Scala analysis: xen18-erlich-nautilus-14
1L 13s MOS for Nautilus, L=124.05, 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: 580.790 cents 580.790000 8: 704.840 cents 704.840000 9: 787.810 cents 787.810000 10: 870.780 cents 870.780000 11: 953.750 cents 953.750000 12: 1036.720 cents 1036.720000 13: 1119.690 cents 1119.690000 14: 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: 82.9700 cents 82.9700 8: 124.0500 cents 124.0500 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 14: 82.9700 cents 82.9700
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 13 82.97000 cents 1: 1 124.05000 cents 2: 12 165.94000 cents 2: 2 207.02000 cents 3: 11 248.91000 cents 3: 3 289.99000 cents 4: 10 331.88000 cents 4: 4 372.96000 cents 5: 9 414.85000 cents 5: 5 455.93000 cents 6: 8 497.82000 cents 6: 6 538.90000 cents 7: 7 580.79000 cents 7: 7 621.87000 cents 8: 6 663.76000 cents 8: 8 704.84000 cents 9: 5 746.73000 cents 9: 9 787.81000 cents 10: 4 829.70000 cents 10: 10 870.78000 cents 11: 3 912.67000 cents 11: 11 953.75000 cents 12: 2 995.64000 cents 12: 12 1036.72000 cents 13: 1 1078.61000 cents 13: 13 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 14 0.0 : 83.0 165.9 248.9 331.9 414.8 497.8 580.8 704.8 787.8 870.8 953.8 1036.7 1119.7 1202.7 83.0 : 83.0 165.9 248.9 331.9 414.8 497.8 621.9 704.8 787.8 870.8 953.8 1036.7 1119.7 1202.7 165.9 : 83.0 165.9 248.9 331.9 414.8 538.9 621.9 704.8 787.8 870.8 953.8 1036.7 1119.7 1202.7 248.9 : 83.0 165.9 248.9 331.9 455.9 538.9 621.9 704.8 787.8 870.8 953.8 1036.7 1119.7 1202.7 331.9 : 83.0 165.9 248.9 373.0 455.9 538.9 621.9 704.8 787.8 870.8 953.8 1036.7 1119.7 1202.7 414.8 : 83.0 165.9 290.0 373.0 455.9 538.9 621.9 704.8 787.8 870.8 953.8 1036.7 1119.7 1202.7 497.8 : 83.0 207.0 290.0 373.0 455.9 538.9 621.9 704.8 787.8 870.8 953.8 1036.7 1119.7 1202.7 580.8 : 124.0 207.0 290.0 373.0 455.9 538.9 621.9 704.8 787.8 870.8 953.8 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 1078.6 1202.7 787.8 : 83.0 165.9 248.9 331.9 414.9 497.8 580.8 663.8 746.7 829.7 912.7 995.6 1119.7 1202.7 870.8 : 83.0 165.9 248.9 331.9 414.9 497.8 580.8 663.8 746.7 829.7 912.7 1036.7 1119.7 1202.7 953.8 : 83.0 165.9 248.9 331.9 414.9 497.8 580.8 663.8 746.7 829.7 953.8 1036.7 1119.7 1202.7 1036.7: 83.0 165.9 248.9 331.9 414.8 497.8 580.8 663.8 746.7 870.8 953.8 1036.7 1119.7 1202.7 1119.7: 83.0 165.9 248.9 331.9 414.9 497.8 580.8 663.8 787.8 870.8 953.8 1036.7 1119.7 1202.7 1202.7
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 82.9700 .. 124.0500 cents 41.08000 cents 82.97000 cents 2: 165.9400 .. 207.0200 cents 41.08000 cents 41.89000 cents 3: 248.9100 .. 289.9900 cents 41.08000 cents 41.89000 cents 4: 331.8800 .. 372.9600 cents 41.08000 cents 41.89000 cents 5: 414.8500 .. 455.9300 cents 41.08000 cents 41.89000 cents 6: 497.8200 .. 538.9000 cents 41.08000 cents 41.89000 cents 7: 580.7900 .. 621.8700 cents 41.08000 cents 41.89000 cents 8: 663.7600 .. 704.8400 cents 41.08000 cents 41.89000 cents 9: 746.7300 .. 787.8100 cents 41.08000 cents 41.89000 cents 10: 829.7000 .. 870.7800 cents 41.08000 cents 41.89000 cents 11: 912.6700 .. 953.7500 cents 41.08000 cents 41.89000 cents 12: 995.6400 .. 1036.7200 cents 41.08000 cents 41.89000 cents 13: 1078.6100 .. 1119.6900 cents 41.08000 cents 41.89000 cents
