Scala analysis: xen18-erlich-nautilus-13
1L 12s MOS for Nautilus, L=207.02, s=82.97
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 82.970 cents 82.970000 2: 165.940 cents 165.940000 3: 248.910 cents 248.910000 4: 331.880 cents 331.880000 5: 414.850 cents 414.850000 6: 497.820 cents 497.820000 7: 704.840 cents 704.840000 8: 787.810 cents 787.810000 9: 870.780 cents 870.780000 10: 953.750 cents 953.750000 11: 1036.720 cents 1036.720000 12: 1119.690 cents 1119.690000 13: 1202.660 cents 1202.660000
SHOW/INTERVAL
0: 82.9700 cents 82.9700 1: 82.9700 cents 82.9700 2: 82.9700 cents 82.9700 3: 82.9700 cents 82.9700 4: 82.9700 cents 82.9700 5: 82.9700 cents 82.9700 6: 82.9700 cents 82.9700 7: 207.0200 cents 207.0200 8: 82.9700 cents 82.9700 9: 82.9700 cents 82.9700 10: 82.9700 cents 82.9700 11: 82.9700 cents 82.9700 12: 82.9700 cents 82.9700 13: 82.9700 cents 82.9700
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 12 82.97000 cents 1: 1 207.02000 cents 2: 11 165.94000 cents 2: 2 289.99000 cents 3: 10 248.91000 cents 3: 3 372.96000 cents 4: 9 331.88000 cents 4: 4 455.93000 cents 5: 8 414.85000 cents 5: 5 538.90000 cents 6: 7 497.82000 cents 6: 6 621.87000 cents 7: 6 580.79000 cents 7: 7 704.84000 cents 8: 5 663.76000 cents 8: 8 787.81000 cents 9: 4 746.73000 cents 9: 9 870.78000 cents 10: 3 829.70000 cents 10: 10 953.75000 cents 11: 2 912.67000 cents 11: 11 1036.72000 cents 12: 1 995.64000 cents 12: 12 1119.69000 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 : 83.0 165.9 248.9 331.9 414.8 497.8 704.8 787.8 870.8 953.8 1036.7 1119.7 1202.7 83.0 : 83.0 165.9 248.9 331.9 414.8 621.9 704.8 787.8 870.8 953.8 1036.7 1119.7 1202.7 165.9 : 83.0 165.9 248.9 331.9 538.9 621.9 704.8 787.8 870.8 953.8 1036.7 1119.7 1202.7 248.9 : 83.0 165.9 248.9 455.9 538.9 621.9 704.8 787.8 870.8 953.8 1036.7 1119.7 1202.7 331.9 : 83.0 165.9 373.0 455.9 538.9 621.9 704.8 787.8 870.8 953.8 1036.7 1119.7 1202.7 414.8 : 83.0 290.0 373.0 455.9 538.9 621.9 704.8 787.8 870.8 953.8 1036.7 1119.7 1202.7 497.8 : 207.0 290.0 373.0 455.9 538.9 621.9 704.8 787.8 870.8 953.8 1036.7 1119.7 1202.7 704.8 : 83.0 165.9 248.9 331.9 414.8 497.8 580.8 663.8 746.7 829.7 912.7 995.6 1202.7 787.8 : 83.0 165.9 248.9 331.9 414.9 497.8 580.8 663.8 746.7 829.7 912.7 1119.7 1202.7 870.8 : 83.0 165.9 248.9 331.9 414.9 497.8 580.8 663.8 746.7 829.7 1036.7 1119.7 1202.7 953.8 : 83.0 165.9 248.9 331.9 414.9 497.8 580.8 663.8 746.7 953.8 1036.7 1119.7 1202.7 1036.7: 83.0 165.9 248.9 331.9 414.8 497.8 580.8 663.8 870.8 953.8 1036.7 1119.7 1202.7 1119.7: 83.0 165.9 248.9 331.9 414.9 497.8 580.8 787.8 870.8 953.8 1036.7 1119.7 1202.7 1202.7
