8193edo
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Prime factorization
3 × 2731
Step size
0.146466¢
Fifth
4793\8193 (702.014¢)
Semitones (A1:m2)
779:614 (114.1¢ : 89.93¢)
Dual sharp fifth
4793\8193 (702.014¢)
Dual flat fifth
4792\8193 (701.867¢)
Dual major 2nd
1392\8193 (203.881¢) (→464\2731)
Consistency limit
7
Distinct consistency limit
7
| ← 8192edo | 8193edo | 8194edo → |
8193 equal divisions of the octave (abbreviated 8193edo or 8193ed2), also called 8193-tone equal temperament (8193tet) or 8193 equal temperament (8193et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 8193 equal parts of about 0.146 ¢ each. Each step represents a frequency ratio of 21/8193, or the 8193rd root of 2.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0589 | +0.0649 | +0.0500 | -0.0286 | -0.0181 | +0.0436 | -0.0227 | +0.0611 | -0.0396 | -0.0376 | +0.0669 |
| Relative (%) | +40.2 | +44.3 | +34.1 | -19.6 | -12.3 | +29.7 | -15.5 | +41.7 | -27.0 | -25.7 | +45.7 | |
| Steps (reduced) |
12986 (4793) |
19024 (2638) |
23001 (6615) |
25971 (1392) |
28343 (3764) |
30318 (5739) |
32009 (7430) |
33489 (717) |
34803 (2031) |
35986 (3214) |
37062 (4290) | |
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