165edt

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165edt

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Prime factorization	3 × 5 × 11
Step size	11.527 ¢
Octave	104\165edt (1198.81 ¢)
Consistency limit	6
Distinct consistency limit	6

165 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 165edt or 165ed3), is a nonoctave tuning system that divides the interval of 3/1 into 165 equal parts of about 11.5 ¢ each. Each step represents a frequency ratio of 3^1/165, or the 165th root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	11.53	7.88
2	23.05	15.76
3	34.58	23.64	49/48, 51/50
4	46.11	31.52	37/36, 38/37, 39/38
5	57.64	39.39	30/29, 31/30
6	69.16	47.27
7	80.69	55.15	22/21
8	92.22	63.03	39/37, 58/55
9	103.74	70.91	52/49
10	115.27	78.79	31/29, 47/44
11	126.8	86.67
12	138.32	94.55	13/12
13	149.85	102.42	12/11
14	161.38	110.3	45/41
15	172.91	118.18	21/19
16	184.43	126.06
17	195.96	133.94	47/42
18	207.49	141.82	44/39
19	219.01	149.7	42/37
20	230.54	157.58	8/7
21	242.07	165.45	23/20
22	253.59	173.33	22/19
23	265.12	181.21
24	276.65	189.09	27/23, 34/29
25	288.18	196.97	13/11
26	299.7	204.85	44/37
27	311.23	212.73
28	322.76	220.61	41/34, 47/39
29	334.28	228.48	40/33, 57/47
30	345.81	236.36
31	357.34	244.24	43/35
32	368.86	252.12	26/21, 47/38
33	380.39	260
34	391.92	267.88
35	403.45	275.76	24/19
36	414.97	283.64	47/37
37	426.5	291.52	55/43
38	438.03	299.39	58/45
39	449.55	307.27	35/27, 48/37
40	461.08	315.15	30/23, 47/36
41	472.61	323.03	46/35
42	484.13	330.91	41/31, 45/34
43	495.66	338.79
44	507.19	346.67	55/41
45	518.72	354.55	27/20, 58/43
46	530.24	362.42
47	541.77	370.3	26/19, 41/30
48	553.3	378.18
49	564.82	386.06
50	576.35	393.94	46/33, 60/43
51	587.88	401.82	52/37
52	599.4	409.7	41/29, 58/41
53	610.93	417.58	37/26, 47/33
54	622.46	425.45	43/30
55	633.99	433.33
56	645.51	441.21	45/31
57	657.04	449.09	19/13
58	668.57	456.97	25/17
59	680.09	464.85	40/27
60	691.62	472.73
61	703.15	480.61	3/2
62	714.67	488.48
63	726.2	496.36	35/23
64	737.73	504.24	49/32
65	749.26	512.12	37/24, 57/37
66	760.78	520	45/29
67	772.31	527.88
68	783.84	535.76	11/7
69	795.36	543.64	19/12
70	806.89	551.52	43/27
71	818.42	559.39
72	829.94	567.27	21/13
73	841.47	575.15	13/8
74	853	583.03	18/11
75	864.53	590.91
76	876.05	598.79
77	887.58	606.67
78	899.11	614.55	37/22
79	910.63	622.42	22/13
80	922.16	630.3	46/27
81	933.69	638.18	12/7
82	945.21	646.06	19/11
83	956.74	653.94	33/19, 40/23
84	968.27	661.82	7/4
85	979.8	669.7	37/21
86	991.32	677.58	39/22, 55/31
87	1002.85	685.45
88	1014.38	693.33
89	1025.9	701.21	38/21, 47/26
90	1037.43	709.09
91	1048.96	716.97	11/6
92	1060.48	724.85	24/13
93	1072.01	732.73	13/7
94	1083.54	740.61	43/23, 58/31
95	1095.07	748.48
96	1106.59	756.36	36/19
97	1118.12	764.24	21/11
98	1129.65	772.12
99	1141.17	780	29/15
100	1152.7	787.88	37/19
101	1164.23	795.76	47/24
102	1175.75	803.64
103	1187.28	811.52
104	1198.81	819.39	2/1
105	1210.34	827.27
106	1221.86	835.15
107	1233.39	843.03	51/25
108	1244.92	850.91	39/19
109	1256.44	858.79	31/15
110	1267.97	866.67
111	1279.5	874.55	44/21
112	1291.02	882.42
113	1302.55	890.3
114	1314.08	898.18	47/22
115	1325.61	906.06	43/20
116	1337.13	913.94
117	1348.66	921.82
118	1360.19	929.7	57/26
119	1371.71	937.58
120	1383.24	945.45	20/9
121	1394.77	953.33	47/21
122	1406.29	961.21
123	1417.82	969.09	34/15
124	1429.35	976.97
125	1440.88	984.85	23/10
126	1452.4	992.73	37/16
127	1463.93	1000.61
128	1475.46	1008.48
129	1486.98	1016.36
130	1498.51	1024.24	19/8
131	1510.04	1032.12	55/23
132	1521.56	1040
133	1533.09	1047.88
134	1544.62	1055.76
135	1556.15	1063.64
136	1567.67	1071.52	47/19
137	1579.2	1079.39
138	1590.73	1087.27
139	1602.25	1095.15	58/23
140	1613.78	1103.03	33/13
141	1625.31	1110.91	23/9
142	1636.83	1118.79
143	1648.36	1126.67	57/22
144	1659.89	1134.55	60/23
145	1671.42	1142.42	21/8
146	1682.94	1150.3	37/14
147	1694.47	1158.18
148	1706	1166.06
149	1717.52	1173.94
150	1729.05	1181.82	19/7
151	1740.58	1189.7	41/15
152	1752.1	1197.58	11/4
153	1763.63	1205.45	36/13
154	1775.16	1213.33
155	1786.69	1221.21
156	1798.21	1229.09
157	1809.74	1236.97	37/13
158	1821.27	1244.85
159	1832.79	1252.73
160	1844.32	1260.61	29/10
161	1855.85	1268.48	38/13
162	1867.37	1276.36	50/17
163	1878.9	1284.24
164	1890.43	1292.12
165	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 165edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-1.19	+0.00	-2.38	+3.22	-1.19	-2.94	-3.58	+0.00	+2.03	-1.60	-2.38
	Relative (%)	-10.3	+0.0	-20.7	+27.9	-10.3	-25.5	-31.0	+0.0	+17.6	-13.9	-20.7
Steps (reduced)		104 (104)	165 (0)	208 (43)	242 (77)	269 (104)	292 (127)	312 (147)	330 (0)	346 (16)	360 (30)	373 (43)

Approximation of harmonics in 165edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.63	-4.13	+3.22	-4.77	+5.55	-1.19	-2.58	+0.84	-2.94	-2.79	+0.94
	Relative (%)	-22.8	-35.9	+27.9	-41.4	+48.1	-10.3	-22.4	+7.3	-25.5	-24.2	+8.2
Steps (reduced)		385 (55)	396 (66)	407 (77)	416 (86)	426 (96)	434 (104)	442 (112)	450 (120)	457 (127)	464 (134)	471 (141)