812edo

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← 811edo812edo813edo →
Prime factorization 22 × 7 × 29
Step size 1.47783¢
Fifth 475\812 (701.97¢)
Semitones (A1:m2) 77:61 (113.8¢ : 90.15¢)
Consistency limit 5
Distinct consistency limit 5

812 equal divisions of the octave (abbreviated 812edo), or 812-tone equal temperament (812tet), 812 equal temperament (812et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 812 equal parts of about 1.48 ¢ each. Each step of 812edo represents a frequency ratio of 21/812, or the 812th root of 2.

812edo is a tuning for the copper temperament in the 5-limit, although it has a high error on the 5th harmonic. It is much better considered as a 2.3.11.17 subgroup tuning, where it is strong, with errors of 6% or less.


Approximation of prime harmonics in 812edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error absolute (¢) +0.000 +0.015 -0.599 +0.632 -0.086 +0.359 -0.029 -0.469 -0.196 +0.472 +0.285
relative (%) +0 +1 -41 +43 -6 +24 -2 -32 -13 +32 +19
Steps
(reduced)
812
(0)
1287
(475)
1885
(261)
2280
(656)
2809
(373)
3005
(569)
3319
(71)
3449
(201)
3673
(425)
3945
(697)
4023
(775)