167edt

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167 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 167edt or 167ed3), is a nonoctave tuning system that divides the interval of 3/1 into 167 equal parts of about 11.4 ¢ each. Each step represents a frequency ratio of 3^1/167, or the 167th root of 3.

← 166edt

167edt

168edt →

Prime factorization	167 (prime)
Step size	11.389 ¢
Octave	105\167edt (1195.84 ¢)
Consistency limit	3
Distinct consistency limit	3

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	11.39	7.78
2	22.78	15.57
3	34.17	23.35	50/49, 51/50
4	45.56	31.14	38/37, 39/38
5	56.94	38.92	31/30
6	68.33	46.71	51/49
7	79.72	54.49	22/21, 45/43
8	91.11	62.28	39/37
9	102.5	70.06	35/33
10	113.89	77.84	47/44
11	125.28	85.63
12	136.67	93.41
13	148.06	101.2	49/45
14	159.45	108.98	34/31
15	170.83	116.77
16	182.22	124.55	10/9
17	193.61	132.34	19/17, 47/42
18	205	140.12
19	216.39	147.9	17/15
20	227.78	155.69	57/50
21	239.17	163.47	31/27, 54/47
22	250.56	171.26
23	261.95	179.04	50/43, 57/49
24	273.33	186.83
25	284.72	194.61	46/39
26	296.11	202.4	51/43
27	307.5	210.18	37/31
28	318.89	217.96
29	330.28	225.75	23/19
30	341.67	233.53
31	353.06	241.32	38/31
32	364.45	249.1	58/47
33	375.84	256.89	46/37
34	387.22	264.67
35	398.61	272.46	34/27, 39/31
36	410	280.24	19/15
37	421.39	288.02	37/29
38	432.78	295.81
39	444.17	303.59
40	455.56	311.38	13/10
41	466.95	319.16	38/29
42	478.34	326.95	29/22
43	489.72	334.73
44	501.11	342.51
45	512.5	350.3	39/29
46	523.89	358.08	23/17
47	535.28	365.87
48	546.67	373.65	37/27
49	558.06	381.44	29/21
50	569.45	389.22
51	580.84	397.01
52	592.23	404.79	38/27
53	603.61	412.57
54	615	420.36
55	626.39	428.14
56	637.78	435.93	13/9
57	649.17	443.71
58	660.56	451.5	41/28, 60/41
59	671.95	459.28
60	683.34	467.07	46/31, 49/33
61	694.73	474.85
62	706.12	482.63
63	717.5	490.42
64	728.89	498.2
65	740.28	505.99	23/15
66	751.67	513.77
67	763.06	521.56
68	774.45	529.34
69	785.84	537.13
70	797.23	544.91
71	808.62	552.69
72	820	560.48
73	831.39	568.26	21/13
74	842.78	576.05
75	854.17	583.83
76	865.56	591.62
77	876.95	599.4
78	888.34	607.19
79	899.73	614.97	37/22
80	911.12	622.75	22/13
81	922.51	630.54	46/27
82	933.89	638.32
83	945.28	646.11	19/11
84	956.67	653.89	33/19
85	968.06	661.68
86	979.45	669.46	37/21
87	990.84	677.25	39/22
88	1002.23	685.03
89	1013.62	692.81
90	1025.01	700.6	47/26
91	1036.39	708.38
92	1047.78	716.17
93	1059.17	723.95
94	1070.56	731.74	13/7
95	1081.95	739.52	43/23
96	1093.34	747.31
97	1104.73	755.09
98	1116.12	762.87
99	1127.51	770.66
100	1138.9	778.44
101	1150.28	786.23
102	1161.67	794.01	45/23
103	1173.06	801.8
104	1184.45	809.58
105	1195.84	817.37
106	1207.23	825.15
107	1218.62	832.93
108	1230.01	840.72
109	1241.4	848.5	41/20, 43/21
110	1252.78	856.29
111	1264.17	864.07	27/13
112	1275.56	871.86
113	1286.95	879.64
114	1298.34	887.43
115	1309.73	895.21	49/23
116	1321.12	902.99
117	1332.51	910.78
118	1343.9	918.56	50/23
119	1355.29	926.35
120	1366.67	934.13
121	1378.06	941.92	51/23
122	1389.45	949.7	29/13
123	1400.84	957.49
124	1412.23	965.27
125	1423.62	973.05
126	1435.01	980.84
127	1446.4	988.62	30/13
128	1457.79	996.41
129	1469.17	1004.19
130	1480.56	1011.98
131	1491.95	1019.76	45/19
132	1503.34	1027.54	31/13
133	1514.73	1035.33
134	1526.12	1043.11
135	1537.51	1050.9
136	1548.9	1058.68
137	1560.29	1066.47
138	1571.68	1074.25	57/23
139	1583.06	1082.04
140	1594.45	1089.82
141	1605.84	1097.6	43/17
142	1617.23	1105.39
143	1628.62	1113.17
144	1640.01	1120.96	49/19
145	1651.4	1128.74
146	1662.79	1136.53	47/18
147	1674.18	1144.31	50/19
148	1685.56	1152.1	45/17
149	1696.95	1159.88
150	1708.34	1167.66	51/19
151	1719.73	1175.45	27/10
152	1731.12	1183.23
153	1742.51	1191.02
154	1753.9	1198.8
155	1765.29	1206.59
156	1776.68	1214.37
157	1788.07	1222.16
158	1799.45	1229.94
159	1810.84	1237.72	37/13
160	1822.23	1245.51	43/15
161	1833.62	1253.29	49/17
162	1845.01	1261.08
163	1856.4	1268.86	38/13
164	1867.79	1276.65	50/17
165	1879.18	1284.43
166	1890.57	1292.22
167	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 167edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-4.16	+0.00	+3.07	+3.98	-4.16	+2.30	-1.09	+0.00	-0.18	+5.65	+3.07
	Relative (%)	-36.5	+0.0	+26.9	+34.9	-36.5	+20.2	-9.6	+0.0	-1.6	+49.6	+26.9
Steps (reduced)		105 (105)	167 (0)	211 (44)	245 (78)	272 (105)	296 (129)	316 (149)	334 (0)	350 (16)	365 (31)	378 (44)

Approximation of harmonics in 167edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+1.16	-1.86	+3.98	-5.25	+3.68	-4.16	+4.74	-4.34	+2.30	+1.49	+4.26
	Relative (%)	+10.2	-16.3	+34.9	-46.1	+32.3	-36.5	+41.6	-38.1	+20.2	+13.1	+37.4
Steps (reduced)		390 (56)	401 (67)	412 (78)	421 (87)	431 (97)	439 (105)	448 (114)	455 (121)	463 (129)	470 (136)	477 (143)