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 82.9700 .. 207.0200 cents 124.05000 cents 82.97000 cents 2: 165.9400 .. 289.9900 cents 124.05000 cents -41.08000 cents 3: 248.9100 .. 372.9600 cents 124.05000 cents -41.08000 cents 4: 331.8800 .. 455.9300 cents 124.05000 cents -41.08000 cents 5: 414.8500 .. 538.9000 cents 124.05000 cents -41.08000 cents 6: 497.8200 .. 621.8700 cents 124.05000 cents -41.08000 cents 7: 580.7900 .. 704.8400 cents 124.05000 cents -41.08000 cents 8: 663.7600 .. 787.8100 cents 124.05000 cents -41.08000 cents 9: 746.7300 .. 870.7800 cents 124.05000 cents -41.08000 cents 10: 829.7000 .. 953.7500 cents 124.05000 cents -41.08000 cents 11: 912.6700 .. 1036.7200 cents 124.05000 cents -41.08000 cents 12: 995.6400 .. 1119.6900 cents 124.05000 cents -41.08000 cents
SHOW DATA
Number of notes : 13 -- Interval properties -- Smallest interval : 82.97000 cents, class 1 Average step (divided formal octave): 92.5123 cents Largest one step interval : 207.02000 cents Average / Smallest step : 1.115009 Largest / Average step : 2.237756 Largest / Smallest step : 2.495119 Median interval of one step : 82.97000 cents, amount: 12 Most common interval of one step : 82.97000 cents, amount: 12 Least squares average step : 93.57256 cents, oct.: 1216.44333 cents Scale is not proper Scale has Myhill's property chromas: 124.05000 cents and 41.08000 cents, ratio: 3.019718 generators: 1 of 82.97000 cents and 12 of 1119.69000 cents ET pair of linear temperament : 14&29 Scale is distributional even Scale is a mode of a 1435-tone equal temperament with octave 1202.660 cents degrees: 99 198 297 396 495 594 841 940 1039 1138 1237 1336 1435 generators: 99 and 1336 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAAAAABAAAAAA Step pattern size order : SSSSSSLSSSSSS Scale is a Constant Structure, by a margin of 41.08000 cents Scale diversity : 1.215009 Lumma stability : 0.137977 Lumma impropriety factor : 0.375734 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 : 41.08000 cents Most common intervals : 82.97000 cents & inv., amount: 12 Scale is a chain of 6 triads 0.0 497.820 1119.690 cents Number of recognisable fifths : 7, average 704.8400 cents Number of recognisable fourths : 7, average 497.8200 cents Scale contains two identical disjunct heptachords Formal octave complements present : 13 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 6-7 -- Rational properties --
FIT/MODE
13: 1 0 1 1 1 1 2 1 1 1 1 1 1 N T3 SD: 43.0148 c. M: 73.4277 c. 14: 1 1 1 1 1 1 2 1 1 1 1 1 1 P M ME I SD: 10.9791 c. M: 17.6057 c. 15: 1 1 1 1 1 1 3 1 1 1 1 1 1 N M DE I SD: 10.4492 c. M: 16.7560 c. 29: 2 2 2 2 2 2 5 2 2 2 2 2 2 N M DE I SD: 0.1045 c. M: 0.1676 c. 768: 53 53 53 53 53 53 132 53 53 53 53 53 53 N M DE I SD: 0.0975 c. M: 0.1564 c. 797: 55 55 55 55 55 55 137 55 55 55 55 55 55 N M DE I SD: 0.0902 c. M: 0.1446 c. 826: 57 57 57 57 57 57 142 57 57 57 57 57 57 N M DE I SD: 0.0833 c. M: 0.1337 c. 855: 59 59 59 59 59 59 147 59 59 59 59 59 59 N M DE I SD: 0.0770 c. M: 0.1234 c. 884: 