User:Sintel/Triad ranking

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A big list of JI triads (max. span of 2 octaves, max. n=20, excluding unisons), with their Tenney norm [math]\displaystyle{ \log_2(r_1 \cdot r_2 \cdot r_3) }[/math] and harmonic entropy (c = 17 ¢). For simple ratios the rankings agree very closely.

Triads
ratio Tenney HE
1:2:3 2.58 3.48
1:2:4 3.00 3.73
1:3:4 3.58 4.08
2:3:4 4.58 4.70
2:3:5 4.91 4.90
2:3:6 5.17 5.07
2:3:7 5.39 5.21
2:3:8 5.58 5.33
2:4:5 5.32 5.17
2:4:7 5.81 5.47
2:5:6 5.91 5.54
2:5:7 6.13 5.68
2:5:8 6.32 5.80
2:6:7 6.39 5.84
2:7:8 6.81 6.10
3:4:5 5.91 5.53
3:4:6 6.17 5.70
3:4:7 6.39 5.84
3:4:8 6.58 5.96
3:4:9 6.75 6.07
3:4:10 6.91 6.16
3:4:11 7.04 6.25
3:4:12 7.17 6.32
3:5:6 6.49 5.90
3:5:7 6.71 6.04
3:5:8 6.91 6.16
3:5:9 7.08 6.27
3:5:10 7.23 6.36
3:5:11 7.37 6.44
3:5:12 7.49 6.52
3:6:7 6.98 6.20
3:6:8 7.17 6.31
3:6:10 7.49 6.49
3:6:11 7.63 6.56
3:7:8 7.39 6.46
3:7:9 7.56 6.55
3:7:10 7.71 6.64
3:7:11 7.85 6.73
3:7:12 7.98 6.80
3:8:9 7.75 6.66
3:8:10 7.91 6.76
3:8:11 8.04 6.82
3:8:12 8.17 6.90
3:9:10 8.08 6.83
3:9:11 8.21 6.90
3:10:11 8.37 7.02
3:10:12 8.49 7.07
3:11:12 8.63 7.13
4:5:6 6.91 6.16
4:5:7 7.13 6.30
4:5:8 7.32 6.41
4:5:9 7.49 6.51
4:5:10 7.64 6.60
4:5:11 7.78 6.69
4:5:12 7.91 6.76
4:5:13 8.02 6.82
4:5:14 8.13 6.88
4:5:15 8.23 6.94
4:5:16 8.32 6.99
4:6:7 7.39 6.46
4:6:9 7.75 6.67
4:6:11 8.04 6.83
4:6:13 8.29 6.96
4:6:15 8.49 7.07
4:7:8 7.81 6.68
4:7:9 7.98 6.80
4:7:10 8.13 6.88
4:7:11 8.27 6.93
4:7:12 8.39 7.02
4:7:13 8.51 7.09
4:7:14 8.61 7.14
4:7:15 8.71 7.18
4:7:16 8.81 7.24
4:8:9 8.17 6.86
4:8:11 8.46 6.99
4:8:13 8.70 7.07
4:8:15 8.91 7.14
4:9:10 8.49 7.08
4:9:11 8.63 7.15
4:9:12 8.75 7.19
4:9:13 8.87 7.23
4:9:14 8.98 7.32
4:9:15 9.08 7.38
4:9:16 9.17 7.41
4:10:11 8.78 7.23
4:10:13 9.02 7.35
4:10:15 9.23 7.45
4:11:12 9.04 7.31
4:11:13 9.16 7.42
4:11:14 9.27 7.46
4:11:15 9.37 7.45
4:11:16 9.46 7.51
4:12:13 9.29 7.39
4:12:15 9.49 7.45
4:13:14 9.51 7.57
4:13:15 9.61 7.61
4:13:16 9.70 7.60
4:14:15 9.71 7.66
4:15:16 9.91 7.65
5:6:7 7.71 6.65
5:6:8 7.91 6.76
5:6:9 8.08 6.85
5:6:10 8.23 6.92
5:6:11 8.37 6.98
5:6:12 8.49 7.07
5:6:13 8.61 7.14
5:6:14 8.71 7.20
5:6:15 8.81 7.24
5:6:16 8.91 7.28
5:6:17 8.99 7.32
5:6:18 9.08 7.37
5:6:19 9.15 7.41
5:6:20 9.23 7.45
