# 426edo

 ← 425edo 426edo 427edo →
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 426ed2), also called 426-tone equal temperament (426tet) or 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 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 (%) +0.0 -19.4 -14.1 +6.7 +28.2 -38.7 -25.9 +38.3 -3.7 -50.0 -48.8
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