Lumatone mapping for 91edo: Difference between revisions
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Add Bryan Deister's *2* Lumatone mappings for 91edo, along with the obligatory diatonic mappings |
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{{Lumatone mapping intro}} | |||
== Diatonic == | == Diatonic == | ||
The large number of notes results in both the flat ([[patent val]]) and sharp (b val) fifths failing to cover the gamut, with both skipping many notes. If not for this problem, the flat version would be a respectable [[Schismic–Pythagorean_equivalence_continuum#Python|Python]] or [[Meantone]] (91c) mapping, while the sharp version would be a respectable mapping for [[Quasiultra]] (as 91bd). | |||
{{Lumatone EDO mapping|n=91|start= | {{Lumatone EDO mapping|n=91|start=89|xstep=15|ystep=-7}} | ||
{{Lumatone EDO mapping|n=91|start= | {{Lumatone EDO mapping|n=91|start=22|xstep=17|ystep=-14}} | ||
== Quartkeenlig-related rank-3 mappings == | == Quartkeenlig-related rank-3 mappings == | ||
=== Pseudo-isomorphic === | === Pseudo-isomorphic === | ||
[[Bryan Deister]] has demonstrated a pseudo-isomorphic mapping for [[91edo]] in [https://www.youtube.com/shorts/HaYUAg30298 ''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. | [[Bryan Deister]] has demonstrated a pseudo-isomorphic mapping for [[91edo]] in [https://www.youtube.com/shorts/HaYUAg30298 ''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. | ||
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=== Isomorphic === | === Isomorphic === | ||
[[Bryan Deister]] has demonstrated an isomorphic [[9L 2s]] mapping for [[91edo]] in [https://www.youtube.com/shorts/z6PeEocYMV8 ''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 | [[Bryan Deister]] has demonstrated an isomorphic [[9L 2s]] mapping for [[91edo]] in [https://www.youtube.com/shorts/z6PeEocYMV8 ''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. | ||
{{Lumatone EDO mapping|n=91|start=0|xstep=9|ystep=-4}} | {{Lumatone EDO mapping|n=91|start=0|xstep=9|ystep=-4}} | ||
{{Navbox Lumatone}} | {{Navbox Lumatone}} | ||
Latest revision as of 13:50, 23 June 2025
There are many conceivable ways to map 91edo onto the onto the Lumatone keyboard. Only one, however, agrees with the Standard Lumatone mapping for Pythagorean.
Diatonic
The large number of notes results in both the flat (patent val) and sharp (b val) fifths failing to cover the gamut, with both skipping many notes. If not for this problem, the flat version would be a respectable Python or Meantone (91c) mapping, while the sharp version would be a respectable mapping for Quasiultra (as 91bd).
89
13
6
21
36
51
66
90
14
29
44
59
74
89
13
7
22
37
52
67
82
6
21
36
51
66
0
15
30
45
60
75
90
14
29
44
59
74
89
13
8
23
38
53
68
83
7
22
37
52
67
82
6
21
36
51
66
1
16
31
46
61
76
0
15
30
45
60
75
90
14
29
44
59
74
89
13
9
24
39
54
69
84
8
23
38
53
68
83
7
22
37
52
67
82
6
21
36
51
66
2
17
32
47
62
77
1
16
31
46
61
76
0
15
30
45
60
75
90
14
29
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59
74
89
13
25
40
55
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85
9
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38
53
68
83
7
22
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82
6
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63
78
2
17
32
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1
16
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0
15
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74
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55
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85
9
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22
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52
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63
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17
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77
1
16
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0
15
30
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60
75
25
40
55
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85
9
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84
8
23
38
53
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63
78
2
17
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62
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1
16
31
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61
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40
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85
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24
39
54
69
84
63
78
2
17
32
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25
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85
63
78
22
39
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2
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5
22
39
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76
2
0
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5
22
39
3
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80
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0
17
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51
68
85
11
28
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22
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83
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26
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60
77
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20
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29
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80
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0
17
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51
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28
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62
79
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22
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83
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26
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8
25
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76
2
35
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63
80
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23
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0
17
34
51
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85
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28
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5
89
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32
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43
60
77
3
20
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31
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82
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35
52
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86
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63
80
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23
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57
74
0
17
34
51
68
85
89
15
32
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66
83
9
26
43
60
77
3
20
37
54
71
88
35
52
69
86
12
29
46
63
80
6
23
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57
74
89
15
32
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83
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26
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60
77
35
52
69
86
12
29
46
63
89
15
32
49
66
35
52
Pseudo-isomorphic
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
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6
15
24
33
42
51
60
69
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87
4
2
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20
29
38
47
56
65
74
83
0
9
18
27
7
16
25
34
43
52
61
70
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88
5
14
23
32
41
50
59
3
12
21
30
39
48
57
66
75
84
1
10
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28
37
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55
64
73
82
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17
26
35
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53
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89
6
15
24
33
42
51
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4
13
22
4
13
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40
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85
2
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74
83
0
9
18
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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
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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
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70
79
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59
68
77
86
3
12
21
30
39
48
57
66
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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
Isomorphic
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.
0
9
5
14
23
32
41
1
10
19
28
37
46
55
64
6
15
24
33
42
51
60
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78
87
5
2
11
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29
38
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56
65
74
83
1
10
19
28
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16
25
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61
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79
88
6
15
24
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42
51
60
3
12
21
30
39
48
57
66
75
84
2
11
20
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47
56
65
74
83
8
17
26
35
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89
7
16
25
34
43
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70
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6
15
24
4
13
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2
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90
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80
89
7
16
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77
86
4
13
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85
3
12
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30
39
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0
9
18
27
36
45
54
63
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81
90
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17
26
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44
53
62
71
80
89
5
14
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32
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50
59
68
77
86
4
13
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31
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49
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82
0
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1
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0
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