# 512edo

 ← 511edo 512edo 513edo →
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

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

Approximation of odd harmonics in 512edo
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.