# Theory

540 tone equal temperament, also called 540-EDO divides the octave in 540 equal steps. Since 540 = 2 * 270 and 540 = 45 * 12, it contains 270edo and 12edo as subsets, both belonging to the zeta peak edos, zeta integral edos and zeta gap edos sequences. The 31-limit patent val for 540-EDO is <540 856 1254 1516 1868 1998 2207 2294 2443 2623 2675|.

# Divisors

The prime factorization of 540 is $540 = 2^{2} \cdot 3^{3} \cdot 5$

Its divisors are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540.

# Intervals

## Harmonic primes

Prime Closest step Error (steps) Error (cents)
2 540 0.000000000 0.000000000
3 856 0.120249611 0.267221357
5 1254 0.158828761 0.352952802
7 1516 0.028342089 0.062982420
11 1868 -0.093074064 -0.206831254
13 1998 -0.237447796 -0.527661769
17 2207 -0.229934275 -0.510965056
19 2294 0.119142740 0.264761645
23 2443 0.276543729 0.614541620
29 2623 -0.309737369 -0.688305264
31 2675 -0.266007609 -0.591128020

## Patent val mapping

Size (steps) Size (extended 12-edo notation) Size (cents) ______ Just (ratio) Just (factorization) Just (FJS notation) Just (cents) ______ Error (steps) Error (cents) ______ Comments
0 0.000
1 2.222
2 4.444
3 6.667
4 8.889
5 11.111
6 13.333
7 15.556
8 17.778
9 20.000
10 22.222
11 24.444
12 26.667
13 28.889
14 31.111
15 33.333
16 35.556
17 37.778
18 40.000
19 42.222
20 44.444
21 46.667
22 48.889
23 51.111
24 53.333
25 55.556
26 57.778
27 60.000
28 62.222
29 64.444
30 66.667
31 68.889
32 71.111
33 73.333
34 75.556
35 77.778
36 80.000
37 82.222
38 84.444
39 86.667
40 88.889
41 91.111
42 93.333
43 95.556
44 97.778
45 100.000
46 102.222
47 104.444
48 106.667
49 108.889
50 111.111
51 113.333
52 115.556
53 117.778
54 120.000
55 122.222
56 124.444
57 126.667
58 128.889
59 131.111
60 133.333
61 135.556
62 137.778
63 140.000
64 142.222
65 144.444
66 146.667
67 148.889
68 151.111
69 153.333
70 155.556
71 157.778
72 160.000
73 162.222
74 164.444
75 166.667
76 168.889
77 171.111
78 173.333
79 175.556
80 177.778
81 180.000
82 182.222
83 184.444
84 186.667
85 188.889
86 191.111
87 193.333
88 195.556
89 197.778
90 200.000
91 202.222
92 204.444
93 206.667
94 208.889
95 211.111
96 213.333
97 215.556
98 217.778
99 220.000
100 222.222
101 224.444
102 226.667
103 228.889
104 231.111
105 233.333
106 235.556
107 237.778
108 240.000
109 242.222
110 244.444
111 246.667
112 248.889
113 251.111
114 253.333
115 255.556
116 257.778
117 260.000
118 262.222
119 264.444
120 266.667
121 268.889
122 271.111
123 273.333
124 275.556
125 277.778
126 280.000
127 282.222
128 284.444
129 286.667
130 288.889
131 291.111
132 293.333
133 295.556
134 297.778
135 300.000
136 302.222
137 304.444
138 306.667
139 308.889
140 311.111
141 313.333
142 315.556
143 317.778
144 320.000
145 322.222
146 324.444
147 326.667
148 328.889
149 331.111
150 333.333
151 335.556
152 337.778
153 340.000
154 342.222
155 344.444
156 346.667
157 348.889
158 351.111
159 353.333
160 355.556
161 357.778
162 360.000
163 362.222
164 364.444
165 366.667
166 368.889
167 371.111
168 373.333
169 375.556
170 377.778
171 380.000
172 382.222
173 384.444
174 386.667
175 388.889
176 391.111
177 393.333
178 395.556
179 397.778
180 400.000
181 402.222
182 404.444
183 406.667
184 408.889
185 411.111
186 413.333
187 415.556
188 417.778
189 420.000
190 422.222
191 424.444
192 426.667
193 428.889
194 431.111
195 433.333
196 435.556
197 437.778
198 440.000
199 442.222
200 444.444
201 446.667
202 448.889
203 451.111
204 453.333
205 455.556
206 457.778
207 460.000
208 462.222
209 464.444
210 466.667
211 468.889
212 471.111
213 473.333
214 475.556
215 477.778
216 480.000
217 482.222
218 484.444
219 486.667
220 488.889
221 491.111
222 493.333
223 495.556
224 497.778
225 500.000
226 502.222
227 504.444
228 506.667
229 508.889
230 511.111
231 513.333
232 515.556
