# 404edo

 ← 403edo 404edo 405edo →
Prime factorization 22 × 101
Step size 2.9703¢
Fifth 236\404 (700.99¢) (→59\101)
Semitones (A1:m2) 36:32 (106.9¢ : 95.05¢)
Consistency limit 7
Distinct consistency limit 7

404 equal divisions of the octave (abbreviated 404edo or 404ed2), also called 404-tone equal temperament (404tet) or 404 equal temperament (404et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 404 equal parts of about 2.97 ¢ each. Each step represents a frequency ratio of 21/404, or the 404th root of 2.

## Theory

404edo is enfactored in the 11-limit, with the same tuning as 202edo. The alternative 404e val, with lower overall error, tempers out 3025/3024 and 41503/41472 in the 11-limit; and 847/845, 1001/1000, and 1716/1715 in the 13-limit, whereas the patent val in the 13-limit tempers out 4225/4224.

### Odd harmonics

Approximation of odd harmonics in 404edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -0.96 -0.18 -0.51 +1.04 +1.16 +0.07 -1.14 -1.00 -0.48 -1.47 +1.43
Relative (%) -32.5 -5.9 -17.1 +35.0 +39.0 +2.2 -38.4 -33.5 -16.3 -49.6 +48.1
Steps
(reduced)
640
(236)
938
(130)
1134
(326)
1281
(69)
1398
(186)
1495
(283)
1578
(366)
1651
(35)
1716
(100)
1774
(158)
1828
(212)

### Subsets and supersets

Since 404 factors into 22 × 101, 404edo has subset edos 2, 4, 101, and 202.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3.5.7.11.13 243/242, 441/440, 4000/3993, 4225/4224, 65625/65536 [404 ​640​ 938​ 1134 ​1398 ​1495]] (404) +0.0854 0.2821 9.50

## Trivia

A Scala file for this EDO is used as the 404 page of Sevish's website.

Francium