Lumatone mapping for 90edo: Difference between revisions

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→Diaschismic: Add temperament text and demo video for the 10L 2s mapping
 
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{{Lumatone EDO mapping|n=90|start=12|xstep=16|ystep=-11}}
{{Lumatone EDO mapping|n=90|start=12|xstep=16|ystep=-11}}


== Diaschismic ==
== Diaschismic + Charismic ==
On the other hand, the golden [[diaschismic]] mapping can cover the whole gamut, has better melodic properties than the diatonic mapping and makes harmonics easier to play together, although it needs to be expanded from [[2L 8s]] to [[10L 2s]] to hit every single note.
On the other hand, the golden [[diaschismic]] mapping can cover the whole gamut, has better melodic properties than the diatonic mapping and makes harmonics easier to play together, although it needs to be expanded from [[2L 8s]] to [[10L 2s]] to hit every single note. The rightward generator 8\90 is a semitone that functions as both ~[[16/15]] and ~[[17/16]] (the charisma [[256/255]] is tempered out). Splitting the octave in half (the [[diaschisma]] 2048/2025 is tempered out) enables this generator to produce these mappings without [[contorsion]].
 
=== 2L 8s ===
With [[2L 8s]], the range is three octaves with a very mild upwards slope, but some notes are missing.
{{Lumatone EDO mapping|n=90|start=36|xstep=8|ystep=5}}
{{Lumatone EDO mapping|n=90|start=36|xstep=8|ystep=5}}


 
=== 10L 2s ===
[[Bryan Deister]] has demonstrated the [[Diaschismic]]-[[256/255|Charismic]] [[10L 2s]] mapping for [[90edo]] (with 8:5 step ratio), in [https://www.youtube.com/shorts/0j33e4F-4jY ''microtonal improvisation in 90edo''] (20025). The range is about 2⅔ octaves with no missed notes, with a mild upward slope.
{{Lumatone EDO mapping|n=90|start=84|xstep=8|ystep=-3}}
{{Lumatone EDO mapping|n=90|start=84|xstep=8|ystep=-3}}


{{Navbox Lumatone}}
{{Navbox Lumatone}}

Latest revision as of 11:26, 28 July 2025

There are many conceivable ways to map 90edo onto the onto the Lumatone keyboard. Only one, however, agrees with the Standard Lumatone mapping for Pythagorean.

Diatonic

Due to the size of the edo, this mapping does not cover all the notes. In addition, the best approximation to 5/4 is a hextuply augmented fifth or septuply-diminished second, which is impossible to play with the root note of the scale.

12
28
17
33
49
65
81
6
22
38
54
70
86
12
28
11
27
43
59
75
1
17
33
49
65
81
0
16
32
48
64
80
6
22
38
54
70
86
12
28
5
21
37
53
69
85
11
27
43
59
75
1
17
33
49
65
81
84
10
26
42
58
74
0
16
32
48
64
80
6
22
38
54
70
86
12
28
89
15
31
47
63
79
5
21
37
53
69
85
11
27
43
59
75
1
17
33
49
65
81
78
4
20
36
52
68
84
10
26
42
58
74
0
16
32
48
64
80
6
22
38
54
70
86
12
28
9
25
41
57
73
89
15
31
47
63
79
5
21
37
53
69
85
11
27
43
59
75
1
17
33
49
65
81
46
62
78
4
20
36
52
68
84
10
26
42
58
74
0
16
32
48
64
80
6
22
38
54
70
86
9
25
41
57
73
89
15
31
47
63
79
5
21
37
53
69
85
11
27
43
59
75
1
46
62
78
4
20
36
52
68
84
10
26
42
58
74
0
16
32
48
64
80
9
25
41
57
73
89
15
31
47
63
79
5
21
37
53
69
85
46
62
78
4
20
36
52
68
84
10
26
42
58
74
9
25
41
57
73
89
15
31
47
63
79
46
62
78
4
20
36
52
68
9
25
41
57
73
46
62

Diaschismic + Charismic

On the other hand, the golden diaschismic mapping can cover the whole gamut, has better melodic properties than the diatonic mapping and makes harmonics easier to play together, although it needs to be expanded from 2L 8s to 10L 2s to hit every single note. The rightward generator 8\90 is a semitone that functions as both ~16/15 and ~17/16 (the charisma 256/255 is tempered out). Splitting the octave in half (the diaschisma 2048/2025 is tempered out) enables this generator to produce these mappings without contorsion.

2L 8s

With 2L 8s, the range is three octaves with a very mild upwards slope, but some notes are missing.

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

10L 2s

Bryan Deister has demonstrated the Diaschismic-Charismic 10L 2s mapping for 90edo (with 8:5 step ratio), in microtonal improvisation in 90edo (20025). The range is about 2⅔ octaves with no missed notes, with a mild upward slope.

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


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