31ed7/3

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← 30ed7/331ed7/332ed7/3 →
Prime factorization 31 (prime)
Step size 47.3184¢ 
Octave 25\31ed7/3 (1182.96¢)
Twelfth 40\31ed7/3 (1892.74¢)
Consistency limit 3
Distinct consistency limit 3

31 equal divisions of 7/3 (abbreviated 31ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 31 equal parts of about 47.3 ¢ each. Each step represents a frequency ratio of (7/3)1/31, or the 31st root of 7/3.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 47.318
2 94.637
3 141.955 25/23
4 189.274 10/9, 19/17
5 236.592
6 283.91 13/11
7 331.229 23/19
8 378.547 26/21
9 425.866 9/7
10 473.184 17/13, 25/19
11 520.503 23/17, 27/20
12 567.821
13 615.139 10/7
14 662.458 19/13, 22/15, 25/17
15 709.776 3/2
16 757.095 14/9, 17/11
17 804.413
18 851.731
19 899.05
20 946.368 19/11, 26/15
21 993.687 23/13
22 1041.005
23 1088.324
24 1135.642 25/13, 27/14
25 1182.96
26 1230.279
27 1277.597 21/10, 23/11
28 1324.916 15/7
29 1372.234 11/5
30 1419.552 25/11
31 1466.871 7/3

Harmonics

Approximation of harmonics in 31ed7/3
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -17.0 -9.2 +13.2 +5.5 +21.1 -9.2 -3.8 -18.4 -11.6 +12.7 +4.0
Relative (%) -36.0 -19.5 +28.0 +11.6 +44.5 -19.5 -8.0 -39.0 -24.4 +26.8 +8.5
Steps
(reduced)
25
(25)
40
(9)
51
(20)
59
(28)
66
(4)
71
(9)
76
(14)
80
(18)
84
(22)
88
(26)
91
(29)
Approximation of harmonics in 31ed7/3
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +7.4 +21.1 -3.7 -20.8 +16.2 +11.8 +12.9 +18.7 -18.4 -4.3 +13.3
Relative (%) +15.6 +44.5 -7.9 -44.0 +34.2 +25.0 +27.2 +39.5 -39.0 -9.2 +28.2
Steps
(reduced)
94
(1)
97
(4)
99
(6)
101
(8)
104
(11)
106
(13)
108
(15)
110
(17)
111
(18)
113
(20)
115
(22)