SHOW DATA
Number of notes : 14 -- Interval properties -- Smallest interval : 82.97000 cents, class 1 Average step (divided formal octave): 85.9043 cents Largest one step interval : 124.05000 cents Average / Smallest step : 1.035366 Largest / Average step : 1.444049 Largest / Smallest step : 1.495119 Median interval of one step : 82.97000 cents, amount: 13 Most common interval of one step : 82.97000 cents, amount: 13 Least squares average step : 86.08641 cents, oct.: 1205.20979 cents Scale is strictly proper Scale has Myhill's property chromas: 41.08000 cents and 41.89000 cents, ratio: 1.019718 generators: 1 of 82.97000 cents and 13 of 1119.69000 cents ET pair of linear temperament : 14&29 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1464-tone equal temperament with octave 1202.660 cents degrees: 101 202 303 404 505 606 707 858 959 1060 1161 1262 1363 1464 generators: 101 and 1363 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAAAAAABAAAAAA Step pattern size order : SSSSSSSLSSSSSS Scale is a Constant Structure, by a margin of 41.89000 cents Scale diversity : 1.223938 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.555951 Rothenberg efficiency : 0.714286 redundancy: 0.285714 Efficiency x scale size : 10.000000 Number of different interval sizes : 26 = 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: 13 Scale is a chain of 7 triads 0.0 497.820 1119.690 cents Number of recognisable fifths : 8, average 704.8400 cents Number of recognisable fourths : 8, average 497.8200 cents Scale contains two identical disjunct heptachords Formal octave complements present : 13 = 92.8571% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 1 Inversional symmetry on intervals : 0-1 7-8 -- Rational properties --
FIT/MODE
14: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 11.9191 c. M:-20.5400 c. 15: 1 1 1 1 1 1 1 2 1 1 1 1 1 1 P M ME SD: 11.3439 c. M: 19.5487 c. 29: 2 2 2 2 2 2 2 3 2 2 2 2 2 2 SP M ME SD: 0.1135 c. M: 0.1955 c. 768: 53 53 53 53 53 53 53 79 53 53 53 53 53 53 SP M DE SD: 0.1059 c. M:-0.1825 c. 797: 55 55 55 55 55 55 55 82 55 55 55 55 55 55 SP M DE SD: 0.0979 c. M:-0.1687 c. 826: 57 57 57 57 57 57 57 85 57 57 57 57 57 57 SP M DE SD: 0.0905 c. M:-0.1559 c. 855: 59 59 59 59 59 59 59 88 59 59 59 59 59 59 SP M DE SD: 0.0836 c. M:-0.1440 c. 884: 61 61 61 61 61 61 61 91 61 61 61 61 61 61 SP M DE SD: 0.0771 c. M:-0.1329 c. 913: 63 63 63 63 63 63 63 94 63 63 63 63 63 63 SP M DE SD: 0.0711 c. M:-0.1224 c. 942: 65 65 65 65 65 65 65 97 65 65 65 65 65 65 SP M DE SD: 0.0654 c. M:-0.1127 c. 971: 67 67 67 67 67 67 67 100 67 67 67 67 67 67 SP M DE SD: 0.0600 c. M:-0.1035 c. 1000: 69 