63ed7/3
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Prime factorization
32 × 7
Step size
23.2837¢
Octave
52\63ed7/3 (1210.75¢)
Twelfth
82\63ed7/3 (1909.26¢)
Consistency limit
3
Distinct consistency limit
3
 |
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| ← 62ed7/3 | 63ed7/3 | 64ed7/3 → |
63 equal divisions of 7/3 (abbreviated 63ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 63 equal parts of about 23.3 ¢ each. Each step represents a frequency ratio of (7/3)1/63, or the 63rd root of 7/3.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 23.284 | |
| 2 | 46.567 | 35/34 |
| 3 | 69.851 | 26/25 |
| 4 | 93.135 | |
| 5 | 116.418 | 15/14, 31/29 |
| 6 | 139.702 | |
| 7 | 162.986 | |
| 8 | 186.269 | 10/9 |
| 9 | 209.553 | |
| 10 | 232.837 | |
| 11 | 256.12 | 22/19 |
| 12 | 279.404 | |
| 13 | 302.688 | 25/21 |
| 14 | 325.971 | |
| 15 | 349.255 | |
| 16 | 372.539 | 26/21 |
| 17 | 395.822 | 34/27 |
| 18 | 419.106 | |
| 19 | 442.39 | 22/17 |
| 20 | 465.673 | 17/13 |
| 21 | 488.957 | |
| 22 | 512.241 | 35/26 |
| 23 | 535.524 | 34/25 |
| 24 | 558.808 | |
| 25 | 582.092 | 7/5 |
| 26 | 605.375 | |
| 27 | 628.659 | 33/23 |
| 28 | 651.943 | |
| 29 | 675.226 | |
| 30 | 698.51 | 3/2 |
| 31 | 721.794 | |
| 32 | 745.077 | |
| 33 | 768.361 | 14/9 |
| 34 | 791.645 | |
| 35 | 814.928 | |
| 36 | 838.212 | 34/21 |
| 37 | 861.496 | |
| 38 | 884.779 | 5/3 |
| 39 | 908.063 | 22/13 |
| 40 | 931.347 | |
| 41 | 954.63 | 26/15, 33/19 |
| 42 | 977.914 | |
| 43 | 1001.198 | 25/14 |
| 44 | 1024.481 | |
| 45 | 1047.765 | |
| 46 | 1071.049 | 13/7 |
| 47 | 1094.332 | |
| 48 | 1117.616 | |
| 49 | 1140.9 | 27/14 |
| 50 | 1164.183 | |
| 51 | 1187.467 | |
| 52 | 1210.751 | |
| 53 | 1234.034 | |
| 54 | 1257.318 | |
| 55 | 1280.602 | 21/10, 23/11 |
| 56 | 1303.885 | |
| 57 | 1327.169 | |
| 58 | 1350.453 | |
| 59 | 1373.736 | |
| 60 | 1397.02 | |
| 61 | 1420.304 | 34/15 |
| 62 | 1443.587 | |
| 63 | 1466.871 | 7/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +10.8 | +7.3 | -1.8 | +7.7 | -5.2 | +7.3 | +9.0 | -8.7 | -4.8 | -6.8 | +5.5 |
| Relative (%) | +46.2 | +31.4 | -7.7 | +33.2 | -22.5 | +31.4 | +38.5 | -37.2 | -20.6 | -29.3 | +23.7 | |
| Steps (reduced) |
52 (52) |
82 (19) |
103 (40) |
120 (57) |
133 (7) |
145 (19) |
155 (29) |
163 (37) |
171 (45) |
178 (52) |
185 (59) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +6.7 | -5.2 | -8.3 | -3.6 | +7.9 | +2.1 | +1.6 | +5.9 | -8.7 | +3.9 | -3.2 |
| Relative (%) | +28.6 | -22.5 | -35.4 | -15.3 | +33.9 | +8.9 | +6.9 | +25.5 | -37.2 | +16.9 | -13.7 | |
| Steps (reduced) |
191 (2) |
196 (7) |
201 (12) |
206 (17) |
211 (22) |
215 (26) |
219 (30) |
223 (34) |
226 (37) |
230 (41) |
233 (44) | |