160edt

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160edt

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Prime factorization	25 × 5
Step size	11.8872¢
Octave	101\160edt (1200.61¢)
Consistency limit	5
Distinct consistency limit	5

160 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 160edt or 160ed3), is a nonoctave tuning system that divides the interval of 3/1 into 160 equal parts of about 11.9⁠ ⁠¢ each. Each step represents a frequency ratio of 3^1/160, or the 160th root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	11.9	8.1
2	23.8	16.3
3	35.7	24.4	48/47, 50/49
4	47.5	32.5	37/36, 38/37
5	59.4	40.6	29/28, 30/29
6	71.3	48.8
7	83.2	56.9	21/20, 43/41
8	95.1	65
9	107	73.1	33/31
10	118.9	81.3	15/14
11	130.8	89.4	41/38
12	142.6	97.5	51/47
13	154.5	105.6	47/43
14	166.4	113.8	11/10
15	178.3	121.9	41/37, 51/46
16	190.2	130	48/43
17	202.1	138.1
18	214	146.3	43/38
19	225.9	154.4	41/36
20	237.7	162.5	31/27, 39/34, 47/41
21	249.6	170.6
22	261.5	178.8	43/37
23	273.4	186.9	48/41
24	285.3	195	33/28, 46/39
25	297.2	203.1	19/16
26	309.1	211.3
27	321	219.4
28	332.8	227.5	40/33, 57/47
29	344.7	235.6
30	356.6	243.8
31	368.5	251.9	47/38
32	380.4	260
33	392.3	268.1
34	404.2	276.3	24/19
35	416.1	284.4
36	427.9	292.5	41/32
37	439.8	300.6	58/45
38	451.7	308.8	48/37
39	463.6	316.9	17/13
40	475.5	325	54/41
41	487.4	333.1	57/43
42	499.3	341.3	4/3
43	511.2	349.4	43/32
44	523	357.5	23/17
45	534.9	365.6
46	546.8	373.8	37/27
47	558.7	381.9	29/21
48	570.6	390	32/23, 57/41
49	582.5	398.1	7/5
50	594.4	406.3	31/22
51	606.2	414.4	44/31
52	618.1	422.5	10/7
53	630	430.6
54	641.9	438.8	29/20, 42/29
55	653.8	446.9	54/37
56	665.7	455	47/32
57	677.6	463.1	34/23
58	689.5	471.3
59	701.3	479.4	3/2
60	713.2	487.5
61	725.1	495.6
62	737	503.7
63	748.9	511.9	37/24, 57/37
64	760.8	520	45/29
65	772.7	528.1
66	784.6	536.3
67	796.4	544.4	19/12
68	808.3	552.5	51/32
69	820.2	560.6	45/28
70	832.1	568.8
71	844	576.9
72	855.9	585
73	867.8	593.1	33/20
74	879.7	601.3
75	891.5	609.4
76	903.4	617.5	32/19
77	915.3	625.6	39/23, 56/33
78	927.2	633.8	41/24
79	939.1	641.9
80	951	650
81	962.9	658.1
82	974.8	666.3
83	986.6	674.4	23/13
84	998.5	682.5	57/32
85	1010.4	690.6	43/24
86	1022.3	698.8
87	1034.2	706.9	20/11
88	1046.1	715
89	1058	723.1
90	1069.8	731.3
91	1081.7	739.4	28/15
92	1093.6	747.5	32/17
93	1105.5	755.6	36/19
94	1117.4	763.8
95	1129.3	771.9
96	1141.2	780	29/15
97	1153.1	788.1	37/19
98	1164.9	796.3	47/24, 49/25
99	1176.8	804.4
100	1188.7	812.5
101	1200.6	820.6	2/1
102	1212.5	828.8
103	1224.4	836.9
104	1236.3	845	47/23
105	1248.2	853.1	37/18
106	1260	861.3	29/14, 60/29
107	1271.9	869.4
108	1283.8	877.5	21/10
109	1295.7	885.6
110	1307.6	893.8
111	1319.5	901.9	15/7
112	1331.4	910	41/19
113	1343.3	918.1
114	1355.1	926.3
115	1367	934.4
116	1378.9	942.5	51/23
117	1390.8	950.6
118	1402.7	958.7	9/4
119	1414.6	966.9	43/19
120	1426.5	975	41/18
121	1438.4	983.1	39/17
122	1450.2	991.3	37/16
123	1462.1	999.4
124	1474	1007.5
125	1485.9	1015.6
126	1497.8	1023.8	19/8
127	1509.7	1031.9
128	1521.6	1040
129	1533.5	1048.1
130	1545.3	1056.3
131	1557.2	1064.4
132	1569.1	1072.5	47/19
133	1581	1080.6
134	1592.9	1088.8
135	1604.8	1096.9	48/19
136	1616.7	1105	28/11
137	1628.5	1113.1	41/16
138	1640.4	1121.3
139	1652.3	1129.4
140	1664.2	1137.5	34/13
141	1676.1	1145.6
142	1688	1153.8
143	1699.9	1161.9
144	1711.8	1170	43/16
145	1723.6	1178.1	46/17
146	1735.5	1186.3	30/11
147	1747.4	1194.4
148	1759.3	1202.5	47/17, 58/21
149	1771.2	1210.6
150	1783.1	1218.8	14/5
151	1795	1226.9	31/11
152	1806.9	1235
153	1818.7	1243.1	20/7
154	1830.6	1251.3
155	1842.5	1259.4	29/10
156	1854.4	1267.5
157	1866.3	1275.6	47/16
158	1878.2	1283.8
159	1890.1	1291.9
160	1902	1300	3/1

Harmonics

Approximation of harmonics in 160edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+0.61	+0.00	+1.22	-4.70	+0.61	-4.74	+1.83	+0.00	-4.10	-2.68	+1.22
	Relative (%)	+5.1	+0.0	+10.2	-39.6	+5.1	-39.9	+15.4	+0.0	-34.5	-22.5	+10.2
Steps (reduced)		101 (101)	160 (0)	202 (42)	234 (74)	261 (101)	283 (123)	303 (143)	320 (0)	335 (15)	349 (29)	362 (42)

Approximation of harmonics in 160edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+5.29	-4.13	-4.70	+2.44	+4.47	+0.61	+2.10	-3.49	-4.74	-2.07	+4.18
	Relative (%)	+44.5	-34.8	-39.6	+20.5	+37.6	+5.1	+17.7	-29.3	-39.9	-17.4	+35.2
Steps (reduced)		374 (54)	384 (64)	394 (74)	404 (84)	413 (93)	421 (101)	429 (109)	436 (116)	443 (123)	450 (130)	457 (137)