User:Overthink/Table of 311edo intervals

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This table assumes the 41-limit patent val ⟨311 493 722 873 1076 1151 1271 1321 1407 1511 1541 1620 1666] of 311edo. Intervals that differ by their assigned steps by more than 50%, but less than 100%, are marked with italics. Intervals that differ by more than 100% are not shown. Since 311edo supports true hemififths, a hemipyth marking is provided.

Intervals of 311edo
Steps Cents Marks Approximate Ratios
13-limit 23-limit 41-limit
0 0.000 P1 1/1
1 3.859 325/324, 385/384 513/512, 715/714
2 7.717 196/195, 225/224 256/255
3 11.576 144/143, 169/168
4 15.434 100/99, 121/120
5 19.293 91/90, 99/98 85/84, 92/91, 96/95 82/81, 88/87, 93/92
6 23.151 78/77, 81/80 70/69, 76/75, 77/76 75/74
7 27.010 64/63, 65/64, 66/65 69/68 63/62
8 30.868 sd2 55/54, 56/55 57/56 58/57
9 34.727 49/48, 50/49 51/50, 52/51
10 38.585 45/44 46/45
11 42.444 40/39 41/40, 42/41
12 46.302 39/38, 77/75 37/36, 38/37
13 50.161 36/35 34/33, 35/34
14 54.019 33/32, 65/63 32/31
15 57.878 sA1 30/29, 31/30
16 61.736 28/27 57/55 29/28
17 65.595 27/26, 80/77
18 69.453 25/24, 26/25 51/49
19 73.312 24/23
20 77.170 23/22
21 81.029 22/21
22 84.887 21/20 41/39
23 88.746 m2 256/243 20/19
24 92.605 135/128 19/18 39/37, 58/55
25 96.463 37/35
26 100.322 35/33 18/17
27 104.180 17/16
28 108.039 33/31
29 111.897 16/15
30 115.756 A1 2187/2048 31/29
31 119.614 15/14
32 123.473 29/27
33 127.331 14/13
34 131.190 41/38
35 135.048 27/25 40/37
36 138.907 13/12
37 142.765 25/23 38/35
38 146.624 n2 49/45, 160/147 37/34
39 150.482 12/11
40 154.341 35/32 82/75
41 158.199 23/21 34/31
42 162.058 45/41
43 165.916 11/10
44 169.775 32/29
45 173.633 21/19
46 177.492 d3 31/28, 41/37
47 181.350 10/9
48 185.209 49/44 69/62
49 189.068 29/26
50 192.926 19/17
51 196.785 28/25
52 200.643 55/49 64/57
53 204.502 M2 9/8
54 208.360 44/39 35/31
55 212.219 26/23
56 216.077 17/15
57 219.936 25/22 42/37
58 223.794 33/29
59 227.653 57/50, 65/57
60 231.511 8/7
61 235.370 sd3 55/48, 63/55
62 239.228 147/128 31/27
63 243.087 23/20, 38/33
64 246.945 15/13 98/85
65 250.804 52/45 37/32
66 254.662 22/19, 80/69
67 258.521 29/25, 36/31
68 262.379 sA2 64/55 57/49
69 266.238 7/6
70 270.096 90/77 76/65
71 273.955 75/64 34/29, 41/35
72 277.814 27/23
73 281.672 20/17
74 285.531 33/28
75 289.389 13/11
76 293.248 m3 32/27, 77/65 45/38
77 297.106 19/16
78 300.965 25/21 44/37
79 304.823 31/26, 37/31
80 308.682 49/41
81 312.540 91/76
82 316.399 6/5
83 320.257 A2 77/64
84 324.116 135/112 35/29
85 327.974 29/24
86 331.833 40/33, 63/52 23/19
87 335.691 17/14
88 339.550 243/200 28/23
89 343.408 39/32, 128/105 50/41
90 347.267 11/9
91 351.125 n3 49/40, 60/49
92 354.984 27/22
93 358.842 16/13
94 362.701 100/81 69/56 37/30
95 366.559 21/17, 68/55
96 370.418 26/21, 99/80 31/25
97 374.277 36/29, 41/33
98 378.135 56/45 46/37, 51/41
99 381.994 d4 81/65, 96/77
100 385.852 5/4
101 389.711 114/91
102 393.569 49/39 64/51, 69/55
103 397.428 44/35 34/27 39/31
104 401.286 29/23
105 405.145 91/72 24/19
106 409.003 M3 81/64 19/15
107 412.862 33/26
108 416.720 14/11
109 420.579 51/40
110 424.437 23/18
111 428.296 32/25, 50/39 41/32
112 432.154 77/60
113 436.013 9/7
114 439.871 sd4 49/38 40/31
115 443.730 128/99 31/24
116 447.588 35/27 22/17, 57/44
117 451.447 135/104
118 455.305 13/10
119 459.164 30/23
120 463.023 64/49, 98/75 17/13 81/62
121 466.881 sA3 55/42, 72/55 38/29
122 470.740 21/16
123 474.598 25/19
124 478.457 29/22
