166edt

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166edt

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Prime factorization	2 × 83
Step size	11.4576 ¢
Octave	105\166edt (1203.04 ¢)
Consistency limit	3
Distinct consistency limit	3

166 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 166edt or 166ed3), is a nonoctave tuning system that divides the interval of 3/1 into 166 equal parts of about 11.5 ¢ each. Each step represents a frequency ratio of 3^1/166, or the 166th root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	11.46	7.83
2	22.92	15.66
3	34.37	23.49	50/49, 51/50
4	45.83	31.33	38/37, 39/38
5	57.29	39.16	31/30
6	68.75	46.99	51/49
7	80.2	54.82	22/21
8	91.66	62.65	39/37
9	103.12	70.48	35/33
10	114.58	78.31	31/29, 47/44
11	126.03	86.14
12	137.49	93.98	13/12
13	148.95	101.81
14	160.41	109.64	34/31, 45/41
15	171.86	117.47
16	183.32	125.3	10/9
17	194.78	133.13	47/42
18	206.24	140.96
19	217.69	148.8	17/15
20	229.15	156.63
21	240.61	164.46	23/20, 54/47
22	252.07	172.29
23	263.52	180.12
24	274.98	187.95	34/29, 41/35
25	286.44	195.78	46/39
26	297.9	203.61
27	309.35	211.45	49/41
28	320.81	219.28
29	332.27	227.11
30	343.73	234.94	50/41
31	355.18	242.77	27/22, 43/35
32	366.64	250.6	21/17, 47/38
33	378.1	258.43	46/37, 51/41
34	389.56	266.27
35	401.01	274.1	29/23
36	412.47	281.93
37	423.93	289.76	23/18, 60/47
38	435.39	297.59	9/7
39	446.84	305.42	22/17, 57/44
40	458.3	313.25	43/33
41	469.76	321.08
42	481.22	328.92	33/25, 37/28
43	492.68	336.75
44	504.13	344.58
45	515.59	352.41	31/23
46	527.05	360.24	42/31
47	538.51	368.07
48	549.96	375.9
49	561.42	383.73	47/34
50	572.88	391.57	39/28
51	584.34	399.4
52	595.79	407.23
53	607.25	415.06	27/19, 44/31
54	618.71	422.89	10/7
55	630.17	430.72
56	641.62	438.55	42/29
57	653.08	446.39	51/35
58	664.54	454.22
59	676	462.05	34/23
60	687.45	469.88	58/39
61	698.91	477.71
62	710.37	485.54
63	721.83	493.37	41/27, 44/29, 47/31
64	733.28	501.2	29/19
65	744.74	509.04	20/13
66	756.2	516.87
67	767.66	524.7
68	779.11	532.53	58/37
69	790.57	540.36	30/19
70	802.03	548.19	27/17
71	813.49	556.02
72	824.94	563.86	29/18
73	836.4	571.69	47/29, 60/37
74	847.86	579.52	31/19
75	859.32	587.35	23/14
76	870.77	595.18
77	882.23	603.01
78	893.69	610.84	57/34
79	905.15	618.67
80	916.6	626.51
81	928.06	634.34
82	939.52	642.17	43/25
83	950.98	650
84	962.44	657.83
85	973.89	665.66
86	985.35	673.49
87	996.81	681.33
88	1008.27	689.16	34/19
89	1019.72	696.99
90	1031.18	704.82	49/27
91	1042.64	712.65	42/23
92	1054.1	720.48	57/31
93	1065.55	728.31	37/20, 50/27
94	1077.01	736.14	41/22, 54/29
95	1088.47	743.98
96	1099.93	751.81	17/9
97	1111.38	759.64	19/10
98	1122.84	767.47	44/23
99	1134.3	775.3
100	1145.76	783.13
101	1157.21	790.96	39/20, 41/21
102	1168.67	798.8	57/29
103	1180.13	806.63
104	1191.59	814.46
105	1203.04	822.29
106	1214.5	830.12
107	1225.96	837.95
108	1237.42	845.78	47/23
109	1248.87	853.61	35/17
110	1260.33	861.45	29/14
111	1271.79	869.28
112	1283.25	877.11	21/10
113	1294.7	884.94	19/9
114	1306.16	892.77
115	1317.62	900.6
116	1329.08	908.43	28/13
117	1340.53	916.27
118	1351.99	924.1
119	1363.45	931.93
120	1374.91	939.76	31/14
121	1386.36	947.59	49/22
122	1397.82	955.42
123	1409.28	963.25
124	1420.74	971.08	25/11
125	1432.2	978.92
126	1443.65	986.75
127	1455.11	994.58	44/19, 51/22
128	1466.57	1002.41	7/3
129	1478.03	1010.24	47/20, 54/23
130	1489.48	1018.07
131	1500.94	1025.9	50/21
132	1512.4	1033.73
133	1523.86	1041.57	41/17
134	1535.31	1049.4	17/7
135	1546.77	1057.23	22/9
136	1558.23	1065.06
137	1569.69	1072.89
138	1581.14	1080.72
139	1592.6	1088.55
140	1604.06	1096.39
141	1615.52	1104.22
142	1626.97	1112.05
143	1638.43	1119.88
144	1649.89	1127.71
145	1661.35	1135.54	47/18, 60/23
146	1672.8	1143.37
147	1684.26	1151.2	45/17
148	1695.72	1159.04
149	1707.18	1166.87
150	1718.63	1174.7	27/10
151	1730.09	1182.53
152	1741.55	1190.36	41/15
153	1753.01	1198.19
154	1764.46	1206.02	36/13
155	1775.92	1213.86
156	1787.38	1221.69
157	1798.84	1229.52
158	1810.29	1237.35	37/13
159	1821.75	1245.18
160	1833.21	1253.01	49/17
161	1844.67	1260.84
162	1856.12	1268.67	38/13
163	1867.58	1276.51	50/17
164	1879.04	1284.34
165	1890.5	1292.17
166	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 166edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+3.04	+0.00	-5.37	-2.13	+3.04	-0.30	-2.33	+0.00	+0.92	-3.68	-5.37
	Relative (%)	+26.6	+0.0	-46.9	-18.6	+26.6	-2.6	-20.3	+0.0	+8.0	-32.1	-46.9
Steps (reduced)		105 (105)	166 (0)	209 (43)	243 (77)	271 (105)	294 (128)	314 (148)	332 (0)	348 (16)	362 (30)	375 (43)

Approximation of harmonics in 166edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+5.01	+2.74	-2.13	+0.72	-1.12	+3.04	+1.10	+3.96	-0.30	-0.64	+2.61
	Relative (%)	+43.7	+23.9	-18.6	+6.3	-9.8	+26.6	+9.6	+34.6	-2.6	-5.6	+22.8
Steps (reduced)		388 (56)	399 (67)	409 (77)	419 (87)	428 (96)	437 (105)	445 (113)	453 (121)	460 (128)	467 (135)	474 (142)