Scala analysis: xen18-erlich-blacksmith-15
10L 5s MOS for Blacksmith, L=83.83, s=71.52
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 83.830 cents 83.830000 2: 155.350 cents 155.350000 3: 239.180 cents 239.180000 4: 323.010 cents 323.010000 5: 394.530 cents 394.530000 6: 478.360 cents 478.360000 7: 562.190 cents 562.190000 8: 633.710 cents 633.710000 9: 717.540 cents 717.540000 10: 801.370 cents 801.370000 11: 872.890 cents 872.890000 12: 956.720 cents 956.720000 13: 1040.550 cents 1040.550000 14: 1112.070 cents 1112.070000 15: 1195.900 cents 1195.900000
SHOW/INTERVAL
0: 83.8300 cents 83.8300 1: 83.8300 cents 83.8300 2: 71.5200 cents 71.5200 3: 83.8300 cents 83.8300 4: 83.8300 cents 83.8300 5: 71.5200 cents 71.5200 6: 83.8300 cents 83.8300 7: 83.8300 cents 83.8300 8: 71.5200 cents 71.5200 9: 83.8300 cents 83.8300 10: 83.8300 cents 83.8300 11: 71.5200 cents 71.5200 12: 83.8300 cents 83.8300 13: 83.8300 cents 83.8300 14: 71.5200 cents 71.5200 15: 83.8300 cents 83.8300
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 71.52000 cents 1: 10 83.83000 cents 2: 10 155.35000 cents 2: 5 167.66000 cents 3: 15 239.18000 cents 4: 5 310.70000 cents 4: 10 323.01000 cents 5: 10 394.53000 cents 5: 5 406.84000 cents 6: 15 478.36000 cents 7: 5 549.88000 cents 7: 10 562.19000 cents 8: 10 633.71000 cents 8: 5 646.02000 cents 9: 15 717.54000 cents 10: 5 789.06000 cents 10: 10 801.37000 cents 11: 10 872.89000 cents 11: 5 885.20000 cents 12: 15 956.72000 cents 13: 5 1028.24000 cents 13: 10 1040.55000 cents 14: 10 1112.07000 cents 14: 5 1124.38000 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 : 83.8 155.3 239.2 323.0 394.5 478.4 562.2 633.7 717.5 801.4 872.9 956.7 1040.5 1112.1 1195.9 83.8 : 71.5 155.3 239.2 310.7 394.5 478.4 549.9 633.7 717.5 789.1 872.9 956.7 1028.2 1112.1 1195.9 155.3 : 83.8 167.7 239.2 323.0 406.8 478.4 562.2 646.0 717.5 801.4 885.2 956.7 1040.5 1124.4 1195.9 239.2 : 83.8 155.4 239.2 323.0 394.5 478.4 562.2 633.7 717.5 801.4 872.9 956.7 1040.5 1112.1 1195.9 323.0 : 71.5 155.3 239.2 310.7 394.5 478.4 549.9 633.7 717.5 789.1 872.9 956.7 1028.2 1112.1 1195.9 394.5 : 83.8 167.7 239.2 323.0 406.8 478.4 562.2 646.0 717.5 801.4 885.2 956.7 1040.5 1124.4 1195.9 478.4 : 83.8 155.3 239.2 323.0 394.5 478.4 562.2 633.7 717.5 801.4 872.9 956.7 1040.5 1112.1 1195.9 562.2 : 71.5 155.3 239.2 310.7 394.5 478.4 549.9 633.7 717.5 789.1 872.9 956.7 1028.2 1112.1 1195.9 633.7 : 83.8 167.7 239.2 323.0 406.8 478.4 562.2 646.0 717.5 801.4 885.2 956.7 1040.5 1124.4 1195.9 717.5 : 83.8 155.3 239.2 323.0 394.5 478.4 562.2 633.7 717.5 801.4 872.9 956.7 1040.5 1112.1 1195.9 801.4 : 71.5 155.3 239.2 310.7 394.5 478.4 549.9 633.7 717.5 789.1 872.9 956.7 1028.2 1112.1 1195.9 872.9 : 83.8 167.7 239.2 323.0 406.8 478.4 562.2 646.0 717.5 801.4 885.2 956.7 1040.5 1124.4 1195.9 956.7 : 83.8 155.3 239.2 323.0 394.5 478.4 562.2 633.7 717.5 801.4 872.9 956.7 1040.5 1112.1 1195.9 1040.5: 71.5 155.4 239.2 310.7 394.5 478.4 549.9 633.7 717.5 789.1 872.9 956.7 1028.2 1112.1 1195.9 1112.1: 83.8 167.7 239.2 323.0 406.8 478.4 562.2 646.0 717.5 801.4 885.2 956.7 1040.5 1124.4 1195.9 1195.9
