Scala analysis: wilcmarv11
Wilson Class scale in 11-limit minimax Marvel
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 85.393 cents 85.393114 2: 151.994 cents 151.994179 3: 316.998 cents 316.998408 4: 383.599 cents 383.599473 5: 468.993 cents 468.992587 6: 584.795 cents 584.795233 7: 700.598 cents 700.597880 8: 767.199 cents 767.198946 9: 901.794 cents 901.793641 10: 968.395 cents 968.394706 11: 1084.197 cents 1084.197353 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 115.8026 cents 115.8026 1: 85.3931 cents 85.3931 2: 66.6011 cents 66.6011 3: 165.0042 cents 165.0042 4: 66.6011 cents 66.6011 5: 85.3931 cents 85.3931 6: 115.8026 cents 115.8026 7: 115.8026 cents 115.8026 8: 66.6011 cents 66.6011 9: 134.5947 cents 134.5947 10: 66.6011 cents 66.6011 11: 115.8026 cents 115.8026 12: 115.8026 cents 115.8026
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 66.60107 cents 1: 2 85.39311 cents 1: 4 115.80265 cents 1: 1 134.59469 cents 1: 1 165.00423 cents 2: 2 151.99418 cents 2: 2 182.40371 cents 2: 4 201.19576 cents 2: 4 231.60529 cents 3: 3 267.79683 cents 3: 3 298.20636 cents 3: 6 316.99841 cents 4: 8 383.59947 cents 4: 4 432.80105 cents 5: 2 450.20054 cents 5: 1 468.99259 cents 5: 5 499.40212 cents 5: 2 518.19417 cents 5: 2 548.60370 cents 6: 6 584.79523 cents 6: 6 615.20477 cents 7: 2 651.39630 cents 7: 2 681.80583 cents 7: 5 700.59788 cents 7: 1 731.00741 cents 7: 2 749.79946 cents 8: 4 767.19895 cents 8: 8 816.40053 cents 9: 6 883.00159 cents 9: 3 901.79364 cents 9: 3 932.20317 cents 10: 4 968.39471 cents 10: 4 998.80424 cents 10: 2 1017.59629 cents 10: 2 1048.00582 cents 11: 1 1034.99577 cents 11: 1 1065.40531 cents 11: 4 1084.19735 cents 11: 2 1114.60689 cents 11: 4 1133.39893 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 3.63636 = 40/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 85.4 152.0 317.0 383.6 469.0 584.8 700.6 767.2 901.8 968.4 1084.2 1200.0 85.4 : 66.6 231.6 298.2 383.6 499.4 615.2 681.8 816.4 883.0 998.8 1114.6 1200.0 152.0 : 165.0 231.6 317.0 432.8 548.6 615.2 749.8 816.4 932.2 1048.0 1133.4 1200.0 317.0 : 66.6 152.0 267.8 383.6 450.2 584.8 651.4 767.2 883.0 968.4 1035.0 1200.0 383.6 : 85.4 201.2 317.0 383.6 518.2 584.8 700.6 816.4 901.8 968.4 1133.4 1200.0 469.0 : 115.8 231.6 298.2 432.8 499.4 615.2 731.0 816.4 883.0 1048.0 1114.6 1200.0 584.8 : 115.8 182.4 317.0 383.6 499.4 615.2 700.6 767.2 932.2 998.8 1084.2 1200.0 700.6 : 66.6 201.2 267.8 383.6 499.4 584.8 651.4 816.4 883.0 968.4 1084.2 1200.0 767.2 : 134.6 201.2 317.0 432.8 518.2 584.8 749.8 816.4 901.8 1017.6 1133.4 1200.0 901.8 : 66.6 182.4 298.2 383.6 450.2 615.2 681.8 767.2 883.0 998.8 1065.4 1200.0 968.4 : 115.8 231.6 317.0 383.6 548.6 615.2 700.6 816.4 932.2 998.8 1133.4 1200.0 1084.2: 115.8 201.2 267.8 432.8 499.4 584.8 700.6 816.4 883.0 1017.6 1084.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 66.6011 .. 165.0042 cents 98.40316 cents 66.60107 cents 2: 151.9942 .. 231.6053 cents 79.61111 cents -13.01005 cents 3: 267.7968 .. 316.9984 cents 49.20158 cents 36.19153 cents 4: 383.5995 .. 