70ed7/3
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Prime factorization
2 × 5 × 7
Step size
20.9553¢
Octave
57\70ed7/3 (1194.45¢)
Twelfth
91\70ed7/3 (1906.93¢) (→13\10ed7/3)
Consistency limit
2
Distinct consistency limit
2
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| ← 69ed7/3 | 70ed7/3 | 71ed7/3 → |
70 equal divisions of 7/3 (abbreviated 70ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 70 equal parts of about 21 ¢ each. Each step represents a frequency ratio of (7/3)1/70, or the 70th root of 7/3.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 21 | |
| 2 | 41.9 | |
| 3 | 62.9 | 29/28 |
| 4 | 83.8 | |
| 5 | 104.8 | 33/31, 35/33 |
| 6 | 125.7 | 14/13 |
| 7 | 146.7 | 25/23, 37/34 |
| 8 | 167.6 | 11/10 |
| 9 | 188.6 | 29/26 |
| 10 | 209.6 | 26/23, 35/31 |
| 11 | 230.5 | |
| 12 | 251.5 | 15/13, 22/19 |
| 13 | 272.4 | 34/29 |
| 14 | 293.4 | |
| 15 | 314.3 | 6/5 |
| 16 | 335.3 | 17/14 |
| 17 | 356.2 | |
| 18 | 377.2 | 36/29 |
| 19 | 398.2 | 29/23 |
| 20 | 419.1 | 14/11, 37/29 |
| 21 | 440.1 | |
| 22 | 461 | 17/13, 30/23 |
| 23 | 482 | 29/22, 33/25, 37/28 |
| 24 | 502.9 | |
| 25 | 523.9 | 23/17 |
| 26 | 544.8 | 26/19 |
| 27 | 565.8 | 18/13, 25/18 |
| 28 | 586.7 | |
| 29 | 607.7 | 37/26 |
| 30 | 628.7 | 33/23, 36/25 |
| 31 | 649.6 | |
| 32 | 670.6 | 25/17, 28/19, 31/21 |
| 33 | 691.5 | |
| 34 | 712.5 | |
| 35 | 733.4 | 26/17, 29/19 |
| 36 | 754.4 | 17/11 |
| 37 | 775.3 | 36/23 |
| 38 | 796.3 | 19/12 |
| 39 | 817.3 | |
| 40 | 838.2 | |
| 41 | 859.2 | 23/14 |
| 42 | 880.1 | |
| 43 | 901.1 | 37/22 |
| 44 | 922 | 17/10, 29/17 |
| 45 | 943 | 19/11, 31/18 |
| 46 | 963.9 | |
| 47 | 984.9 | 23/13, 30/17 |
| 48 | 1005.9 | 25/14, 34/19 |
| 49 | 1026.8 | |
| 50 | 1047.8 | 11/6 |
| 51 | 1068.7 | 13/7, 37/20 |
| 52 | 1089.7 | |
| 53 | 1110.6 | 19/10 |
| 54 | 1131.6 | 25/13 |
| 55 | 1152.5 | 35/18, 37/19 |
| 56 | 1173.5 | |
| 57 | 1194.5 | |
| 58 | 1215.4 | |
| 59 | 1236.4 | |
| 60 | 1257.3 | 29/14, 31/15 |
| 61 | 1278.3 | 23/11 |
| 62 | 1299.2 | 36/17 |
| 63 | 1320.2 | 15/7 |
| 64 | 1341.1 | 13/6 |
| 65 | 1362.1 | 11/5 |
| 66 | 1383 | |
| 67 | 1404 | |
| 68 | 1425 | 25/11 |
| 69 | 1445.9 | 30/13 |
| 70 | 1466.9 | 7/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -5.55 | +4.98 | +9.86 | +0.74 | -0.57 | +4.98 | +4.31 | +9.95 | -4.81 | -2.17 | -6.12 |
| Relative (%) | -26.5 | +23.8 | +47.0 | +3.5 | -2.7 | +23.8 | +20.6 | +47.5 | -22.9 | -10.3 | -29.2 | |
| Steps (reduced) |
57 (57) |
91 (21) |
115 (45) |
133 (63) |
148 (8) |
161 (21) |
172 (32) |
182 (42) |
190 (50) |
198 (58) |
205 (65) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.00 | -0.57 | +5.72 | -1.24 | -1.42 | +4.41 | -5.38 | -10.35 | +9.95 | -7.72 | -0.85 |
| Relative (%) | +9.5 | -2.7 | +27.3 | -5.9 | -6.8 | +21.0 | -25.7 | -49.4 | +47.5 | -36.8 | -4.1 | |
| Steps (reduced) |
212 (2) |
218 (8) |
224 (14) |
229 (19) |
234 (24) |
239 (29) |
243 (33) |
247 (37) |
252 (42) |
255 (45) |
259 (49) | |