User:Lucius Chiaraviglio/Keyboard Layout Lab/Non-Isomorphic Lumatone mappings: Difference between revisions

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=== 70edo (demonstrated to work) ===
=== 70edo (demonstrated to work) ===


==== Pseudo-Isomorphic Pseudo-Diatonic ====
==== Pseudo-Diatonic ====


[[Bryan Deister]] has demonstrated a pseudo-isomorphic mapping for [[70edo]] in [https://www.youtube.com/watch?v=-NEq3jKHjzs ''Improv in 70edo''] (2025) that uses one duplicated note in each octave to achieve a pseudo-diatonic layout for ease of access to common consonant intervals, although it does not include all the notes of the tuning system. Each note 70 is actually another note 0, so as to reset octave pitch down by ~[[81/80]] (moderately deflated).
[[Bryan Deister]] has demonstrated a pseudo-isomorphic mapping for [[70edo]] in [https://www.youtube.com/watch?v=-NEq3jKHjzs ''Improv in 70edo''] (2025) that uses one duplicated note in each octave to achieve a pseudo-diatonic layout for ease of access to common consonant intervals, although it does not include all the notes of the tuning system. Each note 70 is actually another note 0, so as to reset octave pitch down by ~[[81/80]] (moderately deflated).
Line 45: Line 45:


Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:09, 20 September 2025 (UTC)<br>
Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:09, 20 September 2025 (UTC)<br>
Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 20:41, 1 October 2025 (UTC)
Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 20:42, 1 October 2025 (UTC)


==== Pseudo-Isomorphic Pseudo-Antidiatonic ====
==== Pseudo-Antidiatonic ====


[[Bryan Deister]] has demonstrated a pseudo-isomorphic mapping for [[70edo]] in [https://www.youtube.com/shorts/ZDU75YabROE ''70edo prelude''] (2025) that uses three duplicated notes in each octave to achieve a pseudo-antidiatonic layout. Notes 70, 71, and 72 are duplicates of 0, 1, and 2, respectively; of these, the ones appearing on the layout are 0 and 70, 1, and 72. Playing as on a true antidiatonic layout results in a 1L<sub>1</sub>&nbsp;1L<sub>2</sub>&nbsp;5s [[MODMOS]] having a step ratio of 21:14:9.
[[Bryan Deister]] has demonstrated a pseudo-isomorphic mapping for [[70edo]] in [https://www.youtube.com/shorts/ZDU75YabROE ''70edo prelude''] (2025) that uses three duplicated notes in each octave to achieve a pseudo-antidiatonic layout. Notes 70, 71, and 72 are duplicates of 0, 1, and 2, respectively; of these, the ones appearing on the layout are 0 and 70, 1, and 72. Playing as on a true antidiatonic layout results in a 1L<sub>1</sub>&nbsp;1L<sub>2</sub>&nbsp;5s [[MODMOS]] having a step ratio of 21:14:9.
Line 54: Line 54:


Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 06:46, 30 September 2025 (UTC)<br>
Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 06:46, 30 September 2025 (UTC)<br>
Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 20:41, 1 October 2025 (UTC)
Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 20:42, 1 October 2025 (UTC)


=== 87edo (demonstrated to work) ===
=== 87edo (demonstrated to work) ===

Revision as of 20:42, 1 October 2025

As the page title implies, this page gets non-isomorphic Lumatone mappings, including those that can be generated by the isomorphic mechanism by specifying a number of notes per interval of equivalence that is different from the actual number of notes.

Named Note Lumatone Mappings

(This section is a placeholder.)

Pseudo-Isomorphic Lumatone Mappings

Mappings that can be generated by the isomorphic mechanism by specifying a number of notes per interval of equivalence that is different from the actual number of notes (generally, 1 extra note which is actually a duplicate of the next note 0).

