29ed5/4
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Prime factorization
29 (prime)
Step size
13.3212¢
Octave
90\29ed5/4 (1198.9¢)
Twelfth
143\29ed5/4 (1904.93¢)
Consistency limit
8
Distinct consistency limit
6
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29 equal divisions of 5/4 (abbreviated 29ed5/4) is a nonoctave tuning system that divides the interval of 5/4 into 29 equal parts of about 13.3 ¢ each. Each step represents a frequency ratio of (5/4)1/29, or the 29th root of 5/4.
Intervals
Steps | Cents | Approximate ratios |
---|---|---|
0 | 0 | 1/1 |
1 | 13.3 | |
2 | 26.6 | |
3 | 40 | |
4 | 53.3 | |
5 | 66.6 | 23/22, 25/24, 26/25 |
6 | 79.9 | 20/19, 22/21, 24/23 |
7 | 93.2 | 19/18, 21/20 |
8 | 106.6 | 16/15, 17/16, 18/17 |
9 | 119.9 | 15/14 |
10 | 133.2 | 13/12, 14/13 |
11 | 146.5 | 12/11, 25/23 |
12 | 159.9 | |
13 | 173.2 | 10/9, 11/10, 21/19 |
14 | 186.5 | |
15 | 199.8 | 19/17 |
16 | 213.1 | 9/8, 17/15, 25/22, 26/23 |
17 | 226.5 | 8/7 |
18 | 239.8 | 23/20 |
19 | 253.1 | 15/13, 22/19 |
20 | 266.4 | 7/6 |
21 | 279.7 | 13/11, 20/17 |
22 | 293.1 | 25/21 |
23 | 306.4 | 19/16 |
24 | 319.7 | 6/5 |
25 | 333 | 17/14 |
26 | 346.4 | 11/9 |
27 | 359.7 | 16/13, 26/21, 27/22 |
28 | 373 | 21/17 |
29 | 386.3 | 5/4 |
Harmonics
Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | -1.10 | +2.97 | -2.19 | -2.19 | +1.88 | +1.43 | -3.29 | +5.94 | -3.29 | +4.88 | +0.78 |
Relative (%) | -8.2 | +22.3 | -16.4 | -16.4 | +14.1 | +10.7 | -24.7 | +44.6 | -24.7 | +36.7 | +5.9 | |
Steps (reduced) |
90 (3) |
143 (27) |
180 (6) |
209 (6) |
233 (1) |
253 (21) |
270 (9) |
286 (25) |
299 (9) |
312 (22) |
323 (4) |
Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | -4.58 | +0.33 | +0.78 | -4.38 | -2.77 | +4.85 | +4.49 | -4.38 | +4.40 | +3.79 | -6.56 |
Relative (%) | -34.4 | +2.5 | +5.9 | -32.9 | -20.8 | +36.4 | +33.7 | -32.9 | +33.0 | +28.4 | -49.3 | |
Steps (reduced) |
333 (14) |
343 (24) |
352 (4) |
360 (12) |
368 (20) |
376 (28) |
383 (6) |
389 (12) |
396 (19) |
402 (25) |
407 (1) |