14618edo

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← 14617edo

14618edo

14619edo →

Prime factorization	2 × 7309
Step size	0.0820906 ¢
Fifth	8551\14618 (701.956 ¢)
Semitones (A1:m2)	1385:1099 (113.7 ¢ : 90.22 ¢)
Consistency limit	17
Distinct consistency limit	17

14618edo is an extremely strong 13-limit system, with a lower relative error than any previous equal temperaments, beating 6079 and not until 73591 do we find a better equal temperament in the same subgroup. A comma basis is {123201/123200, 1990656/1990625, 3294225/3294172, 4084223/4084101, 781258401/781250000}. It is much less impressive beyond that limit, though it does well in the 2.3.5.7.11.13.19.29 subgroup.

Prime harmonics

Approximation of prime harmonics in 14618edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.0000	+0.0015	+0.0045	+0.0070	+0.0023	-0.0023	+0.0384	-0.0168	-0.0352	+0.0028	-0.0363
	Relative (%)	+0.0	+1.8	+5.5	+8.6	+2.9	-2.8	+46.8	-20.4	-42.9	+3.4	-44.2
Steps (reduced)		14618 (0)	23169 (8551)	33942 (4706)	41038 (11802)	50570 (6716)	54093 (10239)	59751 (1279)	62096 (3624)	66125 (7653)	71014 (12542)	72420 (13948)

Subsets and supersets

29236edo, which doubles 14618edo, provides a good correction to the harmonics 17 and 23.