161edt

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161edt

162edt →

Prime factorization	7 × 23
Step size	11.8134 ¢
Octave	102\161edt (1204.97 ¢)
Consistency limit	3
Distinct consistency limit	3

161 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 161edt or 161ed3), is a nonoctave tuning system that divides the interval of 3/1 into 161 equal parts of about 11.8 ¢ each. Each step represents a frequency ratio of 3^1/161, or the 161st root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	11.8	8.1
2	23.6	16.1
3	35.4	24.2
4	47.3	32.3
5	59.1	40.4
6	70.9	48.4	49/47
7	82.7	56.5	43/41
8	94.5	64.6	19/18
9	106.3	72.7
10	118.1	80.7	15/14
11	129.9	88.8	55/51
12	141.8	96.9	51/47
13	153.6	105	47/43
14	165.4	113
15	177.2	121.1	41/37
16	189	129.2
17	200.8	137.3	55/49
18	212.6	145.3	26/23
19	224.5	153.4	33/29
20	236.3	161.5	39/34, 47/41
21	248.1	169.6	15/13
22	259.9	177.6	43/37
23	271.7	185.7	55/47
24	283.5	193.8
25	295.3	201.9	51/43
26	307.1	209.9	37/31
27	319	218
28	330.8	226.1	23/19
29	342.6	234.2
30	354.4	242.2	27/22
31	366.2	250.3	21/17
32	378	258.4	51/41
33	389.8	266.5
34	401.7	274.5
35	413.5	282.6	47/37
36	425.3	290.7	23/18, 55/43
37	437.1	298.8
38	448.9	306.8	35/27, 57/44
39	460.7	314.9	30/23
40	472.5	323
41	484.3	331.1	41/31, 45/34
42	496.2	339.1
43	508	347.2	55/41
44	519.8	355.3
45	531.6	363.4	34/25
46	543.4	371.4	26/19
47	555.2	379.5	51/37
48	567	387.6	43/31
49	578.9	395.7
50	590.7	403.7
51	602.5	411.8
52	614.3	419.9
53	626.1	428
54	637.9	436	13/9
55	649.7	444.1
56	661.5	452.2
57	673.4	460.2	31/21
58	685.2	468.3	49/33, 55/37
59	697	476.4
60	708.8	484.5
61	720.6	492.5	47/31
62	732.4	500.6
63	744.2	508.7
64	756.1	516.8
65	767.9	524.8
66	779.7	532.9
67	791.5	541	30/19, 49/31
68	803.3	549.1	35/22
69	815.1	557.1
70	826.9	565.2
71	838.8	573.3
72	850.6	581.4
73	862.4	589.4	51/31
74	874.2	597.5	58/35
75	886	605.6
76	897.8	613.7	42/25
77	909.6	621.7	22/13
78	921.4	629.8
79	933.3	637.9
80	945.1	646
81	956.9	654
82	968.7	662.1
83	980.5	670.2	37/21
84	992.3	678.3	39/22, 55/31
85	1004.1	686.3	25/14
86	1016	694.4
87	1027.8	702.5
88	1039.6	710.6	31/17
89	1051.4	718.6
90	1063.2	726.7
91	1075	734.8
92	1086.8	742.9
93	1098.6	750.9
94	1110.5	759	19/10
95	1122.3	767.1	44/23
96	1134.1	775.2
97	1145.9	783.2
98	1157.7	791.3	41/21
99	1169.5	799.4
100	1181.3	807.5
101	1193.2	815.5
102	1205	823.6
103	1216.8	831.7
104	1228.6	839.8
105	1240.4	847.8	43/21
106	1252.2	855.9
107	1264	864	27/13
108	1275.8	872
109	1287.7	880.1
110	1299.5	888.2
111	1311.3	896.3
112	1323.1	904.3	58/27
113	1334.9	912.4
114	1346.7	920.5	37/17
115	1358.5	928.6	57/26
116	1370.4	936.6
117	1382.2	944.7
118	1394	952.8	47/21
119	1405.8	960.9
120	1417.6	968.9	34/15
121	1429.4	977
122	1441.2	985.1	23/10
123	1453	993.2	44/19
124	1464.9	1001.2
125	1476.7	1009.3	54/23
126	1488.5	1017.4
127	1500.3	1025.5
128	1512.1	1033.5
129	1523.9	1041.6	41/17
130	1535.7	1049.7	17/7
131	1547.6	1057.8	22/9
132	1559.4	1065.8
133	1571.2	1073.9	57/23
134	1583	1082
135	1594.8	1090.1
136	1606.6	1098.1	43/17
137	1618.4	1106.2
138	1630.2	1114.3
139	1642.1	1122.4
140	1653.9	1130.4	13/5
141	1665.7	1138.5	34/13, 55/21
142	1677.5	1146.6	29/11
143	1689.3	1154.7
144	1701.1	1162.7
145	1712.9	1170.8
146	1724.8	1178.9
147	1736.6	1187
148	1748.4	1195
149	1760.2	1203.1	47/17, 58/21
150	1772	1211.2
151	1783.8	1219.3	14/5
152	1795.6	1227.3
153	1807.4	1235.4	54/19
154	1819.3	1243.5
155	1831.1	1251.6
156	1842.9	1259.6
157	1854.7	1267.7
158	1866.5	1275.8
159	1878.3	1283.9
160	1890.1	1291.9
161	1902	1300	3/1

Harmonics

Approximation of harmonics in 161edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+4.97	+0.00	-1.88	+1.65	+4.97	-2.01	+3.08	+0.00	-5.20	-4.82	-1.88
	Relative (%)	+42.0	+0.0	-15.9	+13.9	+42.0	-17.0	+26.1	+0.0	-44.0	-40.8	-15.9
Steps (reduced)		102 (102)	161 (0)	203 (42)	236 (75)	263 (102)	285 (124)	305 (144)	322 (0)	337 (15)	351 (29)	364 (42)

Approximation of harmonics in 161edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+1.31	+2.95	+1.65	-3.77	-2.40	+4.97	+5.87	-0.24	-2.01	+0.15	+5.88
	Relative (%)	+11.0	+25.0	+13.9	-31.9	-20.3	+42.0	+49.7	-2.0	-17.0	+1.2	+49.8
Steps (reduced)		376 (54)	387 (65)	397 (75)	406 (84)	415 (93)	424 (102)	432 (110)	439 (117)	446 (124)	453 (131)	460 (138)