1024edo
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Prime factorization
210
Step size
1.17188¢
Fifth
599\1024 (701.953¢)
Semitones (A1:m2)
97:77 (113.7¢ : 90.23¢)
Consistency limit
9
Distinct consistency limit
9
| ← 1023edo | 1024edo | 1025edo → |
1024 equal divisions of the octave (abbreviated 1024edo or 1024ed2), also called 1024-tone equal temperament (1024tet) or 1024 equal temperament (1024et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1024 equal parts of about 1.172 ¢ each. Each step represents a frequency ratio of 21/1024, or the 1024th root of 2.
Theory
1024edo has a near-perfect 3/2, and, as the 10th power of two EDO, offers some much-needed correction for the flaws of 512edo.
It is consistent in the 9-odd-limit. It is great for the 2.3.5.7.13.19.23 subgroup.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.000 | -0.002 | +0.405 | +0.315 | -0.537 | -0.293 | +0.513 | +0.143 | -0.149 | +0.501 | -0.114 |
| relative (%) | +0 | -0 | +35 | +27 | -46 | -25 | +44 | +12 | -13 | +43 | -10 | |
| Steps (reduced) |
1024 (0) |
1623 (599) |
2378 (330) |
2875 (827) |
3542 (470) |
3789 (717) |
4186 (90) |
4350 (254) |
4632 (536) |
4975 (879) |
5073 (977) | |