6650edo
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Prime factorization
2 × 52 × 7 × 19
Step size
0.180451¢
Fifth
3890\6650 (701.955¢) (→389\665)
Semitones (A1:m2)
630:500 (113.7¢ : 90.23¢)
Consistency limit
15
Distinct consistency limit
15
| ← 6649edo | 6650edo | 6651edo → |
6650 equal divisions of the octave (abbreviated 6650edo or 6650ed2), also called 6650-tone equal temperament (6650tet) or 6650 equal temperament (6650et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 6650 equal parts of about 0.18 ¢ each. Each step represents a frequency ratio of 21/6650, or the 6650th root of 2.
This system is consistent up to the 15-odd-limit and shares the same super accurate fifth with 665edo. In the 11-limit, it tempers out 9801/9800, and in the 13-limit, 123201/123200.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | -0.0001 | +0.0322 | +0.0162 | -0.0397 | +0.0137 | +0.0671 | +0.0509 | +0.0565 | +0.0769 | -0.0732 |
| Relative (%) | +0.0 | -0.1 | +17.8 | +9.0 | -22.0 | +7.6 | +37.2 | +28.2 | +31.3 | +42.6 | -40.5 | |
| Steps (reduced) |
6650 (0) |
10540 (3890) |
15441 (2141) |
18669 (5369) |
23005 (3055) |
24608 (4658) |
27182 (582) |
28249 (1649) |
30082 (3482) |
32306 (5706) |
32945 (6345) | |
Subsets and supersets
Since 6650 factors into 2 × 52 × 7 × 19, 6650edo has subset edos 2, 5, 7, 10, 14, 19, 25, 35, 38, 50, 70, 95, 133, 175, 190, 266, 350, 475, 665, 950, 1330, and 3325.