Relative errors of small EDOs

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This article contains two lists. The first shows relative errors of the first 9 prime harmonics for EDOs up to 99. There is no point for showing higher primes because no EDO under 99 is consistent up to them. For other intervals, the relative error follows the additive rule, so they can be derived easily.

The second shows the TE simple badnesses aka relative errors in a certain JI subgroup for EDOs up to 99.

List of relative errors of prime harmonics for small EDOs

EDO Relative Errors (Percent)
3/1 5/1 7/1 11/1 13/1 17/1 19/1 23/1
1 41.50 -32.19 19.26 -45.94 29.96 -8.75 -24.79 47.64
2 -16.99 35.61 38.53 8.11 -40.09 -17.49 -49.59 -4.71
3 24.51 3.42 -42.21 -37.83 -10.13 -26.24 25.62 42.93
4 -33.99 -28.77 -22.94 16.23 19.82 -34.99 0.83 -9.42
5 7.52 39.04 -3.68 -29.72 49.78 -43.73 -23.96 38.22
6 49.02 6.84 15.59 24.34 -20.26 47.52 -48.76 -14.14
7 -9.47 -25.35 34.85 -21.60 9.69 38.78 26.45 33.51
8 32.03 42.46 -45.88 32.45 39.65 30.03 1.66 -18.85
9 -26.47 10.26 -26.62 -13.49 -30.40 21.28 -23.13 28.79
10 15.04 -21.93 -7.35 40.57 -0.44 12.54 -47.93 -23.56
11 -43.46 45.88 11.91 -5.37 29.52 3.79 27.28 24.08
12 -1.96 13.69 31.17 48.68 -40.53 -4.96 2.49 -28.27
13 39.55 -18.51 -49.56 2.74 -10.57 -13.70 -22.31 19.37
14 -18.95 49.30 -30.30 -43.20 19.38 -22.45 -47.10 -32.99
15 22.56 17.11 -11.03 10.85 49.34 -31.19 28.11 14.66
16 -35.94 -15.08 8.23 -35.09 -20.70 -39.94 3.32 -37.70
17 5.56 -47.28 27.50 18.97 9.25 -48.69 -21.48 9.94
18 47.07 20.53 46.76 -26.98 39.21 42.57 -46.27 -42.41
19 -11.43 -11.66 -33.97 27.08 -30.84 33.82 28.94 5.23
20 30.07 -43.86 -14.71 -18.86 -0.88 25.07 4.14 -47.12
21 -28.42 23.95 4.55 35.19 29.08 16.33 -20.65 0.52
22 13.08 -8.24 23.82 -10.75 -40.97 7.58 -45.44 48.16
23 -45.41 -40.43 43.08 43.31 -11.01 -1.16 29.77 -4.19
24 -3.91 27.37 -37.65 -2.64 18.94 -9.91 4.97 43.45
25 37.59 -4.82 -18.39 -48.58 48.90 -18.66 -19.82 -8.90
26 -20.90 -37.01 0.88 5.48 -21.14 -27.40 -44.61 38.74
27 20.60 30.79 20.14 -40.47 8.81 -36.15 30.60 -13.62
28 -37.90 -1.40 39.41 13.59 38.77 -44.90 5.80 34.03
29 3.61 -33.59 -41.33 -32.35 -31.28 46.36 -18.99 -18.33
30 45.11 34.22 -22.06 21.71 -1.32 37.61 -43.78 29.31
31 -13.38 2.02 -2.80 -24.24 28.64 28.87 31.42 -23.04
32 28.12 -30.17 16.46 29.82 -41.41 20.12 6.63 24.60
33 -30.38 37.64 35.73 -16.12 -11.45 11.37 -18.16 -27.75
34 11.13 5.44 -45.01 37.93 18.50 2.63 -42.95 19.89
35 -47.37 -26.75 -25.74 -8.01 48.46 -6.12 32.25 -32.47
36 -5.87 41.06 -6.48 46.05 -21.58 -14.87 7.46 15.18
37 35.64 8.87 12.79 0.10 8.37 -23.61 -17.33 -37.18
38 -22.86 -23.33 32.05 -45.84 38.33 -32.36 -42.12 10.46
39 18.65 44.48 -48.68 8.22 -31.71 -41.11 33.08 -41.89
40 -39.85 12.29 -29.42 -37.73 -1.76 -49.85 8.29 5.75
41 1.65 -19.91 -10.16 16.33 28.20 41.40 -16.50 -46.60
42 43.16 47.90 9.11 -29.61 -41.85 32.66 -41.30 1.04
43 -15.34 15.71 28.37 24.44 -11.89 23.91 33.91 48.68
44 26.16 -16.48 47.64 -21.50 18.07 15.16 9.12 -3.67
