31ed11/5
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Prime factorization
31 (prime)
Step size
44.0324¢
Octave
27\31ed11/5 (1188.87¢)
Twelfth
43\31ed11/5 (1893.39¢)
Consistency limit
3
Distinct consistency limit
3
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31 equal divisions of 11/5 (abbreviated 31ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 31 equal parts of about 44 ¢ each. Each step represents a frequency ratio of (11/5)1/31, or the 31st root of 11/5.
Intervals
Steps | Cents | Approximate Ratios |
---|---|---|
0 | 0 | 1/1 |
1 | 44.032 | |
2 | 88.065 | |
3 | 132.097 | 14/13, 27/25 |
4 | 176.13 | 10/9, 21/19 |
5 | 220.162 | 17/15, 25/22, 26/23 |
6 | 264.194 | |
7 | 308.227 | 6/5 |
8 | 352.259 | 11/9, 27/22 |
9 | 396.292 | |
10 | 440.324 | 22/17 |
11 | 484.356 | |
12 | 528.389 | 15/11, 19/14, 23/17, 27/20 |
13 | 572.421 | 25/18 |
14 | 616.454 | |
15 | 660.486 | 19/13, 22/15, 25/17 |
16 | 704.518 | 3/2 |
17 | 748.551 | 17/11, 23/15 |
18 | 792.583 | 27/17 |
19 | 836.615 | 21/13 |
20 | 880.648 | 5/3 |
21 | 924.68 | 17/10 |
22 | 968.713 | |
23 | 1012.745 | 9/5 |
24 | 1056.777 | 11/6 |
25 | 1100.81 | 17/9 |
26 | 1144.842 | |
27 | 1188.875 | |
28 | 1232.907 | |
29 | 1276.939 | 23/11, 25/12 |
30 | 1320.972 | |
31 | 1365.004 | 11/5 |
Harmonics
Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | -11.1 | -8.6 | +21.8 | -12.3 | -19.7 | +21.7 | +10.7 | -17.1 | +20.6 | -12.3 | +13.2 |
Relative (%) | -25.3 | -19.4 | +49.5 | -27.9 | -44.7 | +49.2 | +24.2 | -38.9 | +46.9 | -27.9 | +30.0 | |
Steps (reduced) |
27 (27) |
43 (12) |
55 (24) |
63 (1) |
70 (8) |
77 (15) |
82 (20) |
86 (24) |
91 (29) |
94 (1) |
98 (5) |
Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | +6.7 | +10.5 | -20.8 | -0.5 | -17.4 | +15.8 | +10.2 | +9.5 | +13.1 | +20.6 | -12.3 |
Relative (%) | +15.3 | +23.9 | -47.3 | -1.1 | -39.4 | +35.8 | +23.3 | +21.6 | +29.8 | +46.9 | -27.9 | |
Steps (reduced) |
101 (8) |
104 (11) |
106 (13) |
109 (16) |
111 (18) |
114 (21) |
116 (23) |
118 (25) |
120 (27) |
122 (29) |
123 (30) |