404edo
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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
| ← 403edo | 404edo | 405edo → |
404 equal divisions of the octave (404edo), or 404-tone equal temperament (404tet), 404 equal temperament (404et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 404 equal parts of about 2.97 ¢ each.
Theory
404et tempers out 703125/702464, 1959552/1953125, 65625/65536, 2401/2400, 2100875/2097152 and 201768035/201326592 in the 7-limit and 4000/3993, 540/539, 441/440, 8019/8000, 9801/9800 and 160083/160000 in the 11-limit.
| 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 | -6 | -17 | +35 | +39 | +2 | -38 | -33 | -16 | -50 | +48 | |
| Steps (reduced) |
640 (236) |
938 (130) |
1134 (326) |
1281 (69) |
1398 (186) |
1495 (283) |
1578 (366) |
1651 (35) |
1716 (100) |
1774 (158) |
1828 (212) | |
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-160 101⟩ | ⟨404 640] | +0.3044 | 0.3045 | 10.25 |
| 2.3.5 | [-13 17 -6⟩, [23 6 -14⟩ | ⟨404 640 938] | +0.2280 | 0.2710 | 9.12 |
| 2.3.5.7 | 2401/2400, 19683/19600, 65625/65536 | ⟨404 640 938 1134] | +0.2164 | 0.2356 | 7.93 |
| 2.3.5.7.11 | 441/440, 540/539, 8019/8000, 65625/65536 | ⟨404 640 938 1134 1398] | +0.1061 | 0.3049 | 10.26 |
| 2.3.5.7.11.13 | 441/440, 540/539, 8019/8000, 4225/4224, 86625/86528 | ⟨404 640 938 1134 1398 1495] | +0.0854 | 0.2821 | 9.50 |
Music
- Error 404: Tuning Not Found by Francium