
35
41
5
11
17
4
10
16
22
28
34
40
4
10
16
22
28
34
40
4
10
16
22
28
34
9
15
21
27
33
39
3
9
15
21
27
33
39
3
9
15
21
27
33
39
3
9
15
8
14
20
26
32
38
2
8
14
20
26
32
38
2
8
14
20
26
32
38
2
8
14
20
26
32
19
25
31
37
1
7
13
19
25
31
37
1
7
13
19
25
31
37
1
7
13
19
25
31
37
1
7
13
36
0
6
12
18
24
30
36
0
6
12
18
24
30
36
0
6
12
18
24
30
36
0
6
12
18
17
23
29
35
41
5
11
17
23
29
35
41
5
11
17
23
29
35
41
5
11
17
23
34
40
4
10
16
22
28
34
40
4
10
16
22
28
34
40
4
10
16
22
15
21
27
33
39
3
9
15
21
27
33
39
3
9
15
21
27
32
38
2
8
14
20
26
32
38
2
8
14
20
26
13
19
25
31
37
1
7
13
19
25
31
30
36
0
6
12
18
24
30
11
17
23
29
35
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
7
4
11
18
25
32
1
8
15
22
29
36
1
8
5
12
19
26
33
40
5
12
19
26
33
2
9
16
23
30
37
2
9
16
23
30
37
2
9
6
13
20
27
34
41
6
13
20
27
34
41
6
13
20
27
34
3
10
17
24
31
38
3
10
17
24
31
38
3
10
17
24
31
38
3
10
7
14
21
28
35
0
7
14
21
28
35
0
7
14
21
28
35
0
7
14
21
28
35
4
11
18
25
32
39
4
11
18
25
32
39
4
11
18
25
32
39
4
11
18
25
32
39
4
11
15
22
29
36
1
8
15
22
29
36
1
8
15
22
29
36
1
8
15
22
29
36
1
8
15
22
29
36
33
40
5
12
19
26
33
40
5
12
19
26
33
40
5
12
19
26
33
40
5
12
19
26
33
40
16
23
30
37
2
9
16
23
30
37
2
9
16
23
30
37
2
9
16
23
30
37
2
34
41
6
13
20
27
34
41
6
13
20
27
34
41
6
13
20
27
34
41
17
24
31
38
3
10
17
24
31
38
3
10
17
24
31
38
3
35
0
7
14
21
28
35
0
7
14
21
28
35
0
18
25
32
39
4
11
18
25
32
39
4
36
1
8
15
22
29
36
1
19
26
33
40
5
37
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.