233 517.778
234 520.000
235 522.222
236 524.444
237 526.667
238 528.889
239 531.111
240 533.333
241 535.556
242 537.778
243 540.000
244 542.222
245 544.444
246 546.667
247 548.889
248 551.111
249 553.333
250 555.556
251 557.778
252 560.000
253 562.222
254 564.444
255 566.667
256 568.889
257 571.111
258 573.333
259 575.556
260 577.778
261 580.000
262 582.222
263 584.444
264 586.667
265 588.889
266 591.111
267 593.333
268 595.556
269 597.778
270 600.000
271 602.222
272 604.444
273 606.667
274 608.889
275 611.111
276 613.333
277 615.556
278 617.778
279 620.000
280 622.222
281 624.444
282 626.667
283 628.889
284 631.111
285 633.333
286 635.556
287 637.778
288 640.000
289 642.222
290 644.444
291 646.667
292 648.889
293 651.111
294 653.333
295 655.556
296 657.778
297 660.000
298 662.222
299 664.444
300 666.667
301 668.889
302 671.111
303 673.333
304 675.556
305 677.778
306 680.000
307 682.222
308 684.444
309 686.667
310 688.889
311 691.111
312 693.333
313 695.556
314 697.778
315 700.000
316 702.222
317 704.444
318 706.667
319 708.889
320 711.111
321 713.333
322 715.556
323 717.778
324 720.000
325 722.222
326 724.444
327 726.667
328 728.889
329 731.111
330 733.333
331 735.556
332 737.778
333 740.000
334 742.222
335 744.444
336 746.667
337 748.889
338 751.111
339 753.333
340 755.556
341 757.778
342 760.000
343 762.222
344 764.444
345 766.667
346 768.889
347 771.111
348 773.333
349 775.556
350 777.778
351 780.000
352 782.222
353 784.444
354 786.667
355 788.889
356 791.111
357 793.333
358 795.556
359 797.778
360 800.000
361 802.222
362 804.444
363 806.667
364 808.889
365 811.111
366 813.333
367 815.556
368 817.778
369 820.000
370 822.222
371 824.444
372 826.667
373 828.889
374 831.111
375 833.333
376 835.556
377 837.778
378 840.000
379 842.222
380 844.444
381 846.667
382 848.889
383 851.111
384 853.333
385 855.556
386 857.778
387 860.000
388 862.222
389 864.444
390 866.667
391 868.889
392 871.111
393 873.333
394 875.556
395 877.778
396 880.000
397 882.222
398 884.444
399 886.667
400 888.889
401 891.111
402 893.333
403 895.556
404 897.778
405 900.000
406 902.222
407 904.444
408 906.667
409 908.889
410 911.111
411 913.333
412 915.556
413 917.778
414 920.000
415 922.222
416 924.444
417 926.667
418 928.889
419 931.111
420 933.333
421 935.556
422 937.778
423 940.000
424 942.222
425 944.444
426 946.667
427 948.889
428 951.111
429 953.333
430 955.556
431 957.778
432 960.000
433 962.222
434 964.444
435 966.667
436 968.889
437 971.111
438 973.333
439 975.556
440 977.778
441 980.000
442 982.222
443 984.444
444 986.667
445 988.889
446 991.111
447 993.333
448 995.556
449 997.778
450 1000.000
451 1002.222
452 1004.444
453 1006.667
454 1008.889
455 1011.111
456 1013.333
457 1015.556
458 1017.778
459 1020.000
460 1022.222
461 1024.444
462 1026.667
463 1028.889
464 1031.111
465 1033.333
466 1035.556
467 1037.778
468 1040.000
469 1042.222
470 1044.444
471 1046.667
472 1048.889
473 1051.111
474 1053.333
475 1055.556
476 1057.778
477 1060.000
478 1062.222
479 1064.444
480 1066.667
481 1068.889
482 1071.111
483 1073.333
484 1075.556
485 1077.778
486 1080.000
487 1082.222
488 1084.444
489 1086.667
490 1088.889
491 1091.111
492 1093.333
493 1095.556
494 1097.778
495 1100.000
496 1102.222
497 1104.444
498 1106.667
499 1108.889
500 1111.111
501 1113.333
502 1115.556
503 1117.778
504 1120.000
505 1122.222
506 1124.444
507 1126.667
508 1128.889
509 1131.111
510 1133.333
511 1135.556
512 1137.778
513 1140.000
514 1142.222
515 1144.444
516 1146.667
517 1148.889
518 1151.111
519 1153.333
520 1155.556
521 1157.778
522 1160.000
523 1162.222
524 1164.444
525 1166.667
526 1168.889
527 1171.111
528 1173.333
529 1175.556
530 1177.778
531 1180.000
532 1182.222
533 1184.444
534 1186.667
535 1188.889
536 1191.111
537 1193.333
538 1195.556
539 1197.778
540 1200.000