432.8011 cents 49.20158 cents 66.60107 cents 5: 450.2005 .. 548.6037 cents 98.40316 cents 17.39948 cents 6: 584.7952 .. 615.2048 cents 30.40953 cents 36.19153 cents 7: 651.3963 .. 749.7995 cents 98.40316 cents 36.19153 cents 8: 767.1989 .. 816.4005 cents 49.20158 cents 17.39948 cents 9: 883.0016 .. 932.2032 cents 49.20158 cents 66.60107 cents 10: 968.3947 .. 1048.0058 cents 79.61111 cents 36.19153 cents 11: 1034.9958 .. 1133.3989 cents 98.40316 cents -13.01005 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 66.60107 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 165.00423 cents Average / Smallest step : 1.501477 Largest / Average step : 1.650042 Largest / Smallest step : 2.477501 Median interval of one step : 100.59788 cents, amount: 0 Least squares average step : 98.30238 cents, oct.: 1179.62855 cents Scale is not proper Step pattern alph. order: ABCBADDBEBDD Step pattern size order : BAEABCCADACC Scale is a Constant Structure, by a margin of 13.01005 cents Scale diversity : 1.400221 Lumma stability : 0.371641 Lumma impropriety factor : 0.021683 Rothenberg efficiency : 0.362608 redundancy: 0.637392 Efficiency x scale size : 4.351299 Number of different interval sizes : 40 = 3.63636 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 3.63636 = 40/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 13.01005 cents Most common intervals : 383.59947 cents & inv., amount: 8 Most common triad is 0.0 383.599 816.401 cents, amount: 4 Number of recognisable fifths : 5, average 700.5979 cents Best fifths form a closed circle Formal octave complements present : 1 = 8.3333% Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 8-9 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 23.4460 c. M:-48.0058 c. Twelve-tone Chromatic (1/11-comma) 13: 1 1 1 1 1 1 2 0 2 0 2 1 N D3 SD: 27.7730 c. M: 45.3178 c. 15: 1 1 2 1 1 1 2 1 1 1 2 1 P B ME SD: 19.1197 c. M:-35.8026 c. Augene-12 16: 1 1 2 1 1 2 1 1 2 1 1 2 P B ME S SD: 16.4168 c. M: 34.1974 c. 19: 1 1 3 1 1 2 2 1 2 1 2 2 N D3 SD: 16.2035 c. M: 26.8873 c. 22: 2 1 3 1 2 2 2 1 3 1 2 2 P B D3 SD: 14.3661 c. M:-25.4791 c. 23: 2 1 3 1 2 2 2 2 2 2 2 2 P D3 SD: 14.3314 c. M:-22.9096 c. 25: 2 1 4 1 2 2 3 1 3 1 3 2 N SD: 11.8322 c. M:-19.8026 c. 28: 2 2 3 2 2 3 2 2 3 2 2 3 SP B ME S SD: 11.5973 c. M:-19.4344 c. Demolished-12 29: 2 2 4 1 2 3 3 2 3 1 3 3 N SD: 11.2656 c. M:-19.0080 c. 31: 2 2 4 2 2 3 3 2 3 2 3 3 P D3 SD: 5.5560 c. M: 11.4711 c. 41: 3 2 6 2 3 4 4 2 5 2 4 4 N SD: 3.5765 c. M: 6.2233 c. 53: 4 3 7 3 4 5 5 3 6 3 5 5 P SD: 3.9247 c. M:-6.4964 c. 69: 5 4 9 4 5 7 6 4 8 4 6 7 P SD: 3.9037 c. M:-6.5091 c. 72: 5 4 10 4 5 7 7 4 8 4 7 7 N SD: 1.4005 c. M: 2.3259 c. 125: 9 7 17 7 9 12 12 7 14 7 12 12 N SD: 0.8797 c. M:-1.6058 c. 166: 12 9 23 9 12 16 16 9 19 9 16 16 N SD: 0.8774 c. M:-1.8208 c. 197: 14 11 27 11 14 19 19 11 22 11 19 19 N SD: 0.1797 c. M:-0.3137 c. 435: 31 24 60 24 31 42 42 24 49 24 42 42 N SD: 0.1745 c. M: 0.3024 c. 560: 40 31 77 31 40 54 54 31 63 31 54 54 N SD: 0.1942 c. M:-0.3492 c. 632: 45 35 87 35 45 61 61 35 71 35 61 61 N SD: 0.0642 c. M: 0.1103 c. 829: 