45 -32.33 -48.68 -33.10 32.56 48.02 6.42 -15.67 43.97
46 9.17 19.13 -13.83 -13.39 -22.02 -2.33 -40.47 -8.38
47 -49.32 -13.06 5.43 40.67 7.93 -11.08 34.74 39.26
48 -7.82 -45.25 24.70 -5.27 37.89 -19.82 9.95 -13.10
49 33.68 22.55 43.96 48.79 -32.15 -28.57 -14.84 34.55
50 -24.81 -9.64 -36.77 2.84 -2.20 -37.31 -39.64 -17.81
51 16.69 -41.83 -17.51 -43.10 27.76 -46.06 35.57 29.83
52 -41.81 25.97 1.75 10.96 -42.29 45.19 10.78 -22.52
53 -0.30 -6.22 21.02 -34.99 -12.33 36.45 -14.02 25.12
54 41.20 -38.41 40.28 19.07 17.63 27.70 -38.81 -27.23
55 -17.29 29.40 -40.45 -26.87 47.58 18.95 36.40 20.41
56 24.21 -2.80 -21.19 27.18 -22.46 10.21 11.61 -31.95
57 -34.29 -34.99 -1.92 -18.76 7.49 1.46 -13.19 15.70
58 7.22 32.82 17.34 35.30 37.45 -7.28 -37.98 -36.66
59 48.72 0.62 36.61 -10.65 -32.59 -16.03 37.23 10.98
60 -9.78 -31.57 -44.13 43.41 -2.64 -24.78 12.43 -41.37
61 31.73 36.24 -24.87 -2.53 27.32 -33.52 -12.36 6.27
62 -26.77 4.05 -5.60 -48.48 -42.73 -42.27 -37.15 -46.08
63 14.74 -28.15 13.66 5.58 -12.77 48.98 38.06 1.56
64 -43.76 39.66 32.93 -40.36 17.19 40.24 13.26 49.20
65 -2.26 7.47 -47.81 13.69 47.14 31.49 -11.53 -3.15
66 39.25 -24.73 -28.54 -32.25 -22.90 22.75 -36.32 44.49
67 -19.25 43.08 -9.28 21.81 7.05 14.00 38.89 -7.87
68 22.25 10.89 9.99 -24.14 37.01 5.25 14.09 39.78
69 -36.24 -21.30 29.25 29.92 -33.03 -3.49 -10.70 -12.58
70 5.26 46.50 48.52 -16.02 -3.08 -12.24 -35.49 35.07
71 46.77 14.31 -32.22 38.04 26.88 -20.99 39.71 -17.29
72 -11.73 -17.88 -12.96 -7.91 -43.17 -29.73 14.92 30.35
73 29.77 49.92 6.31 46.15 -13.21 -38.48 -9.87 -22.00
74 -28.72 17.73 25.57 0.21 16.75 -47.23 -34.66 25.64
75 12.78 -14.46 44.84 -45.74 46.70 44.03 40.54 -26.71
76 -45.72 -46.65 -35.90 8.32 -23.34 35.28 15.75 20.93
77 -4.21 21.15 -16.63 -37.62 6.61 26.54 -9.04 -31.43
78 37.29 -11.04 2.63 16.43 36.57 17.79 -33.83 16.22
79 -21.20 -43.23 21.90 -29.51 -33.47 9.04 41.37 -36.14
80 20.30 24.58 41.16 24.55 -3.52 0.30 16.58 11.50
81 -38.20 -7.62 -39.57 -21.40 26.44 -8.45 -8.21 -40.85
82 3.31 -39.81 -20.31 32.66 -43.61 -17.20 -33.01 6.79
83 44.81 28.00 -1.05 -13.28 -13.65 -25.94 42.20 -45.56
84 -13.69 -4.20 18.22 40.77 16.31 -34.69 17.41 2.08
85 27.82 -36.39 37.48 -5.17 46.26 -43.43 -7.38 49.72
86 -30.68 31.42 -43.25 48.89 -23.78 47.82 -32.18 -2.63
87 10.83 -0.77 -23.99 2.94 6.17 39.07 43.03 45.01
88 -47.67 -32.97 -4.72 -43.00 36.13 30.33 18.24 -7.35
89 -6.17 34.84 14.54 11.06 -33.91 21.58 -6.55 40.30
90 35.34 2.65 33.81 -34.88 -3.96 12.83 -31.35 -12.06
91 -23.16 -29.55 -46.93 19.17 26.00 4.09 43.86 35.59
92 18.34 38.26 -27.67 -26.77 -44.05 -4.66 19.07 -16.77
93 -40.15 6.07 -8.40 27.29 -14.09 -13.40 -5.73 30.87
94 1.35 -26.12 10.86 -18.66 15.87 -22.15 -30.52 -21.48
95 42.86 41.68 30.13 35.40 45.82 -30.90 44.69 26.16
96 -15.64 9.49 49.39 -10.54 -24.22 -39.64 19.90 -26.19
97 25.86 -22.70 -31.34 43.51 5.73 -48.39 -4.90 21.45
98 -32.63 45.10 -12.08 -2.43 35.69 42.86 -29.69 -30.91
99 8.87 12.91 7.19 -48.37 -34.35 34.12 45.52 16.74