18edo (demonstrated to work)

A pseudo-isomorphic pseudo-diatonic mapping for 18edo that duplicates note 0 (as note 18) enables diatonic playing while keeping octaves level — it is the 19edo diatonic layout, but with only 18 unique notes per octave. Alternatively, it can be interpreted as the 4L 3s Janko layout, but with a duplicate of note 0 added, which allows it to support both the 4L 3s scale (3:2 step ratio) and a 5L 1s1 1s2 MODMOS scale (3:2:1 step ratio). This is demonstrated in Bryan Deister's 18edo improv (2025).

17
1
0
3
6
9
12
18
2
5
8
11
14
17
1
1
4
7
10
13
16
0
3
6
9
12
0
3
6
9
12
15
18
2
5
8
11
14
17
1
2
5
8
11
14
17
1
4
7
10
13
16
0
3
6
9
12
1
4
7
10
13
16
0
3
6
9
12
15
18
2
5
8
11
14
17
1
3
6
9
12
15
18
2
5
8
11
14
17
1
4
7
10
13
16
0
3
6
9
12
2
5
8
11
14
17
1
4
7
10
13
16
0
3
6
9
12
15
18
2
5
8
11
14
17
1
7
10
13
16
0
3
6
9
12
15
18
2
5
8
11
14
17
1
4
7
10
13
16
0
3
6
9
12
15
18
2
5
8
11
14
17
1
4
7
10
13
16
0
3
6
9
12
15
18
2
5
8
11
14
7
10
13
16
0
3
6
9
12
15
18
2
5
8
11
14
17
1
4
7
10
13
16
15
18
2
5
8
11
14
17
1
4
7
10
13
16
0
3
6
9
12
15
7
10
13
16
0
3
6
9
12
15
18
2
5
8
11
14
17
15
18
2
5
8
11
14
17
1
4
7
10
13
16
7
10
13
16
0
3
6
9
12
15
18
15
18
2
5
8
11
14
17
7
10
13
16
0
15
18

Added: Lucius Chiaraviglio (talk) 05:44, 25 September 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 20:57, 27 September 2025 (UTC)

52edo (demonstrated to work)

A version of the Pseudo-Pentacircle mapping for 52edo that duplicates note 0 (as note 52, as if making a layout for 53edo) keeps the octaves level. This is demonstrated in Bryan Deister's 52edo improv (2025).

4
13
8
17
26
35
44
3
12
21
30
39
48
4
13
7
16
25
34
43
52
8
17
26
35
44
2
11
20
29
38
47
3
12
21
30
39
48
4
13
6
15
24
33
42
51
7
16
25
34
43
52
8
17
26
35
44
1
10
19
28
37
46
2
11
20
29
38
47
3
12
21
30
39
48
4
13
5
14
23
32
41
50
6
15
24
33
42
51
7
16
25
34
43
52
8
17
26
35
44
0
9
18
27
36
45
1
10
19
28
37
46
2
11
20
29
38
47
3
12
21
30
39
48
4
13
13
22
31
40
49
5
14
23
32
41
50
6
15
24
33
42
51
7
16
25
34
43
52
8
17
26
35
44
35
44
0
9
18
27
36
45
1
10
19
28
37
46
2
11
20
29
38
47
3
12
21
30
39
48
13
22
31
40
49
5
14
23
32
41
50
6
15
24
33
42
51
7
16
25
34
43
52
35
44
0
9
18
27
36
45
1
10
19
28
37
46
2
11
20
29
38
47
13
22
31
40
49
5
14
23
32
41
50
6
15
24
33
42
51
35
44
0
9
18
27
36
45
1
10
19
28
37
46
13
22
31
40
49
5
14
23
32
41
50
35
44
0
9
18
27
36
45
13
22
31
40
49
35
44

Added: Lucius Chiaraviglio (talk) 05:44, 25 September 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 07:27, 27 September 2025 (UTC)

61edo (demonstrated to work)

Bryan Deister has demonstrated a pseudo-isomorphic mapping for 61edo in 61edo prelude (2025). This mapping retains a diatonic-style layout for ease of access to common consonant intervals, although it does not include all the notes of the tuning system. Each note 61 is actually another note 0, so as to reset octave pitch down by half of ~81/80 (considerably deflated).

