Scala analysis: xen18-erlich-blackwood-15
10L 5s MOS for Blackwood, L=80.09, s=78.69
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 80.090 cents 80.090000 2: 158.780 cents 158.780000 3: 238.870 cents 238.870000 4: 318.960 cents 318.960000 5: 397.650 cents 397.650000 6: 477.740 cents 477.740000 7: 557.830 cents 557.830000 8: 636.520 cents 636.520000 9: 716.610 cents 716.610000 10: 796.700 cents 796.700000 11: 875.390 cents 875.390000 12: 955.480 cents 955.480000 13: 1035.570 cents 1035.570000 14: 1114.260 cents 1114.260000 15: 1194.350 cents 1194.350000
SHOW/INTERVAL
0: 80.0900 cents 80.0900 1: 80.0900 cents 80.0900 2: 78.6900 cents 78.6900 3: 80.0900 cents 80.0900 4: 80.0900 cents 80.0900 5: 78.6900 cents 78.6900 6: 80.0900 cents 80.0900 7: 80.0900 cents 80.0900 8: 78.6900 cents 78.6900 9: 80.0900 cents 80.0900 10: 80.0900 cents 80.0900 11: 78.6900 cents 78.6900 12: 80.0900 cents 80.0900 13: 80.0900 cents 80.0900 14: 78.6900 cents 78.6900 15: 80.0900 cents 80.0900
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 78.69000 cents 1: 10 80.09000 cents 2: 10 158.78000 cents 2: 5 160.18000 cents 3: 15 238.87000 cents 4: 5 317.56000 cents 4: 10 318.96000 cents 5: 10 397.65000 cents 5: 5 399.05000 cents 6: 15 477.74000 cents 7: 5 556.43000 cents 7: 10 557.83000 cents 8: 10 636.52000 cents 8: 5 637.92000 cents 9: 15 716.61000 cents 10: 5 795.30000 cents 10: 10 796.70000 cents 11: 10 875.39000 cents 11: 5 876.79000 cents 12: 15 955.48000 cents 13: 5 1034.17000 cents 13: 10 1035.57000 cents 14: 10 1114.26000 cents 14: 5 1115.66000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.71429 = 12/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0.0 : 80.1 158.8 238.9 319.0 397.6 477.7 557.8 636.5 716.6 796.7 875.4 955.5 1035.6 1114.3 1194.3 80.1 : 78.7 158.8 238.9 317.6 397.6 477.7 556.4 636.5 716.6 795.3 875.4 955.5 1034.2 1114.3 1194.3 158.8 : 80.1 160.2 238.9 319.0 399.0 477.7 557.8 637.9 716.6 796.7 876.8 955.5 1035.6 1115.7 1194.3 238.9 : 80.1 158.8 238.9 319.0 397.6 477.7 557.8 636.5 716.6 796.7 875.4 955.5 1035.6 1114.3 1194.3 319.0 : 78.7 158.8 238.9 317.6 397.6 477.7 556.4 636.5 716.6 795.3 875.4 955.5 1034.2 1114.3 1194.3 397.6 : 80.1 160.2 238.9 319.0 399.0 477.7 557.8 637.9 716.6 796.7 876.8 955.5 1035.6 1115.7 1194.3 477.7 : 80.1 158.8 238.9 319.0 397.6 477.7 557.8 636.5 716.6 796.7 875.4 955.5 1035.6 1114.3 1194.3 557.8 : 78.7 158.8 238.9 317.6 397.6 477.7 556.4 636.5 716.6 795.3 875.4 955.5 1034.2 1114.3 1194.3 636.5 : 80.1 160.2 238.9 319.0 399.0 477.7 557.8 637.9 716.6 796.7 876.8 955.5 1035.6 1115.7 1194.3 716.6 : 80.1 158.8 238.9 319.0 397.6 477.7 557.8 636.5 716.6 796.7 875.4 955.5 1035.6 1114.3 1194.3 796.7 : 78.7 158.8 238.9 317.6 397.6 477.7 556.4 636.5 716.6 795.3 875.4 955.5 1034.2 1114.3 1194.3 875.4 : 80.1 160.2 238.9 319.0 399.0 477.7 557.8 637.9 716.6 796.7 876.8 955.5 1035.6 1115.7 1194.3 955.5 : 80.1 158.8 238.9 319.0 397.6 477.7 557.8 636.5 716.6 796.7 875.4 955.5 1035.6 1114.3 1194.3 1035.6: 78.7 158.8 238.9 317.6 397.6 477.7 556.4 636.5 716.6 795.3 875.4 955.5 1034.2 1114.3 1194.3 1114.3: 80.1 160.2 238.9 319.0 399.0 477.7 557.8 637.9 716.6 796.7 876.8 955.5 1035.6 1115.7 1194.3 1194.3
