284edo
| ← 283edo | 284edo | 285edo → |
284 equal divisions of the octave (abbreviated 284edo or 284ed2), also called 284-tone equal temperament (284tet) or 284 equal temperament (284et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 284 equal parts of about 4.23 ¢ each. Each step represents a frequency ratio of 21/284, or the 284th root of 2.
The equal temperament tempers out the kleisma, 15625/15552, and the breedsma, 2401/2400, and is a good tuning for quadritikleismic temperament which tempers out both. This is particularly true for the 11-limit version of quadritikleismic, which also tempers out 385/384, for which it provides the optimal patent val. In fact, if 385/384 is tempered out essentially the same tuning accuracy can be obtained using quadritikleismic, since 284 provides the optimal patent val for quadritikleismic, the rank-3 temperaments agni and enlil and keenanismic, the 385/384 rank-4 temperament.
Prime harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.55 | -1.81 | -1.22 | -1.09 | -2.02 | +0.32 | +1.87 | +0.68 | -1.74 | -1.77 | +1.30 |
| Relative (%) | -12.9 | -42.8 | -28.9 | -25.9 | -47.9 | +7.5 | +44.3 | +16.1 | -41.1 | -41.8 | +30.8 | |
| Steps (reduced) |
450 (166) |
659 (91) |
797 (229) |
900 (48) |
982 (130) |
1051 (199) |
1110 (258) |
1161 (25) |
1206 (70) |
1247 (111) |
1285 (149) | |
Subsets and supersets
Since 284 factors into 22 × 71, 284edo has subset edos 2, 4, 71, and 142.