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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
==Theory== | |||
== Theory == | |||
404edo is [[enfactoring|enfactored]] in the 11-limit, with the same tuning as [[202edo]]. The alternative 404e [[val]], with lower overall error, [[tempering out|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 === | |||
{{Harmonics in equal|404}} | {{Harmonics in equal|404}} | ||
==Regular temperament properties== | |||
=== Subsets and supersets === | |||
Since 404 factors into {{factorization|404}}, 404edo has subset edos {{EDOs| 2, 4, 101, and 202 }}. | |||
== Regular temperament properties == | |||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
|- | |- | ||
! rowspan="2" | [[Subgroup]] | |||
| | ! rowspan="2" | [[Comma list]] | ||
| | ! rowspan="2" | [[Mapping]] | ||
| | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
| | ! colspan="2" | Tuning error | ||
| | |||
|- | |- | ||
| | ! [[TE error|Absolute]] (¢) | ||
| | ! [[TE simple badness|Relative]] (%) | ||
|- | |- | ||
|2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
|441/440, | | 243/242, 441/440, 4000/3993, 4225/4224, 65625/65536 | ||
|{{ | | {{mapping| 404 640 938 1134 1398 1495 }} (404) | ||
| +0.0854 | | +0.0854 | ||
| 0.2821 | | 0.2821 | ||
| Line 51: | Line 31: | ||
|} | |} | ||
==Music== | == Trivia == | ||
* [https:// | A Scala file for this EDO is used as the 404 page of [[Sevish]]'s website. | ||
== Music == | |||
; [[User:Francium|Francium]] | |||
* [https://youtu.be/CDQMtcI542U?si=gvXoTa6CGuT36hCu ''Error 404: Tuning Not Found''] (2023) | |||
[[Category:Listen]] | [[Category:Listen]] | ||
Latest revision as of 13:21, 21 February 2025
| ← 403edo | 404edo | 405edo → |
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
| 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
- Error 404: Tuning Not Found (2023)