29ed11/5
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Prime factorization
29 (prime)
Step size
47.0691¢
Octave
25\29ed11/5 (1176.73¢)
Twelfth
40\29ed11/5 (1882.76¢)
Consistency limit
3
Distinct consistency limit
3
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← 28ed11/5 | 29ed11/5 | 30ed11/5 → |
29 equal divisions of 11/5 (abbreviated 29ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 29 equal parts of about 47.1 ¢ each. Each step represents a frequency ratio of (11/5)1/29, or the 29th root of 11/5.
Intervals
Steps | Cents | Approximate Ratios |
---|---|---|
0 | 0 | 1/1 |
1 | 47.069 | |
2 | 94.138 | |
3 | 141.207 | 25/23 |
4 | 188.276 | 10/9, 19/17 |
5 | 235.346 | |
6 | 282.415 | 13/11 |
7 | 329.484 | 17/14, 23/19 |
8 | 376.553 | |
9 | 423.622 | 14/11 |
10 | 470.691 | 17/13, 25/19 |
11 | 517.76 | 23/17, 27/20 |
12 | 564.829 | |
13 | 611.898 | |
14 | 658.968 | 19/13, 22/15, 25/17 |
15 | 706.037 | 3/2 |
16 | 753.106 | 17/11 |
17 | 800.175 | |
18 | 847.244 | |
19 | 894.313 | 5/3 |
20 | 941.382 | 19/11 |
21 | 988.451 | 23/13 |
22 | 1035.52 | |
23 | 1082.59 | |
24 | 1129.659 | 21/11, 25/13 |
25 | 1176.728 | |
26 | 1223.797 | |
27 | 1270.866 | 23/11 |
28 | 1317.935 | |
29 | 1365.004 | 11/5 |
Harmonics
Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | -23.3 | -19.2 | +0.5 | -9.2 | +4.6 | +20.2 | -22.7 | +8.7 | +14.6 | -9.2 | -18.7 |
Relative (%) | -49.4 | -40.8 | +1.1 | -19.6 | +9.8 | +42.8 | -48.3 | +18.5 | +30.9 | -19.6 | -39.7 | |
Steps (reduced) |
25 (25) |
40 (11) |
51 (22) |
59 (1) |
66 (8) |
72 (14) |
76 (18) |
81 (23) |
85 (27) |
88 (1) |
91 (4) |
Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | -16.0 | -3.1 | +18.6 | +1.0 | -9.8 | -14.6 | -14.0 | -8.7 | +1.0 | +14.6 | -15.3 |
Relative (%) | -34.1 | -6.6 | +39.6 | +2.2 | -20.8 | -31.0 | -29.8 | -18.5 | +2.0 | +30.9 | -32.6 | |
Steps (reduced) |
94 (7) |
97 (10) |
100 (13) |
102 (15) |
104 (17) |
106 (19) |
108 (21) |
110 (23) |
112 (25) |
114 (27) |
115 (28) |