5:7:8 8.13 6.88
5:7:9 8.30 6.97
5:7:10 8.45 7.03
5:7:11 8.59 7.13
5:7:12 8.71 7.15
5:7:13 8.83 7.26
5:7:14 8.94 7.29
5:7:15 9.04 7.34
5:7:16 9.13 7.40
5:7:17 9.22 7.41
5:7:18 9.30 7.48
5:7:19 9.38 7.50
5:7:20 9.45 7.54
5:8:9 8.49 7.08
5:8:10 8.64 7.11
5:8:11 8.78 7.22
5:8:12 8.91 7.29
5:8:13 9.02 7.29
5:8:14 9.13 7.40
5:8:15 9.23 7.42
5:8:16 9.32 7.47
5:8:17 9.41 7.53
5:8:18 9.49 7.52
5:8:19 9.57 7.59
5:8:20 9.64 7.61
5:9:10 8.81 7.18
5:9:11 8.95 7.31
5:9:12 9.08 7.38
5:9:13 9.19 7.42
5:9:14 9.30 7.40
5:9:15 9.40 7.48
5:9:16 9.49 7.56
5:9:17 9.58 7.60
5:9:18 9.66 7.61
5:9:19 9.74 7.61
5:9:20 9.81 7.67
5:10:11 9.10 7.28
5:10:12 9.23 7.31
5:10:13 9.34 7.34
5:10:14 9.45 7.35
5:10:16 9.64 7.36
5:10:17 9.73 7.42
5:10:18 9.81 7.44
5:10:19 9.89 7.36
5:11:12 9.37 7.50
5:11:13 9.48 7.56
5:11:14 9.59 7.60
5:11:15 9.69 7.58
5:11:16 9.78 7.57
5:11:17 9.87 7.69
5:11:18 9.95 7.75
5:11:19 10.03 7.77
5:11:20 10.10 7.76
5:12:13 9.61 7.61
5:12:14 9.71 7.64
5:12:15 9.81 7.60
5:12:16 9.91 7.73
5:12:17 9.99 7.66
5:12:18 10.08 7.79
5:12:19 10.15 7.79
5:12:20 10.23 7.79
5:13:14 9.83 7.70
5:13:15 9.93 7.63
5:13:16 10.02 7.75
5:13:17 10.11 7.80
5:13:18 10.19 7.73
5:13:19 10.27 7.86
5:13:20 10.34 7.81
5:14:15 10.04 7.63
5:14:16 10.13 7.81
5:14:17 10.22 7.84
5:14:18 10.30 7.85
5:14:19 10.38 7.74
5:14:20 10.45 7.83
5:15:16 10.23 7.66
5:15:17 10.32 7.70
5:15:18 10.40 7.72
5:15:19 10.48 7.65
5:16:17 10.41 7.89
5:16:18 10.49 7.93
5:16:19 10.57 7.95
5:16:20 10.64 7.84
5:17:18 10.58 7.95
5:17:19 10.66 7.96
5:17:20 10.73 7.89
5:18:19 10.74 7.99
5:18:20 10.81 7.89
5:19:20 10.89 7.84
6:7:8 8.39 7.02
6:7:9 8.56 7.12
6:7:10 8.71 7.20
6:7:11 8.85 7.26
6:7:12 8.98 7.29
6:7:13 9.09 7.31
6:7:14 9.20 7.40
6:7:15 9.30 7.47
6:7:16 9.39 7.52
6:7:17 9.48 7.56
6:7:18 9.56 7.57
6:7:19 9.64 7.59
6:7:20 9.71 7.63
6:8:9 8.75 7.22
6:8:11 9.04 7.36
6:8:13 9.29 7.47
6:8:15 9.49 7.57
6:8:17 9.67 7.64
6:8:19 9.83 7.70
6:9:10 9.08 7.37
6:9:11 9.21 7.43
6:9:13 9.46 7.53
6:9:14 9.56 7.57
6:9:16 9.75 7.64
6:9:17 9.84 7.66
6:9:19 10.00 7.71
6:9:20 10.08 7.73
6:10:11 9.37 7.50
6:10:13 9.61 7.61
6:10:15 9.81 7.70
6:10:17 9.99 7.77
6:10:19 10.15 7.82
6:11:12 9.63 7.47
6:11:13 9.74 7.65
6:11:14 9.85 7.71
6:11:15 9.95 7.75
6:11:16 10.04 7.74
6:11:17 10.13 7.65