69 69 69 69 69 69 103 69 69 69 69 69 69 SP M DE SD: 0.0550 c. M:-0.0948 c. 1029: 71 71 71 71 71 71 71 106 71 71 71 71 71 71 SP M DE SD: 0.0503 c. M:-0.0866 c. 1058: 73 73 73 73 73 73 73 109 73 73 73 73 73 73 SP M DE SD: 0.0458 c. M:-0.0789 c. 1087: 75 75 75 75 75 75 75 112 75 75 75 75 75 75 SP M DE SD: 0.0415 c. M:-0.0715 c. 1116: 77 77 77 77 77 77 77 115 77 77 77 77 77 77 SP M DE SD: 0.0375 c. M:-0.0646 c. 1145: 79 79 79 79 79 79 79 118 79 79 79 79 79 79 SP M DE SD: 0.0337 c. M:-0.0580 c. 1174: 81 81 81 81 81 81 81 121 81 81 81 81 81 81 SP M DE SD: 0.0300 c. M:-0.0518 c. 1203: 83 83 83 83 83 83 83 124 83 83 83 83 83 83 SP M DE SD: 0.0266 c. M:-0.0458 c. 1232: 85 85 85 85 85 85 85 127 85 85 85 85 85 85 SP M DE SD: 0.0233 c. M:-0.0401 c. 1261: 87 87 87 87 87 87 87 130 87 87 87 87 87 87 SP M DE SD: 0.0201 c. M:-0.0347 c. 1290: 89 89 89 89 89 89 89 133 89 89 89 89 89 89 SP M DE SD: 0.0171 c. M:-0.0295 c. 1319: 91 91 91 91 91 91 91 136 91 91 91 91 91 91 SP M DE SD: 0.0143 c. M:-0.0246 c. 1348: 93 93 93 93 93 93 93 139 93 93 93 93 93 93 SP M DE SD: 0.0115 c. M:-0.0198 c. 1377: 95 95 95 95 95 95 95 142 95 95 95 95 95 95 SP M DE SD: 0.0089 c. M:-0.0153 c. 1406: 97 97 97 97 97 97 97 145 97 97 97 97 97 97 SP M DE SD: 0.0064 c. M:-0.0110 c. 1435: 99 99 99 99 99 99 99 148 99 99 99 99 99 99 SP M DE SD: 0.0039 c. M:-0.0068 c. 1464: 101 101 101 101 101 101 101 151 101 101 101 101 101 101 SP M DE SD: 0.0016 c. M:-0.0028 c. 1493: 103 103 103 103 103 103 103 154 103 103 103 103 103 103 SP M DE SD: 0.0006 c. M: 0.0011 c.
FIT/HARMONIC
1 x 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 x 3 x x x x x 4 S SD: 1.9621 cents 3 x x x x x 4 x x x 5 x x x 6 S SD: 4.6129 cents 4 x x x x 5 x x 6 x x 7 x x 8 S SD: 8.1279 cents 5 x x x 6 x x 7 x 8 x x 9 x 10 S SD: 7.2361 cents 6 x x 7 x x 8 x 9 x 10 x 11 x 12 S SD: 4.3534 cents 7 x x 8 x 9 x 10 x 11 x 12:13 x 14 S SD: 8.7540 cents 8 x 9 x x 10 x 11:12 x 13:14 x 15:16 S SD: 9.0742 cents 9 x 10 x 11 x 12:13 x 14:15 x 16:17:18 S SD: 8.8492 cents 10 x 11 x 12:13 x 14:15:16 x 17:18:19:20 S SD: 6.4594 cents 11 x 12:13 x 14:15 x x 17:18:19:20:21:22 SD: 7.0443 cents 12 x 13:14 x 15:16:17:18:19:20:21:22:23:24 S SD: 4.6174 cents 13 x 14:15:16 x 17:18:20 x 22:23:24:25:26 S SD: 8.5292 cents 14:15 x 16:17:18:19:20:21:22:23:24:25:27:28 SD: 6.1316 cents 15:16 x 17:18:19:20:21:23:24:25:26:27:29:30 SD: 5.4916 cents 16:17:18 x 19:20:21:22:24:25:26:28:29:31:32 SD: 6.7069 cents 17:18:19:20:21:22:23:24:26:27:28:29:31:32:34 SD: 6.2732 cents 18:19:20:21:22:23:24:25:27:28:30:31:33:34:36 SD: 3.6245 cents 26:27:29:30:31:33:35:36:39:41:43:45:47:50:52 SD: 3.5780 cents 27:28:30:31:33:34:36:38:41:43:45:47:49:52:54 SD: 3.5741 cents 28:29:31:32:34:36:37:39:42:44:46:49:51:53:56 SD: 3.3902 cents 30:31:33:35:36:38:40:42:45:47:50:52:55:57:60 SD: 3.0755 cents 32:34:35:37:39:41:43:45:48:50:53:56:58:61:64 SD: 2.9765 cents 33:35:36:38:40:42:44:46:50:52:55:57:60:63:66 SD: 2.3879 cents 37:39:41:43:45:47:49:52:56:58:61:64:67:71:74 