424edo

← 423edo

424edo

425edo →

Prime factorization	23 × 53
Step size	2.83019 ¢
Fifth	248\424 (701.887 ¢) (→ 31\53)
Semitones (A1:m2)	40:32 (113.2 ¢ : 90.57 ¢)
Consistency limit	9
Distinct consistency limit	9

Theory

424et is consistent to the 9-odd-limit and the harmonic 5 is halfway between its steps. It tempers out 32805/32768 in the 5-limit; 184528125/184473632, 2460375/2458624, 1280000000/1275989841, 2401/2400 and 5250987/5242880 in the 7-limit, supporting enki.

Odd harmonics

Approximation of odd harmonics in 424edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.07	-1.41	-0.90	-0.14	+0.57	+0.04	+1.35	-0.24	-0.34	-0.97	+0.03
	Relative (%)	-2.4	-49.8	-31.8	-4.8	+20.1	+1.4	+47.8	-8.4	-12.1	-34.3	+1.0
Steps (reduced)		672 (248)	984 (136)	1190 (342)	1344 (72)	1467 (195)	1569 (297)	1657 (385)	1733 (37)	1801 (105)	1862 (166)	1918 (222)

Subsets and supersets

424 factors into 2³ × 53, with subset edos Template:2, 4, 8, 53, 106, and 212. 848edo, which doubles it, gives a good correction to the harmonic 11.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[-84 53⟩	[⟨424 672]]	0.0215	0.0215	0.76