280edo
| ← 279edo | 280edo | 281edo → |
280 equal divisions of the octave (abbreviated 280edo or 280ed2), also called 280-tone equal temperament (280tet) or 280 equal temperament (280et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 280 equal parts of about 4.29 ¢ each. Each step represents a frequency ratio of 21/280, or the 280th root of 2.
280edo is enfactored in the 7-limit, with the same tuning as 140edo. It has a consistency limit of only 7. The approximation of 11 is improved over 140edo, tempering out 3025/3024. It supplies the optimal patent val for 13-limit enki, the rank-3 temperament tempering out 325/324, 364/363 and 625/624.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.90 | -0.60 | -0.25 | +1.54 | -0.53 | -2.10 | -1.80 | +1.73 | -1.01 | -0.75 |
| Relative (%) | +0.0 | +21.0 | -14.0 | -5.9 | +35.9 | -12.3 | -49.0 | -42.0 | +40.3 | -23.5 | -17.5 | |
| Steps (reduced) |
280 (0) |
444 (164) |
650 (90) |
786 (226) |
969 (129) |
1036 (196) |
1144 (24) |
1189 (69) |
1267 (147) |
1360 (240) |
1387 (267) | |
Subsets and supersets
Since 280 factors into 23 × 5 × 7, it has subset edos 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, and 140.