User:FloraC/Table of 540edo intervals

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This table of 540edo intervals assumes the 43-limit patent val of 540edo ⟨540 856 1254 1516 1868 1998 2207 2294 2443 2623 2675 2813 2893 2930]. Prime harmonics are in bold; inconsistently mapped intervals are in italic. As is analysed in the main article, the 2.3.5.7.11.13.19-subgroup of 540edo is the same as 270edo, but primes 17 and 23 are much improved. Furthermore, 540edo can be used in the full 43-limit, but as a no-29 no-31 43-limit system, it is almost consistent to the 45-odd-limit. For this reason, intervals of 29 and 31 are given in parentheses.

# Cents Marks 13-limit 23-limit 31-limit 43-limit
0 0.0 P1 1/1 " " "
1 2.2 760/759 " "
2 4.4 385/384 " " "
3 6.6 256/255 " "
4 8.8 196/195 " " "
5 11.1 ? " "
6 13.3 126/125 " " "
7 15.5 ? " "
8 17.7 99/98 " " "
9 20.0 ? " "
10 22.2 78/77 " " "
11 24.4 ? " "
12 26.6 65/64 " " "
13 28.8 ? " "
14 31.1 56/55 " " "
15 33.3 51/50, 52/51 " "
16 35.5 49/48, 50/49 " " "
17 37.7 46/45 " "
18 40.0 45/44 " " 43/42, 44/43
19 42.2 ? " 41/40, 42/41
20 44.4 39/38, 40/39 " " "
21 46.6 ? " 37/36, 38/37
22 48.8 36/35 " " "
23 51.1 34/33, 35/34 " "
24 53.3 33/32 " " "
25 55.5 ? (31/30, 32/31) "
26 57.7 91/88 " " "
27 60.0 ? (29/28, 30/29) "
28 62.2 28/27 " " "
29 64.4 ? " "
30 66.6 26/25, 27/26 " " "
31 68.8 51/49 " "
32 71.1 25/24 " " "
33 73.3 24/23 " "
34 75.5 117/112 " " "
35 77.7 23/22 " "
36 80.0 22/21 " " "
37 82.2 ? " 43/41
38 84.4 21/20 " " "
39 86.6 ? " 41/39
40 88.8 m2 81/77 20/19 " "
41 91.1 ? " 39/37
42 93.3 96/91 19/18 " "
43 95.5 ? " 37/35
44 97.7 55/52 " " "
45 100.0 18/17 " "
46 102.2 35/33 " " "
47 104.4 17/16 " "
48 106.6 117/110 " " "
49 108.8 49/46 (33/31) "
50 111.1 16/15 " " "
51 113.3 ? " "
52 115.5 77/72 " 31/29 "
53 117.7 ? " 46/43
54 120.0 15/14 " " "
55 122.2 ? (29/27) 44/41
56 124.4 130/121 " " 43/40
57 126.6 ? " "
58 128.8 14/13 " " "
59 131.1 ? " 41/38
60 133.3 27/25 " " "
61 135.5 ? " 40/37
62 137.7 13/12 " " "
63 140.0 ? " "
64 142.2 88/81 38/35 " "
65 144.4 25/23 " "
66 146.6 49/45 " " 37/34
67 148.8 ? " "
68 151.1 12/11 " " "
69 153.3 ? " "
70 155.5 35/32 " " "
71 157.7 23/21 " "
72 160.0 169/154 " (34/31) "
73 162.2 56/51 " 45/41
74 164.4 11/10 " " "
75 166.6 ? " "
76 168.8 54/49 " " 43/39
77 171.1 ? (32/29) "
78 173.3 243/220 21/19 " "
79 175.5 ? (31/28) "
80 177.7 72/65 51/46 " 41/37
81 180.0 ? " "
82 182.2 10/9 " " "
83 184.4 ? " "
84 186.6 39/35 " " "
85 188.8 ? (29/26) "
86 191.1 125/112 " " 48/43
87 193.3 19/17 " "
