124edf
| ← 123edf | 124edf | 125edf → |
124 equal divisions of the perfect fifth (abbreviated 124edf or 124ed3/2) is a nonoctave tuning system that divides the interval of 3/2 into 124 equal parts of about 5.66 ¢ each. Each step represents a frequency ratio of (3/2)1/124, or the 124th root of 3/2.
Theory
124edf is closely related to 212edo, but with the perfect fifth instead of the octave tuned just. The octave is stretched by about 0.117 cents. Like 212edo, 124edf is consistent to the 16-integer-limit. While the 3-limit part is tuned sharp plus a sharper 23, the 5, 7, 11, and 13 remain flat but significantly less so than in 212edo, and the flat mappings of 17 and 19 now become closer than the sharp mappings.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.12 | +0.12 | +0.23 | -1.14 | +0.23 | -0.57 | +0.35 | +0.23 | -1.02 | -1.86 | +0.35 |
| Relative (%) | +2.1 | +2.1 | +4.1 | -20.1 | +4.1 | -10.1 | +6.2 | +4.1 | -18.0 | -32.8 | +6.2 | |
| Steps (reduced) |
212 (88) |
336 (88) |
424 (52) |
492 (120) |
548 (52) |
595 (99) |
636 (16) |
672 (52) |
704 (84) |
733 (113) |
760 (16) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.36 | -0.46 | -1.02 | +0.47 | -2.59 | +0.35 | -2.68 | -0.90 | -0.46 | -1.74 | +0.56 | +0.47 |
| Relative (%) | -41.7 | -8.1 | -18.0 | +8.2 | -45.8 | +6.2 | -47.3 | -16.0 | -8.1 | -30.8 | +9.8 | +8.2 | |
| Steps (reduced) |
784 (40) |
807 (63) |
828 (84) |
848 (104) |
866 (122) |
884 (16) |
900 (32) |
916 (48) |
931 (63) |
945 (77) |
959 (91) |
972 (104) | |
Subsets and supersets
Since 124 factors into primes as 22 × 31, 124edf contains subset edfs 2, 4, 31, and 62.