1224edo

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← 1223edo

1224edo

1225edo →

Prime factorization	23 × 32 × 17
Step size	0.980392 ¢
Fifth	716\1224 (701.961 ¢) (→ 179\306)
Semitones (A1:m2)	116:92 (113.7 ¢ : 90.2 ¢)
Consistency limit	21
Distinct consistency limit	21

1224edo is enfactored in the 11-limit, with the same tuning as 612edo, but it corrects the harmonics 13 and 17 to work better with the other harmonics. It provides the optimal patent val for the 19-limit semihemiennealimmal temperament with fine tunes of 23, 29 and 31.

Prime harmonics

Approximation of prime harmonics in 1224edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.006	-0.039	-0.198	-0.338	-0.332	-0.053	-0.454	+0.157	-0.165	+0.062
	Relative (%)	+0.0	+0.6	-4.0	-20.2	-34.4	-33.8	-5.5	-46.3	+16.0	-16.9	+6.4
Steps (reduced)		1224 (0)	1940 (716)	2842 (394)	3436 (988)	4234 (562)	4529 (857)	5003 (107)	5199 (303)	5537 (641)	5946 (1050)	6064 (1168)

Subsets and supersets

Since 1224 factors into 2³ × 3² × 17, 1224edo has subset edos 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 68, 72, 102, 136, 153, 204, 306, 408, and 612.