SD: 2.3129 cents 38:40:42:44:46:48:51:53:57:60:63:66:69:73:76 SD: 1.6816 cents 52:55:57:60:63:66:69:73:78:82:86:90:95:99:104 SD: 1.5370 cents 57:60:63:66:69:72:76:80:86:90:94:99:104:109:114 SD: 1.3890 cents 60:63:66:69:73:76:80:84:90:95:99:104:109:115:120 SD: 1.2174 cents 66:69:73:76:80:84:88:92:99:104:109:114:120:126:132 SD: 1.1390 cents 77:81:85:89:93:98:103:108:116:121:127:134:140:147:154 SD: 1.1344 cents 78:82:86:90:94:99:104:109:117:123:129:135:142:149:156 SD: 0.8522 cents 90:94:99:104:109:114:120:126:135:142:149:156:164:172:180 SD: 0.8077 cents 99:104:109:114:120:126:132:138:149:156:164:172:180:189:198 SD: 0.7299 cents 118:124:130:136:143:150:157:165:177:186:195:205:215:225:236 SD: 0.5804 cents 141:148:155:163:171:179:188:197:212:222:233:245:257:269:282 SD: 0.5055 cents 161:169:177:186:195:205:215:225:242:254:266:279:293:307:322 SD: 0.4985 cents 180:189:198:208:218:229:240:252:270:284:298:312:328:344:361 SD: 0.4574 cents 181:190:199:209:219:230:241:253:272:285:299:314:329:346:363 SD: 0.4172 cents 188:197:207:217:228:239:251:263:282:296:311:326:342:359:377 SD: 0.4161 cents 189:198:208:218:229:240:252:264:284:298:313:328:344:361:379 SD: 0.3721 cents 199:209:219:230:241:253:265:278:299:314:329:345:362:380:399 SD: 0.3467 cents 219:230:241:253:265:278:292:306:329:345:362:380:399:418:439 SD: 0.3280 cents 240:252:264:277:291:305:320:336:361:378:397:416:437:458:481 SD: 0.3194 cents 241:253:265:278:292:306:321:337:362:380:399:418:439:460:483 SD: 0.3178 cents 246:258:271:284:298:313:328:344:370:388:407:427:448:470:493 SD: 0.2937 cents 265:278:292:306:321:337:353:371:398:418:438:460:482:506:531 SD: 0.2850 cents 266:279:293:307:322:338:355:372:400:419:440:461:484:508:533 SD: 0.2757 cents 279:293:307:322:338:355:372:390:419:440:461:484:508:533:559 SD: 0.2750 cents 285:299:314:329:345:362:380:399:428:449:471:494:519:544:571 SD: 0.2741 cents 288:302:317:333:349:366:384:403:433:454:476:500:524:550:577 SD: 0.2488 cents 306:321:337:353:371:389:408:428:460:482:506:531:557:584:613 SD: 0.2233 cents 309:324:340:357:374:393:412:432:464:487:511:536:562:590:619 SD: 0.2161 cents 328:344:361:379:397:417:437:459:493:517:542:569:597:626:657 SD: 0.2147 cents 366:384:403:423:443:465:488:512:550:577:605:635:666:699:733 SD: 0.1821 cents 387:406:426:447:469:492:516:541:581:610:640:671:704:739:775 SD: 0.1787 cents 388:407:427:448:470:493:517:543:583:612:642:673:706:741:777 SD: 0.1613 cents 406:426:447:469:492:516:541:568:610:640:671:704:739:775:813 SD: 0.1573 cents 487:511:536:562:590:619:649:681:732:768:805:845:886:930:975 SD: 0.1545 cents 505:530:556:583:612:642:673:706:759:796:835:876:919:964:1012 SD: 0.1451 cents 517:542:569:597:626:657:689:723:777:815:855:897:941:987:1036 SD: 0.1279 cents 529:555:582:611:641:672:705:740:795:834:875:918:963:1010:1060 SD: 0.1275 cents 587:616:646:678:711:746:783:821:882:925:971:1018:1068:1121:1176 SD: 0.1234 cents 595:624:655:687:721:756:793:832:894:938:984:1032:1083:1136:1192 SD: 0.0922 cents