986edo

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← 985edo986edo987edo →
Prime factorization 2 × 17 × 29
Step size 1.21704¢
Fifth 577\986 (702.231¢)
Semitones (A1:m2) 95:73 (115.6¢ : 88.84¢)
Consistency limit 3
Distinct consistency limit 3

986 equal divisions of the octave (abbreviated 986edo), or 986-tone equal temperament (986tet), 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 of 986edo 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

Approximation of prime harmonics in 986edo
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

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 409\986 497.769 4/3 Gary