125 482.315 33/25 37/28
126 486.174 45/34 49/37
127 490.032 65/49 69/52, 85/64
128 493.891
129 497.749 P4 4/3
130 501.608
131 505.466
132 509.325
133 513.183 35/26 39/29
134 517.042 31/23
135 520.900 27/20 50/37
136 524.759 A3 23/17
137 528.617 19/14
138 532.476 34/25
139 536.334 15/11
140 540.193 41/30
141 544.051 26/19
142 547.910 48/35
143 551.768 11/8
144 555.627 sA4
145 559.486
146 563.344 18/13
147 567.203 25/18
148 571.061
149 574.920 39/28
150 578.778
151 582.637 7/5
152 586.495 d5 1024/729
153 590.354 45/32 38/27
154 594.212 55/39 31/22
155 598.071 24/17 41/29
156 601.929 17/12 58/41
157 605.788 78/55 44/31
158 609.646 64/45 27/19
159 613.505 A4 729/512
160 617.363 10/7
161 621.222
162 625.080
163 628.939 23/16
164 632.797 36/25
165 636.656 13/9
166 640.514
167 644.373 sd5
168 648.232 16/11
169 652.090 35/24
170 655.949
171 659.807
172 663.666 22/15
173 667.524 25/17
174 671.383 28/19
175 675.241 d6 34/23
176 679.100 40/27
177 682.958
178 686.817 52/35
179 690.675
180 694.534 112/75
181 698.392
182 702.251 P5 3/2
183 706.109 176/117, 182/121
184 709.968 128/85
185 713.826
186 717.685 50/33
187 721.543
188 725.402 38/25
189 729.260 32/21
190 733.119 sd6 55/36, 84/55 29/19
191 736.977 49/32 26/17
192 740.836 23/15
193 744.695 20/13
194 748.553
195 752.412 54/35 17/11
196 756.270 99/64
197 760.129 sA5
198 763.987 14/9
199 767.846 120/77
200 771.704 25/16, 39/25
201 775.563 36/23
202 779.421 80/51
203 783.280 11/7
204 787.138 52/33
205 790.997 m6 128/81 30/19
206 794.855 19/12
207 798.714
208 802.572
209 806.431
210 810.289
211 814.148 8/5
212 818.006 A5 77/48, 130/81
213 821.865 45/28
214 825.723
215 829.582 21/13, 160/99
216 833.441 34/21, 55/34
217 837.299 81/50
218 841.158 13/8
219 845.016 44/27
220 848.875 n6 49/30, 80/49
221 852.733 18/11
222 856.592 64/39, 105/64
223 860.450 23/14
224 864.309 28/17
225 868.167 33/20, 104/63 38/23
226 872.026
227 875.884
228 879.743 d7
229 883.601 5/3
230 887.460
231 891.318
232 895.177
233 899.035 42/25
234 902.894 32/19
235 906.752 M6 27/16
236 910.611
237 914.469
238 918.328
239 922.186
240 926.045
241 929.904
242 933.762 12/7
243 937.621 sd7
244 941.479
245 945.338
246 949.196 64/37
247 953.055 26/15
248 956.913
249 960.772
250 964.630 sA6
251 968.489 7/4
252 972.347
253 976.206
254 980.064
255 983.923
256 987.781
257 991.640
258 995.498 m7 16/9
259 999.357
260 1003.215
261 1007.074 34/19
262 1010.932
263 1014.791
264 1018.650 9/5
265 1022.508 A6
266 1026.367
267 1030.225 29/16
268 1034.084 20/11
269 1037.942
270 1041.801
271 1045.659
272 1049.518 11/6
273 1053.376 n7 90/49
274 1057.235
275 1061.093 24/13
276 1064.952
277 1068.810
278 1072.669 13/7
279 1076.527
280 1080.386 28/15
281 1084.244 d8
282 1088.103 15/8
283 1091.961
284 1095.820 32/17
285 1099.678 17/9
286 1103.537
287 1107.395 36/19
288 1111.254 M7 243/128 19/10
289 1115.113 40/21
290 1118.971 21/11
291 1122.830 44/23
292 1126.688 23/12
293 1130.547 25/13, 48/25
294 1134.405 27/13, 77/40
295 1138.264 27/14 56/29
296 1142.122 sd8 29/15, 60/31
297 1145.981 64/33 31/16
298 1149.839 35/18 33/17, 68/35
299 1153.698 76/39 37/19, 72/37
300 1157.556 39/20 41/21, 80/41
301 1161.415 88/45 45/23
302 1165.273 49/25, 96/49 51/26, 100/51
303 1169.132 sA7 55/28, 108/55 112/57 57/29
304 1172.990 63/32
305 1176.849 160/81
306 1180.707 196/99
307 1184.566 99/50, 208/105
308 1188.424 143/72
309 1192.283 448/225 255/128
310 1196.141 768/385
311 1200.000 P8 2/1
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