Scala analysis: magic13
Magic[13] in 41-et (7-limit poptimal)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 204.878 cents 204.878049 2: 263.415 cents 263.414634 3: 321.951 cents 321.951220 4: 380.488 cents 380.487805 5: 585.366 cents 585.365854 6: 643.902 cents 643.902439 7: 702.439 cents 702.439024 8: 760.976 cents 760.975610 9: 965.854 cents 965.853659 10: 1024.390 cents 1024.390244 11: 1082.927 cents 1082.926829 12: 1141.463 cents 1141.463415 13: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 58.5366 cents 58.5366 1: 204.8780 cents 204.8780 2: 58.5366 cents 58.5366 3: 58.5366 cents 58.5366 4: 58.5366 cents 58.5366 5: 204.8780 cents 204.8780 6: 58.5366 cents 58.5366 7: 58.5366 cents 58.5366 8: 58.5366 cents 58.5366 9: 204.8780 cents 204.8780 10: 58.5366 cents 58.5366 11: 58.5366 cents 58.5366 12: 58.5366 cents 58.5366 13: 58.5366 cents 58.5366
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 10 58.53658 cents 1: 3 204.87805 cents 2: 7 117.07317 cents 2: 6 263.41463 cents 3: 4 175.60976 cents 3: 9 321.95122 cents 4: 1 234.14634 cents 4: 12 380.48781 cents 5: 11 439.02439 cents 5: 2 585.36585 cents 6: 8 497.56098 cents 6: 5 643.90244 cents 7: 5 556.09756 cents 7: 8 702.43902 cents 8: 2 614.63415 cents 8: 11 760.97561 cents 9: 12 819.51220 cents 9: 1 965.85366 cents 10: 9 878.04878 cents 10: 4 1024.39024 cents 11: 6 936.58537 cents 11: 7 1082.92683 cents 12: 3 995.12195 cents 12: 10 1141.46341 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 0.0 : 204.9 263.4 322.0 380.5 585.4 643.9 702.4 761.0 965.9 1024.4 1082.9 1141.5 1200.0 204.9 : 58.5 117.1 175.6 380.5 439.0 497.6 556.1 761.0 819.5 878.0 936.6 995.1 1200.0 263.4 : 58.5 117.1 322.0 380.5 439.0 497.6 702.4 761.0 819.5 878.0 936.6 1141.5 1200.0 322.0 : 58.5 263.4 322.0 380.5 439.0 643.9 702.4 761.0 819.5 878.0 1082.9 1141.5 1200.0 380.5 : 204.9 263.4 322.0 380.5 585.4 643.9 702.4 761.0 819.5 1024.4 1082.9 1141.5 1200.0 585.4 : 58.5 117.1 175.6 380.5 439.0 497.6 556.1 614.6 819.5 878.0 936.6 995.1 1200.0 643.9 : 58.5 117.1 322.0 380.5 439.0 497.6 556.1 761.0 819.5 878.0 936.6 1141.5 1200.0 702.4 : 58.5 263.4 322.0 380.5 439.0 497.6 702.4 761.0 819.5 878.0 1082.9 1141.5 1200.0 761.0 : 204.9 263.4 322.0 380.5 439.0 643.9 702.4 761.0 819.5 1024.4 1082.9 1141.5 1200.0 965.9 : 58.5 117.1 175.6 234.1 439.0 497.6 556.1 614.6 819.5 878.0 936.6 995.1 1200.0 1024.4: 58.5 117.1 175.6 380.5 439.0 497.6 556.1 761.0 819.5 878.0 936.6 1141.5 1200.0 1082.9: 58.5 117.1 322.0 380.5 439.0 497.6 702.4 761.0 819.5 878.0 1082.9 1141.5 1200.0 1141.5: 58.5 263.4 322.0 380.5 439.0 643.9 702.4 761.0 819.5 1024.4 1082.9 1141.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 58.5366 .. 204.8780 cents 146.34146 cents 58.53658 cents 2: 117.0732 .. 263.4146 cents 146.34146 cents -87.80488 cents 3: 175.6098 .. 321.9512 cents 146.34146 cents -87.80488 cents 4: 234.1463 .. 380.4878 cents 146.34146 cents -87.80488 cents 5: 439.0244 .. 585.3659 cents 146.34146 cents 58.53659 cents 6: 497.5610 .. 643.9024 cents 146.34146 cents -87.80488 cents 7: 556.0976 .. 702.4390 cents 146.34146 cents -87.80488 cents 8: 614.6341 .. 760.9756 cents 146.34146 cents -87.80488 cents 9: 819.5122 .. 965.8537 cents 146.34146 cents 58.53659 cents 10: 878.0488 .. 1024.3902 cents 146.34146 cents -87.80488 cents 11: 936.5854 .. 1082.9268 cents 146.34146 cents -87.80488 cents 12: 995.1220 .. 1141.4634 cents 146.34146 cents -87.80488 cents