61 61 61 61 61 61 152 61 61 61 61 61 61 N M DE I SD: 0.0710 c. M: 0.1139 c. 913: 63 63 63 63 63 63 157 63 63 63 63 63 63 N M DE I SD: 0.0654 c. M: 0.1050 c. 942: 65 65 65 65 65 65 162 65 65 65 65 65 65 N M DE I SD: 0.0602 c. M:-0.0966 c. 971: 67 67 67 67 67 67 167 67 67 67 67 67 67 N M DE I SD: 0.0553 c. M:-0.0887 c. 1000: 69 69 69 69 69 69 172 69 69 69 69 69 69 N M DE I SD: 0.0507 c. M: 0.0812 c. 1029: 71 71 71 71 71 71 177 71 71 71 71 71 71 N M DE I SD: 0.0463 c. M: 0.0742 c. 1058: 73 73 73 73 73 73 182 73 73 73 73 73 73 N M DE I SD: 0.0422 c. M: 0.0676 c. 1087: 75 75 75 75 75 75 187 75 75 75 75 75 75 N M DE I SD: 0.0382 c. M: 0.0613 c. 1116: 77 77 77 77 77 77 192 77 77 77 77 77 77 N M DE I SD: 0.0345 c. M: 0.0554 c. 1145: 79 79 79 79 79 79 197 79 79 79 79 79 79 N M DE I SD: 0.0310 c. M: 0.0497 c. 1174: 81 81 81 81 81 81 202 81 81 81 81 81 81 N M DE I SD: 0.0277 c. M: 0.0444 c. 1203: 83 83 83 83 83 83 207 83 83 83 83 83 83 N M DE I SD: 0.0245 c. M: 0.0393 c. 1232: 85 85 85 85 85 85 212 85 85 85 85 85 85 N M DE I SD: 0.0214 c. M: 0.0344 c. 1261: 87 87 87 87 87 87 217 87 87 87 87 87 87 N M DE I SD: 0.0185 c. M: 0.0297 c. 1290: 89 89 89 89 89 89 222 89 89 89 89 89 89 N M DE I SD: 0.0158 c. M: 0.0253 c. 1319: 91 91 91 91 91 91 227 91 91 91 91 91 91 N M DE I SD: 0.0131 c. M: 0.0211 c. 1348: 93 93 93 93 93 93 232 93 93 93 93 93 93 N M DE I SD: 0.0106 c. M: 0.0170 c. 1377: 95 95 95 95 95 95 237 95 95 95 95 95 95 N M DE I SD: 0.0082 c. M: 0.0131 c. 1406: 97 97 97 97 97 97 242 97 97 97 97 97 97 N M DE I SD: 0.0059 c. M: 0.0094 c. 1435: 99 99 99 99 99 99 247 99 99 99 99 99 99 N M DE I SD: 0.0036 c. M: 0.0058 c. 1464: 101 101 101 101 101 101 252 101 101 101 101 101 101 N M DE I SD: 0.0015 c. M: 0.0024 c. 1493: 103 103 103 103 103 103 257 103 103 103 103 103 103 N M DE I SD: 0.0006 c. M: 0.0009 c.
FIT/HARMONIC
1 x x x x x x x x x x x x 2 S SD: 2.6600 cents 2 x x x x x x 3 x x x x x 4 S SD: 1.9621 cents 3 x x x x x 4 x x 5 x x x 6 S SD: 4.6129 cents 4 x x x x 5 x 6 x x 7 x x 8 S SD: 8.1279 cents 5 x x x 6 x 7 x 8 x x 9 x 10 S SD: 18.4161 cents 6 x x 7 x x 8:9 x 10 x 11 x 12 S SD: 4.3534 cents 7 x x 8 x 9 x x 11 x 12:13 x 14 SD: 8.1790 cents 8 x 9 x x 10:11:12 x 13:14 x 15:16 S SD: 10.6531 cents 9 x 10 x 11 x 12 x 14:15 x 16:17:18 S SD: 7.1000 cents 10 x 11 x 12:13 x 15:16 x 17:18:19:20 SD: 7.1746 cents 11 x 12:13 x 14:15 x 17:18:19:20:21:22 SD: 7.0443 cents 12 x 13:14 x 15:16:18:19:20:21:22:23:24 S SD: 4.6148 cents 13 x 14:15:16 x 17:20 x 22:23:24:25:26 SD: 9.2192 cents 14:15 x 16:17:18:19:21:22:23:24:25:27:28 SD: 5.8967 cents 15:16 x 17:18:19:20:23:24:25:26:27:29:30 SD: 5.9475 cents 16:17:18 x 19:20:21:24:25:26:28:29:31:32 SD: 6.8381 cents 17:18:19:20:21:22:23:26:27:28:29:31:32:34 SD: 6.6397 cents 18:19:20:21:22:23:24:27:28:30:31:33:34:36 SD: 3.7913 cents 26:27:29:30:31:33:35:39:41:43:45:47:50:52 