182edt

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← 181edt 182edt 183edt →
Prime factorization 2 × 7 × 13
Step size 10.4503¢ 
Octave 115\182edt (1201.78¢)
Consistency limit 5
Distinct consistency limit 5

182 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 182edt or 182ed3), is a nonoctave tuning system that divides the interval of 3/1 into 182 equal parts of about 10.5 ¢ each. Each step represents a frequency ratio of 31/182, or the 182nd root of 3.

Intervals

Steps Cents Approximate ratios
0 0 1/1
1 10.45
2 20.9
3 31.35 55/54, 56/55, 57/56
4 41.8 42/41, 43/42
5 52.25 34/33
6 62.7 28/27, 57/55
7 73.15
8 83.6 43/41
9 94.05 19/18
10 104.5
11 114.95 31/29, 47/44
12 125.4
13 135.85
14 146.3 37/34, 62/57
15 156.75 23/21
16 167.2
17 177.66 41/37, 51/46
18 188.11 29/26, 39/35
19 198.56 37/33, 46/41
20 209.01 35/31, 44/39
21 219.46 42/37
22 229.91
23 240.36 31/27, 54/47
24 250.81 52/45
25 261.26 43/37
26 271.71 55/47
27 282.16
28 292.61 45/38
29 303.06 56/47
30 313.51
31 323.96 41/34, 47/39
32 334.41 57/47
33 344.86
34 355.31 27/22, 43/35
35 365.76 21/17
36 376.21 41/33, 46/37
37 386.66 5/4
38 397.11 39/31, 44/35
39 407.56 43/34
40 418.01 14/11
41 428.46 32/25
42 438.91 58/45
43 449.36 35/27, 57/44
44 459.81
45 470.26
46 480.71 62/47
47 491.16
48 501.61
49 512.06 39/29
50 522.52 23/17
51 532.97
52 543.42 26/19, 63/46
53 553.87 62/45
54 564.32 18/13
55 574.77 39/28, 46/33
56 585.22
57 595.67 55/39
58 606.12 44/31
59 616.57
60 627.02 56/39
61 637.47 13/9
62 647.92
63 658.37
64 668.82
65 679.27
66 689.72
67 700.17
68 710.62
69 721.07 44/29, 47/31
70 731.52 29/19
71 741.97 43/28
72 752.42 17/11
73 762.87
74 773.32 25/16
75 783.77
76 794.22
77 804.67 35/22, 43/27
78 815.12
79 825.57 29/18
80 836.02 47/29
81 846.47 31/19, 44/27
82 856.92
83 867.38
84 877.83
85 888.28
86 898.73
87 909.18
88 919.63
89 930.08 65/38
90 940.53 31/18
91 950.98
92 961.43 54/31
93 971.88
94 982.33
95 992.78 55/31
96 1003.23
97 1013.68
98 1024.13 47/26, 56/31, 65/36
99 1034.58
100 1045.03
101 1055.48 57/31
102 1065.93
103 1076.38 54/29
104 1086.83
105 1097.28
106 1107.73 55/29
107 1118.18
108 1128.63 48/25
109 1139.08 56/29
110 1149.53 33/17
111 1159.98 43/22
112 1170.43 57/29
113 1180.88
114 1191.33
115 1201.78
116 1212.24
117 1222.69
118 1233.14
119 1243.59
120 1254.04
121 1264.49 27/13
122 1274.94
123 1285.39
124 1295.84
125 1306.29
126 1316.74
127 1327.19 28/13
128 1337.64 13/6
129 1348.09
130 1358.54 46/21, 57/26
131 1368.99
132 1379.44 51/23
133 1389.89 29/13
134 1400.34
135 1410.79
136 1421.24
137 1431.69
138 1442.14
139 1452.59 44/19
140 1463.04
141 1473.49
142 1483.94 33/14
143 1494.39
144 1504.84 31/13
145 1515.29 12/5
146 1525.74
147 1536.19 17/7
148 1546.64 22/9
149 1557.1
150 1567.55 47/19
151 1578
152 1588.45
153 1598.9
154 1609.35 38/15
155 1619.8
156 1630.25
157 1640.7
158 1651.15
159 1661.6 47/18
160 1672.05
161 1682.5 37/14
162 1692.95
163 1703.4
164 1713.85 35/13
165 1724.3 46/17, 65/24
166 1734.75
167 1745.2 63/23
168 1755.65
169 1766.1
170 1776.55
171 1787
172 1797.45
173 1807.9 54/19
174 1818.35
175 1828.8
176 1839.25 55/19
177 1849.7
178 1860.15 41/14
179 1870.6 56/19
180 1881.05
181 1891.5
182 1901.96 3/1

Harmonics

Approximation of harmonics in 182edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +1.78 +0.00 +3.57 +3.92 +1.78 -3.83 -5.10 +0.00 -4.75 -2.55 +3.57
Relative (%) +17.1 +0.0 +34.2 +37.5 +17.1 -36.6 -48.8 +0.0 -45.4 -24.4 +34.2
Steps
(reduced)
115
(115)
182
(0)
230
(48)
267
(85)
297
(115)
322
(140)
344
(162)
364
(0)
381
(17)
397
(33)
412
(48)
Approximation of harmonics in 182edt
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +0.85 -2.04 +3.92 -3.31 -3.76 +1.78 +2.23 -2.96 -3.83 -0.76 -4.57
Relative (%) +8.1 -19.6 +37.5 -31.7 -36.0 +17.1 +21.4 -28.4 -36.6 -7.3 -43.7
Steps
(reduced)
425
(61)
437
(73)
449
(85)
459
(95)
469
(105)
479
(115)
488
(124)
496
(132)
504
(140)
512
(148)
519
(155)