316edt

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← 315edt 316edt 317edt →
Prime factorization 22 × 79
Step size 6.01884¢ 
Octave 199\316edt (1197.75¢)
Consistency limit 2
Distinct consistency limit 2

316 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 316edt or 316ed3), is a nonoctave tuning system that divides the interval of 3/1 into 316 equal parts of about 6.02 ¢ each. Each step represents a frequency ratio of 31/316, or the 316th root of 3.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 6.019
2 12.038
3 18.057 99/98
4 24.075
5 30.094 58/57
6 36.113
7 42.132 42/41
8 48.151
9 54.17 65/63, 98/95
10 60.188
11 66.207
12 72.226
13 78.245 45/43, 91/87
14 84.264
15 90.283 98/93
16 96.302 37/35
17 102.32 35/33
18 108.339 33/31
19 114.358 47/44
20 120.377
21 126.396
22 132.415
23 138.433
24 144.452 25/23
25 150.471
26 156.49 81/74
27 162.509
28 168.528 43/39
29 174.547 52/47
30 180.565
31 186.584
32 192.603 19/17
33 198.622 37/33, 46/41
34 204.641
35 210.66 35/31
36 216.678 17/15
37 222.697 58/51
38 228.716
39 234.735 63/55
40 240.754 54/47
41 246.773 98/85
42 252.791 81/70
43 258.81
44 264.829
45 270.848
46 276.867
47 282.886
48 288.905 13/11
49 294.923 51/43
50 300.942 69/58
51 306.961
52 312.98
53 318.999
54 325.018 35/29
55 331.036 23/19
56 337.055
57 343.074 50/41
58 349.093
59 355.112 27/22, 70/57
60 361.131 85/69
61 367.15
62 373.168
63 379.187
64 385.206
65 391.225
66 397.244 39/31
67 403.263
68 409.281 19/15
69 415.3
70 421.319 37/29
71 427.338
72 433.357
73 439.376 58/45
74 445.395 75/58
75 451.413 74/57
76 457.432
77 463.451 98/75
78 469.47
79 475.489 25/19
80 481.508
81 487.526 57/43
82 493.545
83 499.564
84 505.583
85 511.602
86 517.621 58/43
87 523.64 23/17
88 529.658
89 535.677
90 541.696
91 547.715 70/51
92 553.734 95/69
93 559.753
94 565.771
95 571.79
96 577.809 81/58
97 583.828
98 589.847
99 595.866
100 601.884
101 607.903 27/19, 98/69
102 613.922
103 619.941 93/65
104 625.96
105 631.979
106 637.998
107 644.016 74/51
108 650.035
109 656.054
110 662.073 85/58
111 668.092 25/17
112 674.111 31/21
113 680.129
114 686.148 55/37
115 692.167 85/57
116 698.186
117 704.205
118 710.224 98/65
119 716.243 62/41
120 722.261
121 728.28 99/65
122 734.299
123 740.318 23/15
124 746.337
125 752.356
126 758.374
127 764.393 14/9
128 770.412 39/25
129 776.431
130 782.45 11/7
131 788.469 41/26
132 794.488 87/55
133 800.506 27/17
134 806.525
135 812.544
136 818.563 69/43
137 824.582 66/41
138 830.601 21/13
139 836.619
140 842.638
141 848.657
142 854.676 95/58
143 860.695 74/45
144 866.714
145 872.733
146 878.751
147 884.77 5/3
148 890.789
149 896.808 47/28
150 902.827
151 908.846 93/55
152 914.864
153 920.883 63/37
154 926.902
155 932.921
156 938.94 43/25
157 944.959
158 950.978
159 956.996
160 963.015 75/43, 82/47
161 969.034
162 975.053 65/37
163 981.072 37/21
164 987.091
165 993.109 55/31
166 999.128
167 1005.147 84/47
168 1011.166
169 1017.185 9/5
170 1023.204
171 1029.222
172 1035.241
173 1041.26
174 1047.279
