User:Francium/313edt
| ← 312edt | 313edt | 314edt → |
313 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 313edt or 313ed3), is a nonoctave tuning system that divides the interval of 3/1 into 313 equal parts of about 6.08 ¢ each. Each step represents a frequency ratio of 31/313, or the 313th root of 3.
Theory
313edt corresponds to 197.481128edo, so it falls almost exactly between 197edo and 198edo.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.92 | +0.00 | +0.23 | +2.82 | -2.92 | -2.43 | -2.69 | +0.00 | -0.11 | -1.05 | +0.23 |
| Relative (%) | -48.1 | +0.0 | +3.8 | +46.3 | -48.1 | -39.9 | -44.3 | +0.0 | -1.8 | -17.2 | +3.8 | |
| Steps (reduced) |
197 (197) |
313 (0) |
395 (82) |
459 (146) |
510 (197) |
554 (241) |
592 (279) |
626 (0) |
656 (30) |
683 (57) |
708 (82) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.42 | +0.73 | +2.82 | +0.46 | -1.19 | -2.92 | +0.70 | -3.03 | -2.43 | +2.11 | -1.93 | -2.69 |
| Relative (%) | +23.3 | +12.0 | +46.3 | +7.6 | -19.6 | -48.1 | +11.5 | -49.9 | -39.9 | +34.7 | -31.8 | -44.3 | |
| Steps (reduced) |
731 (105) |
752 (126) |
772 (146) |
790 (164) |
807 (181) |
823 (197) |
839 (213) |
853 (227) |
867 (241) |
881 (255) |
893 (267) |
905 (279) | |
Subsets and supersets
313edt is the 65th prime edt. It does not contain any nontrivial subset edts.