404edo: Difference between revisions

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== Trivia ==
A Scala file for this EDO is used as the 404 page of [[Sevish]]'s website.
== Music ==
== Music ==
; [[User:Francium|Francium]]
; [[User:Francium|Francium]]

Revision as of 07:34, 12 February 2024

← 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

Template:EDO intro

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.

Music

Francium