28000edo
| ← 27999edo | 28000edo | 28001edo → |
28000 equal divisions of the octave (abbreviated 28000edo or 28000ed2), also called 28000-tone equal temperament (28000tet) or 28000 equal temperament (28000et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 28000 equal parts of about 0.0429 ¢ each. Each step represents a frequency ratio of 21/28000, or the 28000th root of 2.
This edo is notable for both being quite composite and having great approximations of every prime harmonic up to 19 apart from the 13th, which 84000edo corrects by slicing a step of 28000edo into 3 equal parts. Given its size and that there are other edos that are a potentially better approximation of the harmonic series in its size range, 28000edo doesn't seem to be especially practical for musical applications.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | +0.0021 | +0.0006 | +0.0027 | -0.0037 | -0.0134 | +0.0017 | +0.0013 | +0.0114 | -0.0201 | -0.0213 |
| Relative (%) | +0.0 | +5.0 | +1.3 | +6.2 | -8.5 | -31.2 | +4.0 | +3.0 | +26.5 | -46.8 | -49.7 | |
| Steps (reduced) |
28000 (0) |
44379 (16379) |
65014 (9014) |
78606 (22606) |
96864 (12864) |
103612 (19612) |
114449 (2449) |
118942 (6942) |
126660 (14660) |
136023 (24023) |
138717 (26717) | |