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User:Lucius Chiaraviglio/Keyboard Layout Lab/Unnamed rank-3 temperament Lumatone mappings

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Revision as of 08:46, 14 December 2025 by Lucius Chiaraviglio (talk | contribs) (Fix section heading case)

Various Kit-Bashed Lumatone mappings for rank-3 Temperaments

These Lumatone mappings were not created for a particular temperament (however, with the proviso that whatever corresponding temperament is discovered must be rank-3 because either generator by itself would produce contorsion), but as experiments in modifying the Lumatone mapping of one EDO to work for a nearby size without regard to whether they have any temperaments in common.

30edo (demonstrated to work)

Bryan Deister has used a layout for 30edo that was also inspired by the layout for 29edo (rather than being made for any specific temperament), as demonstrated in minuet in 30edo (2025). The right-moving generator is a somewhat flat Pythagorean whole tone (~9/8, 5\30; and in the video, the row segments that include note 0 are colored solid red). The up-moving generator is a somewhat flat tridecimal supraminor second (~14/13, 3\30); neither would be able access the full gamut on its own, but together they cover the full gamut with a generous allotment of repeated notes (indicating that if this layout was to represent a particular temperament, that would have to be a rank-3 temperament if having an octave period, or a rank-2 temperament dividing the octave into multiple periods). The range is a bit under five octaves, with octaves slanting up (while wrapping around) at the same angle as the right-moving generator.

 
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Added: Lucius Chiaraviglio (talk) 07:59, 25 March 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 21:39, 29 March 2025 (UTC)
Moved here from Various other Lumatone mappings page: Lucius Chiaraviglio (talk) 19:34, 23 July 2025 (UTC)

Reversed positions of chroma and diatone (demonstrated to work but awaiting approval)

Related to the above mapping, Bryan Deister has also used a mapping in which the upwards generator of the previous mapping is instead made to be the down-right mapping, in 30edo improv (2025). (Rest of description goes here.)

 
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Added: Lucius Chiaraviglio (talk) 08:20, 14 December 2025 (UTC)

Moved here from Unnamed rank-3 temperament Lumatone mappings: Lucius Chiaraviglio (talk) 08:45, 14 December 2025 (UTC)

Various Unnamed rank-3 temperament Lumatone mappings

Various Lumatone mappings that do not match the mapping for another size of EDO, and were not designed for a particular temperament (however, with the proviso that whatever corresponding temperament is discovered must be rank-3 because either generator by itself would produce contorsion).

Moved here from Unnamed rank-3 temperament Lumatone mappings: Lucius Chiaraviglio (talk) 08:45, 14 December 2025 (UTC)

98edo (demonstrated to work)

Bryan Deister has demonstrated a rotated 7L 1s (13:7 step ratio) mapping for 98edo in 98edo waltz (2025). This mapping was designed to get as much range as possible without regard to temperament (the resulting temperament being an unnamed rank-3 temperament, since either single-step generator used alone will produce contorsion). The range is a bit over two octaves with no missed notes and no repeated notes, although the upper left and lower right corners contain considerable numbers of notes from incomplete octaves chopped off by the left and right edges; the octaves slope up and have a vertical wraparound.

 
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Added: Lucius Chiaraviglio (talk) 10:20, 4 August 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 08:50, 6 August 2025 (UTC)

75edo (demonstrated to work)

Bryan Deister has demonstrated the 7L 3s (step size ratio 9:4) Lumatone mapping for 75edo, in microtonal improvisation in 75edo (2025-06-24). So Right = 9\75 and down-right = 4\75, which means that Up = 5\75. Like 97edo, 75edo has mainly bad harmonics for its size (but with different harmonics being exceptions), so to find useful intervals, it is necessary to try to stick to primes 3, 5, and 23 (those having the least relative error) and/or take advantage of error cancellation as much as possible. Going right (9\75) 1 key is ~25/23 (error canceling, but starting out with some of the least bad harmonics); right 2 keys (18\75) is a subminor third ~625/529 (no simple ratio maps to this interval in the patent val of 75edo, but it merits mention anyway due to extensive use in the video); right 3 keys (27\75) = ~9/7 (errors only partially cancel, so somewhat flat); and right 7 keys (63\75) = ~34/19 (errors nearly cancel). Going down-right (4\75) 1 key functions as both ~27/26 and ~28/27; down-right 2 keys = ~14/13 (errors largely cancel), 3 keys = ~19/17 (errors largely cancel), and 5 keys = ~5/4 (the 5th harmonic has a small relative error). Going up (5\75) 1 key is ~23/22 (errors only partially canceling, so somewhat sharp). The range is just over 3½ octaves, and the octaves are very close to level, with just a slight down slope. This corresponds to the Neutral Thirds mapping on the Lumatone mapping for 75edo page.

