Table of 431edo intervals: Difference between revisions

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Latest revision as of 13:39, 16 June 2026

This table of 431edo intervals assumes the 13-limit patent val ⟨431 683 1001 1210 1491 1595] of 431edo.

Intervals highlighted in bold are prime harmonics or subharmonics. Intervals that differ from their assigned steps by more than 50%, but no more than 100%, are shown in italic. Intervals that differ by more than 100% are not shown. For clarity, an entry can contain multiple intervals if they are of comparable complexity.

Degree Cents Marks 5-limit 7-limit 11-limit 13-limit
0 0.000 P1 1/1
1 2.784 6144/6125 441/440 351/350
2 5.568 385/384

1375/1372

3 8.353 1029/1024

225/224

4 11.137 126/125 1331/1323
5 13.921 4125/4096
6 16.705 1344/1331 105/104
7 19.490 81/80
8 22.274 245/242
9 25.058 2079/2048
10 27.842 64/63
11 30.626 56/55
12 33.411 55/54
13 36.395 49/48
14 38.979 128/125
15 41.763 1375/1344
16 44.548 40/39
17 47.332 36/35
18 50.116 1120/1089
19 52.900 33/32
20 55.684 1225/1188
21 58.469 6875/6656
22 61.253 3136/3025
23 64.037 28/27
24 66.821 4900/4719
25 69.606 343/330
26 72.390 25/24
27 75.174 256/245
28 77.958 288/275
29 80.742 22/21
30 83.527 21/20
31 86.311 605/576
32 89.095 539/512
33 91.879 m2 135/128
34 94.664 1568/1485
35 97.448 128/121
36 100.232 297/280
37 103.016 35/33
38 105.800 1029/968
39 108.585 1408/1323
40 111.370 16/15 273/256
41 114.153 294/275
42 116.937 1100/1029
43 119.722 15/14
44 122.506 189/176
45 125.290 275/256
46 128.074 14/13
47 130.858 3087/2860
48 133.643 392/363
49 136.427 1430/1323
50 139.211 13/12
51 141.995 525/484
52 144.780 4608/4235
53 147.564 572/525
54 150.348 12/11
55 153.132 1323/1210
56 155.916 35/32 128/117
57 158.701 3087/2816
58 161.485 484/441
59 164.269 11/10
60 167.053 441/400
61 169.838 847/768
62 172.622 968/875
63 175.406 448/405
64 178.190 256/231
65 180.974 672/605
66 183.759 10/9
67 186.543 49/44
68 189.327 1925/1728
69 192.111 352/315 143/128
70 194.900 28/25
71 197.680 3087/2750
72 200.464 55/49
73 203.248 M2 9/8
74 206.032 7203/6400
75 208.817 1936/1715
76 211.601 325/288
77 214.385
78 217.169 825/728
79 219.954 500/441
80 222.738 256/225 25/22
81 225.522 726/637
82 228.306 3520/3087
83 231.090 8/7
84 233.875 63/55
85 236.659 55/48
86 239.443 147/128
87 242.227 7371/6400
88 245.012 2200/1911
89 247.796 15/13
90 250.580 1323/1144
91 253.364 1815/1568
92 256.148 297/256
93 258.933 1225/1056
94 261.717 64/55
95 264.501 220/189
96 267.285 7/6
97 270.070 1029/880
98 272.854 1375/1176
99 275.638 75/64
100 278.422 168/143
101 281.206 1210/1029
102 283.991 33/28
103 286.775 520/441
104 289.559 13/11
105 292.343
106 295.128
107 297.912 m3 32/27
108 300.696
109 303.480
110 306.265
111 309.049
112 311.833
113 314.617 6/5
114 317.401
115 320.186 77/64
116 322.970
117 325.754
118 328.528
119 331.323
120 334.107 40/33
121 336.891
122 339.675
123 342.459 39/32
124 345.244
125 348.028 11/9
126 350.812 49/40
127 353.596 27/22
128 356.381
129 359.165 315/256 16/13
130 361.949
131 364.733
132 367.517
133 370.302 26/21
134 373.086
135 375.870
136 378.654 56/45
137 381.439 96/77
138 384.223
139 387.007 5/4
140 389.791
141 392.575
142 395.360
143 398.144
144 400.928
145 403.712
146 406.497 M3 81/64
147 409.281
148 412.065
149 414.849 80/63
150 417.633 14/11
151 420.418
152 423.202
153 425.986 32/25
154 428.770
155 431.555
156 434.339 9/7
157 437.123
158 439.907 165/128
159 442.691
160 445.476 128/99
161 448.260
162 451.044
163 453.828 13/10
164 456.613
165 459.397
166 462.181 64/49
167 464.965
168 467.749
169 470.534 21/16
170 473.318
171 476.102
172 478.886
173 481.671 169/128
174 484.455
175 487.239
176 490.023
177 492.807
178 495.592
179 498.375 P4 4/3