SHOW DATA
Number of notes : 13 -- Interval properties -- Smallest interval : 58.53658 cents, class 1 Average step (divided formal octave): 92.3077 cents Largest one step interval : 204.87805 cents Average / Smallest step : 1.576923 Largest / Average step : 2.219512 Largest / Smallest step : 3.500000 Median interval of one step : 58.53658 cents, amount: 10 Most common interval of one step : 58.53658 cents, amount: 10 Least squares average step : 99.09765 cents, oct.: 1288.26945 cents Scale is not proper Scale has Myhill's property chromas: 146.34146 cents and 87.80488 cents, ratio: 1.666667 generators: 4 of 380.48781 cents and 819.51219 cents ET pair of linear temperament : 19&22 Scale is distributional even Scale is a mode of a 41-tone equal temperament with octave 1200.000 cents degrees: 7 9 11 13 20 22 24 26 33 35 37 39 41 generators: 13 and 28 Number of contiguous 1-step segments: 0 Scale is fully connected major-minor triadic in 41-tone equal temperament Step pattern alph. order: ABBBABBBABBBB Step pattern size order : LSSSLSSSLSSSS Interval vector is [ 0 10 0 7 0 4 3 1 6 0 9 0 12 0 11 0 8 0 5 2 ] Scale is a Constant Structure, by a margin of 29.26829 cents Scale diversity : 1.222903 Lumma stability : 0.195122 Lumma impropriety factor : 0.512195 Rothenberg efficiency : 0.717949 redundancy: 0.282051 Efficiency x scale size : 9.333333 Number of different interval sizes : 24 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 29.26829 cents Most common intervals : 380.48781 cents & inv., amount: 12 Scale is a chain of 6 triads 0.0 380.488 760.976 cents Most common triad is 0.0 380.488 819.512 cents, amount: 11 Number of recognisable fifths : 8, average 702.4390 cents Formal octave complements present : 1 = 7.6923% Limited inverse transpositions : 9 Inversional symmetry on degrees : 11 Inversional symmetry on intervals : 4-5 -- Rational properties --
FIT/MODE
13: 2 1 0 1 2 1 0 1 2 1 0 1 1 N T3 SD: 34.0070 c. M: 67.5422 c. 14: 2 1 1 0 3 0 1 1 2 1 0 1 1 N SD: 27.4301 c. M: 54.3554 c. 15: 3 0 1 1 2 1 1 1 2 1 1 0 1 N SD: 22.8192 c. M:-39.0244 c. 17: 3 1 1 0 3 1 1 1 3 1 0 1 1 N SD: 20.1742 c. M:-34.4333 c. 18: 3 1 1 1 3 1 1 0 3 1 1 1 1 N SD: 19.5694 c. M: 32.5203 c. 19: 3 1 1 1 3 1 1 1 3 1 1 1 1 N M DE S SD: 10.8925 c. M: 18.4852 c. Magic-13 22: 4 1 1 1 4 1 1 1 4 1 1 1 1 N M DE S SD: 9.4072 c. M:-15.9645 c. Magic-13 35: 6 2 1 2 6 2 1 2 6 2 2 1 2 N T3 SD: 8.9916 c. M: 16.7247 c. 37: 6 2 2 2 6 2 2 1 7 2 1 2 2 N SD: 8.8059 c. M: 15.0297 c. 40: 7 2 2 2 6 2 2 2 7 2 2 2 2 N S SD: 8.7429 c. M: 15.3659 c. 41: 7 2 2 2 7 2 2 2 7 2 2 2 2 N M DE S SD: 0.0000 c. M: 0.0000 c. Magic-13
FIT/HARMONIC
