186ed6

← 185ed6

186ed6

187ed6 →

Prime factorization	2 × 3 × 31
Step size	16.6772 ¢
Octave	72\186ed6 (1200.76 ¢) (→ 12\31ed6)
Twelfth	114\186ed6 (1901.2 ¢) (→ 19\31ed6)
Consistency limit	18
Distinct consistency limit	13

Division of the sixth harmonic into 186 equal parts (186ED6) is related to 72 edo, but with the 6/1 rather than the 2/1 being just. The octave is about 1.2347 cents stretched and the step size is about 16.6838 cents. It is consistent to the 18-integer-limit, and significantly improves on 72edo's approximation to 13.

Lookalikes: 72edo, 114edt

Harmonics

Approximation of prime harmonics in 186ed6

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.76	-0.76	-1.23	-0.04	+1.30	-4.40	-1.87	+5.70	-8.19	+7.43	-7.96
	Relative (%)	+4.5	-4.5	-7.3	-0.2	+7.8	-26.4	-11.2	+34.2	-49.1	+44.6	-47.7
Steps (reduced)		72 (72)	114 (114)	167 (167)	202 (16)	249 (63)	266 (80)	294 (108)	306 (120)	325 (139)	350 (164)	356 (170)

Approximation of prime harmonics in 186ed6

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+2.60	+8.33	-7.42	+5.36	-2.51	-4.73	+4.27	-8.06	+8.29	-6.45	+6.90
	Relative (%)	+15.6	+49.9	-44.5	+32.2	-15.0	-28.3	+25.6	-48.3	+49.7	-38.6	+41.4
Steps (reduced)		375 (3)	386 (14)	390 (18)	400 (28)	412 (40)	423 (51)	427 (55)	436 (64)	443 (71)	445 (73)	454 (82)

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