88 195.5 28/25 " " "
89 197.7 ? " 37/33
90 200.0 55/49 " " 46/41
91 202.2 ? " "
92 204.4 M2 9/8 " " "
93 206.6 ? " "
94 208.8 44/39 " " "
95 211.1 26/23 " "
96 213.3 112/99 " " 43/38
97 215.5 17/15 " "
98 217.7 143/126 " " "
99 220.0 ? " 42/37
100 222.2 25/22 " " "
101 224.4 ? (33/29) 41/36
102 226.6 154/135 57/50 " 49/43
103 228.8 ? " "
104 231.1 8/7 " " "
105 233.3 ? " "
106 235.5 55/48 " " "
107 237.7 39/34 (31/27) "
108 240.0 147/128 " " "
109 242.2 23/20 " "
110 244.4 121/105 38/33 " "
111 246.6 ? " "
112 248.8 15/13 " " "
113 251.1 ? " 37/32
114 253.3 81/70 22/19 " "
115 255.5 51/44 (29/25) "
116 257.7 65/56 " " "
117 260.0 ? (36/31) 43/37
118 262.2 64/55 57/49 " 50/43
119 264.4 ? " "
120 266.6 7/6 " " "
121 268.8 ? " "
122 271.1 90/77 76/65 " "
123 273.3 ? " 41/35, 48/41
124 275.5 75/64 " (34/29) "
125 277.7 27/23 " "
126 280.0 147/125 " " "
127 282.2 20/17 " "
128 284.4 33/28 " " "
129 286.6 46/39 " "
130 288.8 13/11 " " "
131 291.1 ? (58/49) "
132 293.3 m3 32/27 " " "
133 295.5 ? " 51/43
134 297.7 108/91 19/16 " "
135 300.0 ? " 44/37
136 302.2 25/21 " " "
137 304.4 ? (31/26) "
138 306.6 105/88 " " (37/31), 43/36
139 308.8 ? " 49/41
140 311.1 140/117 91/76 " "
141 313.3 ? " "
142 315.5 6/5 " " "
143 317.7 ? " "
144 320.0 65/54 " " "
145 322.2 ? " "
146 324.4 135/112 76/63 " 41/34
147 326.6 ? (29/24) "
148 328.8 98/81 " " 52/43
149 331.1 23/19 " "
150 333.3 40/33 " " "
151 335.5 17/14 " "
152 337.7 147/121 " (62/51) "
153 340.0 28/23 " "
154 342.2 39/32 " " "
155 344.4 ? " 50/41
156 346.6 11/9 " " "
157 348.8 ? " "
158 351.1 49/40 " " "
159 353.3 ? (38/31) "
160 355.5 27/22 " " "
161 357.7 ? " "
162 360.0 16/13 " " "
163 362.2 ? " 37/30
164 364.4 100/81 " " "
165 366.6 21/17 " "
166 368.8 26/21 " " "
167 371.1 ? (31/25) "
168 373.3 150/121 " " "
169 375.5 ? (36/29) 41/33
170 377.7 56/45 " " 46/37
171 380.0 ? " "
172 382.2 81/65 " " "
173 384.4 ? " "
174 386.6 5/4 " " "
175 388.8 ? " "
176 391.1 351/280 " " "
177 393.3 64/51 " "
178 395.5 44/35 " " "
179 397.7 34/27 " "
180 400.0 63/50 " (29/23) "
181 402.2 ? " "
182 404.4 91/72 24/19 " "
183 406.6 ? (62/49) 43/34
184 408.8 M3 81/64 19/15 " "
185 411.1 ? " 52/41
186 413.3 33/26 " " "
187 415.5 ? " "
188 417.7 14/11 " " "
189 420.0 51/40 " "
190 422.2 125/98 " " (37/29)
191 424.4 23/18 " "
192 426.6 32/25 " " "
193 428.8 ? " 41/32
194 431.1 50/39 " " "
195 433.3 ? " "
196 435.5 9/7 " " "
197 437.7 ? (58/45) "
198 440.0 156/121 49/38 " "
199 442.2 ? (31/24, 40/31) "
200 444.4 84/65 " " "
201 446.6 22/17 " "
202 448.8 35/27 " " "
