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 | 21.3 | |
| 2 | 42.5 | |
| 3 | 63.8 | 28/27 |
| 4 | 85 | 21/20 |
| 5 | 106.3 | |
| 6 | 127.6 | |
| 7 | 148.8 | 37/34 |
| 8 | 170.1 | |
| 9 | 191.3 | 19/17, 29/26 |
| 10 | 212.6 | 26/23 |
| 11 | 233.8 | |
| 12 | 255.1 | 29/25 |
| 13 | 276.4 | 34/29 |
| 14 | 297.6 | |
| 15 | 318.9 | |
| 16 | 340.1 | |
| 17 | 361.4 | |
| 18 | 382.7 | |
| 19 | 403.9 | 29/23 |
| 20 | 425.2 | 37/29 |
| 21 | 446.4 | |
| 22 | 467.7 | 17/13 |
| 23 | 489 | |
| 24 | 510.2 | |
| 25 | 531.5 | 34/25 |
| 26 | 552.7 | |
| 27 | 574 | |
| 28 | 595.3 | |
| 29 | 616.5 | 10/7 |
| 30 | 637.8 | |
| 31 | 659 | 19/13 |
| 32 | 680.3 | 34/23, 37/25 |
| 33 | 701.5 | 3/2 |
| 34 | 722.8 | |
| 35 | 744.1 | |
| 36 | 765.3 | 14/9 |
| 37 | 786.6 | |
| 38 | 807.8 | |
| 39 | 829.1 | |
| 40 | 850.4 | 31/19 |
| 41 | 871.6 | |
| 42 | 892.9 | |
| 43 | 914.1 | |
| 44 | 935.4 | |
| 45 | 956.7 | |
| 46 | 977.9 | |
| 47 | 999.2 | |
| 48 | 1020.4 | |
| 49 | 1041.7 | 31/17 |
| 50 | 1062.9 | |
| 51 | 1084.2 | |
| 52 | 1105.5 | |
| 53 | 1126.7 | |
| 54 | 1148 | |
| 55 | 1169.2 | |
| 56 | 1190.5 | |
| 57 | 1211.8 | |
| 58 | 1233 | |
| 59 | 1254.3 | |
| 60 | 1275.5 | 23/11 |
| 61 | 1296.8 | |
| 62 | 1318.1 | 15/7 |
| 63 | 1339.3 | |
| 64 | 1360.6 | |
| 65 | 1381.8 | 20/9 |
| 66 | 1403.1 | 9/4 |
| 67 | 1424.4 | 25/11 |
| 68 | 1445.6 | 23/10 |
| 69 | 1466.9 | 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) | |