181edt

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← 180edt 181edt 182edt →
Prime factorization 181 (prime)
Step size 10.508 ¢ 
Octave 114\181edt (1197.92 ¢)
Consistency limit 6
Distinct consistency limit 6

181 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 181edt or 181ed3), is a nonoctave tuning system that divides the interval of 3/1 into 181 equal parts of about 10.5 ¢ each. Each step represents a frequency ratio of 31/181, or the 181st root of 3.

Intervals

Steps Cents Hekts Approximate ratios
0 0 0 1/1
1 10.51 7.18
2 21.02 14.36
3 31.52 21.55 55/54, 56/55, 57/56
4 42.03 28.73 42/41
5 52.54 35.91 34/33
6 63.05 43.09 28/27, 57/55
7 73.56 50.28
8 84.06 57.46
9 94.57 64.64 19/18
10 105.08 71.82
11 115.59 79.01 31/29, 46/43
12 126.1 86.19
13 136.6 93.37
14 147.11 100.55 37/34
15 157.62 107.73 23/21
16 168.13 114.92 43/39
17 178.64 122.1 41/37, 51/46
18 189.14 129.28 29/26
19 199.65 136.46 46/41
20 210.16 143.65 35/31
21 220.67 150.83 25/22, 42/37
22 231.18 158.01
23 241.68 165.19
24 252.19 172.38
25 262.7 179.56
26 273.21 186.74 41/35, 55/47
27 283.72 193.92 33/28
28 294.23 201.1 51/43
29 304.73 208.29 31/26
30 315.24 215.47 6/5
31 325.75 222.65 35/29
32 336.26 229.83 17/14
33 346.77 237.02 11/9
34 357.27 244.2 43/35
35 367.78 251.38 47/38
36 378.29 258.56 51/41, 56/45
37 388.8 265.75
38 399.31 272.93 34/27
39 409.81 280.11 19/15
40 420.32 287.29 65/51
41 430.83 294.48
42 441.34 301.66
43 451.85 308.84
44 462.35 316.02 47/36
45 472.86 323.2 46/35
46 483.37 330.39 37/28, 41/31
47 493.88 337.57
48 504.39 344.75
49 514.89 351.93 35/26
50 525.4 359.12 42/31
51 535.91 366.3 15/11
52 546.42 373.48 37/27
53 556.93 380.66
54 567.43 387.85 43/31
55 577.94 395.03
56 588.45 402.21 52/37
57 598.96 409.39 41/29, 65/46
58 609.47 416.57 27/19
59 619.97 423.76
60 630.48 430.94 36/25
61 640.99 438.12 42/29, 55/38
62 651.5 445.3 51/35
63 662.01 452.49 22/15, 63/43
64 672.51 459.67 28/19
65 683.02 466.85 43/29, 46/31
66 693.53 474.03
67 704.04 481.22
68 714.55 488.4 65/43
69 725.05 495.58 38/25
70 735.56 502.76 26/17
71 746.07 509.94
72 756.58 517.13 65/42
73 767.09 524.31
74 777.59 531.49 47/30, 58/37
75 788.1 538.67 41/26, 52/33
76 798.61 545.86 46/29, 65/41
77 809.12 553.04
78 819.63 560.22
79 830.14 567.4 21/13
80 840.64 574.59
81 851.15 581.77
82 861.66 588.95 51/31
83 872.17 596.13 43/26
84 882.68 603.31
85 893.18 610.5 62/37
86 903.69 617.68
87 914.2 624.86 39/23
88 924.71 632.04 29/17
89 935.22 639.23
90 945.72 646.41 19/11
91 956.23 653.59 33/19
92 966.74 660.77
93 977.25 667.96 51/29, 58/33
94 987.76 675.14 23/13
95 998.26 682.32
96 1008.77 689.5
97 1019.28 696.69
98 1029.79 703.87
99 1040.3 711.05 31/17
100 1050.8 718.23
101 1061.31 725.41
102 1071.82 732.6 13/7
103 1082.33 739.78 43/23
104 1092.84 746.96 47/25, 62/33
105 1103.34 754.14
106 1113.85 761.33
107 1124.36 768.51
108 1134.87 775.69 52/27
109 1145.38 782.87
110 1155.88 790.06
111 1166.39 797.24 51/26
112 1176.9 804.42
113 1187.41 811.6
114 1197.92 818.78
115 1208.42 825.97
116 1218.93 833.15
117 1229.44 840.33 57/28
118 1239.95 847.51 43/21, 45/22
119 1250.46 854.7 35/17
120 1260.96 861.88 29/14
121 1271.47 869.06 25/12
122 1281.98 876.24 65/31
123 1292.49 883.43 19/9
124 1303 890.61
125 1313.5 897.79 47/22
126 1324.01 904.97 58/27
127 1334.52 912.15
128 1345.03 919.34
129 1355.54 926.52
130 1366.05 933.7 11/5
131 1376.55 940.88 31/14
132 1387.06 948.07
133 1397.57 955.25 65/29
134 1408.08 962.43
135 1418.59 969.61
136 1429.09 976.8
137 1439.6 983.98 62/27
138 1450.11 991.16
139 1460.62 998.34
140 1471.13 1005.52
141 1481.63 1012.71
142 1492.14 1019.89 45/19
143 1502.65 1027.07
144 1513.16 1034.25
145 1523.67 1041.44 41/17
146 1534.17 1048.62
147 1544.68 1055.8
148 1555.19 1062.98 27/11
149 1565.7 1070.17 42/17
150 1576.21 1077.35
151 1586.71 1084.53 5/2
152 1597.22 1091.71
153 1607.73 1098.9 43/17
154 1618.24 1106.08 28/11
155 1628.75 1113.26
156 1639.25 1120.44
157 1649.76 1127.62
158 1660.27 1134.81
159 1670.78 1141.99
160 1681.29 1149.17 37/14
161 1691.79 1156.35
162 1702.3 1163.54
163 1712.81 1170.72
164 1723.32 1177.9 46/17
165 1733.83 1185.08
166 1744.33 1192.27 63/23
167 1754.84 1199.45
168 1765.35 1206.63
169 1775.86 1213.81
170 1786.37 1220.99
171 1796.87 1228.18
172 1807.38 1235.36 54/19
173 1817.89 1242.54
174 1828.4 1249.72
175 1838.91 1256.91 55/19
176 1849.41 1264.09
177 1859.92 1271.27 41/14
178 1870.43 1278.45 56/19
179 1880.94 1285.64
180 1891.45 1292.82
181 1901.96 1300 3/1

Harmonics

Approximation of harmonics in 181edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -2.08 +0.00 -4.17 -1.68 -2.08 +4.25 +4.26 +0.00 -3.77 -0.64 -4.17
Relative (%) -19.8 +0.0 -39.7 -16.0 -19.8 +40.5 +40.5 +0.0 -35.8 -6.1 -39.7
Steps
(reduced) 		114
(114) 		181
(0) 		228
(47) 		265
(84) 		295
(114) 		321
(140) 		343
(162) 		362
(0) 		379
(17) 		395
(33) 		409
(47)
Approximation of harmonics in 181edt
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +4.37 +2.17 -1.68 +2.17 +2.30 -2.08 -1.11 +4.66 +4.25 -2.73 +4.38
Relative (%) +41.6 +20.7 -16.0 +20.7 +21.9 -19.8 -10.6 +44.3 +40.5 -25.9 +41.7
Steps
(reduced) 		423
(61) 		435
(73) 		446
(84) 		457
(95) 		467
(105) 		476
(114) 		485
(123) 		494
(132) 		502
(140) 		509
(147) 		517
(155)
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