3178edo

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3178edo

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Prime factorization	2 × 7 × 227
Step size	0.377596 ¢
Fifth	1859\3178 (701.951 ¢)
Semitones (A1:m2)	301:239 (113.7 ¢ : 90.25 ¢)
Consistency limit	27
Distinct consistency limit	27

3178edo is quite accurate in the 23-limit, consistent to the 27-odd-limit, and has an exceptional approximation of harmonic 13. However, like most edos of this size, it is rather impractical to use. It tempers out several of the smaller 23-limit superparticular commas, including 9801/9800 in the 11-limit; 10648/10647 and 123201/123200 in the 13-limit; 5832/5831, 14400/14399, and 28561/28560 in the 17-limit; 6175/6174, 10830/10829, 12636/12635, 14080/14079, 14365/14364, 23409/23408, 28900/28899, and 43681/43680 in the 19-limit; 8625/8624, 11271/11270, 12168/12167 and 43264/43263 in the 23-limit.

Prime harmonics

Approximation of prime harmonics in 3178edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	-0.004	-0.033	+0.085	-0.028	+0.001	+0.016	+0.033	+0.045	+0.127	-0.165
	Relative (%)	+0.0	-1.1	-8.7	+22.6	-7.4	+0.3	+4.3	+8.6	+12.0	+33.6	-43.6
Steps (reduced)		3178 (0)	5037 (1859)	7379 (1023)	8922 (2566)	10994 (1460)	11760 (2226)	12990 (278)	13500 (788)	14376 (1664)	15439 (2727)	15744 (3032)