# 8192edo

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 ← 8191edo 8192edo 8193edo →
Prime factorization 213
Step size 0.146484¢
Fifth 4792\8192 (701.953¢) (→599\1024)
Semitones (A1:m2) 776:616 (113.7¢ : 90.23¢)
Consistency limit 9
Distinct consistency limit 9

8192 equal divisions of the octave (8192edo), or 8192-tone equal temperament (8192tet), 8192 equal temperament (8192et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 8192 equal parts of about 0.146 ¢ each.

## Theory

Approximation of prime harmonics in 8192edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error absolute (¢) +0.0000 -0.0019 -0.0344 +0.0217 +0.0492 -0.0003 -0.0726 -0.0033 -0.0029 +0.0615 +0.0328
relative (%) +0 -1 -23 +15 +34 -0 -50 -2 -2 +42 +22
Steps
(reduced)
8192
(0)
12984
(4792)
19021
(2637)
22998
(6614)
28340
(3764)
30314
(5738)
33484
(716)
34799
(2031)
37057
(4289)
39797
(7029)
40585
(7817)

This is the 13th power of two EDO, but with a consistency limit of only 9, it's not as impressive as the one before it, though to be fair, it's representations of the 19-prime and the 23-prime are pretty good.