404edo

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← 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

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.

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)

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