590edo
| ← 589edo | 590edo | 591edo → |
590 equal divisions of the octave (abbreviated 590edo or 590ed2), also called 590-tone equal temperament (590tet) or 590 equal temperament (590et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 590 equal parts of about 2.034 ¢ each. Each step represents a frequency ratio of 21/590, or the 590th root of 2.
590edo has the same tuning as the 118edo in the 5-limit and provides a good correction for the harmonics 7, 11, and 13, altogether being consistent in the 15-odd-limit. Among the 118th-octave temperaments, it by definition tunes parakleischis as well as centenniamajor in the 590ee val.
Besides that, it is a tuning for the quintaschis temperament in the 7-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.000 | -0.260 | +0.127 | -0.690 | -0.132 | -0.528 | +0.807 | -0.564 | +0.200 | -0.425 | +0.049 |
| relative (%) | +0 | -13 | +6 | -34 | -6 | -26 | +40 | -28 | +10 | -21 | +2 | |
| Steps (reduced) |
590 (0) |
935 (345) |
1370 (190) |
1656 (476) |
2041 (271) |
2183 (413) |
2412 (52) |
2506 (146) |
2669 (309) |
2866 (506) |
2923 (563) | |
Subsets and supersets
Since 590 factors into 2 × 5 × 59, 590edo has subset edos 2, 5, 10, 59, 118, and 295.