SD: 3.6131 cents 28:29:31:32:34:36:37:42:44:46:49:51:53:56 SD: 3.6096 cents 30:31:33:35:36:38:40:45:47:50:52:55:57:60 SD: 3.3094 cents 32:34:35:37:39:41:43:48:50:53:56:58:61:64 SD: 3.1222 cents 33:35:36:38:40:42:44:50:52:55:57:60:63:66 SD: 2.5327 cents 37:39:41:43:45:47:49:56:58:61:64:67:71:74 SD: 2.4057 cents 38:40:42:44:46:48:51:57:60:63:66:69:73:76 SD: 1.7730 cents 52:55:57:60:63:66:69:78:82:86:90:95:99:104 SD: 1.5786 cents 57:60:63:66:69:72:76:86:90:94:99:104:109:114 SD: 1.4214 cents 60:63:66:69:73:76:80:90:95:99:104:109:115:120 SD: 1.3043 cents 66:69:73:76:80:84:88:99:104:109:114:120:126:132 SD: 1.1430 cents 78:82:86:90:94:99:104:117:123:129:135:142:149:156 SD: 0.9109 cents 90:94:99:104:109:114:120:135:142:149:156:164:172:180 SD: 0.8597 cents 99:104:109:114:120:126:132:149:156:164:172:180:189:198 SD: 0.6478 cents 118:124:130:136:143:150:157:177:186:195:205:215:225:236 SD: 0.6244 cents 129:135:142:149:156:164:172:194:203:213:224:235:246:258 SD: 0.6054 cents 141:148:155:163:171:179:188:212:222:233:245:257:269:282 SD: 0.5267 cents 162:170:178:187:196:206:216:243:255:268:281:295:309:324 SD: 0.4864 cents 180:189:198:208:218:229:240:270:284:298:312:328:344:361 SD: 0.4744 cents 181:190:199:209:219:230:241:272:285:299:314:329:346:363 SD: 0.4425 cents 189:198:208:218:229:240:252:284:298:313:328:344:361:379 SD: 0.3629 cents 199:209:219:230:241:253:265:299:314:329:345:362:380:399 SD: 0.3398 cents 207:217:228:239:251:263:276:311:326:342:359:377:395:415 SD: 0.3134 cents 265:278:292:306:321:337:353:398:418:438:460:482:506:531 SD: 0.2768 cents 285:299:314:329:345:362:380:428:449:471:494:519:544:571 SD: 0.2638 cents 288:302:317:333:349:366:384:433:454:476:500:524:550:577 SD: 0.2596 cents 306:321:337:353:371:389:408:460:482:506:531:557:584:613 SD: 0.2404 cents 309:324:340:357:374:393:412:464:487:511:536:562:590:619 SD: 0.2268 cents 328:344:361:379:397:417:437:493:517:542:569:597:626:657 SD: 0.2189 cents 350:367:385:404:424:445:467:526:552:579:607:637:668:701 SD: 0.2064 cents 366:384:403:423:443:465:488:550:577:605:635:666:699:733 SD: 0.1940 cents 387:406:426:447:469:492:516:581:610:640:671:704:739:775 SD: 0.1814 cents 388:407:427:448:470:493:517:583:612:642:673:706:741:777 SD: 0.1523 cents 505:530:556:583:612:642:673:759:796:835:876:919:964:1012 SD: 0.1459 cents 517:542:569:597:626:657:689:777:815:855:897:941:987:1036 SD: 0.1369 cents 529:555:582:611:641:672:705:795:834:875:918:963:1010:1060 SD: 0.1351 cents 549:576:604:634:665:698:732:825:865:908:952:999:1048:1100 SD: 0.1348 cents 555:582:611:641:672:705:740:834:875:918:963:1010:1060:1112 SD: 0.1331 cents 587:616:646:678:711:746:783:882:925:971:1018:1068:1121:1176 SD: 0.1328 cents 588:617:647:679:712:747:784:883:927:972:1020:1070:1123:1178 SD: 0.1266 cents 595:624:655:687:721:756:793:894:938:984:1032:1083:1136:1192 SD: 0.0954 cents