8192edo
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Prime factorization
213
Step size
0.146484¢
Fifth
4792\8192 (701.953¢) (→599\1024)
Semitones (A1:m2)
776:616 (113.7¢ : 90.23¢)
Consistency limit
9
Distinct consistency limit
9
| ← 8191edo | 8192edo | 8193edo → |
8192 equal divisions of the octave (abbreviated 8192edo or 8192ed2), also called 8192-tone equal temperament (8192tet) or 8192 equal temperament (8192et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 8192 equal parts of about 0.146 ¢ each. Each step represents a frequency ratio of 21/8192, or the 8192nd root of 2.
Theory
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | -0.0019 | -0.0344 | +0.0217 | +0.0492 | -0.0003 | -0.0726 | -0.0033 | -0.0029 | +0.0615 | +0.0328 |
| Relative (%) | +0.0 | -1.3 | -23.5 | +14.8 | +33.6 | -0.2 | -49.6 | -2.2 | -2.0 | +42.0 | +22.4 | |
| Steps (reduced) |
8192 (0) |
12984 (4792) |
19021 (2637) |
22998 (6614) |
28340 (3764) |
30314 (5738) |
33484 (716) |
34799 (2031) |
37057 (4289) |
39797 (7029) |
40585 (7817) | |
This is the 13th power of two EDO, but with a consistency limit of only 9, it's not as impressive as the one before it, though to be fair, its representations of harmonics 3, 13, 19, and 23 are very good.