1178edo

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← 1177edo

1178edo

1179edo →

Prime factorization	2 × 19 × 31
Step size	1.01868 ¢
Fifth	689\1178 (701.868 ¢)
Semitones (A1:m2)	111:89 (113.1 ¢ : 90.66 ¢)
Consistency limit	21
Distinct consistency limit	21

1178edo is a very strong 19-limit system, and is a zeta peak, integral and gap edo. It is also distinctly consistent through to the 21-odd-limit, and is the first edo past 742 with a lower 19-limit relative error. A basis for its 19-limit commas is 2500/2499, 3025/3024, 3250/3249, 4200/4199, 4375/4374, 4914/4913 and 5985/5984. It supports and provides a great tuning for semihemienneadecal.

Prime harmonics

Approximation of prime harmonics in 1178edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	-0.087	-0.236	-0.065	-0.214	-0.120	-0.032	-0.060	+0.249	+0.304	-0.044
	Relative (%)	+0.0	-8.6	-23.1	-6.4	-21.0	-11.8	-3.1	-5.9	+24.4	+29.8	-4.3
Steps (reduced)		1178 (0)	1867 (689)	2735 (379)	3307 (951)	4075 (541)	4359 (825)	4815 (103)	5004 (292)	5329 (617)	5723 (1011)	5836 (1124)

Subsets and supersets

Since 1178 = 2 × 19 × 31, 1178edo is notable for containing both 19 and 31. Its subset edos are 2, 19, 31, 38, 62, and 589.