58
6
2
12
22
32
42
60
8
18
28
38
48
58
6
4
14
24
34
44
54
2
12
22
32
42
0
10
20
30
40
50
60
8
18
28
38
48
58
6
6
16
26
36
46
56
4
14
24
34
44
54
2
12
22
32
42
2
12
22
32
42
52
0
10
20
30
40
50
60
8
18
28
38
48
58
6
8
18
28
38
48
58
6
16
26
36
46
56
4
14
24
34
44
54
2
12
22
32
42
4
14
24
34
44
54
2
12
22
32
42
52
0
10
20
30
40
50
60
8
18
28
38
48
58
6
20
30
40
50
60
8
18
28
38
48
58
6
16
26
36
46
56
4
14
24
34
44
54
2
12
22
32
42
46
56
4
14
24
34
44
54
2
12
22
32
42
52
0
10
20
30
40
50
60
8
18
28
38
48
20
30
40
50
60
8
18
28
38
48
58
6
16
26
36
46
56
4
14
24
34
44
54
46
56
4
14
24
34
44
54
2
12
22
32
42
52
0
10
20
30
40
50
20
30
40
50
60
8
18
28
38
48
58
6
16
26
36
46
56
46
56
4
14
24
34
44
54
2
12
22
32
42
52
20
30
40
50
60
8
18
28
38
48
58
46
56
4
14
24
34
44
54
20
30
40
50
60
46
56

Added: Lucius Chiaraviglio (talk) 08:21, 20 September 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 06:54, 21 September 2025 (UTC)

70edo (demonstrated to work)

Pseudo-Diatonic

Bryan Deister has demonstrated a pseudo-isomorphic mapping for 70edo in Improv in 70edo (2025) that uses one duplicated note in each octave to achieve a pseudo-diatonic layout for ease of access to common consonant intervals, although it does not include all the notes of the tuning system. Each note 70 is actually another note 0, so as to reset octave pitch down by ~81/80 (moderately deflated).

61
1
69
9
20
31
42
66
6
17
28
39
50
61
1
3
14
25
36
47
58
69
9
20
31
42
0
11
22
33
44
55
66
6
17
28
39
50
61
1
8
19
30
41
52
63
3
14
25
36
47
58
69
9
20
31
42
5
16
27
38
49
60
0
11
22
33
44
55
66
6
17
28
39
50
61
1
13
24
35
46
57
68
8
19
30
41
52
63
3
14
25
36
47
58
69
9
20
31
42
10
21
32
43
54
65
5
16
27
38
49
60
0
11
22
33
44
55
66
6
17
28
39
50
61
1
29
40
51
62
2
13
24
35
46
57
68
8
19
30
41
52
63
3
14
25
36
47
58
69
9
20
31
42
59
70
10
21
32
43
54
65
5
16
27
38
49
60
0
11
22
33
44
55
66
6
17
28
39
50
29
40
51
62
2
13
24
35
46
57
68
8
19
30
41
52
63
3
14
25
36
47
58
59
70
10
21
32
43
54
65
5
16
27
38
49
60
0
11
22
33
44
55
29
40
51
62
2
13
24
35
46
57
68
8
19
30
41
52
63
59
70
10
21
32
43
54
65
5
16
27
38
49
60
29
40
51
62
2
13
24
35
46
57
68
59
70
10
21
32
43
54
65
29
40
51
62
2
59
70

Added: Lucius Chiaraviglio (talk) 08:09, 20 September 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 20:42, 1 October 2025 (UTC)

Pseudo-Antidiatonic

Bryan Deister has demonstrated a pseudo-isomorphic mapping for 70edo in 70edo prelude (2025) that uses three duplicated notes in each octave to achieve a pseudo-antidiatonic layout. Notes 70, 71, and 72 are duplicates of 0, 1, and 2, respectively; of these, the ones appearing on the layout are 0 and 70, 1, and 72. Playing as on a true antidiatonic layout results in a 1L1 1L2 5s MODMOS having a step ratio of 21:14:9.

