# 14618edo

 ← 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

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 0.0821 ¢ 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 (%) +0.0 +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.