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 78.6900 .. 80.0900 cents 1.40000 cents 78.69000 cents 2: 158.7800 .. 160.1800 cents 1.40000 cents 78.69000 cents 3: 238.8700 .. 238.8700 cents 1/1, 0.0000 cents 78.69000 cents 4: 317.5600 .. 318.9600 cents 1.40000 cents 78.69000 cents 5: 397.6500 .. 399.0500 cents 1.40000 cents 78.69000 cents 6: 477.7400 .. 477.7400 cents 1/1, 0.0000 cents 78.69000 cents 7: 556.4300 .. 557.8300 cents 1.40000 cents 78.69000 cents 8: 636.5200 .. 637.9200 cents 1.40000 cents 78.69000 cents 9: 716.6100 .. 716.6100 cents 1/1, 0.0000 cents 78.69000 cents 10: 795.3000 .. 796.7000 cents 1.40000 cents 78.69000 cents 11: 875.3900 .. 876.7900 cents 1.40000 cents 78.69000 cents 12: 955.4800 .. 955.4800 cents 1/1, 0.0000 cents 78.69000 cents 13: 1034.1700 .. 1035.5700 cents 1.40000 cents 78.69000 cents 14: 1114.2600 .. 1115.6600 cents 1.40000 cents 78.69000 cents
SHOW DATA
Number of notes : 15 -- Interval properties -- Smallest interval : 78.69000 cents, class 1 Average step (divided formal octave): 79.6233 cents Largest one step interval : 80.09000 cents Average / Smallest step : 1.011861 Largest / Average step : 1.005861 Largest / Smallest step : 1.017791 Median interval of one step : 80.09000 cents, amount: 10 Most common interval of one step : 80.09000 cents, amount: 10 Least squares average step : 79.62145 cents, oct.: 1194.32177 cents Scale is strictly proper Scale is maximally even in 850-tone equal temperament Scale has 5 repeating blocks of 3 notes Blocks have Myhill's property chromas: 1.40000 cents and 77.29000 cents, ratio: 55.207143 generators: 1 of 80.09000 cents and 2 of 158.78000 cents ET pair of linear temperament : 850&3415 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 850-tone equal temperament with octave 1194.350 cents degrees: 57 113 170 227 283 340 397 453 510 567 623 680 737 793 850 Least number of segments generator : 427 of 599.985 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 453 of 636.518 cents and inv. generated superset size: 683 = 668 more = 4553.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABAABAABAABA Step pattern size order : LSLLSLLSLLSLLSL Scale is a Constant Structure, by a margin of 78.69000 cents Scale diversity : 1.012038 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.988278 Number of different interval sizes : 24 = 1.71429 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.71429 = 12/7 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 1.40000 cents Most common triad is 0.0 238.870 477.740 cents, amount: 15 Number of recognisable fifths : 15, average 716.6100 cents Number of appreciable fifths : 0 Number of recognisable fourths : 0 Scale contains two identical disjunct heptachords Best minor thirds form a closed circle Formal octave complements present : 15 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 3 6 9 12 Limited inverse transpositions : 3 6 9 12 Inversional symmetry on degrees : 0 3 6 9 12 Inversional symmetry on intervals : 1-2 4-5 7-8 10-11 13-14 -- Rational properties --
FIT/MODE
15: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 0.3810 c. M: 0.4667 c. 430: 29 28 29 29 28 29 29 28 29 29 28 29 29 28 29 SP B ME I SD: 0.3749 c. M: 0.4592 c. 445: 30 29 30 30 29 30 30 29 30 30 29 30 30 29 30 SP B ME I SD: 0.3494 c. M:-0.4280 c. 460: 31 30 31 31 30 31 31 30 31 31 30 31 31 30 31 SP B ME I SD: 0.3256 c. M: 0.3988 c. 475: 32 31 32 32 31 32 32 31 32 32 31 32 32 31 32 SP B ME I SD: 0.3033 c. M:-0.3715 c. 490: 33 32 33 33 32 33 33 32 33 33 32 33 33 32 33 SP B ME I SD: 0.2824 c. M:-0.3458 c. 505: 34 33 34 34 33 34 34 33 34 34 33 34 34 33 34 SP B ME I SD: 0.2627 c. M:-0.3217 c. 520: 35 34 35 35 34 35 35 34 35 35 34 35 35 34 35 SP B ME I SD: 0.2441 c. M:-0.2989 c. 535: 36 35 36 36 35 36 36 35 36 36 35 36 36 35 36 SP B ME I SD: 0.2266 c. M:-0.2775 c. 550: 37 36 37 37 36 37 37 36 37 37 36 37 37 36 37 SP B ME I SD: 0.2100 c. M:-0.2572 c. 565: 38 37 38 38 37 38 38 37 38 38 37 38 38 37 38 SP B ME I SD: 0.1943 c. M: 0.2380 c. 580: 39 38 39 39 38 39 39 38 39 39 38 39 39 38 39 SP B ME I SD: 0.1794 c. M: 0.2197 c. 595: 40 39 40 40 39 40 40 39 40 40 39 40 40 39 40 SP B ME I SD: 0.1653 c. M:-0.2024 c. 610: 41 40 41 41 40 41 41 40 41 41 40 41 41 40 41 SP B ME I SD: 0.1519 c. M:-0.1860 c. 625: 42 41 42 42 41 42 42 41 42 42 41 42 42 41 42 SP B ME I SD: 0.1391 c. M:-0.1703 c. 640: 43 42 43 43 42 43 43 42 43 43 42 43 43 42 43 SP B ME I SD: 0.1269 c. M: 0.1554 c. 655: 44 43 44 44 43 44 44 43 44 44 43 44 44 43 44 SP B ME I SD: 0.1152 c. M:-0.1411 c. 670: 45 44 45 45 44 45 45 44 45 45 44 45 45 44 45 SP B ME I SD: 0.1041 c. M: 0.1275 c. 685: 46 45 46 46 45 46 46 45 46 46 45 46 46 45 46 SP B ME I SD: 0.0935 c. M:-0.1145 c. 700: 47 46 47 47 46 47 47 46 47 47 46 47 47 46 47 SP B ME I SD: 0.0833 c. M: 0.1021 c. 715: 48 47 48 48 47 48 48 47 48 48 47 48 48 47 48 SP B ME I SD: 0.0736 c. M:-0.0901 c. 730: 49 48 49 49 48 49 49 48 49 49 48 49 49 48 49 SP B ME I SD: 0.0643 c. M:-0.0787 c. 745: 50 49 50 50 49 50 50 49 50 50 49 50 50 49 50 SP B ME I SD: 0.0553 c. M: 0.0677 c. 760: 51 50 51 51 50 51 51 50 51 51 50 51 51 50 51 SP B ME I SD: 0.0467 c. M: 0.0572 c. 775: 52 51 52 52 51 52 52 51 52 52 51 52 52 51 52 SP B ME I SD: 0.0384 c. M: 0.0470 c. 790: 53 52 53 53 52 53 53 52 53 53 52 53 53 52 53 SP B ME I SD: 0.0304 c. M: 0.0373 c. 805: 54 53 54 54 53 54 54 53 54 54 53 54 54 53 54 SP B ME I SD: 0.0228 c. M: 0.0279 c. 820: 55 54 55 55 54 55 55 54 55 55 54 55 55 54 55 SP B ME I SD: 0.0154 c. M:-0.0188 c. 835: 56 55 56 56 55 56 56 55 56 56 55 56 56 55 56 SP B ME I SD: 0.0083 c. M: 0.0101 c. 850: 57 56 57 57 56 57 57 56 57 57 56 57 57 56 57 SP B ME I SD: 0.0014 c. M: 0.0017 c.
FIT/HARMONIC
1 x x x x x x x x x x x x x x 2 S SD: 5.6500 cents 2 x x x x x x x x 3 x x x x x 4 S SD: 7.8532 cents 3 x x x x x 4 x x x x 5 x x x 6 S SD: 7.6351 cents 4 x x x x 5 x x x 6 x x 7 x x 8 S SD: 5.8807 cents 5 x x x 6 x x 7 x x 8 x x 9 x 10 S SD: 7.1098 cents 6 x x 7 x x 8 x x 9 x 10 x 11 x 12 S SD: 6.8995 cents 7 x x 8 x 9 x x 10 x 11 x 12:13 x 14 S SD: 8.8774 cents 8 x x 9 x 10 x 11 x 12 x 13:14 x 15:16 S SD: 7.6125 cents 9 x 10 x 11 x 12 x 13 x 14:15 x 16:17:18 S SD: 7.5650 cents 10 x 11 x 12 x 13:14 x 15:16 x 17:18:19:20 S SD: 5.8627 cents 11 x 12 x 13:14 x 15:16:17 x 18:19:20:21:22 S SD: 5.7250 cents 12 x 13:14 x 15:16 x 17:18:19:20:21:22:23:24 S SD: 5.0683 cents 13 x 14:15 x 16:17:18:19:20:21:22:23:24:25:26 S SD: 7.0427 cents 14 x 15:16:17:18 x 19:20:21:22:23:24:25:27:28 SD: 6.5473 cents 15:16 x 17:18:19:20:21:22:23:24:25:26:27:29:30 SD: 5.2379 cents 16:17 x 18:19:20:21:22:23:24:25:27:28:29:30:32 SD: 5.1668 cents 17:18:19 x 20:21:22:23:25:26:27:28:30:31:32:34 SD: 6.6913 cents 18:19:20:21:22:23:24:25:26:27:29:30:31:33:34:36 SD: 4.8606 cents 19:20:21:22:23:24:25:26:27:29:30:32:33:35:36:38 SD: 3.8313 cents 20:21:22:23:24:25:26:28:29:30:32:33:35:36:38:40 SD: 3.3546 cents 27:28:30:31:32:34:36:37:39:41:43:45:47:49:51:54 SD: 3.3179 cents 29:30:32:33:35:36:38:40:42:44:46:48:50:53:55:58 SD: 2.8786 cents 31:32:34:36:37:39:41:43:45:47:49:51:54:56:59:62 SD: 2.8252 cents 34:36:37:39:41:43:45:47:49:51:54:56:59:62:65:68 SD: 2.2833 cents 39:41:43:45:47:49:51:54:56:59:62:65:68:71:74:78 SD: 1.8710 cents 41:43:45:47:49:52:54:57:59:62:65:68:71:75:78:82 SD: 1.7290 cents 50:52:55:57:60:63:66:69:72:76:79:83:87:91:95:100 SD: 1.5419 cents 60:63:66:69:72:75:79:83:87:91:95:99:104:109:114:120 SD: 1.3636 cents 61:64:67:70:73:77:80:84:88:92:97:101:106:111:116:122 SD: 1.1877 cents 79:83:87:91:95:99:104:109:114:120:125:131:137:144:150:157 SD: 1.1721 cents 81:85:89:93:97:102:107:112:117:123:128:134:141:147:154:161 SD: 1.0478 cents 82:86:90:94:99:103:108:113:118:124:130:136:142:149:156:163 SD: 0.8938 cents 84:88:92:96:101:106:111:116:121:127:133:139:146:153:160:167 SD: 0.8912 cents 94:98:103:108:113:118:124:130:136:142:149:156:163:171:179:187 SD: 0.7732 cents 103:108:113:118:124:130:136:142:149:156:163:171:179:187:196:205 SD: 0.6934 cents 113:118:124:130:136:142:149:156:163:171:179:187:196:206:215:225 SD: 0.6508 cents 123:129:135:141:148:155:162:170:178:186:195:204:214:224:234:245 SD: 0.5345 cents 144:151:158:165:173:181:190:199:208:218:228:239:250:262:274:287 SD: 0.4185 cents 187:196:205:215:225:235:246:258:270:283:296:310:325:340:356:373 SD: 0.3745 cents 189:198:207:217:227:238:249:261:273:286:299:313:328:344:360:377 SD: 0.3344 cents 216:226:237:248:260:272:285:298:312:327:342:358:375:393:411:431 SD: 0.3328 cents 236:247:259:271:284:297:311:326:341:357:374:391:410:429:449:470 SD: 0.2882 cents 248:260:272:285:298:312:327:342:358:375:393:411:431:451:472:494 SD: 0.2817 cents 252:264:276:289:303:317:332:348:364:381:399:418:438:458:480:502 SD: 0.2652 cents 271:284:297:311:326:341:357:374:391:410:429:449:471:493:516:540 SD: 0.2418 cents 292:306:320:335:351:367:385:403:422:442:463:484:507:531:556:582 SD: 0.2274 cents 337:353:369:387:405:424:444:465:487:510:534:559:585:613:641:672 SD: 0.1919 cents 365:382:400:419:439:459:481:504:527:552:578:605:634:664:695:728 SD: 0.1755 cents 406:425:445:466:488:511:535:560:586:614:643:673:705:738:773:809 SD: 0.1751 cents 419:439:459:481:504:527:552:578:605:634:664:695:728:762:798:835 SD: 0.1727 cents 425:445:466:488:511:535:560:587:614:643:673:705:738:773:809:847 SD: 0.1510 cents 445:466:488:511:535:560:586:614:643:673:705:738:773:809:847:887 SD: 0.1461 cents 479:502:525:550:576:603:631:661:692:725:759:794:832:871:912:955 SD: 0.1440 cents 500:524:548:574:601:629:659:690:722:756:792:829:868:909:952:997 SD: 0.1348 cents 529:554:580:607:636:666:697:730:764:800:838:877:919:962:1007:1055 SD: 0.1284 cents 573:600:628:658:689:721:755:791:828:867:908:950:995:1042:1091:1142 SD: 0.0987 cents