185edt

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185edt

186edt →

Prime factorization	5 × 37
Step size	10.2808 ¢
Octave	117\185edt (1202.86 ¢)
Consistency limit	3
Distinct consistency limit	3

185 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 185edt or 185ed3), is a nonoctave tuning system that divides the interval of 3/1 into 185 equal parts of about 10.3 ¢ each. Each step represents a frequency ratio of 3^1/185, or the 185th root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	10.28	7.03
2	20.56	14.05
3	30.84	21.08	55/54, 58/57
4	41.12	28.11
5	51.4	35.14	34/33
6	61.69	42.16	57/55
7	71.97	49.19
8	82.25	56.22	43/41, 65/62
9	92.53	63.24	19/18, 58/55
10	102.81	70.27	35/33, 52/49
11	113.09	77.3
12	123.37	84.32	29/27
13	133.65	91.35	27/25
14	143.93	98.38	25/23, 63/58
15	154.21	105.41	47/43
16	164.49	112.43	11/10
17	174.77	119.46
18	185.06	126.49
19	195.34	133.51
20	205.62	140.54
21	215.9	147.57	17/15
22	226.18	154.59	57/50, 65/57
23	236.46	161.62	39/34, 47/41
24	246.74	168.65	15/13
25	257.02	175.68	29/25
26	267.3	182.7	7/6
27	277.58	189.73	27/23
28	287.86	196.76
29	298.14	203.78
30	308.43	210.81	55/46
31	318.71	217.84
32	328.99	224.86
33	339.27	231.89	45/37, 62/51
34	349.55	238.92	60/49
35	359.83	245.95
36	370.11	252.97	26/21, 57/46
37	380.39	260
38	390.67	267.03
39	400.95	274.05	29/23, 63/50
40	411.23	281.08
41	421.51	288.11	37/29
42	431.8	295.14
43	442.08	302.16
44	452.36	309.19
45	462.64	316.22
46	472.92	323.24	46/35
47	483.2	330.27	41/31
48	493.48	337.3
49	503.76	344.32
50	514.04	351.35	35/26, 39/29
51	524.32	358.38	23/17
52	534.6	365.41	49/36
53	544.88	372.43	37/27, 63/46
54	555.17	379.46	51/37, 62/45
55	565.45	386.49	43/31
56	575.73	393.51	46/33
57	586.01	400.54
58	596.29	407.57	55/39
59	606.57	414.59
60	616.85	421.62	10/7
61	627.13	428.65
62	637.41	435.68	13/9
63	647.69	442.7
64	657.97	449.73	19/13
65	668.25	456.76	25/17
66	678.54	463.78	37/25
67	688.82	470.81
68	699.1	477.84
69	709.38	484.86
70	719.66	491.89	47/31, 50/33
71	729.94	498.92
72	740.22	505.95	23/15
73	750.5	512.97	54/35
74	760.78	520	45/29
75	771.06	527.03	39/25
76	781.34	534.05	11/7
77	791.62	541.08	30/19
78	801.91	548.11	27/17, 62/39
79	812.19	555.14
80	822.47	562.16	37/23
81	832.75	569.19	55/34
82	843.03	576.22
83	853.31	583.24	18/11
84	863.59	590.27
85	873.87	597.3	58/35
86	884.15	604.32	5/3
87	894.43	611.35	57/34, 62/37
88	904.71	618.38
89	914.99	625.41	39/23
90	925.28	632.43	29/17
91	935.56	639.46
92	945.84	646.49	19/11
93	956.12	653.51	33/19
94	966.4	660.54
95	976.68	667.57	51/29, 58/33, 65/37
96	986.96	674.59	23/13
97	997.24	681.62
98	1007.52	688.65	34/19
99	1017.8	695.68	9/5
100	1028.08	702.7
101	1038.36	709.73
102	1048.65	716.76	11/6
103	1058.93	723.78
104	1069.21	730.81
105	1079.49	737.84
106	1089.77	744.86
107	1100.05	751.89	17/9
108	1110.33	758.92	19/10
109	1120.61	765.95	21/11
110	1130.89	772.97	25/13
111	1141.17	780	29/15
112	1151.45	787.03	35/18
113	1161.73	794.05	45/23
114	1172.02	801.08
115	1182.3	808.11
116	1192.58	815.14
117	1202.86	822.16
118	1213.14	829.19
119	1223.42	836.22
120	1233.7	843.24	51/25
121	1243.98	850.27	39/19
122	1254.26	857.3
123	1264.54	864.32	27/13
124	1274.82	871.35
125	1285.1	878.38	21/10
126	1295.39	885.41
127	1305.67	892.43
128	1315.95	899.46	62/29
129	1326.23	906.49
130	1336.51	913.51
131	1346.79	920.54	37/17
132	1357.07	927.57	46/21
133	1367.35	934.59
134	1377.63	941.62	51/23
135	1387.91	948.65	29/13
136	1398.19	955.68	65/29
137	1408.47	962.7
138	1418.76	969.73
139	1429.04	976.76
140	1439.32	983.78	62/27
141	1449.6	990.81
142	1459.88	997.84
143	1470.16	1004.86
144	1480.44	1011.89
145	1490.72	1018.92
146	1501	1025.95	50/21
147	1511.28	1032.97
148	1521.56	1040	65/27
149	1531.84	1047.03	46/19, 63/26
150	1542.13	1054.05
151	1552.41	1061.08	49/20
152	1562.69	1068.11	37/15
153	1572.97	1075.14	62/25
154	1583.25	1082.16
155	1593.53	1089.19
156	1603.81	1096.22
157	1614.09	1103.24
158	1624.37	1110.27	23/9
159	1634.65	1117.3	18/7
160	1644.93	1124.32
161	1655.21	1131.35	13/5
162	1665.5	1138.38	34/13
163	1675.78	1145.41	50/19
164	1686.06	1152.43	45/17
165	1696.34	1159.46
166	1706.62	1166.49
167	1716.9	1173.51	62/23
168	1727.18	1180.54
169	1737.46	1187.57	30/11
170	1747.74	1194.59
171	1758.02	1201.62	58/21
172	1768.3	1208.65	25/9
173	1778.58	1215.68
174	1788.87	1222.7
175	1799.15	1229.73	65/23
176	1809.43	1236.76	54/19
177	1819.71	1243.78
178	1829.99	1250.81
179	1840.27	1257.84	55/19
180	1850.55	1264.86
181	1860.83	1271.89
182	1871.11	1278.92
183	1881.39	1285.95
184	1891.67	1292.97
185	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 185edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+2.86	+0.00	-4.56	-0.21	+2.86	+3.29	-1.71	+0.00	+2.65	+2.14	-4.56
	Relative (%)	+27.8	+0.0	-44.4	-2.0	+27.8	+32.0	-16.6	+0.0	+25.8	+20.8	-44.4
Steps (reduced)		117 (117)	185 (0)	233 (48)	271 (86)	302 (117)	328 (143)	350 (165)	370 (0)	388 (18)	404 (34)	418 (48)

Approximation of harmonics in 185edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+0.79	-4.13	-0.21	+1.15	-1.00	+2.86	+1.78	-4.77	+3.29	+5.00	+0.01
	Relative (%)	+7.7	-40.2	-2.0	+11.2	-9.7	+27.8	+17.3	-46.4	+32.0	+48.6	+0.1
Steps (reduced)		432 (62)	444 (74)	456 (86)	467 (97)	477 (107)	487 (117)	496 (126)	504 (134)	513 (143)	521 (151)	528 (158)