162edt

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162edt

163edt →

Prime factorization	2 × 34
Step size	11.7405 ¢
Octave	102\162edt (1197.53 ¢) (→ 17\27edt)
Consistency limit	7
Distinct consistency limit	7

162 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 162edt or 162ed3), is a nonoctave tuning system that divides the interval of 3/1 into 162 equal parts of about 11.7 ¢ each. Each step represents a frequency ratio of 3^1/162, or the 162nd root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	11.7	8
2	23.5	16
3	35.2	24.1
4	47	32.1	37/36, 38/37
5	58.7	40.1
6	70.4	48.1	25/24, 51/49
7	82.2	56.2	43/41
8	93.9	64.2	19/18
9	105.7	72.2
10	117.4	80.2
11	129.1	88.3	14/13
12	140.9	96.3	51/47
13	152.6	104.3	47/43
14	164.4	112.3
15	176.1	120.4	31/28
16	187.8	128.4	39/35
17	199.6	136.4	55/49
18	211.3	144.4	26/23, 35/31
19	223.1	152.5	33/29, 58/51
20	234.8	160.5
21	246.5	168.5	15/13
22	258.3	176.5	36/31
23	270	184.6
24	281.8	192.6
25	293.5	200.6	45/38
26	305.3	208.6	31/26, 37/31
27	317	216.7	6/5
28	328.7	224.7
29	340.5	232.7	28/23
30	352.2	240.7	38/31
31	364	248.8	37/30, 58/47
32	375.7	256.8	41/33, 46/37
33	387.4	264.8	5/4
34	399.2	272.8	34/27
35	410.9	280.9
36	422.7	288.9
37	434.4	296.9	9/7
38	446.1	304.9	22/17
39	457.9	313	43/33
40	469.6	321
41	481.4	329	37/28
42	493.1	337
43	504.8	345.1
44	516.6	353.1	31/23
45	528.3	361.1	19/14
46	540.1	369.1
47	551.8	377.2
48	563.5	385.2	18/13
49	575.3	393.2
50	587	401.2
51	598.8	409.3	41/29
52	610.5	417.3	37/26
53	622.2	425.3
54	634	433.3	49/34
55	645.7	441.4	45/31
56	657.5	449.4	19/13
57	669.2	457.4
58	680.9	465.4	43/29
59	692.7	473.5
60	704.4	481.5
61	716.2	489.5	56/37
62	727.9	497.5	35/23
63	739.6	505.6	23/15
64	751.4	513.6	54/35
65	763.1	521.6
66	774.9	529.6	36/23
67	786.6	537.7
68	798.4	545.7
69	810.1	553.7
70	821.8	561.7	37/23, 45/28
71	833.6	569.8	34/21, 55/34
72	845.3	577.8	44/27, 57/35
73	857.1	585.8
74	868.8	593.8	38/23
75	880.5	601.9
76	892.3	609.9
77	904	617.9
78	915.8	625.9
79	927.5	634
80	939.2	642
81	951	650	26/15, 45/26
82	962.7	658
83	974.5	666
84	986.2	674.1
85	997.9	682.1
86	1009.7	690.1
87	1021.4	698.1
88	1033.2	706.2	49/27
89	1044.9	714.2
90	1056.6	722.2	35/19, 46/25
91	1068.4	730.2
92	1080.1	738.3	28/15
93	1091.9	746.3
94	1103.6	754.3
95	1115.3	762.3
96	1127.1	770.4	23/12
97	1138.8	778.4
98	1150.6	786.4	35/18
99	1162.3	794.4	45/23
100	1174	802.5
101	1185.8	810.5
102	1197.5	818.5
103	1209.3	826.5
104	1221	834.6
105	1232.7	842.6	55/27
106	1244.5	850.6	39/19
107	1256.2	858.6	31/15
108	1268	866.7	52/25
109	1279.7	874.7	44/21
110	1291.5	882.7
111	1303.2	890.7
112	1314.9	898.8	47/22
113	1326.7	906.8
114	1338.4	914.8	13/6
115	1350.2	922.8
116	1361.9	930.9
117	1373.6	938.9	42/19
118	1385.4	946.9	49/22
119	1397.1	954.9	56/25
120	1408.9	963
121	1420.6	971
122	1432.3	979
123	1444.1	987
124	1455.8	995.1	51/22
125	1467.6	1003.1	7/3
126	1479.3	1011.1
127	1491	1019.1
128	1502.8	1027.2
129	1514.5	1035.2	12/5
130	1526.3	1043.2
131	1538	1051.2
132	1549.7	1059.3
133	1561.5	1067.3
134	1573.2	1075.3
135	1585	1083.3	5/2
136	1596.7	1091.4
137	1608.4	1099.4	38/15
138	1620.2	1107.4
139	1631.9	1115.4
140	1643.7	1123.5	31/12
141	1655.4	1131.5	13/5
142	1667.1	1139.5	55/21
143	1678.9	1147.5	29/11
144	1690.6	1155.6
145	1702.4	1163.6
146	1714.1	1171.6	35/13
147	1725.8	1179.6
148	1737.6	1187.7
149	1749.3	1195.7
150	1761.1	1203.7	47/17
151	1772.8	1211.7	39/14
152	1784.6	1219.8
153	1796.3	1227.8
154	1808	1235.8	54/19
155	1819.8	1243.8
156	1831.5	1251.9	49/17
157	1843.3	1259.9
158	1855	1267.9
159	1866.7	1275.9
160	1878.5	1284
161	1890.2	1292
162	1902	1300	3/1

Harmonics

Approximation of harmonics in 162edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-2.47	+0.00	-4.95	-3.82	-2.47	+0.69	+4.32	+0.00	+5.44	+4.81	-4.95
	Relative (%)	-21.1	+0.0	-42.1	-32.6	-21.1	+5.9	+36.8	+0.0	+46.4	+40.9	-42.1
Steps (reduced)		102 (102)	162 (0)	204 (42)	237 (75)	264 (102)	287 (125)	307 (145)	324 (0)	340 (16)	354 (30)	366 (42)

Approximation of harmonics in 162edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.63	-1.79	-3.82	+1.85	+2.56	-2.47	-2.15	+2.97	+0.69	+2.33	-4.18
	Relative (%)	-22.4	-15.2	-32.6	+15.8	+21.8	-21.1	-18.3	+25.3	+5.9	+19.9	-35.6
Steps (reduced)		378 (54)	389 (65)	399 (75)	409 (85)	418 (94)	426 (102)	434 (110)	442 (118)	449 (125)	456 (132)	462 (138)