6:11:18 10.21 7.75
6:11:19 10.29 7.86
6:11:20 10.37 7.89
6:12:13 9.87 7.50
6:12:17 10.26 7.50
6:12:19 10.42 7.52
6:13:14 10.09 7.78
6:13:15 10.19 7.83
6:13:16 10.29 7.86
6:13:17 10.37 7.88
6:13:18 10.46 7.76
6:13:19 10.53 7.73
6:13:20 10.61 7.90
6:14:15 10.30 7.87
6:14:17 10.48 7.92
6:14:19 10.64 7.97
6:15:16 10.49 7.92
6:15:17 10.58 7.95
6:15:19 10.74 7.98
6:15:20 10.81 8.00
6:16:17 10.67 7.97
6:16:19 10.83 8.02
6:17:18 10.84 7.78
6:17:19 10.92 8.02
6:17:20 10.99 8.06
6:18:19 11.00 7.80
6:19:20 11.15 8.06
7:8:9 8.98 7.31
7:8:10 9.13 7.40
7:8:11 9.27 7.46
7:8:12 9.39 7.52
7:8:13 9.51 7.55
7:8:14 9.61 7.54
7:8:15 9.71 7.53
7:8:16 9.81 7.62
7:8:17 9.89 7.71
7:8:18 9.98 7.76
7:8:19 10.06 7.79
7:8:20 10.13 7.80
7:9:10 9.30 7.48
7:9:11 9.44 7.50
7:9:12 9.56 7.57
7:9:13 9.68 7.64
7:9:14 9.78 7.58
7:9:15 9.88 7.72
7:9:16 9.98 7.63
7:9:17 10.06 7.79
7:9:18 10.15 7.74
7:9:19 10.23 7.83
7:9:20 10.30 7.84
7:10:11 9.59 7.58
7:10:12 9.71 7.64
7:10:13 9.83 7.66
7:10:14 9.94 7.60
7:10:15 10.04 7.78
7:10:16 10.13 7.81
7:10:17 10.22 7.67
7:10:18 10.30 7.85
7:10:19 10.38 7.90
7:10:20 10.45 7.83
7:11:12 9.85 7.71
7:11:13 9.97 7.76
7:11:14 10.07 7.63
7:11:15 10.17 7.77
7:11:16 10.27 7.85
7:11:17 10.35 7.87
7:11:18 10.44 7.71
7:11:19 10.51 7.93
7:11:20 10.59 7.96
7:12:13 10.09 7.78
7:12:14 10.20 7.66
7:12:15 10.30 7.87
7:12:16 10.39 7.87
7:12:17 10.48 7.86
7:12:18 10.56 7.95
7:12:19 10.64 7.79
7:12:20 10.71 7.99
7:13:14 10.32 7.60
7:13:15 10.41 7.87
7:13:16 10.51 7.93
7:13:17 10.60 7.95
7:13:18 10.68 7.98
7:13:19 10.76 7.91
7:13:20 10.83 7.77
7:14:15 10.52 7.62
7:14:16 10.61 7.60
7:14:17 10.70 7.59
7:14:18 10.78 7.62
7:14:19 10.86 7.51
7:14:20 10.94 7.62
7:15:16 10.71 7.95
7:15:17 10.80 8.02
7:15:18 10.88 8.02
7:15:19 10.96 8.06
7:15:20 11.04 8.03
7:16:17 10.89 8.04
7:16:18 10.98 8.03
7:16:19 11.06 8.05
7:16:20 11.13 8.10
7:17:18 11.06 8.04
7:17:19 11.14 8.08
7:17:20 11.22 8.05
7:18:19 11.23 8.11
7:18:20 11.30 8.13
7:19:20 11.38 8.09
8:9:10 9.49 7.52
8:9:11 9.63 7.62
8:9:12 9.75 7.67
8:9:13 9.87 7.71
8:9:14 9.98 7.76
8:9:15 10.08 7.77
8:9:16 10.17 7.68
8:9:17 10.26 7.64
8:9:18 10.34 7.76
8:9:19 10.42 7.87
8:9:20 10.49 7.93
8:10:11 9.78 7.68
8:10:13 10.02 7.76
8:10:15 10.23 7.84
8:10:17 10.41 7.90
8:10:19 10.57 7.95
8:11:12 10.04 7.77
