669edo
| ← 668edo | 669edo | 670edo → |
669 equal divisions of the octave (669edo), or 669-tone equal temperament (669tet), 669 equal temperament (669et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 669 equal parts of about 1.79 ¢ each.
669edo is consistent in the 7-odd-limit, although it has significant errors on the 3rd and the 5th harmonics. Besides that, 669c val is a tuning for the sensipent temperament in the 5-limit.
669edo appears much more useful as a higher-limit system, with harmonics 37 through 53 all having an error of 20% or less, with a comma basis for the 2.37.41.43.47.53 subgroup being {75809/75776, 1874161/1873232, 151124317/151101728, 9033613312/9032089499, 9795995841727/9788230467584}.
Overall, the subgroup which provides satisfactory results for 669edo is 2.7.19.29.37.41.43.47.53.
Harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | -0.610 | -0.663 | -0.216 | +0.574 | -0.645 | +0.728 | +0.521 | +0.874 | +0.245 | -0.826 | -0.472 |
| relative (%) | -34 | -37 | -12 | +32 | -36 | +41 | +29 | +49 | +14 | -46 | -26 | |
| Steps (reduced) |
1060 (391) |
1553 (215) |
1878 (540) |
2121 (114) |
2314 (307) |
2476 (469) |
2614 (607) |
2735 (59) |
2842 (166) |
2938 (262) |
3026 (350) | |