Relative errors of small EDOs: Difference between revisions

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


== List of relative errors of prime harmonics for small edos ==
== List of relative errors of prime harmonics for small EDOs ==
{| class="wikitable sortable mw-collapsible" style="text-align:right"
{| class="wikitable sortable mw-collapsible" style="text-align:right"
! rowspan="2" | Edo
! rowspan="2" | EDO
! colspan="8" |Relative Errors (Percent)
! colspan="8" | Relative Errors (Percent)
|-
|-
!  3/1
!  3/1
Line 1,008: Line 1,008:
|}
|}


== List of TE simple badnesses for small edos ==
== List of TE simple badnesses for small EDOs ==
Notes:   
Notes:   
# [[Patent val]] mapping is used throughout.  
# [[Patent val]] mapping is used throughout.
# Each edo is TE-optimally stretched.  
# Each EDO is TE-optimally stretched.
# [[Graham Breed]]'s definition is used, scaled by 100.   
# [[Graham Breed]]'s definition is used, scaled by 100.   
{| class="wikitable sortable mw-collapsible" style="text-align:right"
{| class="wikitable sortable mw-collapsible" style="text-align:right"
! rowspan="2" | Edo
! rowspan="2" | EDO
! colspan="8" | TE simple badness × 100
! colspan="8" | TE simple badness × 100
|-
|-

Revision as of 02:15, 30 August 2021

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