1 x 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 x 4 S SD: 0.2420 cents 3 x x x x 4 x x x 5 x x x 6 S SD: 39.8140 cents 4 x x x 5 x x 6 x 7 x x x 8 S SD: 1.6395 cents 5 x x 6 x 7 x x 8 x 9 x x 10 S SD: 10.7192 cents 6 x 7 x x 8 x 9 x 10:11 x x 12 S SD: 20.3457 cents 7:8 x x 9 x 10 x 11:12 x 13 x 14 S SD: 11.0931 cents 8:9 x x 10:11 x 12 x 14 x 15 x 16 S SD: 5.0137 cents 9:10 x 11 x x 13 x 14 x 16:17 x 18 SD: 6.9266 cents 10:11 x 12 x 14 x 15:16:17:18:19 x 20 S SD: 9.6167 cents 11:12:13 x 14:15:16 x 17:19:20 x 21:22 SD: 9.1551 cents 12 x 14 x 15:17 x 18:19:21:22 x 23:24 SD: 5.4601 cents 13 x 15 x 16:18:19 x 20:23 x 24:25:26 SD: 5.6674 cents 14:16 x 17 x x 20:21:22:24:25:26:27:28 SD: 6.0777 cents 15:17 x 18:19:21:22 x 23:26:27:28:29:30 SD: 4.1234 cents 16:18 x 19:20:22:23:24:25:28:29:30:31:32 SD: 3.9516 cents 17:19:20 x 21:24:25 x 26:30:31:32:33:34 SD: 4.7926 cents 18:20:21:22 x 25:26:27:28:31:33:34:35:36 SD: 4.6918 cents 19:21:22:23:24:27:28 x 29:33:34:36:37:38 SD: 5.8639 cents 20 x 23:24:25:28:29:30:31:35:36:37:39:40 SD: 2.8129 cents 21:24 x 25:26:29:30:32:33:37:38:39:41:42 SD: 5.5437 cents 22:25:26 x 27:31:32:33:34:38:40:41:43:44 SD: 4.2751 cents 24:27:28:29:30:34:35:36:37:42:43:45:46:48 SD: 2.5480 cents 32:36:37:39:40:45:46:48:50:56:58:60:62:64 SD: 2.5314 cents 38:43:44:46:47:53:55:57:59:66:69:71:73:76 SD: 2.1881 cents 40:45:47:48:50:56:58:60:62:70:72:75:77:80 SD: 1.6841 cents 48:54:56:58:60:67:70:72:74:84:87:90:93:96 SD: 1.6152 cents 49:55:57:59:61:69:71:74:76:86:89:92:95:98 SD: 1.6050 cents 54:61:63:65:67:76:78:81:84:94:98:101:104:108 SD: 1.4375 cents 60:68:70:72:75:84:87:90:93:105:108:112:116:120 SD: 1.3316 cents 62:70:72:75:77:87:90:93:96:108:112:116:120:124 SD: 1.0477 cents 74:83:86:89:92:104:107:111:115:129:134:138:143:148 SD: 0.9763 cents 78:88:91:94:97:109:113:117:121:136:141:146:151:156 SD: 0.7776 cents 98:110:114:118:122:137:142:147:152:171:177:183:189:196 SD: 0.7295 cents 102:115:119:123:127:143:148:153:158:178:184:191:197:204 SD: 0.6112 cents 122:137:142:147:152:171:177:183:189:213:220:228:236:244 SD: 0.5121 cents 146:164:170:176:182:205:212:219:227:255:264:273:282:292 SD: 0.4840 cents 151:170:176:182:188:212:219:227:234:264:273:282:292:302 SD: 0.4450 cents 166:187:193:200:207:233:241:249:258:290:300:310:321:332 SD: 0.3853 cents 176:198:205:212:219:247:255:264:273:307:318:329:340:352 SD: 0.3617 cents 182:205:212:219:227:255:264:273:282:318:329:340:352:364 SD: 0.3502 cents 206:232:240:248:257:289:299:309:320:360:372:385:398:412 SD: 0.3116 cents 224:252:261:270:279:314:325:336:348:391:405:419:433:448 SD: 0.2776 cents 244:275:284:294:304:342:354:366:379:426:441:456:472:488 SD: 0.2529 cents 268:302:312:323:334:376:389:402:416:468:484:501:518:536 SD: 0.2419 cents 304:342:354:366:379:426:441:456:472:531:549:568:588:608 SD: 0.2100 cents 328:369:382:395:409:460:476:492:509:573:593:613:634:656 SD: 0.1837 cents 358:403:417:431:446:502:519:537:556:625:647:669:692:716 SD: 0.1787 cents 366:412:426:441:456:513:531:549:568:639:661:684:708:732 SD: 0.1730 cents 382:430:445:460:476:536:554:573:593:667:690:714:739:764 SD: 0.1689 cents 390:439:454:470:486:547:566:585:605:681:705:729:754:780 SD: 0.1612 cents 406:457:473:489:506:569:589:609:630:709:734:759:785:812 SD: 0.1558 cents 415:467:483:500:517:582:602:623:644:725:750:776:802:830 SD: 0.1381 cents 420:473:489:506:523:589:609:630:652:734:759:785:812:840 SD: 0.1312 cents 542:610:631:653:675:760:786:813:841:947:979:1013:1048:1084 SD: 0.1107 cents 597:672:695:719:744:837:866:896:927:1043:1079:1116:1154:1194 SD: 0.1033 cents