203 451.1 ? " 48/37
204 453.3 13/10 " " "
205 455.5 ? " "
206 457.7 125/96 99/76 " 43/33, 56/43
207 460.0 30/23 " "
208 462.2 64/49 " " "
209 464.4 17/13 " "
210 466.6 55/42 " " "
211 468.8 ? (38/29) "
212 471.1 21/16 " " "
213 473.3 46/35 " "
214 475.5 154/117 25/19 " "
215 477.7 ? (29/22) 54/41
216 480.0 33/25 " " "
217 482.2 ? " 37/28
218 484.4 143/108 " " (41/31)
219 486.6 45/34 " "
220 488.8 65/49 " " "
221 491.1 ? " "
222 493.3 117/88 " " "
223 495.5 ? " "
224 497.7 P4 4/3 " " "
225 500.0 ? " "
226 502.2 147/110 " " "
227 504.4 ? " "
228 506.6 75/56 " " "
229 508.8 51/38 " "
230 511.1 121/90 " " 43/32
231 513.3 ? (39/29) "
232 515.5 35/26 " (31/23) "
233 517.7 ? " (58/43)
234 520.0 27/20 " " "
235 522.2 ? " 50/37
236 524.4 65/48 23/17 " "
237 526.6 ? (42/31) "
238 528.8 110/81 19/14 " "
239 531.1 34/25 " "
240 533.3 49/36 " " "
241 535.5 ? " "
242 537.7 15/11 " " "
243 540.0 ? " 41/30, 56/41
244 542.2 160/117 26/19 " "
245 544.4 ? " 37/27
246 546.6 48/35 " " "
247 548.8 70/51 " "
248 551.1 11/8 " " "
249 553.3 ? (62/45) "
250 555.5 91/66 " " 51/37
251 557.7 ? (29/21, 40/29) "
252 560.0 112/81 105/76 " "
253 562.2 ? " "
254 564.4 18/13 " " "
255 566.6 68/49 " (43/31)
256 568.8 25/18 " " "
257 571.1 32/23 " "
258 573.3 39/28 " " "
259 575.5 46/33 " "
260 577.7 88/63 " " 60/43
261 580.0 ? " "
262 582.2 7/5 " " "
263 584.4 ? " "
264 586.6 d5 108/77 80/57 " "
265 588.8 ? " 52/37
266 591.1 45/32 38/27 " "
267 593.3 ? (31/22) "
268 595.5 55/39 " " "
269 597.7 24/17 " "
270 600.0 99/70 " " (41/29, 58/41)
271 602.2 17/12 " "
272 604.4 78/55 " " "
273 606.6 ? (44/31) "
274 608.8 64/45 27/19 " "
275 611.1 ? " 37/26
276 613.3 A4 77/54 57/40 " "
277 615.5 ? " "
278 617.7 10/7 " " "
279 620.0 ? " "
280 622.2 63/44 " " 43/30
281 624.4 33/23 " "
282 626.6 56/39 " " "
283 628.8 23/16 " "
284 631.1 36/25 " " "
285 633.3 49/34 " (62/43)
286 635.5 13/9 " " "
287 637.7 ? " "
288 640.0 81/56 " " "
289 642.2 ? (29/20, 42/29) "
290 644.4 132/91 " " 74/51
291 646.6 ? (45/31) "
292 648.8 16/11 " " "
293 651.1 51/35 " "
294 653.3 35/24 " " "
295 655.5 ? " 54/37
296 657.7 117/80 19/13 " "
297 660.0 ? " 41/28, 60/41
298 662.2 22/15 " " "
299 664.4 ? " "
300 666.6 72/49 " " "
301 668.8 25/17 " "
302 671.1 81/55 28/19 " "
303 673.3 ? (31/21) "
304 675.5 65/44 34/23 " "
305 677.7 ? " 37/25
306 680.0 40/27 " " "
307 682.2 ? " (43/29)
308 684.4 49/33 " (46/31) "
309 686.6 ? (58/39) "
310 688.8 125/84 " " 64/43
311 691.1 76/51 " "
312 693.3 112/75 " " "
313 695.5 ? " "
314 697.7 175/117 " " "
