512edo

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← 511edo512edo513edo →
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 2.344 ¢ 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 (%) +50 +17 -37 -0 -23 +37 -33 +22 +6 +13 -6
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.