51ed7/3
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Prime factorization
3 × 17
Step size
28.7622¢
Octave
42\51ed7/3 (1208.01¢) (→14\17ed7/3)
Twelfth
66\51ed7/3 (1898.3¢) (→22\17ed7/3)
Consistency limit
3
Distinct consistency limit
3
 |
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| ← 50ed7/3 | 51ed7/3 | 52ed7/3 → |
51 equal divisions of 7/3 (abbreviated 51ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 51 equal parts of about 28.8 ¢ each. Each step represents a frequency ratio of (7/3)1/51, or the 51st root of 7/3.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 28.762 | |
| 2 | 57.524 | 29/28, 30/29, 31/30 |
| 3 | 86.287 | |
| 4 | 115.049 | 15/14, 31/29 |
| 5 | 143.811 | 25/23 |
| 6 | 172.573 | 21/19, 31/28 |
| 7 | 201.335 | 28/25 |
| 8 | 230.097 | |
| 9 | 258.86 | 22/19, 29/25 |
| 10 | 287.622 | 13/11 |
| 11 | 316.384 | 6/5 |
| 12 | 345.146 | 11/9, 28/23 |
| 13 | 373.908 | 26/21, 31/25 |
| 14 | 402.67 | 29/23 |
| 15 | 431.433 | 9/7 |
| 16 | 460.195 | 30/23 |
| 17 | 488.957 | |
| 18 | 517.719 | 31/23 |
| 19 | 546.481 | 26/19 |
| 20 | 575.243 | |
| 21 | 604.006 | 17/12, 27/19 |
| 22 | 632.768 | 13/9 |
| 23 | 661.53 | 19/13, 22/15 |
| 24 | 690.292 | |
| 25 | 719.054 | |
| 26 | 747.817 | |
| 27 | 776.579 | |
| 28 | 805.341 | |
| 29 | 834.103 | 21/13 |
| 30 | 862.865 | 23/14, 28/17 |
| 31 | 891.627 | |
| 32 | 920.39 | 17/10, 29/17 |
| 33 | 949.152 | 19/11, 26/15 |
| 34 | 977.914 | 30/17 |
| 35 | 1006.676 | 25/14 |
| 36 | 1035.438 | 31/17 |
| 37 | 1064.2 | |
| 38 | 1092.963 | |
| 39 | 1121.725 | 21/11, 23/12 |
| 40 | 1150.487 | |
| 41 | 1179.249 | |
| 42 | 1208.011 | |
| 43 | 1236.774 | |
| 44 | 1265.536 | 25/12, 27/13, 29/14 |
| 45 | 1294.298 | 19/9 |
| 46 | 1323.06 | 15/7 |
| 47 | 1351.822 | |
| 48 | 1380.584 | 31/14 |
| 49 | 1409.347 | |
| 50 | 1438.109 | 23/10 |
| 51 | 1466.871 | 7/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +8.0 | -3.7 | -12.7 | +3.6 | +4.4 | -3.7 | -4.7 | -7.3 | +11.6 | -9.6 | +12.4 |
| Relative (%) | +27.9 | -12.7 | -44.3 | +12.6 | +15.2 | -12.7 | -16.4 | -25.4 | +40.4 | -33.3 | +43.0 | |
| Steps (reduced) |
42 (42) |
66 (15) |
83 (32) |
97 (46) |
108 (6) |
117 (15) |
125 (23) |
132 (30) |
139 (37) |
144 (42) |
150 (48) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -11.2 | +4.4 | -0.0 | +3.3 | +13.4 | +0.7 | -6.6 | -9.1 | -7.3 | -1.6 | +7.8 |
| Relative (%) | -38.8 | +15.2 | -0.1 | +11.4 | +46.5 | +2.5 | -23.0 | -31.7 | -25.4 | -5.4 | +27.0 | |
| Steps (reduced) |
154 (1) |
159 (6) |
163 (10) |
167 (14) |
171 (18) |
174 (21) |
177 (24) |
180 (27) |
183 (30) |
186 (33) |
189 (36) | |