263edt
Jump to navigation
Jump to search
| ← 262edt | 263edt | 264edt → |
263 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 263edt or 263ed3), is a nonoctave tuning system that divides the interval of 3/1 into 263 equal parts of about 7.23 ¢ each. Each step represents a frequency ratio of 31/263, or the 263rd root of 3.
263edt is related to 166edo, but with the perfect twelfth instead of the octave tuned just. Unlike 166edo, which is consistent to the 14-integer-limit, 263edt is only consistent to the 13-integer-limit, even though it has an overall more balanced tuning profile, with some harmonics tuned flat and others tuned sharp.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.47 | +0.00 | +0.95 | -2.08 | +0.47 | +1.18 | +1.42 | +0.00 | -1.61 | -0.28 | +0.95 |
| Relative (%) | +6.5 | +0.0 | +13.1 | -28.8 | +6.5 | +16.3 | +19.6 | +0.0 | -22.3 | -3.9 | +13.1 | |
| Steps (reduced) |
166 (166) |
263 (0) |
332 (69) |
385 (122) |
429 (166) |
466 (203) |
498 (235) |
526 (0) |
551 (25) |
574 (48) |
595 (69) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.22 | +1.65 | -2.08 | +1.89 | -1.82 | +0.47 | +0.88 | -1.14 | +1.18 | +0.19 | +2.78 | +1.42 |
| Relative (%) | -3.1 | +22.8 | -28.8 | +26.2 | -25.1 | +6.5 | +12.2 | -15.7 | +16.3 | +2.6 | +38.5 | +19.6 | |
| Steps (reduced) |
614 (88) |
632 (106) |
648 (122) |
664 (138) |
678 (152) |
692 (166) |
705 (179) |
717 (191) |
729 (203) |
740 (214) |
751 (225) |
761 (235) | |
Subsets and supersets
263edt is the 56th prime edt. It does not contain any nontrivial subset edts.