User:Overthink/3426edo

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← 3425edo 3426edo 3427edo →
Prime factorization 2 × 3 × 571
Step size 0.350263 ¢ 
Fifth 2004\3426 (701.926 ¢) (→ 334\571)
Semitones (A1:m2) 324:258 (113.5 ¢ : 90.37 ¢)
Consistency limit 15
Distinct consistency limit 15

3426 equal divisions of the octave (abbreviated 3426edo or 3426ed2), also called 3426-tone equal temperament (3426tet) or 3426 equal temperament (3426et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 3426 equal parts of about 0.35 ¢ each. Each step represents a frequency ratio of 21/3426, or the 3426th root of 2.

Theory

3426edo is consistent to the 15-odd-limit and is overall a strong 11- and 13-limit system.

Approximation of prime harmonics in 3426edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 -0.029 +0.026 +0.001 -0.004 +0.103 +0.123 -0.140 +0.097 -0.155 -0.027
Relative (%) +0.0 -8.2 +7.4 +0.2 -1.3 +29.4 +35.2 -40.0 +27.7 -44.3 -7.7
Steps
(reduced)
3426
(0)
5430
(2004)
7955
(1103)
9618
(2766)
11852
(1574)
12678
(2400)
14004
(300)
14553
(849)
15498
(1794)
16643
(2939)
16973
(3269)