618edo
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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
| ← 617edo | 618edo | 619edo → |
618 equal divisions of the octave (618edo), or 618-tone equal temperament (618tet), 618 equal temperament (618et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 618 equal parts of about 1.94 ¢ each.
Theory
As every other step of 1236edo, 618edo is excellent in the 2.9.5.7.11.13.17 subgroup, where it 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
| 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 | +5 | +5 | -1 | +7 | +13 | -46 | -5 | -22 | -45 | +44 | |
| Steps (reduced) |
980 (362) |
1435 (199) |
1735 (499) |
1959 (105) |
2138 (284) |
2287 (433) |
2414 (560) |
2526 (54) |
2625 (153) |
2714 (242) |
2796 (324) | |