512edo
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Prime factorization
29
Step size
2.34375¢
Fifth
300\512 (703.125¢) (→75\128)
Semitones (A1:m2)
52:36 (121.9¢ : 84.38¢)
Dual sharp fifth
300\512 (703.125¢) (→75\128)
Dual flat fifth
299\512 (700.781¢)
Dual major 2nd
87\512 (203.906¢)
(semiconvergent)
Consistency limit
5
Distinct consistency limit
5
| ← 511edo | 512edo | 513edo → |
(semiconvergent)
512 equal divisions of the octave (abbreviated 512edo or 512ed2), also called 512-tone equal temperament (512tet) or 512 equal temperament (512et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 512 equal parts of about 2.34 ¢ each. Each step represents a frequency ratio of 21/512, or the 512th root of 2.
With only a consistency limit of 5, this 9th-power-of-two edo does not have a whole lot to offer in terms of lower harmonics. Harmonic 3 is about halfway between its steps, making it suitable for a 2.9.5.21.17.19.23 subgroup interpretation, with optional addition of either 11 or 13.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.17 | +0.41 | -0.86 | -0.00 | -0.54 | +0.88 | -0.77 | +0.51 | +0.14 | +0.31 | -0.15 |
| Relative (%) | +49.9 | +17.3 | -36.6 | -0.2 | -22.9 | +37.5 | -32.8 | +21.9 | +6.1 | +13.3 | -6.4 | |
| Steps (reduced) |
812 (300) |
1189 (165) |
1437 (413) |
1623 (87) |
1771 (235) |
1895 (359) |
2000 (464) |
2093 (45) |
2175 (127) |
2249 (201) |
2316 (268) | |
Subsets and supersets
Since 512edo factors into 29, 512edo has subset edos 2, 4, 8, 16, 32, 64, 128, and 256.