69ed7/3
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Prime factorization
3 × 23
Step size
21.259¢
Octave
56\69ed7/3 (1190.5¢)
Twelfth
89\69ed7/3 (1892.05¢)
Consistency limit
3
Distinct consistency limit
3
 |
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| ← 68ed7/3 | 69ed7/3 | 70ed7/3 → |
69 equal divisions of 7/3 (abbreviated 69ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 69 equal parts of about 21.3 ¢ each. Each step represents a frequency ratio of (7/3)1/69, or the 69th root of 7/3.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 21.259 | |
| 2 | 42.518 | |
| 3 | 63.777 | 28/27 |
| 4 | 85.036 | 21/20 |
| 5 | 106.295 | |
| 6 | 127.554 | |
| 7 | 148.813 | 37/34 |
| 8 | 170.072 | |
| 9 | 191.331 | 19/17, 29/26 |
| 10 | 212.59 | 26/23 |
| 11 | 233.849 | |
| 12 | 255.108 | 29/25 |
| 13 | 276.367 | 34/29 |
| 14 | 297.626 | |
| 15 | 318.885 | |
| 16 | 340.144 | |
| 17 | 361.403 | |
| 18 | 382.662 | |
| 19 | 403.921 | 29/23 |
| 20 | 425.18 | 37/29 |
| 21 | 446.439 | |
| 22 | 467.698 | 17/13 |
| 23 | 488.957 | |
| 24 | 510.216 | |
| 25 | 531.475 | 34/25 |
| 26 | 552.734 | |
| 27 | 573.993 | |
| 28 | 595.252 | |
| 29 | 616.511 | 10/7 |
| 30 | 637.77 | |
| 31 | 659.029 | 19/13 |
| 32 | 680.288 | 34/23, 37/25 |
| 33 | 701.547 | 3/2 |
| 34 | 722.806 | |
| 35 | 744.065 | |
| 36 | 765.324 | 14/9 |
| 37 | 786.583 | |
| 38 | 807.842 | |
| 39 | 829.101 | |
| 40 | 850.36 | 31/19 |
| 41 | 871.619 | |
| 42 | 892.878 | |
| 43 | 914.137 | |
| 44 | 935.396 | |
| 45 | 956.655 | |
| 46 | 977.914 | |
| 47 | 999.173 | |
| 48 | 1020.432 | |
| 49 | 1041.691 | 31/17 |
| 50 | 1062.95 | |
| 51 | 1084.209 | |
| 52 | 1105.468 | |
| 53 | 1126.727 | |
| 54 | 1147.986 | |
| 55 | 1169.245 | |
| 56 | 1190.504 | |
| 57 | 1211.763 | |
| 58 | 1233.022 | |
| 59 | 1254.281 | |
| 60 | 1275.54 | 23/11 |
| 61 | 1296.799 | |
| 62 | 1318.058 | 15/7 |
| 63 | 1339.317 | |
| 64 | 1360.576 | |
| 65 | 1381.835 | 20/9 |
| 66 | 1403.094 | 9/4 |
| 67 | 1424.353 | 25/11 |
| 68 | 1445.612 | 23/10 |
| 69 | 1466.871 | 7/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -9.50 | -9.90 | +2.27 | -1.38 | +1.86 | -9.90 | -7.23 | +1.45 | +10.38 | -5.81 | -7.64 |
| Relative (%) | -44.7 | -46.6 | +10.7 | -6.5 | +8.7 | -46.6 | -34.0 | +6.8 | +48.8 | -27.3 | -35.9 | |
| Steps (reduced) |
56 (56) |
89 (20) |
113 (44) |
131 (62) |
146 (8) |
158 (20) |
169 (31) |
179 (41) |
188 (50) |
195 (57) |
202 (64) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.60 | +1.86 | +9.97 | +4.53 | +5.87 | -8.05 | +4.65 | +0.88 | +1.45 | +5.95 | -7.23 |
| Relative (%) | +12.2 | +8.7 | +46.9 | +21.3 | +27.6 | -37.8 | +21.9 | +4.1 | +6.8 | +28.0 | -34.0 | |
| Steps (reduced) |
209 (2) |
215 (8) |
221 (14) |
226 (19) |
231 (24) |
235 (28) |
240 (33) |
244 (37) |
248 (41) |
252 (45) |
255 (48) | |