186ed6

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← 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 harmonics in 186ed6

Harmonic		2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18
Error	Absolute (¢)	+0.76	-0.76	+1.51	-1.23	+0.00	-0.04	+2.27	-1.51	-0.47	+1.30	+0.76	-4.40	+0.72	-1.98	+3.03	-1.87	-0.76
	Relative (%)	+4.5	-4.5	+9.1	-7.3	+0.0	-0.2	+13.6	-9.1	-2.8	+7.8	+4.5	-26.4	+4.3	-11.9	+18.2	-11.2	-4.5
Steps (reduced)		72 (72)	114 (114)	144 (144)	167 (167)	186 (0)	202 (16)	216 (30)	228 (42)	239 (53)	249 (63)	258 (72)	266 (80)	274 (88)	281 (95)	288 (102)	294 (108)	300 (114)

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	16.68
2	33.35	51/50, 52/51
3	50.03	35/34
4	66.71	26/25
5	83.39	21/20
6	100.06	18/17
7	116.74	46/43
8	133.42	27/25
9	150.09	12/11
10	166.77
11	183.45	10/9
12	200.13	55/49, 64/57
13	216.8	17/15
14	233.48
15	250.16	37/32, 52/45
16	266.83	7/6
17	283.51	33/28
18	300.19	44/37
19	316.87
20	333.54	40/33, 57/47
21	350.22	49/40, 60/49
22	366.9	21/17, 47/38
23	383.58
24	400.25	34/27, 63/50
25	416.93	14/11
26	433.61
27	450.28	35/27, 48/37
28	466.96	38/29, 55/42
29	483.64	37/28
30	500.32
31	516.99	31/23
32	533.67	49/36, 64/47
33	550.35	11/8
34	567.02	43/31
35	583.7	7/5
36	600.38	41/29, 58/41
37	617.06	10/7
38	633.73	49/34, 62/43
39	650.41
40	667.09	25/17
41	683.76	46/31, 49/33
42	700.44
43	717.12	56/37
44	733.8	55/36
45	750.47	37/24, 54/35
46	767.15
47	783.83
48	800.5	27/17
49	817.18
50	833.86	34/21, 55/34
51	850.54	49/30
52	867.21	33/20
53	883.89	5/3
54	900.57	37/22
55	917.24
56	933.92	12/7
57	950.6	45/26
58	967.28
59	983.95	30/17
60	1000.63	57/32
61	1017.31	9/5
62	1033.99	20/11
63	1050.66
64	1067.34	50/27, 63/34
65	1084.02	43/23
66	1100.69	17/9
67	1117.37
68	1134.05	52/27
69	1150.73	35/18
70	1167.4	51/26
71	1184.08
72	1200.76	2/1
73	1217.43
74	1234.11	51/25
75	1250.79	35/17
76	1267.47	52/25
77	1284.14	21/10
78	1300.82
79	1317.5
80	1334.17	54/25
81	1350.85	24/11
82	1367.53
83	1384.21
84	1400.88
85	1417.56	34/15
86	1434.24
87	1450.91	37/16
88	1467.59	7/3
89	1484.27	33/14
90	1500.95	50/21
91	1517.62
92	1534.3
93	1550.98	49/20
94	1567.65	47/19
95	1584.33
96	1601.01	63/25
97	1617.69	28/11
98	1634.36	18/7
99	1651.04
100	1667.72	55/21
101	1684.39	45/17
102	1701.07
103	1717.75	62/23
104	1734.43	49/18
105	1751.1	11/4
106	1767.78	25/9
107	1784.46
108	1801.14
109	1817.81	20/7
110	1834.49
111	1851.17
112	1867.84	50/17
113	1884.52
114	1901.2	3/1
115	1917.88
116	1934.55	52/17, 55/18
117	1951.23
118	1967.91
119	1984.58
120	2001.26	54/17
121	2017.94
122	2034.62
123	2051.29
124	2067.97	33/10
125	2084.65	10/3
126	2101.32	64/19
127	2118	17/5
128	2134.68
129	2151.36	52/15
130	2168.03	7/2
131	2184.71
132	2201.39
133	2218.06	18/5
134	2234.74	40/11
135	2251.42
136	2268.1	63/17
137	2284.77
138	2301.45	34/9
139	2318.13
140	2334.8
141	2351.48	35/9
142	2368.16	55/14
143	2384.84
144	2401.51
145	2418.19
146	2434.87	49/12
147	2451.55
148	2468.22
149	2484.9	21/5
150	2501.58
151	2518.25	30/7
152	2534.93
153	2551.61	48/11
154	2568.29
155	2584.96
156	2601.64
157	2618.32
158	2634.99	55/12
159	2651.67	37/8
160	2668.35
161	2685.03	33/7
162	2701.7
163	2718.38
164	2735.06	34/7
165	2751.73	49/10
166	2768.41
167	2785.09
168	2801.77
169	2818.44	56/11
170	2835.12	36/7
171	2851.8
172	2868.47
173	2885.15
174	2901.83
175	2918.51	27/5
176	2935.18
177	2951.86	11/2
178	2968.54	50/9
179	2985.21
180	3001.89	17/3
181	3018.57	40/7
182	3035.25
183	3051.92
184	3068.6
185	3085.28
186	3101.96	6/1