93edf
Jump to navigation
Jump to search
| ← 92edf | 93edf | 94edf → |
93 equal divisions of the perfect fifth (abbreviated 93edf or 93ed3/2) is a nonoctave tuning system that divides the interval of 3/2 into 93 equal parts of about 7.55 ¢ each. Each step represents a frequency ratio of (3/2)1/93, or the 93rd root of 3/2.
Theory
93edf is closely related to 159edo, but with the perfect fifth instead of the octave tuned just. The octave is stretched by about 0.117 cents. Like 159edo, 93edf is consistent to the 18-integer-limit. It has a virtually pure 11, and while the 3-limit part is tuned sharp plus a sharper 17, the 5, 7, 13, 19 and 23 remain flat but significantly less so than in 159edo.
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 | -2.46 | +0.35 | +0.23 | -1.02 | +0.03 | +0.35 |
| Relative (%) | +1.5 | +1.5 | +3.1 | -15.1 | +3.1 | -32.6 | +4.6 | +3.1 | -13.5 | +0.4 | +4.6 | |
| Steps (reduced) |
159 (66) |
252 (66) |
318 (39) |
369 (90) |
411 (39) |
446 (74) |
477 (12) |
504 (39) |
528 (63) |
550 (85) |
570 (12) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.36 | -2.34 | -1.02 | +0.47 | +1.18 | +0.35 | -2.68 | -0.90 | -2.34 | +0.15 | -1.33 | +0.47 |
| Relative (%) | -31.3 | -31.1 | -13.5 | +6.2 | +15.7 | +4.6 | -35.5 | -12.0 | -31.1 | +1.9 | -17.6 | +6.2 | |
| Steps (reduced) |
588 (30) |
605 (47) |
621 (63) |
636 (78) |
650 (92) |
663 (12) |
675 (24) |
687 (36) |
698 (47) |
709 (58) |
719 (68) |
729 (78) | |
Subsets and supersets
Since 93 factors into primes as 3 × 31, 93edf contains 3edf and 31edf as subset edfs.