618edo

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← 617edo618edo619edo →
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.