 
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Added: Lucius Chiaraviglio (talk) 07:46, 25 June 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 05:48, 29 June 2025 (UTC)

78edo (demonstrated to work)

Bryan Deister] has demonsrated a Lumatone mapping for 78edo that lays out scales 11L 1s (7:1 step ratio) and 6L 6s (7:6 step ratio), in microtonal improvisation in 78edo (2025). The rightward generator 7\78 is slightly sharp large septendecimal semitone ~17/16; two of them make a slightly flat biyatismic whole tone ~17/15; and six of them readh a slightly flat undecimal minor fifth ~16/11. The down-right generator 6\78 is a somewhat sharp small undevicesimal semitone ~20/19; stacking these can yield both a slightly sharp undecimal major fourth ~11/8 (as 36\78, six generators) and slightly flat undecimal minor fifth ~16/11 (as 42\78, seven down-right generators, same as six rightward generators). The range is somewhat under three octaves, with all notes represented; octaves alternate between far and near, with an overall upwards slant.

 
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Added: Lucius Chiaraviglio (talk) 07:52, 3 July 2025 (UTC)

91edo (demonstrated to work)

Bryan Deister has demonstrated an isomorphic 9L 2s mapping for 91edo in improv 91edo (2025). The range is just one note beyond 3 full octaves, with octaves sloping up mildly (which results in a wraparound of note 0). The rightward generator 9\91 is the septimal diatonic semitone ~15/14. The upward generator 4\91 is a quartertone that functions as ~32/31, ~33/32, ~34/33, and ~36/35; two of them make the minor diatonic semitone ~17/16; six of them make a near-just minor third ~6/5. The use of this generator makes this a mapping for Quartkeenlig; however, since stacking the upward generator quickly leads to wraparounds, and attempting to get the perfect fifth in 91edo with this generator yields 52\91, which is the 7edo (91bb) fifth. Therefore, this mapping really needs to be treated as a rank-3 temperament mapping; for instance, to get the patent fifth 53\92 (a mildly flat ~3/2, almost exactly 1/7-comma meantone), it is easiest to stack five rightward generators and two upward generators.

 
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Added: Lucius Chiaraviglio (talk) 16:02, 4 June 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 08:57, 23 June 2025 (UTC)

93edo (demonstrated to work)

(This mapping has been updated with the changes made to the official version by Yourmusic Productions and ArrowHead294.)

Bryan Deister has demonstrated a mapping for 93edo in microtonal improvisation in 93edo (2025). The rightward generator 6\93 represents 21/20, 23/22, and 25/24, producing a 15L 1s scale as in Valentine, although 93edo is contorted with this scale (L = 6 and s = 3) and temperament; choosing the scale 13L 3s avoids contortion, although neither the bright version (64\93) nor the dark version (29\93) of its generator maps to a convenient ratio, so the following discussion instead uses the generators for the mapping itself. Going right 2 keys makes a ~35/32 neutral second (abundantly used in the later part of the video); 3 right = ~8/7; 5 right = ~5/4; and 8 right = ~10/7. To avoid contortion, it is necessary to use a second generator, making this a rank-3 temperament mapping; the upward generator 7\93 is ~20/19; 4 steps up makes ~16/13; 5 steps up makes ~13/10, and 9 steps up (which always involves a vertical wraparound) makes ~8/5. Down-right is −1\93, enabling easy glissandos (demonstrated in the beginning of the video). In order to avoid having notes of the first note 0 to note 0 octave chopped off at the left edge, the first note 5 is placed half way down the left edge, and note 0 is 5 down-right from that. The range is just over an octave and a half, and the octaves slope from near to far.

 
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3
9
15
21
27
33
39
45
89
2
8
14
20
26
32
38
13
19
25
31
37
24
30

Added: Lucius Chiaraviglio (talk) 20:43, 31 May 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 08:57, 14 June 2025 (UTC)

98edo (proposed and untested)

(Descriptive text needs to go here for 98edo, starting with rightward generator 9\98 = ~16/15 and 5 of them = ~11/8; and upward generator 5\98 = both ~29/28 ~30/29 and 9 of them = ~11/8; may need to streamline down to rank-2.)