59 46 114 46 59 80 80 46 93 46 80 80 N SD: 0.0076 c. M:-0.0158 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 0.6786 cents 3 x x x x 4 x x x 5 x x 6 S SD: 11.2941 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 0.7663 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 13.5483 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 11.6381 cents 7 x 8 x x 9:10 x 11:12 x 13:14 S SD: 14.1853 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 10.8940 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 9.1214 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.7404 cents 11 x 12:13:14 x 15:16:17 x 19:21:22 SD: 10.4401 cents 12 x 13:14:15:16:17:18:19:20:21:22:24 S SD: 7.1579 cents 13 x 14 x 16:17:18:19:20:22:23:24:26 S SD: 7.0409 cents 14 x 15:17 x 18:20:21:22:24 x 26:28 SD: 7.8708 cents 15:16 x 18:19:20:21:22:23:25:26:28:30 SD: 6.3827 cents 16:17 x 19:20:21:22:24:25:27:28:30:32 SD: 4.0230 cents 18:19:20:22 x 24:25:27:28:30:31:34:36 SD: 6.0013 cents 19:20:21:23:24:25:27:28:30:32:33:36:38 SD: 5.1003 cents 20:21:22:24:25:26:28:30:31:34:35:37:40 SD: 2.7989 cents 32:34:35:38:40:42:45:48:50:54:56:60:64 SD: 2.4678 cents 36:38:39:43:45:47:50:54:56:61:63:67:72 SD: 2.4523 cents 40:42:44:48:50:52:56:60:62:67:70:75:80 SD: 1.9911 cents 44:46:48:53:55:58:62:66:69:74:77:82:88 SD: 1.7810 cents 45:47:49:54:56:59:63:67:70:76:79:84:90 SD: 1.6059 cents 54:57:59:65:67:71:76:81:84:91:94:101:108 SD: 1.5480 cents 60:63:66:72:75:79:84:90:93:101:105:112:120 SD: 1.5015 cents 64:67:70:77:80:84:90:96:100:108:112:120:128 SD: 1.0591 cents 80:84:87:96:100:105:112:120:125:135:140:150:160 SD: 0.9466 cents 84:88:92:101:105:110:118:126:131:141:147:157:168 SD: 0.9043 cents 99:104:108:119:124:130:139:148:154:167:173:185:198 SD: 0.8392 cents 100:105:109:120:125:131:140:150:156:168:175:187:200 SD: 0.5776 cents 120:126:131:144:150:157:168:180:187:202:210:224:240 SD: 0.5595 cents 140:147:153:168:175:184:196:210:218:236:245:262:280 SD: 0.5486 cents 154:162:168:185:192:202:216:231:240:259:269:288:308 SD: 0.4220 cents 174:183:190:209:217:228:244:261:271:293:304:325:348 SD: 0.3851 cents 199:209:217:239:248:261:279:298:310:335:348:372:398 SD: 0.3302 cents 219:230:239:263:273:287:307:328:341:369:383:410:438 SD: 0.2916 cents 274:288:299:329:342:359:384:411:427:461:479:513:548 SD: 0.2809 cents 293:308:320:352:366:384:411:439:456:493:513:548:586 SD: 0.2765 cents 294:309:321:353:367:385:412:441:458:495:514:550:588 SD: 0.2543 cents 303:318:331:364:378:397:425:454:472:510:530:567:606 SD: 0.2406 cents 318:334:347:382:397:417:446:477:495:535:556:595:636 SD: 0.2379 cents 319:335:348:383:398:418:447:478:497:537:558:597:638 SD: 0.1978 cents 379:398:414:455:473:497:531:568:590:638:663:709:758 SD: 0.1627 cents 492:517:537:591:614:645:690:737:766:828:861:920:984 SD: 0.1605 cents 493:518:538:592:615:646:691:739:768:830:863:922:986 SD: 0.1587 cents 511:537:558:614:638:670:716:766:796:860:894:956:1022 SD: 0.1397 cents 533:560:582:640:665:699:747:799:830:897:933:997:1066 SD: 0.1251 cents 588:618:642:706:734:771:824:881:916:990:1029:1100:1176 SD: 0.1142 cents