35
44
49
58
67
3
12
54
63
72
8
17
26
35
44
68
4
13
22
31
40
49
58
67
3
12
0
9
18
27
36
45
54
63
72
8
17
26
35
44
14
23
32
41
50
59
68
4
13
22
31
40
49
58
67
3
12
19
28
37
46
55
64
0
9
18
27
36
45
54
63
72
8
17
26
35
44
33
42
51
60
69
5
14
23
32
41
50
59
68
4
13
22
31
40
49
58
67
3
12
38
47
56
65
1
10
19
28
37
46
55
64
0
9
18
27
36
45
54
63
72
8
17
26
35
44
61
70
6
15
24
33
42
51
60
69
5
14
23
32
41
50
59
68
4
13
22
31
40
49
58
67
3
12
20
29
38
47
56
65
1
10
19
28
37
46
55
64
0
9
18
27
36
45
54
63
72
8
17
26
61
70
6
15
24
33
42
51
60
69
5
14
23
32
41
50
59
68
4
13
22
31
40
20
29
38
47
56
65
1
10
19
28
37
46
55
64
0
9
18
27
36
45
61
70
6
15
24
33
42
51
60
69
5
14
23
32
41
50
59
20
29
38
47
56
65
1
10
19
28
37
46
55
64
61
70
6
15
24
33
42
51
60
69
5
20
29
38
47
56
65
1
10
61
70
6
15
24
20
29

Added: Lucius Chiaraviglio (talk) 06:46, 30 September 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 20:42, 1 October 2025 (UTC)

87edo (demonstrated to work)

Bryan Deister has demonstrated a pseudo-isomorphic mapping for 87edo in 87edo waltz (2025). This mapping retains a diatonic-style layout for ease of access to common consonant intervals, although it does not include all the notes of the tuning system. Each note 87 is actually another note 0, so as to reset octave pitch down by half of ~81/80 (moderately inflated).

80
6
1
15
29
43
57
84
10
24
38
52
66
80
6
5
19
33
47
61
75
1
15
29
43
57
0
14
28
42
56
70
84
10
24
38
52
66
80
6
9
23
37
51
65
79
5
19
33
47
61
75
1
15
29
43
57
4
18
32
46
60
74
0
14
28
42
56
70
84
10
24
38
52
66
80
6
13
27
41
55
69
83
9
23
37
51
65
79
5
19
33
47
61
75
1
15
29
43
57
8
22
36
50
64
78
4
18
32
46
60
74
0
14
28
42
56
70
84
10
24
38
52
66
80
6
31
45
59
73
87
13
27
41
55
69
83
9
23
37
51
65
79
5
19
33
47
61
75
1
15
29
43
57
68
82
8
22
36
50
64
78
4
18
32
46
60
74
0
14
28
42
56
70
84
10
24
38
52
66
31
45
59
73
87
13
27
41
55
69
83
9
23
37
51
65
79
5
19
33
47
61
75
68
82
8
22
36
50
64
78
4
18
32
46
60
74
0
14
28
42
56
70
31
45
59
73
87
13
27
41
55
69
83
9
23
37
51
65
79
68
82
8
22
36
50
64
78
4
18
32
46
60
74
31
45
59
73
87
13
27
41
55
69
83
68
82
8
22
36
50
64
78
31
45
59
73
87
68
82

Added: Lucius Chiaraviglio (talk) 08:00, 20 September 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 06:54, 21 September 2025 (UTC)

91edo (demonstrated to work)

Bryan Deister has demonstrated a pseudo-isomorphic mapping for 91edo in microtonal improvisation in 91edo (2025). This layout is numbered as for 92edo, but note 91 is actually a duplicate of note 0. The range is just one note short of 3 full octaves, with octaves sloping down gently, unlike the fully isomorphic version below, which avoids the interruption from the duplicated note 0 and has slightly greater range, but at the cost of greater (and opposite) octave slope and a vertical wraparound of note 0 with ascending octaves (as well as producing a discontinuity in scales). This mapping has the same generators as the fully isomorphic version, as described below.