 
4
13
8
17
26
35
44
3
12
21
30
39
48
57
66
7
16
25
34
43
52
61
70
79
88
97
2
11
20
29
38
47
56
65
74
83
92
3
12
21
6
15
24
33
42
51
60
69
78
87
96
7
16
25
34
43
52
1
10
19
28
37
46
55
64
73
82
91
2
11
20
29
38
47
56
65
74
5
14
23
32
41
50
59
68
77
86
95
6
15
24
33
42
51
60
69
78
87
96
7
0
9
18
27
36
45
54
63
72
81
90
1
10
19
28
37
46
55
64
73
82
91
2
11
20
29
13
22
31
40
49
58
67
76
85
94
5
14
23
32
41
50
59
68
77
86
95
6
15
24
33
42
51
60
35
44
53
62
71
80
89
0
9
18
27
36
45
54
63
72
81
90
1
10
19
28
37
46
55
64
66
75
84
93
4
13
22
31
40
49
58
67
76
85
94
5
14
23
32
41
50
59
68
88
97
8
17
26
35
44
53
62
71
80
89
0
9
18
27
36
45
54
63
21
30
39
48
57
66
75
84
93
4
13
22
31
40
49
58
67
43
52
61
70
79
88
97
8
17
26
35
44
53
62
74
83
92
3
12
21
30
39
48
57
66
96
7
16
25
34
43
52
61
29
38
47
56
65
51
60

Added: Lucius Chiaraviglio (talk) 07:52, 21 June 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 08:57, 23 June 2025 (UTC)

99edo (proposed and untested)

(Descriptive text needs to go here for 99edo, starting with rightward generator 8\99 = ~135/128, ~18/17, ~19/18, and 3 of them make ~13/11, and 4 of them make ~5/4and 6 of them make ~7/5; and upward generator 1\99 = ~126/125; may need to streamline down to rank-2.)

 
75
83
82
90
98
7
15
81
89
97
6
14
22
30
38
88
96
5
13
21
29
37
45
53
61
69
87
95
4
12
20
28
36
44
52
60
68
76
84
92
94
3
11
19
27
35
43
51
59
67
75
83
91
0
8
16
24
93
2
10
18
26
34
42
50
58
66
74
82
90
98
7
15
23
31
39
47
1
9
17
25
33
41
49
57
65
73
81
89
97
6
14
22
30
38
46
54
62
70
78
0
8
16
24
32
40
48
56
64
72
80
88
96
5
13
21
29
37
45
53
61
69
77
85
93
2
15
23
31
39
47
55
63
71
79
87
95
4
12
20
28
36
44
52
60
68
76
84
92
1
9
17
25
33
38
46
54
62
70
78
86
94
3
11
19
27
35
43
51
59
67
75
83
91
0
8
16
24
32
40
69
77
85
93
2
10
18
26
34
42
50
58
66
74
82
90
98
7
15
23
31
39
47
92
1
9
17
25
33
41
49
57
65
73
81
89
97
6
14
22
30
38
46
24
32
40
48
56
64
72
80
88
96
5
13
21
29
37
45
53
47
55
63
71
79
87
95
4
12
20
28
36
44
52
78
86
94
3
11
19
27
35
43
51
59
2
10
18
26
34
42
50
58
33
41
49
57
65
56
64

Added: Lucius Chiaraviglio (talk) 07:52, 21 June 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 08:57, 23 June 2025 (UTC)

100edo (proposed and untested)

(Descriptive text needs to go here for 100edom starting with rightward generator 8\100 = ~37/35, and 2 of them make ~19/17, and 3 of them make ~13/11, and 4 of them make ~5/4; upward generator 1\100 = ?; cannot streamline down to rank-2.)

 
76
84
83
91
99
7
15
82
90
98
6
14
22
30
38
89
97
5
13
21
29
37
45
53
61
69
88
96
4
12
20
28
36
44
52
60
68
76
84
92
95
3
11
19
27
35
43
51
59
67
75
83
91
99
7
15
23
94
2
10
18
26
34
42
50
58
66
74
82
90
98
6
14
22
30
38
46
1
9
17
25
33
41
49
57
65
73
81
89
97
5
13
21
29
37
45
53
61
69
77
0
8
16
24
32
40
48
56
64
72
80
88
96
4
12
20
28
36
44
52
60
68
76
84
92
0
15
23
31
39
47
55
63
71
79
87
95
3
11
19
27
35
43
51
59
67
75
83
91
99
7
15
23
31
38
46
54
62
70
78
86
94
2
10
18
26
34
42
50
58
66
74
82
90
98
6
14
22
30
38
69
77
85
93
1
9
17
25
33
41
49
57
65
73
81
89
97
5
13
21
29
37
45
92
0
8
16
24
32
40
48
56
64
72
80
88
96
4
12
20
28
36
44
23
31
39
47
55
63
71
79
87
95
3
11
19
27
35
43
51
46
54
62
70
78
86
94
2
10
18
26
34
42
50
77
85
93
1
9
17
25
33
41
49
57
0
8
16
24
32
40
48
56
31
39
47
55
63
54
62

Added: Lucius Chiaraviglio (talk) 07:52, 21 June 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 08:57, 23 June 2025 (UTC)

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