User:Overthink/Table of 311edo intervals: Difference between revisions

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Overthink (talk | contribs)
autopatrolled
2,982 edits
Thanks, but no column merges, the first column is within 13-limit, the second column is strictly HC17 through HC23, third column is strictly HC29 through HC41 (1/1 and 2/1 might be exceptions)
Eufalesio (talk | contribs)
autopatrolled
786 edits
more intervals up to 4/3, except for 103\311, 117\311, 128\311 of which I couldn't find good mapping
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Revision as of 18:56, 24 February 2026

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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.

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, 352/351, 364/363,
385/384, 441/440, 540/539,
676/675, 729/728, 847/845 		289/288, 361/360, 400/399,

484/483, 513/512, 529/528, 561/560, 576/575, 715/714

2 7.717 196/195, 225/224, 243/242,
351/350, 896/891 		256/255, 324/323
3 11.576 144/143, 169/168, 176/175
4 15.434 100/99, 105/104, 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 37/36, 38/37
13 50.161 36/35 34/33, 35/34
14 54.019 33/32 32/31
15 57.878 sA1 30/29, 31/30
16 61.736 28/27 29/28
17 65.595 27/26
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
23 88.746 m2 256/243 20/19
24 92.605 19/18 58/55
25 96.463 37/35
26 100.322 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 40/37
36 138.907 13/12
37 142.765 38/35
38 146.624 n2 160/147
39 150.482 12/11
40 154.341 82/75
41 158.199 23/21
42 162.058 45/41
43 165.916 11/10
44 169.775 32/29
45 173.633 21/19
46 177.492 d3 41/37
47 181.350 10/9
48 185.209 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 31/27
63 243.087 23/20
64 246.945 15/13 98/85
65 250.804 37/32
66 254.662 22/19
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 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
77 297.106 19/16
78 300.965 25/21
79 304.823 31/26
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
85 327.974 29/24
86 331.833 40/33
87 335.691 17/14
88 339.550 28/23
89 343.408 39/32
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 37/30
95 366.559 21/17
96 370.418 26/21
97 374.277 36/29
98 378.135 51/41
99 381.994 d4 81/65, 96/77
100 385.852 5/4
101 389.711
102 393.569 49/39
103 397.428 34/27 39/31
104 401.286 29/23
105 405.145 91/72 24/19
106 409.003 M3 81/64
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
116 447.588 22/17, 57/44
117 451.447
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 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
128 493.891
129 497.749 P4 4/3
130 501.608
131 505.466
132 509.325
133 513.183
134 517.042
135 520.900 27/20
136 524.759 A3
137 528.617
138 532.476
139 536.334
140 540.193
141 544.051
142 547.910
143 551.768 11/8
144 555.627 sA4
145 559.486
146 563.344
147 567.203
148 571.061
149 574.920
150 578.778
151 582.637 7/5
152 586.495 d5 1024/729
153 590.354 45/32
154 594.212
155 598.071
156 601.929
157 605.788
158 609.646 64/45
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
165 636.656
166 640.514
167 644.373 sd5
168 648.232 16/11
169 652.090
170 655.949
171 659.807
172 663.666
173 667.524
174 671.383
175 675.241 d6
176 679.100 40/27
177 682.958
178 686.817
179 690.675
180 694.534
181 698.392
182 702.251 P5 3/2
183 706.109
184 709.968
185 713.826
186 717.685
187 721.543
188 725.402
189 729.260 32/21
190 733.119 sd6
191 736.977
192 740.836
193 744.695 20/13
194 748.553
195 752.412
196 756.270 99/64
197 760.129 sA5
198 763.987 14/9
199 767.846
200 771.704 25/16, 39/25
201 775.563
202 779.421
203 783.280
204 787.138
205 790.997 m6 128/81
206 794.855
207 798.714
208 802.572
209 806.431
210 810.289
211 814.148 8/5
212 818.006 A5
213 821.865
214 825.723
215 829.582
216 833.441
217 837.299
218 841.158 13/8
219 845.016
220 848.875 n6
221 852.733
222 856.592
223 860.450
224 864.309
225 868.167
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
234 902.894
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
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
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
276 1064.952
277 1068.810
278 1072.669
279 1076.527
280 1080.386 28/15
281 1084.244 d8
282 1088.103 15/8
283 1091.961
284 1095.820
285 1099.678
286 1103.537
287 1107.395
288 1111.254 M7 243/128 19/10
289 1115.113
290 1118.971
291 1122.830
292 1126.688
293 1130.547
294 1134.405
295 1138.264
296 1142.122 sd8
297 1145.981 31/16
298 1149.839
299 1153.698
300 1157.556
301 1161.415
302 1165.273
303 1169.132 sA7
304 1172.990 63/32
305 1176.849
306 1180.707
307 1184.566
308 1188.424
309 1192.283
310 1196.141
311 1200.000 P8 2/1
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