0
9
5
14
23
32
41
1
10
19
28
37
46
55
64
6
15
24
33
42
51
60
69
78
87
4
2
11
20
29
38
47
56
65
74
83
0
9
18
27
7
16
25
34
43
52
61
70
79
88
5
14
23
32
41
50
59
3
12
21
30
39
48
57
66
75
84
1
10
19
28
37
46
55
64
73
82
8
17
26
35
44
53
62
71
80
89
6
15
24
33
42
51
60
69
78
87
4
13
22
4
13
22
31
40
49
58
67
76
85
2
11
20
29
38
47
56
65
74
83
0
9
18
27
36
45
18
27
36
45
54
63
72
81
90
7
16
25
34
43
52
61
70
79
88
5
14
23
32
41
50
59
68
77
41
50
59
68
77
86
3
12
21
30
39
48
57
66
75
84
1
10
19
28
37
46
55
64
73
82
73
82
91
8
17
26
35
44
53
62
71
80
89
6
15
24
33
42
51
60
69
78
87
4
13
22
31
40
49
58
67
76
85
2
11
20
29
38
47
56
65
74
83
36
45
54
63
72
81
90
7
16
25
34
43
52
61
70
79
88
59
68
77
86
3
12
21
30
39
48
57
66
75
84
91
8
17
26
35
44
53
62
71
80
89
22
31
40
49
58
67
76
85
54
63
72
81
90
77
86

Added: Lucius Chiaraviglio (talk) 16:02, 4 June 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 07:54, 8 June 2025 (UTC)
Moved here from User:Lucius_Chiaraviglio/Keyboard_Layout_Lab/Various_other_Lumatone_mappings: Lucius Chiaraviglio (talk) 07:32, 20 September 2025 (UTC)

MOS Subset Lumatone Mappings

These work like the pseudo-isomorphic mappings above, but with the additional consideration of deliberately using non-coprime generators on all axes to take a MOS subset of their tuning systems.

92edo (demonstrated to work)

Bryan Deister has demonstrated a pseudo-isomorphic pseudo-diatonic mapping for 92edo in 92edo waltz (2025) that deliberately uses non-coprime generators on all axes to use a subset of 92edo to make 31 non-equal divisions of the octave in the form of a 30L 1s MOS scale with a 3:2 step ratio. This layout is numbered as for 93edo, but note 92 is actually a duplicate of note 0; due to missing notes, it does not actually appear here.

87
9
3
18
33
48
63
90
12
27
42
57
72
87
9
6
21
36
51
66
81
3
18
33
48
63
0
15
30
45
60
75
90
12
27
42
57
72
87
9
9
24
39
54
69
84
6
21
36
51
66
81
3
18
33
48
63
3
18
33
48
63
78
0
15
30
45
60
75
90
12
27
42
57
72
87
9
12
27
42
57
72
87
9
24
39
54
69
84
6
21
36
51
66
81
3
18
33
48
63
6
21
36
51
66
81
3
18
33
48
63
78
0
15
30
45
60
75
90
12
27
42
57
72
87
9
30
45
60
75
90
12
27
42
57
72
87
9
24
39
54
69
84
6
21
36
51
66
81
3
18
33
48
63
69
84
6
21
36
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66
81
3
18
33
48
63
78
0
15
30
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75
90
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27
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57
72
30
45
60
75
90
12
27
42
57
72
87
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24
39
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69
84
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69
84
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21
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51
66
81
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18
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78
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15
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75
30
45
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75
90
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27
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57
72
87
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24
39
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69
84
69
84
6
21
36
51
66
81
3
18
33
48
63
78
30
45
60
75
90
12
27
42
57
72
87
69
84
6
21
36
51
66
81
30
45
60
75
90
69
84

Added: Lucius Chiaraviglio (talk) 07:46, 27 September 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 05:55, 30 September 2025 (UTC)

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