14618edo

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← 14617edo14618edo14619edo →
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

14618 equal divisions of the octave (abbreviated 14618edo or 14618ed2), also called 14618-tone equal temperament (14618tet) or 14618 equal temperament (14618et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 14618 equal parts of about 0.082 ¢ each. Each step represents a frequency ratio of 21/14618, or the 14618th root of 2.

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 +2 +6 +9 +3 -3 +47 -20 -43 +3 -44
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.