178edo

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178edo

179edo →

Prime factorization	2 × 89
Step size	6.74157 ¢
Fifth	104\178 (701.124 ¢) (→ 52\89)
Semitones (A1:m2)	16:14 (107.9 ¢ : 94.38 ¢)
Consistency limit	5
Distinct consistency limit	5

178edo tempers out 15625/15555 (kleisma) and 571919811374025/562949953421312 in the 5-limit. Using the patent val, it tempers out 225/224, 4375/4374, and 40960000/40353607 in the 7-limit; 243/242, 3025/3024, 4375/4356, and 16896/16807 in the 11-limit; 640/637, 1188/1183, 1625/1617, 1716/1715, and 4096/4095 in the 13-limit. Using the 178def val, it tempers out 10976/10935, 33075/32768, and 50421/50000 in the 7-limit; 441/440, 3388/3375, 4125/4096, and 8019/8000 in the 11-limit; 325/324, 625/624, 847/845, 1287/1280, and 1573/1568 in the 13-limit.

Odd harmonics

Approximation of prime harmonics in 178edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	-0.83	-2.04	+1.96	+1.49	+2.17	+2.91	-0.88	-1.31	+1.88	+1.03
	Relative (%)	+0.0	-12.3	-30.3	+29.1	+22.1	+32.2	+43.2	-13.1	-19.4	+27.9	+15.3
Steps (reduced)		178 (0)	282 (104)	413 (57)	500 (144)	616 (82)	659 (125)	728 (16)	756 (44)	805 (93)	865 (153)	882 (170)