# 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 2^{1/986}, 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 log_{2}11, 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 (%) | +0.0 | +22.7 | -42.1 | -5.2 | +0.0 | +36.6 | -23.8 | -45.7 | -23.2 | +3.1 | +16.2 | |

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 |