175 1053.298
176 1059.317
177 1065.336
178 1071.354 13/7
179 1077.373 41/22, 95/51
180 1083.392 43/23
181 1089.411
182 1095.43
183 1101.449 17/9
184 1107.467 55/29
185 1113.486 78/41
186 1119.505 21/11
187 1125.524
188 1131.543 25/13
189 1137.562 27/14
190 1143.581
191 1149.599
192 1155.618
193 1161.637 45/23
194 1167.656
195 1173.675 65/33
196 1179.694 85/43
197 1185.712
198 1191.731
199 1197.75
200 1203.769
201 1209.788
202 1215.807
203 1221.826
204 1227.844 63/31
205 1233.863 51/25
206 1239.882
207 1245.901
208 1251.92
209 1257.939
210 1263.957
211 1269.976
212 1275.995
213 1282.014 65/31, 86/41
214 1288.033
215 1294.052 19/9
216 1300.071
217 1306.089
218 1312.108
219 1318.127
220 1324.146 58/27
221 1330.165
222 1336.184
223 1342.202
224 1348.221 85/39
225 1354.24
226 1360.259
227 1366.278
228 1372.297 95/43
229 1378.315 51/23
230 1384.334
231 1390.353
232 1396.372
233 1402.391
234 1408.41
235 1414.429 43/19
236 1420.447
237 1426.466 57/25, 98/43
238 1432.485
239 1438.504
240 1444.523
241 1450.542
242 1456.56 58/25
243 1462.579
244 1468.598
245 1474.617
246 1480.636 87/37
247 1486.655
248 1492.674 45/19
249 1498.692
250 1504.711 31/13
251 1510.73
252 1516.749
253 1522.768
254 1528.787
255 1534.805
256 1540.824 95/39
257 1546.843 22/9
258 1552.862
259 1558.881
260 1564.9
261 1570.919 57/23
262 1576.937 87/35
263 1582.956
264 1588.975
265 1594.994 98/39
266 1601.013 58/23
267 1607.032 43/17
268 1613.05 33/13
269 1619.069
270 1625.088
271 1631.107
272 1637.126
273 1643.145
274 1649.164 70/27
275 1655.182
276 1661.201 47/18
277 1667.22 55/21
278 1673.239
279 1679.258
280 1685.277 45/17
281 1691.295 93/35
282 1697.314
283 1703.333 99/37
284 1709.352 51/19
285 1715.371
286 1721.39
287 1727.408
288 1733.427
289 1739.446
290 1745.465 74/27
291 1751.484
292 1757.503 69/25
293 1763.522
294 1769.54
295 1775.559
296 1781.578
297 1787.597
298 1793.616 31/11
299 1799.635 99/35
300 1805.653
301 1811.672
302 1817.691
303 1823.71 43/15
304 1829.729
305 1835.748
306 1841.767
307 1847.785
308 1853.804
309 1859.823 41/14
310 1865.842
311 1871.861
312 1877.88
313 1883.898 98/33
314 1889.917
315 1895.936
316 1901.955 3/1

Harmonics

Approximation of prime harmonics in 316edt
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) -2.25 +0.00 +0.41 +1.73 +1.69 +1.38 +0.40 +0.45 +0.72
Relative (%) -37.4 +0.0 +6.8 +28.7 +28.0 +22.9 +6.7 +7.5 +12.0
Steps
(reduced)
199
(199)
316
(0)
463
(147)
560
(244)
690
(58)
738
(106)
815
(183)
847
(215)
902
(270)
Approximation of odd harmonics in 316edt
Harmonic 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55
Error Absolute (¢) +0.82 +0.00 +2.68 +1.58 +1.69 +2.14 +2.24 +1.38 -0.94 +0.87 +0.41 -2.65 -2.56 +0.40 +0.02 +2.10
Relative (%) +13.7 +0.0 +44.6 +26.3 +28.0 +35.5 +37.1 +22.9 -15.6 +14.5 +6.8 -43.9 -42.6 +6.7 +0.3 +34.8
Steps
(reduced)
926
(294)
948
(0)
969
(21)
988
(40)
1006
(58)
1023
(75)
1039
(91)
1054
(106)
1068
(120)
1082
(134)
1095
(147)
1107
(159)
1119
(171)
1131
(183)
1142
(194)
1153
(205)