426edo

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← 425edo426edo427edo →
Prime factorization 2 × 3 × 71
Step size 2.8169¢
Fifth 249\426 (701.408¢) (→83\142)
Semitones (A1:m2) 39:33 (109.9¢ : 92.96¢)
Consistency limit 9
Distinct consistency limit 9

426 equal divisions of the octave (abbreviated 426edo), or 426-tone equal temperament (426tet), 426 equal temperament (426et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 426 equal parts of about 2.82 ¢ each. Each step of 426edo represents a frequency ratio of 21/426, or the 426th root of 2.

Theory

426edo is consistent to the 9-odd-limit. Using the patent val, the equal temperament tempers out 65625/65536, 118098/117649, 250047/250000 in the 7-limit; 540/539, 4000/3993, 9801/9800, 24057/24010, 137781/137500, and 151263/151250 in the 11-limit. It supports the 5-limit version of untriton.

Prime harmonics

Approximation of prime harmonics in 426edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error absolute (¢) +0.00 -0.55 -0.40 +0.19 +0.79 -1.09 -0.73 +1.08 -0.11 -1.41 -1.37
relative (%) +0 -19 -14 +7 +28 -39 -26 +38 -4 -50 -49
Steps
(reduced)
426
(0)
675
(249)
989
(137)
1196
(344)
1474
(196)
1576
(298)
1741
(37)
1810
(106)
1927
(223)
2069
(365)
2110
(406)

Subsets and supersets

Since 426 factors into 2 × 3 × 71, 426edo has subset edos 2, 3, 6, 71, 142, and 213.

Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [-225 142 [426 675]] +0.1724 0.1724 6.12
2.3.5 [-7 22 -12, [-44 -3 21 [426 675 989]] +0.1721 0.1408 5.00
2.3.5.7 65625/65536, 118098/117649, 250047/250000 [426 675 989 1196]] +0.1123 0.1600 5.68

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 199\426 560.56 864/625 Whoosh
1 209\426 588.73 45/32 Untriton (5-limit)
3 137\426
(5\426)
385.92
(14.08)
5/4
(126/125)
Mutt (7-limit)

* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct