Scala analysis: xen18-erlich-nautilus-09
1L 8s MOS for Nautilus, L=538.90, 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: 870.780 cents 870.780000 6: 953.750 cents 953.750000 7: 1036.720 cents 1036.720000 8: 1119.690 cents 1119.690000 9: 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: 538.9000 cents 538.9000 6: 82.9700 cents 82.9700 7: 82.9700 cents 82.9700 8: 82.9700 cents 82.9700 9: 82.9700 cents 82.9700
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 8 82.97000 cents 1: 1 538.90000 cents 2: 7 165.94000 cents 2: 2 621.87000 cents 3: 6 248.91000 cents 3: 3 704.84000 cents 4: 5 331.88000 cents 4: 4 787.81000 cents 5: 4 414.85000 cents 5: 5 870.78000 cents 6: 3 497.82000 cents 6: 6 953.75000 cents 7: 2 580.79000 cents 7: 7 1036.72000 cents 8: 1 663.76000 cents 8: 8 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 0.0 : 83.0 165.9 248.9 331.9 870.8 953.8 1036.7 1119.7 1202.7 83.0 : 83.0 165.9 248.9 787.8 870.8 953.8 1036.7 1119.7 1202.7 165.9 : 83.0 165.9 704.8 787.8 870.8 953.8 1036.7 1119.7 1202.7 248.9 : 83.0 621.9 704.8 787.8 870.8 953.8 1036.7 1119.7 1202.7 331.9 : 538.9 621.9 704.8 787.8 870.8 953.8 1036.7 1119.7 1202.7 870.8 : 83.0 165.9 248.9 331.9 414.9 497.8 580.8 663.8 1202.7 953.8 : 83.0 165.9 248.9 331.9 414.9 497.8 580.8 1119.7 1202.7 1036.7: 83.0 165.9 248.9 331.9 414.8 497.8 1036.7 1119.7 1202.7 1119.7: 83.0 165.9 248.9 331.9 414.9 953.8 1036.7 1119.7 1202.7 1202.7
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 82.9700 .. 538.9000 cents 455.93000 cents 82.97000 cents 2: 165.9400 .. 621.8700 cents 455.93000 cents -372.96000 cents 3: 248.9100 .. 704.8400 cents 455.93000 cents -372.96000 cents 4: 331.8800 .. 787.8100 cents 455.93000 cents -372.96000 cents 5: 414.8500 .. 870.7800 cents 455.93000 cents -372.96000 cents 6: 497.8200 .. 953.7500 cents 455.93000 cents -372.96000 cents 7: 580.7900 .. 1036.7200 cents 455.93000 cents -372.96000 cents 8: 663.7600 .. 1119.6900 cents 455.93000 cents -372.96000 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 82.97000 cents, class 1 Average step (divided formal octave): 133.6289 cents Largest one step interval : 538.90000 cents Average / Smallest step : 1.610569 Largest / Average step : 4.032811 Largest / Smallest step : 6.495119 Median interval of one step : 82.97000 cents, amount: 8 Most common interval of one step : 82.97000 cents, amount: 8 Least squares average step : 138.96140 cents, oct.: 1250.65263 cents Scale is not proper Scale has Myhill's property chromas: 455.93000 cents and 372.96000 cents, ratio: 1.222464 generators: 1 of 82.97000 cents and 8 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 1039 1138 1237 1336 1435 generators: 99 and 1336 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAAABAAAA Step pattern size order : SSSSLSSSS Scale is a Constant Structure, by a margin of 41.08000 cents Scale diversity : 1.255706 Lumma stability : 0.137977 Lumma impropriety factor : 0.724045 Rothenberg efficiency : 0.740741 redundancy: 0.259259 Efficiency x scale size : 6.666667 Number of different interval sizes : 16 = 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: 8 Scale is a chain of 4 triads 0.0 331.880 1119.690 cents Number of recognisable fifths : 3, average 704.8400 cents Number of recognisable fourths : 3, average 497.8200 cents Scale contains two identical disjunct pentachords Formal octave complements present : 9 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 4-5 -- Rational properties --
FIT/MODE
9: 0 1 0 1 4 1 0 1 1 N SD: 69.3814 c. M: 115.2811 c. 10: 1 0 1 1 4 1 1 0 1 N I SD: 31.2109 c. M:-45.6740 c. 13: 1 1 1 1 5 1 1 1 1 N M DE I SD: 24.6381 c. M:-38.1692 c. 14: 1 1 1 1 6 1 1 1 1 N M DE I SD: 7.5763 c. M:-11.7371 c. 15: 1 1 1 1 7 1 1 1 1 N M DE I SD: 7.2106 c. M:-11.1707 c. 29: 2 2 2 2 13 2 2 2 2 N M DE I SD: 0.0721 c. M:-0.1117 c. 768: 53 53 53 53 344 53 53 53 53 N M DE I SD: 0.0673 c. M:-0.1043 c. 797: 55 55 55 55 357 55 55 55 55 N M DE I SD: 0.0622 c. M:-0.0964 c. 826: 57 57 57 57 370 57 57 57 57 N M DE I SD: 0.0575 c. M:-0.0891 c. 855: 59 59 59 59 383 59 59 59 59 N M DE I SD: 0.0531 c. M:-0.0823 c. 884: 61 61 61 61 396 61 61 61 61 N M DE I SD: 0.0490 c. M:-0.0759 c. 913: 63 63 63 63 409 63 63 63 63 N M DE I SD: 0.0452 c. M:-0.0700 c. 942: 65 65 65 65 422 65 65 65 65 N M DE I SD: 0.0416 c. M:-0.0644 c. 971: 67 67 67 67 435 67 67 67 67 N M DE I SD: 0.0382 c. M:-0.0591 c. 1000: 69 69 69 69 448 69 69 69 69 N M DE I SD: 0.0350 c. M:-0.0542 c. 1029: 71 71 71 71 461 71 71 71 71 N M DE I SD: 0.0319 c. M:-0.0495 c. 1058: 73 73 73 73 474 73 73 73 73 N M DE I SD: 0.0291 c. M:-0.0451 c. 1087: 75 75 75 75 487 75 75 75 75 N M DE I SD: 0.0264 c. M:-0.0409 c. 1116: 77 77 77 77 500 77 77 77 77 N M DE I SD: 0.0238 c. M:-0.0369 c. 1145: 79 79 79 79 513 79 79 79 79 N M DE I SD: 0.0214 c. M:-0.0332 c. 1174: 81 81 81 81 526 81 81 81 81 N M DE I SD: 0.0191 c. M:-0.0296 c. 1203: 83 83 83 83 539 83 83 83 83 N M DE I SD: 0.0169 c. M:-0.0262 c. 1232: 85 85 85 85 552 85 85 85 85 N M DE I SD: 0.0148 c. M:-0.0229 c. 1261: 87 87 87 87 565 87 87 87 87 N M DE I SD: 0.0128 c. M:-0.0198 c. 1290: 89 89 89 89 578 89 89 89 89 N M DE I SD: 0.0109 c. M:-0.0169 c. 1319: 91 91 91 91 591 91 91 91 91 N M DE I SD: 0.0091 c. M:-0.0140 c. 1348: 93 93 93 93 604 93 93 93 93 N M DE I SD: 0.0073 c. M:-0.0113 c. 1377: 95 95 95 95 617 95 95 95 95 N M DE I SD: 0.0056 c. M:-0.0087 c. 1406: 97 97 97 97 630 97 97 97 97 N M DE I SD: 0.0040 c. M:-0.0063 c. 1435: 99 99 99 99 643 99 99 99 99 N M DE I SD: 0.0025 c. M:-0.0039 c. 1464: 101 101 101 101 656 101 101 101 101 N M DE I SD: 0.0010 c. M:-0.0016 c. 1493: 103 103 103 103 669 103 103 103 103 N M DE I SD: 0.0004 c. M: 0.0006 c.
FIT/HARMONIC
1 x x x x x x x x 2 S SD: 2.6600 cents 2 x x x x 3 x x x 4 S SD: 84.4230 cents 3 x x x 4:5 x x x 6 S SD: 55.5800 cents 4 x x x 5 x 7 x x 8 SD: 18.8485 cents 5 x x x 6:8 x 9 x 10 S SD: 15.6048 cents 6 x x 7 x 10 x 11 x 12 SD: 6.4899 cents 7 x x 8 x x 12:13 x 14 S SD: 11.0978 cents 8 x 9 x 10:13:14 x 15:16 SD: 13.4800 cents 9 x 10 x 11:15 x 16:17:18 SD: 8.6635 cents 10 x 11 x 12 x 17:18:19:20 SD: 7.3448 cents 11 x 12:13 x 18:19:20:21:22 SD: 6.7857 cents 12 x 13:14:15:20:21:22:23:24 S SD: 8.5304 cents 13 x 14:15:16:22:23:24:25:26 SD: 9.4437 cents 14:15 x 16:17:23:24:25:27:28 SD: 7.5085 cents 15:16 x 17:18:25:26:27:29:30 SD: 7.0223 cents 16:17:18 x 19:26:28:29:31:32 SD: 8.7938 cents 17:18:19:20:21:28:29:31:32:34 SD: 7.6102 cents 18:19:20:21:22:30:31:33:34:36 SD: 4.7221 cents 19:20:21:22:23:31:33:35:36:38 SD: 3.9732 cents 20:21:22:23:24:33:35:36:38:40 SD: 3.5169 cents 33:35:36:38:40:55:57:60:63:66 SD: 3.2697 cents 37:39:41:43:45:61:64:67:71:74 SD: 2.7069 cents 38:40:42:44:46:63:66:69:73:76 SD: 1.8320 cents 57:60:63:66:69:94:99:104:109:114 SD: 1.4590 cents 76:80:84:88:92:126:132:138:145:152 SD: 1.4121 cents 77:81:85:89:93:127:134:140:147:154 SD: 1.3023 cents 78:82:86:90:94:129:135:142:149:156 SD: 1.2516 cents 79:83:87:91:96:131:137:144:151:158 SD: 1.0883 cents 90:94:99:104:109:149:156:164:172:180 SD: 1.0083 cents 98:103:108:113:119:162:170:178:187:196 SD: 0.8581 cents 99:104:109:114:120:164:172:180:189:198 SD: 0.8232 cents 118:124:130:136:143:195:205:215:225:236 SD: 0.7484 cents 122:128:134:141:148:202:212:222:233:244 SD: 0.7220 cents 141:148:155:163:171:233:245:257:269:282 SD: 0.6893 cents 142:149:156:164:172:235:246:258:271:284 SD: 0.6514 cents 161:169:177:186:195:266:279:293:307:322 SD: 0.5432 cents 180:189:198:208:218:298:312:328:344:361 SD: 0.5330 cents 188:197:207:217:228:311:326:342:359:377 SD: 0.4262 cents 199:209:219:230:241:329:345:362:380:399 SD: 0.3831 cents 227:238:250:262:275:375:394:413:433:455 SD: 0.3706 cents 245:257:270:283:297:405:425:446:468:491 SD: 0.3410 cents 246:258:271:284:298:407:427:448:470:493 SD: 0.3093 cents 265:278:292:306:321:438:460:482:506:531 SD: 0.3030 cents 289:303:318:334:350:478:501:526:552:579 SD: 0.2784 cents 309:324:340:357:374:511:536:562:590:619 SD: 0.2588 cents 349:366:384:403:423:577:605:635:666:699 SD: 0.2409 cents 350:367:385:404:424:579:607:637:668:701 SD: 0.1978 cents 387:406:426:447:469:640:671:704:739:775 SD: 0.1930 cents 388:407:427:448:470:642:673:706:741:777 SD: 0.1461 cents 407:427:448:470:493:673:706:741:777:815 SD: 0.1038 cents