486edo
| ← 485edo | 486edo | 487edo → |
486 equal divisions of the octave (abbreviated 486edo or 486ed2), also called 486-tone equal temperament (486tet) or 486 equal temperament (486et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 486 equal parts of about 2.47 ¢ each. Each step represents a frequency ratio of 21/486, or the 486th root of 2.
Theory
486edo is contorted in the 7-limit, with the same tuning as 243edo, but it corrects the 11th harmonic. However, due to the doubling of relative error on the fifth, it is inconsistent to the 9-odd-limit. Its approximation of most harmonics are poor for its size, with all odd harmonics from 3 to 23 having more than 25% relative error, but the ratios between harmonics are approximated better. Using the patent val, it tempers out 2401/2400, 3025/3024, and 4375/4374 in the 11-limit, and 625/624, 729/728, and 1575/1573 in the 13-limit. The 486g val with a strong flat tendency is the best way to extend it further, tempering out 833/832 and 1701/1700 in the 17-limit, 513/512 and 1521/1520 in the 19-limit, and 897/896 and 1105/1104 in the 23-limit.
Prime harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | 25 | 27 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.72 | -1.13 | -0.92 | +1.03 | -0.70 | -1.02 | +0.62 | +1.22 | -1.22 | +0.82 | -1.11 | +0.21 | +0.31 | +0.05 | +0.64 |
| Relative (%) | -29.2 | -45.7 | -37.4 | +41.6 | -28.4 | -41.4 | +25.1 | +49.3 | -49.3 | +33.4 | -45.1 | +8.6 | +12.5 | +2.1 | +26.1 | |
| Steps (reduced) |
770 (284) |
1128 (156) |
1364 (392) |
1541 (83) |
1681 (223) |
1798 (340) |
1899 (441) |
1987 (43) |
2064 (120) |
2135 (191) |
2198 (254) |
2257 (313) |
2311 (367) |
2361 (417) |
2408 (464) | |