58edf
| ← 57edf | 58edf | 59edf → |
58 equal divisions of the perfect fifth (abbreviated 58edf or 58ed3/2) is a nonoctave tuning system that divides the interval of 3/2 into 58 equal parts of about 12.1 ¢ each. Each step represents a frequency ratio of (3/2)1/58, or the 58th root of 3/2.
Theory
58edf corresponds to 99.1517…edo. It is related to 99edo, but with the 3/2 rather than the 2/1 being just. The octave is about 1.8354 cents compressed. 58edf is consistent to the 12-integer-limit. In comparison, 99edo is only consistent up to the 10-integer-limit.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.84 | -1.84 | -3.67 | -2.70 | -3.67 | -4.28 | -5.51 | -3.67 | -4.53 | -0.10 | -5.51 |
| Relative (%) | -15.2 | -15.2 | -30.3 | -22.3 | -30.3 | -35.4 | -45.5 | -30.3 | -37.5 | -0.8 | -45.5 | |
| Steps (reduced) |
99 (41) |
157 (41) |
198 (24) |
230 (56) |
256 (24) |
278 (46) |
297 (7) |
314 (24) |
329 (39) |
343 (53) |
355 (7) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.15 | +5.98 | -4.53 | +4.76 | -3.37 | -5.51 | -2.29 | +5.73 | +5.98 | -1.94 | +5.83 | +4.76 |
| Relative (%) | +9.5 | +49.4 | -37.5 | +39.3 | -27.9 | -45.5 | -18.9 | +47.4 | +49.4 | -16.0 | +48.1 | +39.3 | |
| Steps (reduced) |
367 (19) |
378 (30) |
387 (39) |
397 (49) |
405 (57) |
413 (7) |
421 (15) |
429 (23) |
436 (30) |
442 (36) |
449 (43) |
455 (49) | |
Subsets and supersets
Since 58 factors into primes as 2 × 29, 58edf contains 2edf and 29edf as subsets.