8192edo

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← 8191edo8192edo8193edo →
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 (abbreviated 8192edo), or 8192-tone equal temperament (8192tet), 8192 equal temperament (8192et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 8192 equal parts of about 0.146 ¢ each. Each step of 8192edo represents a frequency ratio of 21/8192, or the 8192nd root of 2.

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.