48ed7/3
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Prime factorization
24 × 3
Step size
30.5598¢
Octave
39\48ed7/3 (1191.83¢) (→13\16ed7/3)
Twelfth
62\48ed7/3 (1894.71¢) (→31\24ed7/3)
Consistency limit
3
Distinct consistency limit
3
Special properties
 |
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| ← 47ed7/3 | 48ed7/3 | 49ed7/3 → |
48 equal divisions of 7/3 (abbreviated 48ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 48 equal parts of about 30.6 ¢ each. Each step represents a frequency ratio of (7/3)1/48, or the 48th root of 7/3.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 30.56 | |
| 2 | 61.12 | 27/26, 28/27 |
| 3 | 91.679 | |
| 4 | 122.239 | 15/14 |
| 5 | 152.799 | |
| 6 | 183.359 | 10/9 |
| 7 | 213.919 | |
| 8 | 244.478 | 15/13 |
| 9 | 275.038 | |
| 10 | 305.598 | 25/21 |
| 11 | 336.158 | 23/19 |
| 12 | 366.718 | 26/21 |
| 13 | 397.278 | 29/23 |
| 14 | 427.837 | |
| 15 | 458.397 | 13/10 |
| 16 | 488.957 | |
| 17 | 519.517 | 23/17, 27/20, 31/23 |
| 18 | 550.077 | |
| 19 | 580.636 | 7/5 |
| 20 | 611.196 | |
| 21 | 641.756 | 13/9 |
| 22 | 672.316 | |
| 23 | 702.876 | 3/2 |
| 24 | 733.435 | 29/19 |
| 25 | 763.995 | 14/9 |
| 26 | 794.555 | |
| 27 | 825.115 | 21/13 |
| 28 | 855.675 | |
| 29 | 886.235 | 5/3 |
| 30 | 916.794 | |
| 31 | 947.354 | 19/11, 26/15 |
| 32 | 977.914 | |
| 33 | 1008.474 | 25/14 |
| 34 | 1039.034 | 31/17 |
| 35 | 1069.593 | 13/7 |
| 36 | 1100.153 | |
| 37 | 1130.713 | 25/13 |
| 38 | 1161.273 | |
| 39 | 1191.833 | |
| 40 | 1222.392 | |
| 41 | 1252.952 | |
| 42 | 1283.512 | 21/10 |
| 43 | 1314.072 | 15/7 |
| 44 | 1344.632 | |
| 45 | 1375.191 | |
| 46 | 1405.751 | 9/4 |
| 47 | 1436.311 | |
| 48 | 1466.871 | 7/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -8.2 | -7.2 | +14.2 | -5.4 | +15.1 | -7.2 | +6.1 | -14.5 | -13.5 | +4.8 | +7.0 |
| Relative (%) | -26.7 | -23.7 | +46.5 | -17.6 | +49.6 | -23.7 | +19.8 | -47.4 | -44.3 | +15.8 | +22.8 | |
| Steps (reduced) |
39 (39) |
62 (14) |
79 (31) |
91 (43) |
102 (6) |
110 (14) |
118 (22) |
124 (28) |
130 (34) |
136 (40) |
141 (45) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -9.4 | +15.1 | -12.6 | -2.1 | +15.2 | +7.9 | +6.0 | +8.9 | -14.5 | -3.4 | +11.4 |
| Relative (%) | -30.6 | +49.6 | -41.3 | -6.9 | +49.7 | +25.8 | +19.6 | +29.0 | -47.4 | -11.0 | +37.2 | |
| Steps (reduced) |
145 (1) |
150 (6) |
153 (9) |
157 (13) |
161 (17) |
164 (20) |
167 (23) |
170 (26) |
172 (28) |
175 (31) |
178 (34) | |