List of TE simple badnesses for small EDOs

Notes:

  1. Patent val mapping is used throughout.
  2. Each EDO is TE-optimally stretched.
  3. Graham Breed's definition is used, scaled by 100.
EDO TE simple badness × 100
3 Limit 5 Limit 7 Limit 11 Limit 13 Limit 17 Limit 19 Limit 23 Limit
1 13.09 16.61 14.43 14.79 13.75 12.83 12.25 11.95
2 5.36 10.69 10.66 9.58 10.37 9.82 10.07 9.50
3 7.73 6.97 10.80 10.68 9.76 9.17 9.04 9.20
4 10.72 8.79 7.73 9.20 9.67 9.02 8.67 8.22
5 2.37 7.08 7.15 8.41 8.72 9.61 9.34 9.11
6 15.46 13.94 12.32 11.08 11.52 10.79 11.89 11.51
7 2.99 4.46 8.72 8.06 7.57 7.97 7.72 7.55
8 10.10 9.11 14.89 13.41 12.35 11.44 10.92 10.81
9 8.35 9.09 8.21 7.37 6.83 7.37 6.91 7.32
10 4.74 7.73 6.79 7.83 7.19 6.68 7.58 7.34
11 13.71 19.34 17.01 15.22 14.29 13.23 12.52 11.88
12 0.62 3.11 4.94 5.99 8.35 7.88 7.40 7.47
13 12.48 14.02 15.79 14.13 12.94 12.03 11.34 10.84
14 5.98 13.72 13.32 12.86 12.12 11.31 10.99 10.44
15 7.12 5.81 6.97 6.25 6.65 7.73 7.29 6.88
16 11.34 9.53 9.91 8.98 8.22 7.67 7.67 7.26
17 1.76 10.52 11.30 10.51 9.65 9.88 9.32 8.88
18 14.85 12.45 10.91 13.03 11.90 11.02 12.37 12.77
19 3.61 3.02 4.35 6.79 6.47 7.40 7.56 7.17
20 9.49 15.46 13.58 12.26 11.21 10.75 10.07 9.99
21 8.97 11.67 10.27 10.30 9.76 9.06 8.80 8.31
22 4.13 4.94 5.23 5.33 6.89 6.42 6.99 7.57
23 14.33 11.79 16.76 17.03 15.55 14.44 13.91 13.12
24 1.23 6.22 8.95 8.01 7.66 7.14 6.70 7.02
25 11.86 11.70 11.76 12.70 12.57 11.89 11.30 10.68
26 6.59 6.96 7.43 7.51 6.86 6.37 6.17 7.45
27 6.50 6.19 5.40 9.37 8.58 9.13 8.70 8.41
28 11.95 11.13 13.62 12.46 12.19 12.00 11.25 10.92
29 1.14 7.41 7.91 7.15 6.54 8.94 8.36 7.89
30 14.23 11.62 13.94 12.51 11.87 11.02 11.82 11.15
31 4.22 4.20 3.70 3.84 5.35 5.75 5.93 5.89
32 8.87 12.60 11.07 10.18 10.85 10.13 9.47 9.00
33 9.58 14.46 13.86 12.72 11.71 10.87 10.30 9.91
34 3.51 2.92 8.67 9.26 8.59 7.96 8.36 8.01
35 14.94 12.31 10.85 10.54 13.06 12.22 12.27 11.61
36 1.85 9.33 8.63 8.76 8.96 8.63 8.08 7.62
37 11.24 9.82 8.70 8.37 7.78 8.21 8.13 8.42
38 7.21 6.04 9.96 9.76 10.64 10.02 9.62 9.30
39 5.88 7.89 13.78 12.34 12.08 11.86 11.42 11.21
40 12.57 13.28 11.62 10.48 9.99 9.43 9.38 9.18
41 0.52 4.31 3.76 4.51 5.29 6.00 5.90 6.59
42 13.61 11.60 11.45 13.33 14.24 13.22 13.36 12.64
43 4.84 6.75 7.56 7.08 6.85 6.49 6.35 6.45
44 8.25 9.89 10.45 10.66 9.74 9.02 8.46 8.11
45 10.20 9.75 8.49 11.84 13.50 12.72 11.90 12.03
46 2.89 3.45 5.12 5.20 5.42 5.02 5.62 5.30
47 15.56 13.54 13.24 14.39 13.38 12.39 12.20 11.98