180 501.160
181 503.944
182 506.729
183 509.513
184 512.297
185 515.081
186 517.865 27/20
187 520.650
188 523.434
189 526.218 256/189
190 529.002
191 531.787
192 534.571
193 537.355 15/11
194 540.139
195 542.923 175/128
196 545.708 48/35
197 548.492
198 551.276 11/8
199 554.060
200 556.845
201 559.629
202 562.413 18/13
203 565.197
204 567.981
205 570.766 25/18
206 573.550 39/28
207 576.334
208 579.118
209 581.903 7/5
210 584.687
211 587.471
212 590.255 d5 45/32
213 593.039
214 595.824
215 598.608
216 601.392
217 604.176
218 606.961
219 609.745 A4 64/45
220 612.529
221 615.313
222 618.097 10/7
223 620.882
224 623.666
225 626.450 56/39
226 629.234 36/25
227 632.019
228 634.803
229 637.587 13/9
230 640.371
231 643.155
232 645.940
233 648.724 16/11
234 651.508
235 654.292 35/24
236 657.077 256/175
237 659.861
238 662.645 22/15
239 665.429
240 668.213
241 671.000
242 673.782 189/128
243 676.566
244 679.350
245 682.135 40/27
246 684.919
247 687.703
248 690.487
249 693.271
250 696.056
251 698.840
252 701.624 P5 3/2
253 704.408
254 707.193
255 709.977
256 712.761
257 715.545
258 718.329 256/169
259 721.114
260 723.898
261 726.682
262 729.466 32/21
263 732.251
264 735.035
265 737.819 49/32
266 740.603
267 743.387
268 746.172 20/13
269 748.956
270 751.740
271 754.524 99/64
272 757.309
273 760.093 256/165
274 762.877
275 765.661 14/9
276 768.445
277 771.230
278 774.014 25/16
279 776.798
280 779.582
281 782.367 11/7
282 785.151 63/40
283 787.935
284 790.719
285 793.503 m6 128/81
286 796.288
287 799.072
288 801.856
289 804.640
290 807.425
291 810.209
292 812.993 8/5
293 815.777
294 818.561 77/48
295 821.346 45/28
296 824.130
297 826.914
298 829.698 21/13
299 832.483
300 835.267
301 838.051
302 840.835 512/315 13/8
303 843.619
304 846.404 44/27
305 849.188 80/49
306 851.972 18/11
307 854.756
308 857.541 64/39
309 860.325
310 863.109
311 865.893 33/20
312 868.677
313 871.462
314 874.246
315 877.030
316 879.814 128/77
317 882.599
318 885.383 5/3
319 888.167
320 890.951
321 893.735
322 896.520
323 899.304
324 902.088
325 904.872 M6 27/16
326 907.657
327 910.441 22/13
328 913.225
329 916.009 56/33
330 918.794
331 921.578
332 924.362 128/75
333 927.146
334 929.930
335 932.715 12/7
336 935.499
337 938.283 55/32
338 941.067
339 943.852 512/297
340 946.636
341 949.420
342 952.204 26/15
343 954.988
344 957.773
345 960.557 256/147
346 963.341 96/55
347 966.125
348 968.910 7/4
349 971.694
350 974.478
351 977.262 225/128 44/25
352 980.046
353 982.831
354 985.615
355 988.399
356 991.183
357 993.968
358 996.752 m7 16/9
359 999.536
360 1002.320
361 1005.104 25/14
362 1007.889 256/143
363 1010.673
364 1013.457
365 1016.241 9/5
366 1019.026
367 1021.810 231/128
368 1024.594
369 1027.378
370 1030.162
371 1032.947
372 1035.731 20/11
373 1038.515
374 1041.299
375 1044.084 64/35 117/64
376 1046.868
377 1049.652 11/6
378 1052.436
379 1055.220
380 1058.005
381 1060.789 24/13
382 1063.573
383 1066.357
384 1069.142
385 1071.926 13/7
386 1074.710 512/275
387 1077.494
388 1080.278 28/15
389 1083.063
390 1085.847
391 1088.631 15/8 512/273
392 1091.415
393 1094.200
394 1096.984
395 1099.768
396 1102.552 121/64
397 1105.336
398 1108.121 M7 243/128
399 1110.905
400 1113.689
401 1116.473 40/21
402 1119.258 21/11
403 1122.042
404 1124.826 245/128
405 1127.610 48/25
406 1130.394
407 1133.179
408 1135.963 27/14
409 1138.747
410 1141.531
411 1144.316
412 1147.100 64/33
413 1149.884
414 1152.668 35/18
415 1155.452 39/20
416 1158.237
417 1161.021 125/64
418 1163.805 96/49
419 1166.589
420 1169.374
421 1172.158 63/32
422 1174.942
423 1177.726
424 1180.510
425 1183.295
426 1186.079
427 1188.863
428 1191.647
429 1194.432
430 1197.216
431 1200.000 P8 2/1
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