315 700.0 ? " "
316 702.2 P5 3/2 " " "
317 704.4 ? " "
318 706.6 176/117 " " "
319 708.8 ? " "
320 711.1 98/65 95/63 " "
321 713.3 68/45 " "
322 715.5 121/80 " " (62/41)
323 717.7 ? " 56/37
324 720.0 50/33 " " "
325 722.2 ? (44/29) 41/27
326 724.4 117/77 38/25 " "
327 726.6 35/23 " "
328 728.8 32/21 " " "
329 731.1 ? (29/19) "
330 733.3 55/36 " " "
331 735.5 26/17 " "
332 737.7 49/32 " " "
333 740.0 23/15 " "
334 742.2 135/88 " " 43/28, 66/43
335 744.4 ? " "
336 746.6 20/13 " " "
337 748.8 ? " 37/24
338 751.1 54/35 " " "
339 753.3 17/11 " "
340 755.5 65/42 " " "
341 757.7 ? (31/20, 48/31) "
342 760.0 121/78 76/49 " "
343 762.2 ? (45/29) "
344 764.4 14/9 " " "
345 766.6 ? " "
346 768.8 39/25 " " "
347 771.1 ? " 64/41
348 773.3 25/16 " " "
349 775.5 36/23 " "
350 777.7 196/125 " " (58/37)
351 780.0 80/51 " "
352 782.2 11/7 " " "
353 784.4 ? " "
354 786.6 52/33 " " "
355 788.8 ? " 41/26
356 791.1 m6 128/81 30/19 " "
357 793.3 ? (49/31) 68/37
358 795.5 144/91 19/12 " "
359 797.7 ? " "
360 800.0 100/63 " (46/29) "
361 802.2 27/17 " "
362 804.4 35/22 " " "
363 806.6 51/32 " "
364 808.8 351/220 " " "
365 811.1 ? " "
366 813.3 8/5 " " "
367 815.5 ? " "
368 817.7 77/48 " " "
369 820.0 ? " "
370 822.2 45/28 " " 37/23
371 824.4 ? (29/18) 66/41
372 826.6 121/75 " " "
373 828.8 ? (50/31) "
374 831.1 21/13 " " "
375 833.3 34/21 " "
376 835.5 81/50 " " "
377 837.7 ? " 60/37
378 840.0 13/8 " " "
379 842.2 ? " "
380 844.4 44/27 " " "
381 846.6 ? (31/19) "
382 848.8 49/30 " " "
383 851.1 ? " "
384 853.3 18/11 " " "
385 855.5 ? " 41/25
386 857.7 64/39 " " "
387 860.0 23/14 " "
388 862.2 242/147 " (51/31) "
389 864.4 28/17 " "
390 866.6 33/20 " " "
391 868.8 38/23 " "
392 871.1 81/49 " " 43/26
393 873.3 (48/29) " "
394 875.5 224/135 63/38 " "
395 877.7 ? " "
396 880.0 108/65 " " "
397 882.2 ? " "
398 884.4 5/3 " " "
399 886.6 ? " "
400 888.8 117/70 " " "
401 891.1 ? " 82/49
402 893.3 176/105 " " (62/37), 72/43
403 895.5 ? (52/31) "
404 897.7 42/25 " " "
405 900.0 ? " 37/22
406 902.2 91/54 32/19 " "
407 904.4 ? " 86/51
408 906.6 M6 27/16 " " "
409 908.8 ? (49/29) "
410 911.1 22/13 " " "
411 913.3 39/23 " "
412 915.5 56/33 " " "
413 917.7 17/10 " "
414 920.0 143/84 " " "
415 922.2 46/27 " "
416 924.4 75/44 " (29/17) "
417 926.6 ? " 41/24, 70/41
418 928.8 77/45 " " "
419 931.1 ? " "
420 933.3 12/7 " " "
421 935.5 ? " "
422 937.7 55/32 " " 43/25
423 940.0 ? (31/18) 74/43
424 942.2 112/65 " " "
425 944.4 88/51 (50/29) "
426 946.6 121/70 19/11 " "
427 948.8 ? " 64/37
428 951.1 26/15 " " "
429 953.3 ? " "
