57ed7/3
Jump to navigation
Jump to search
Prime factorization
3 × 19
Step size
25.7346¢
Octave
47\57ed7/3 (1209.53¢)
Twelfth
74\57ed7/3 (1904.36¢)
Consistency limit
3
Distinct consistency limit
3
 |
This page is a stub. You can help the Xenharmonic Wiki by expanding it. |
| ← 56ed7/3 | 57ed7/3 | 58ed7/3 → |
57 equal divisions of 7/3 (abbreviated 57ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 57 equal parts of about 25.7 ¢ each. Each step represents a frequency ratio of (7/3)1/57, or the 57th root of 7/3.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 25.735 | |
| 2 | 51.469 | |
| 3 | 77.204 | 22/21, 23/22 |
| 4 | 102.938 | 18/17 |
| 5 | 128.673 | 14/13 |
| 6 | 154.407 | 23/21 |
| 7 | 180.142 | 10/9 |
| 8 | 205.877 | |
| 9 | 231.611 | |
| 10 | 257.346 | 22/19 |
| 11 | 283.08 | 20/17 |
| 12 | 308.815 | |
| 13 | 334.55 | 17/14, 23/19 |
| 14 | 360.284 | |
| 15 | 386.019 | |
| 16 | 411.753 | 19/15 |
| 17 | 437.488 | 9/7 |
| 18 | 463.222 | 17/13, 30/23 |
| 19 | 488.957 | |
| 20 | 514.692 | 31/23 |
| 21 | 540.426 | 15/11 |
| 22 | 566.161 | 18/13 |
| 23 | 591.895 | 31/22 |
| 24 | 617.63 | 10/7 |
| 25 | 643.364 | 29/20 |
| 26 | 669.099 | |
| 27 | 694.834 | |
| 28 | 720.568 | |
| 29 | 746.303 | 20/13 |
| 30 | 772.037 | |
| 31 | 797.772 | 27/17 |
| 32 | 823.506 | 29/18 |
| 33 | 849.241 | 31/19 |
| 34 | 874.976 | |
| 35 | 900.71 | |
| 36 | 926.445 | 29/17 |
| 37 | 952.179 | 33/19 |
| 38 | 977.914 | |
| 39 | 1003.649 | |
| 40 | 1029.383 | |
| 41 | 1055.118 | |
| 42 | 1080.852 | |
| 43 | 1106.587 | 19/10 |
| 44 | 1132.321 | 27/14 |
| 45 | 1158.056 | |
| 46 | 1183.791 | |
| 47 | 1209.525 | |
| 48 | 1235.26 | |
| 49 | 1260.994 | 27/13, 29/14, 31/15 |
| 50 | 1286.729 | 21/10 |
| 51 | 1312.463 | |
| 52 | 1338.198 | 13/6 |
| 53 | 1363.933 | 11/5 |
| 54 | 1389.667 | 29/13 |
| 55 | 1415.402 | |
| 56 | 1441.136 | 23/10 |
| 57 | 1466.871 | 7/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +9.5 | +2.4 | -6.7 | -7.0 | +11.9 | +2.4 | +2.8 | +4.8 | +2.5 | -8.1 | -4.3 |
| Relative (%) | +37.0 | +9.3 | -26.0 | -27.1 | +46.4 | +9.3 | +11.0 | +18.7 | +9.9 | -31.3 | -16.6 | |
| Steps (reduced) |
47 (47) |
74 (17) |
93 (36) |
108 (51) |
121 (7) |
131 (17) |
140 (26) |
148 (34) |
155 (41) |
161 (47) |
167 (53) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +11.6 | +11.9 | -4.6 | +12.4 | +10.3 | -11.4 | -2.1 | +12.1 | +4.8 | +1.5 | +1.7 |
| Relative (%) | +44.9 | +46.4 | -17.8 | +48.1 | +40.2 | -44.3 | -8.0 | +46.9 | +18.7 | +5.7 | +6.7 | |
| Steps (reduced) |
173 (2) |
178 (7) |
182 (11) |
187 (16) |
191 (20) |
194 (23) |
198 (27) |
202 (31) |
205 (34) |
208 (37) |
211 (40) | |