8:11:13 10.16 7.78
8:11:14 10.27 7.79
8:11:15 10.37 7.88
8:11:16 10.46 7.74
8:11:17 10.55 7.93
8:11:18 10.63 7.97
8:11:19 10.71 7.77
8:11:20 10.78 8.01
8:12:13 10.29 7.84
8:12:15 10.49 7.89
8:12:17 10.67 7.92
8:12:19 10.83 7.94
8:13:14 10.51 7.94
8:13:15 10.61 7.96
8:13:16 10.70 7.75
8:13:17 10.79 8.00
8:13:18 10.87 7.95
8:13:19 10.95 8.02
8:13:20 11.02 8.07
8:14:15 10.71 7.95
8:14:17 10.89 8.04
8:14:19 11.06 8.06
8:15:16 10.91 7.71
8:15:17 10.99 8.00
8:15:18 11.08 8.08
8:15:19 11.15 8.08
8:15:20 11.23 8.11
8:16:17 11.09 7.73
8:16:19 11.25 7.55
8:17:18 11.26 8.03
8:17:19 11.34 8.13
8:17:20 11.41 8.14
8:18:19 11.42 8.15
8:19:20 11.57 8.15
9:10:11 9.95 7.68
9:10:12 10.08 7.79
9:10:13 10.19 7.84
9:10:14 10.30 7.85
9:10:15 10.40 7.90
9:10:16 10.49 7.93
9:10:17 10.58 7.89
9:10:18 10.66 7.76
9:10:19 10.74 7.71
9:10:20 10.81 7.84
9:11:12 10.21 7.84
9:11:13 10.33 7.80
9:11:14 10.44 7.91
9:11:15 10.54 7.93
9:11:16 10.63 7.92
9:11:17 10.72 7.99
9:11:18 10.80 7.84
9:11:19 10.88 8.03
9:11:20 10.95 7.77
9:12:13 10.46 7.92
9:12:14 10.56 7.95
9:12:16 10.75 8.00
9:12:17 10.84 8.02
9:12:19 11.00 8.06
9:12:20 11.08 8.08
9:13:14 10.68 7.91
9:13:15 10.78 8.01
9:13:16 10.87 8.03
9:13:17 10.96 7.91
9:13:18 11.04 7.78
9:13:19 11.12 8.09
9:13:20 11.19 8.10
9:14:15 10.88 8.03
9:14:16 10.98 8.03
9:14:17 11.06 8.08
9:14:18 11.15 7.78
9:14:19 11.23 7.98
9:14:20 11.30 8.13
9:15:16 11.08 8.08
9:15:17 11.16 8.10
9:15:19 11.32 8.13
9:15:20 11.40 8.15
9:16:17 11.26 8.03
9:16:18 11.34 7.61
9:16:19 11.42 8.15
9:16:20 11.49 8.12
9:17:18 11.43 7.81
9:17:19 11.51 8.08
9:17:20 11.58 8.17
9:18:19 11.59 7.82
9:18:20 11.66 7.43
9:19:20 11.74 8.10
10:11:12 10.37 7.78
10:11:13 10.48 7.92
10:11:14 10.59 7.96
10:11:15 10.69 7.97
10:11:16 10.78 7.98
10:11:17 10.87 8.04
10:11:18 10.95 8.04
10:11:19 11.03 7.97
10:11:20 11.10 7.85
10:12:13 10.61 7.96
10:12:15 10.81 8.00
10:12:17 10.99 8.04
10:12:19 11.15 8.10
10:13:14 10.83 8.02
10:13:15 10.93 8.02
10:13:16 11.02 7.92
10:13:17 11.11 8.00
10:13:18 11.19 8.09
10:13:19 11.27 8.10
10:13:20 11.34 7.83
10:14:15 11.04 8.02
10:14:17 11.22 8.05
10:14:19 11.38 8.10
10:15:16 11.23 8.05
10:15:17 11.32 8.08
10:15:18 11.40 8.10
10:15:19 11.48 8.04
10:16:17 11.41 8.15
10:16:19 11.57 8.17
10:17:18 11.58 8.17
10:17:19 11.66 8.19
