986edo

← 985edo

986edo

987edo →

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

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 (%)	+0.0	+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

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated Ratio*	Temperaments
1	409\986	497.769	4/3	Gary