587edo
| ← 586edo | 587edo | 588edo → |
587 equal divisions of the octave (abbreviated 587edo or 587ed2), also called 587-tone equal temperament (587tet) or 587 equal temperament (587et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 587 equal parts of about 2.04 ¢ each. Each step represents a frequency ratio of 21/587, or the 587th root of 2.
587edo is consistent to the 7-odd-limit, but the error of harmonic 3 is quite large. With good approximations to harmonics 5, 7, 9, 11, and 13, it commends itself as a 2.9.5.7.11.13 subgroup tuning.
Using the patent val, however, the equal temperament tempers out 19683/19600 and 703125/702464 in the 7-limit, providing the optimal patent val for the 19 & 183 temperament and the planar temperament cataharry tempering out 19683/19600.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | -0.762 | +0.058 | +0.169 | +0.519 | +0.641 | -0.323 | -0.705 | -0.696 | +0.954 | -0.594 | -0.676 |
| relative (%) | -37 | +3 | +8 | +25 | +31 | -16 | -34 | -34 | +47 | -29 | -33 | |
| Steps (reduced) |
930 (343) |
1363 (189) |
1648 (474) |
1861 (100) |
2031 (270) |
2172 (411) |
2293 (532) |
2399 (51) |
2494 (146) |
2578 (230) |
2655 (307) | |
Subsets and supersets
587edo is the 107th prime edo.