59ed7/3
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Prime factorization
59 (prime)
Step size
24.8622¢
Octave
48\59ed7/3 (1193.39¢)
Twelfth
76\59ed7/3 (1889.53¢)
Consistency limit
3
Distinct consistency limit
3
 |
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| ← 58ed7/3 | 59ed7/3 | 60ed7/3 → |
59 equal divisions of 7/3 (abbreviated 59ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 59 equal parts of about 24.9 ¢ each. Each step represents a frequency ratio of (7/3)1/59, or the 59th root of 7/3.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 24.862 | |
| 2 | 49.724 | 34/33 |
| 3 | 74.587 | 23/22 |
| 4 | 99.449 | |
| 5 | 124.311 | |
| 6 | 149.173 | |
| 7 | 174.036 | |
| 8 | 198.898 | |
| 9 | 223.76 | 25/22, 33/29 |
| 10 | 248.622 | |
| 11 | 273.484 | 34/29 |
| 12 | 298.347 | 32/27 |
| 13 | 323.209 | |
| 14 | 348.071 | |
| 15 | 372.933 | 31/25 |
| 16 | 397.795 | 29/23 |
| 17 | 422.658 | |
| 18 | 447.52 | 22/17 |
| 19 | 472.382 | 21/16, 25/19 |
| 20 | 497.244 | 4/3 |
| 21 | 522.107 | 23/17 |
| 22 | 546.969 | 26/19 |
| 23 | 571.831 | |
| 24 | 596.693 | 31/22 |
| 25 | 621.555 | 10/7, 33/23 |
| 26 | 646.418 | 29/20 |
| 27 | 671.28 | 25/17 |
| 28 | 696.142 | |
| 29 | 721.004 | |
| 30 | 745.867 | |
| 31 | 770.729 | |
| 32 | 795.591 | |
| 33 | 820.453 | |
| 34 | 845.315 | 31/19 |
| 35 | 870.178 | 33/20 |
| 36 | 895.04 | |
| 37 | 919.902 | 17/10 |
| 38 | 944.764 | 19/11 |
| 39 | 969.627 | 7/4 |
| 40 | 994.489 | 16/9 |
| 41 | 1019.351 | |
| 42 | 1044.213 | 31/17 |
| 43 | 1069.075 | |
| 44 | 1093.938 | |
| 45 | 1118.8 | |
| 46 | 1143.662 | 29/15 |
| 47 | 1168.524 | |
| 48 | 1193.386 | |
| 49 | 1218.249 | |
| 50 | 1243.111 | |
| 51 | 1267.973 | |
| 52 | 1292.835 | |
| 53 | 1317.698 | 15/7 |
| 54 | 1342.56 | |
| 55 | 1367.422 | 11/5 |
| 56 | 1392.284 | |
| 57 | 1417.146 | 25/11, 34/15 |
| 58 | 1442.009 | 23/10 |
| 59 | 1466.871 | 7/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -6.6 | -12.4 | +11.6 | -1.7 | +5.8 | -12.4 | +5.0 | +0.0 | -8.4 | +0.7 | -0.8 |
| Relative (%) | -26.6 | -50.0 | +46.8 | -7.0 | +23.4 | -50.0 | +20.2 | +0.0 | -33.6 | +2.7 | -3.2 | |
| Steps (reduced) |
48 (48) |
76 (17) |
97 (38) |
112 (53) |
125 (7) |
135 (17) |
145 (27) |
153 (35) |
160 (42) |
167 (49) |
173 (55) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +9.8 | +5.8 | +10.7 | -1.6 | -7.1 | -6.6 | -0.8 | +9.9 | +0.0 | -5.9 | -8.3 |
| Relative (%) | +39.5 | +23.4 | +43.0 | -6.4 | -28.6 | -26.6 | -3.0 | +39.8 | +0.0 | -23.9 | -33.4 | |
| Steps (reduced) |
179 (2) |
184 (7) |
189 (12) |
193 (16) |
197 (20) |
201 (24) |
205 (28) |
209 (32) |
212 (35) |
215 (38) |
218 (41) | |