430 955.5 125/72 33/19 " "
431 957.7 40/23 " "
432 960.0 195/112 " " "
433 962.2 68/39 (54/31) "
434 964.4 96/55 " " "
435 966.6 ? " "
436 968.8 7/4 " " "
437 971.1 ? " "
438 973.3 135/77 100/57 " 86/49
439 975.5 ? (58/33) 72/41
440 977.7 44/25 " " "
441 980.0 ? " 37/21
442 982.2 143/81 " " "
443 984.8 30/17 " "
444 986.6 99/56 " " 76/43
445 988.8 23/13 " "
446 991.1 39/22 " " "
447 993.3 ? " "
448 995.5 m7 16/9 " " "
449 997.7 ? " "
450 1000.0 98/55 57/32 " 41/23
451 1002.2 ? " 66/37
452 1004.4 25/14 " " "
453 1006.6 34/19 " "
454 1008.8 224/125 " " 43/24
455 1011.1 ? (52/29) "
456 1013.3 70/39 " " "
457 1015.5 ? " "
458 1017.7 9/5 " " "
459 1020.0 ? " "
460 1022.2 65/36 " " "
461 1024.4 ? (56/31) "
462 1026.6 405/224 38/21 " "
463 1028.8 ? (29/16) "
464 1031.1 49/27 " " "
465 1033.3 ? " "
466 1035.5 20/11 " " "
467 1037.7 51/28 " "
468 1040.0 175/96 " (31/17) "
469 1042.2 42/23 " "
470 1044.4 64/35 " " "
471 1046.6 ? " "
472 1048.8 11/6 " " "
473 1051.1 ? " "
474 1053.3 90/49 " " 68/37
475 1055.5 46/25 " "
476 1057.7 81/44 35/19 " "
477 1060.0 ? " "
478 1062.2 24/13 " " "
479 1064.4 ? " 37/20
480 1066.6 50/27 " " "
481 1068.8 ? " 76/41
482 1071.1 13/7 " " "
483 1073.3 ? " "
484 1075.5 121/65 " " 80/43
485 1077.7 ? (54/29) 41/22
486 1080.0 28/15 " " "
487 1082.2 ? " 43/23
488 1084.4 144/77 " " "
489 1086.6 ? " "
490 1088.8 15/8 " " "
491 1091.1 92/49 (62/33) "
492 1093.3 220/117 " " "
493 1095.5 32/17 " "
494 1097.7 49/26 " " "
495 1100.0 17/9 " "
496 1102.2 104/55 " " "
497 1104.4 ? " 70/37
498 1106.6 91/48 36/19 " "
499 1108.8 ? " 74/39
500 1111.1 M7 154/81 19/10 " "
501 1113.3 ? " 78/41
502 1115.5 40/21 " " "
503 1117.7 ? " 82/43
504 1120.0 21/11 " " "
505 1122.2 44/23 " "
506 1124.4 224/117 " " "
507 1126.6 23/12 " "
508 1128.8 48/25 " " "
509 1131.1 98/51 " "
510 1133.3 25/13 " " "
511 1135.5 ? " "
512 1137.7 27/14 " " "
513 1140.0 ? (29/15) "
514 1142.2 176/91 " " "
515 1144.4 ? (31/16) "
516 1146.6 64/33 " " "
517 1148.8 33/17 " "
518 1151.1 35/18 " " "
519 1153.3 ? " 37/19
520 1155.5 39/20 " " "
521 1157.7 ? " 41/21
522 1160.0 88/45 " " 43/22
523 1162.2 45/23 " "
524 1164.4 49/25 " " "
525 1166.6 51/26 " "
526 1168.8 55/28 " " "
527 1171.1 ? " "
528 1173.3 63/32 " " "
529 1175.5 ? " "
530 1177.7 77/39 75/38 " "
531 1180.0 ? " "
532 1182.2 99/50 " " "
533 1184.4 ? " "
534 1186.6 125/63 " " "
535 1188.8 ? " "
536 1191.1 175/88 " " "
537 1193.3 255/128 " "
538 1195.5 351/176 " " "
539 1197.7 483/242 " "
540 1200.0 P8 2/1 " " "
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