986edo
| ← 985edo | 986edo | 987edo → |
986 equal divisions of the octave (abbreviated 986edo or 986ed2), also called 986-tone equal temperament (986tet) or 986 equal temperament (986et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 986 equal parts of about 1.22 ¢ each. Each step represents a frequency ratio of 21/986, or the 986th root of 2.
Theory
986edo is a good 2.3.7.11 subgroup tuning, but it is inconsistent to the 5-odd-limit and larger due to a high error on the 5th harmonic. 986edo has an excellent 11th harmonic, being the denominator of a convergent to log211, after 949 and before 1935. In the 2.3.7.11 subgroup, 986edo can be used with optional additions of either 17, 23, 29, or 31.
In the 2.3.7 subgroup, 986edo tempers out the garischisma, and is a strong tuning for 2.3.7.11-subgroup gary. It also tempers out, 131072/130977, 3195731/3188646, 33554432/33480783, 67110351/67108864, and [5 4 0 28 -26⟩ in the 2.3.7.11 subgroup.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.000 | +0.276 | -0.512 | -0.063 | +0.001 | +0.446 | -0.290 | -0.556 | -0.282 | +0.037 | +0.198 |
| relative (%) | +0 | +23 | -42 | -5 | +0 | +37 | -24 | -46 | -23 | +3 | +16 | |
| Steps (reduced) |
986 (0) |
1563 (577) |
2289 (317) |
2768 (796) |
3411 (453) |
3649 (691) |
4030 (86) |
4188 (244) |
4460 (516) |
4790 (846) |
4885 (941) | |
Subsets and supersets
Since 986 factors as 2 × 17 × 29, 986edo has subset edos 1, 2, 17, 29, 34, 58, 493.
Regular temperament properties
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 409\986 | 497.769 | 4/3 | Gary |