10:17:20 11.73 7.76
10:18:19 11.74 8.09
10:19:20 11.89 7.89
11:12:13 10.74 7.85
11:12:14 10.85 8.01
11:12:15 10.95 8.06
11:12:16 11.04 8.08
11:12:17 11.13 8.04
11:12:18 11.21 8.09
11:12:19 11.29 8.13
11:12:20 11.37 8.12
11:13:14 10.97 8.04
11:13:15 11.07 7.97
11:13:16 11.16 8.10
11:13:17 11.25 8.11
11:13:18 11.33 8.13
11:13:19 11.41 8.15
11:13:20 11.48 8.09
11:14:15 11.17 8.10
11:14:16 11.27 8.12
11:14:17 11.35 8.00
11:14:18 11.44 8.08
11:14:19 11.51 8.05
11:14:20 11.59 8.15
11:15:16 11.37 8.14
11:15:17 11.45 8.16
11:15:18 11.54 8.04
11:15:19 11.61 8.02
11:15:20 11.69 8.20
11:16:17 11.55 8.04
11:16:18 11.63 8.19
11:16:19 11.71 8.12
11:16:20 11.78 8.21
11:17:18 11.72 8.18
11:17:19 11.79 8.22
11:17:20 11.87 8.22
11:18:19 11.88 8.22
11:18:20 11.95 8.13
11:19:20 12.03 8.23
12:13:14 11.09 7.91
12:13:15 11.19 8.07
12:13:16 11.29 8.13
12:13:17 11.37 8.15
12:13:18 11.46 8.11
12:13:19 11.53 8.10
12:13:20 11.61 8.18
12:14:15 11.30 8.10
12:14:17 11.48 8.16
12:14:19 11.64 8.13
12:15:16 11.49 8.16
12:15:17 11.58 8.18
12:15:19 11.74 8.20
12:15:20 11.81 8.22
12:16:17 11.67 8.19
12:16:19 11.83 8.21
12:17:18 11.84 8.13
12:17:19 11.92 8.04
12:17:20 11.99 8.25
12:18:19 12.00 8.15
12:19:20 12.15 8.25
13:14:15 11.41 7.97
13:14:16 11.51 8.11
13:14:17 11.60 8.18
13:14:18 11.68 8.19
13:14:19 11.76 8.19
13:14:20 11.83 8.13
13:15:16 11.61 8.15
13:15:17 11.69 7.91
13:15:18 11.78 8.22
13:15:19 11.86 8.19
13:15:20 11.93 8.25
13:16:17 11.79 8.21
13:16:18 11.87 8.22
13:16:19 11.95 7.99
13:16:20 12.02 8.23
13:17:18 11.96 8.21
13:17:19 12.04 8.25
13:17:20 12.11 8.25
13:18:19 12.12 8.23
13:18:20 12.19 8.28
13:19:20 12.27 8.14
14:15:16 11.71 8.01
14:15:17 11.80 8.15
14:15:18 11.88 8.21
14:15:19 11.96 8.22
14:15:20 12.04 8.24
14:16:17 11.89 8.18
14:16:19 12.06 8.26
14:17:18 12.06 8.24
14:17:19 12.14 8.27
14:17:20 12.22 7.92
14:18:19 12.23 8.23
14:19:20 12.38 8.27
15:16:17 11.99 8.05
15:16:18 12.08 8.19
15:16:19 12.15 8.24
15:16:20 12.23 8.25
15:17:18 12.16 8.21
15:17:19 12.24 7.81
15:17:20 12.32 8.28
15:18:19 12.32 8.27
15:18:20 12.40 8.29
15:19:20 12.48 8.27
16:17:18 12.26 8.09
16:17:19 12.34 8.22
16:17:20 12.41 8.27
16:18:19 12.42 8.23
16:19:20 12.57 8.28
17:18:19 12.51 8.12
17:18:20 12.58 8.25
17:19:20 12.66 8.26
18:19:20 12.74 8.15