# 618edo

 ← 617edo 618edo 619edo →
Prime factorization 2 × 3 × 103
Step size 1.94175¢
Fifth 362\618 (702.913¢) (→181\309)
Semitones (A1:m2) 62:44 (120.4¢ : 85.44¢)
Dual sharp fifth 362\618 (702.913¢) (→181\309)
Dual flat fifth 361\618 (700.971¢)
Dual major 2nd 105\618 (203.883¢) (→35\206)
Consistency limit 7
Distinct consistency limit 7

618 equal divisions of the octave (abbreviated 618edo or 618ed2), also called 618-tone equal temperament (618tet) or 618 equal temperament (618et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 618 equal parts of about 1.94 ¢ each. Each step represents a frequency ratio of 21/618, or the 618th root of 2.

618edo is consistent to the 7-odd-limit, but harmonic 3 is about halfway between its steps. Nonetheless, as every other step of 1236edo, 618edo is excellent in approximating harmonics 5, 7, 9, 11, 13, and 17, making it suitable for a 2.9.5.7.11.13.17 subgroup interpretation, where the equal temperament notably tempers out 2601/2600, 4096/4095, 5832/5831, 6656/6655, 9801/9800, and 10648/10647. With a reasonable approximation of 19, it further tempers out 2926/2925, 5985/5984, and 6175/6174.

### Odd harmonics

Approximation of odd harmonics in 618edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +0.958 +0.094 +0.106 -0.027 +0.138 +0.249 -0.890 -0.101 -0.426 -0.878 +0.852
Relative (%) +49.3 +4.8 +5.5 -1.4 +7.1 +12.8 -45.8 -5.2 -21.9 -45.2 +43.9
Steps
(reduced)
980
(362)
1435
(199)
1735
(499)
1959
(105)
2138
(284)
2287
(433)
2414
(560)
2526
(54)
2625
(153)
2714
(242)
2796
(324)

### Subsets and supersets

Since 618 factors into 2 × 3 × 103, 618edo has subset edos 2, 3, 6, 103, 206, and 309. 1236edo, which doubles it, provides a good correction for harmonic 3.