48 2.47 8.27 10.25 9.22 9.84 9.20 8.71 8.23
49 10.63 8.69 7.87 7.11 10.12 10.85 10.67 10.09
50 7.83 6.62 6.39 6.76 6.54 6.19 5.90 5.62
51 5.27 11.79 10.34 9.93 10.23 9.89 10.15 10.01
52 13.19 15.75 13.86 12.69 12.08 12.33 11.62 11.02
53 0.10 1.22 3.81 5.65 5.22 6.05 5.76 5.75
54 13.00 17.51 15.92 14.24 13.01 12.05 12.31 12.02
55 5.46 9.63 10.57 9.63 10.83 10.23 10.02 9.52
56 7.64 7.50 8.38 7.90 7.95 7.37 6.90 7.07
57 10.82 9.06 9.30 8.47 8.68 8.41 7.92 7.98
58 2.28 5.89 5.10 4.83 4.56 5.33 7.07 7.72
59 15.37 14.43 12.55 12.56 13.10 12.56 11.85 11.19
60 3.08 5.56 6.23 10.22 9.44 8.77 8.54 8.26
61 10.01 8.59 11.66 10.84 9.93 10.38 9.95 9.39
62 8.44 8.40 7.40 7.67 7.28 6.83 6.40 6.09
63 4.65 8.77 8.00 7.17 6.73 7.50 7.41 7.03
64 13.80 18.41 17.26 16.16 14.96 14.36 13.46 13.07
65 0.71 1.94 7.82 7.65 8.94 8.68 8.23 7.77
66 12.38 14.83 14.37 13.50 12.47 11.84 11.36 11.32
67 6.07 12.62 11.18 10.24 9.35 8.67 8.44 8.10
68 7.02 5.84 5.19 6.84 6.75 6.34 5.93 5.81
69 11.43 9.40 12.23 12.30 11.48 10.67 9.98 9.41
70 1.66 8.76 8.63 9.73 9.37 9.21 9.62 9.20
71 14.75 12.71 14.95 13.52 12.34 12.20 11.49 11.25
72 3.70 3.56 3.09 2.96 3.82 3.59 4.57 5.60
73 9.39 9.56 9.59 8.65 9.62 10.93 10.60 10.47
74 9.06 10.80 10.83 9.69 9.02 9.36 9.06 8.88
75 4.03 5.85 8.36 10.29 10.36 9.98 9.51 9.57
76 14.42 12.07 10.57 11.84 11.01 12.28 12.13 11.98
77 1.33 5.04 5.59 6.66 6.25 6.42 6.03 6.03
78 11.76 12.37 10.95 9.80 9.14 8.47 9.09 8.57
79 6.69 7.84 10.49 9.43 8.66 8.64 9.55 9.10
80 6.40 5.59 5.68 5.17 6.01 6.12 5.78 5.56
81 12.05 10.67 9.49 8.65 10.05 9.45 8.94 8.50
82 1.04 8.62 7.52 9.02 8.92 8.26 7.82 7.62
83 14.14 11.58 11.68 11.82 11.53 11.44 10.90 11.25
84 4.32 3.72 5.39 7.02 6.50 7.05 6.70 6.32
85 8.78 13.57 12.98 11.80 11.37 11.76 11.08 10.84
86 9.68 13.50 13.06 14.03 12.95 12.94 12.35 11.64
87 3.42 3.30 5.45 4.90 4.53 5.35 5.77 5.92
88 15.04 12.29 12.05 10.79 12.68 12.94 12.56 11.88
89 1.95 8.15 7.08 6.35 7.57 7.12 6.77 6.77
90 11.15 10.25 9.07 11.10 10.39 9.62 9.75 9.33
91 7.31 6.49 6.51 8.82 9.74 9.28 9.95 9.93
92 5.79 6.91 10.24 10.40 10.83 10.03 9.52 9.06
93 12.67 12.60 11.09 11.46 10.46 9.68 9.09 9.14
94 0.43 5.52 5.74 5.35 5.48 5.28 5.24 4.99
95 13.52 11.23 9.90 8.98 8.20 10.47 9.80 9.34
96 4.93 5.86 9.86 9.14 8.90 8.96 8.59 8.28
97 8.16 10.76 10.97 11.24 10.26 10.60 9.92 9.49
98 10.29 16.34 14.25 12.75 12.32 11.92 11.54 11.15
99 2.80 2.63 2.33 7.27 7.48 7.75 8.09 7.67

See also

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