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 71.5200 .. 83.8300 cents 12.31000 cents 71.52000 cents 2: 155.3500 .. 167.6600 cents 12.31000 cents 71.52000 cents 3: 239.1800 .. 239.1800 cents 1/1, 0.0000 cents 71.52000 cents 4: 310.7000 .. 323.0100 cents 12.31000 cents 71.52000 cents 5: 394.5300 .. 406.8400 cents 12.31000 cents 71.52000 cents 6: 478.3600 .. 478.3600 cents 1/1, 0.0000 cents 71.52000 cents 7: 549.8800 .. 562.1900 cents 12.31000 cents 71.52000 cents 8: 633.7100 .. 646.0200 cents 12.31000 cents 71.52000 cents 9: 717.5400 .. 717.5400 cents 1/1, 0.0000 cents 71.52000 cents 10: 789.0600 .. 801.3700 cents 12.31000 cents 71.52000 cents 11: 872.8900 .. 885.2000 cents 12.31000 cents 71.52000 cents 12: 956.7200 .. 956.7200 cents 1/1, 0.0000 cents 71.52000 cents 13: 1028.2400 .. 1040.5500 cents 12.31000 cents 71.52000 cents 14: 1112.0700 .. 1124.3800 cents 12.31000 cents 71.52000 cents
SHOW DATA
Number of notes : 15 -- Interval properties -- Smallest interval : 71.52000 cents, class 1 Average step (divided formal octave): 79.7267 cents Largest one step interval : 83.83000 cents Average / Smallest step : 1.114746 Largest / Average step : 1.051468 Largest / Smallest step : 1.172120 Median interval of one step : 83.83000 cents, amount: 10 Most common interval of one step : 83.83000 cents, amount: 10 Least squares average step : 79.71012 cents, oct.: 1195.65181 cents Scale is strictly proper Scale has 5 repeating blocks of 3 notes Blocks have Myhill's property chromas: 12.31000 cents and 59.21000 cents, ratio: 4.809911 generators: 1 of 83.83000 cents and 2 of 155.35000 cents ET pair of linear temperament : 85&100 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1070-tone equal temperament with octave 1195.900 cents degrees: 75 139 214 289 353 428 503 567 642 717 781 856 931 995 1070 Least number of segments generator : 537 of 600.185 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 567 of 633.715 cents and inv. generated superset size: 859 = 844 more = 5726.667% 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 71.52000 cents Scale diversity : 1.075693 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.897065 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 : 12.31000 cents Most common triad is 0.0 239.180 478.360 cents, amount: 15 Number of recognisable fifths : 15, average 717.5400 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: 3.3504 c. M: 4.1033 c. 55: 4 3 4 4 3 4 4 3 4 4 3 4 4 3 4 SP B ME I SD: 2.5675 c. M:-3.1445 c. Blackwood-15 70: 5 4 5 5 4 5 5 4 5 5 4 5 5 4 5 SP B ME I SD: 1.2994 c. M:-1.5914 c. 85: 6 5 6 6 5 6 6 5 6 6 5 6 6 5 6 SP B ME I SD: 0.4789 c. M:-0.5865 c. 100: 7 6 7 7 6 7 7 6 7 7 6 7 7 6 7 SP B ME I SD: 0.0955 c. M:-0.1170 c. Blackwood-15 285: 20 17 20 20 17 20 20 17 20 20 17 20 20 17 20 SP B DE I SD: 0.0758 c. M: 0.0928 c. 385: 27 23 27 27 23 27 27 23 27 27 23 27 27 23 27 SP B DE I SD: 0.0313 c. M:-0.0383 c. 485: 34 29 34 34 29 34 34 29 34 34 29 34 34 29 34 SP B DE I SD: 0.0051 c. M: 0.0063 c. 1070: 75 64 75 75 64 75 75 64 75 75 64 75 75 64 75 SP B DE I SD: 0.0043 c. M: 0.0052 c. 1555: 109 93 109 109 93 109 109 93 109 109 93 109 109 93 109 SP B DE I SD: 0.0013 c. M: 0.0016 c. 2040: 143 122 143 143 122 143 143 122 143 143 122 143 143 122 143 SP B DE I SD: 0.0002 c. M:-0.0002 c.
FIT/HARMONIC
1 x x x x x x x x x x x x x x 2 S SD: 4.1000 cents 2 x x x x x x x x 3 x x x x x 4 S SD: 8.0576 cents 3 x x x x x 4 x x x x 5 x x x 6 S SD: 7.7161 cents 4 x x x x 5 x x x 6 x x 7 x x 8 S SD: 5.4415 cents 5 x x x 6 x x 7 x x 8 x x 9 x 10 S SD: 6.8196 cents 6 x x 7 x x 8 x x 9 x 10 x 11 x 12 S SD: 6.7148 cents 7 x x 8 x 9 x x 10 x 11 x 12:13 x 14 S SD: 8.8894 cents 8 x x 9 x 10 x 11 x 12 x 13:14 x 15:16 S SD: 7.3418 cents 9 x 10 x 11 x 12 x 13 x 14:15:16 x 17:18 S SD: 7.7554 cents 10 x 11 x 12 x 13:14 x 15:16 x 17:18:19:20 S SD: 5.9435 cents 11 x 12 x 13:14 x 15:16:17 x 18:19:20:21:22 S SD: 6.0861 cents 12 x 13:14 x 15:16 x 17:18:19:20:21:22:23:24 S SD: 4.7861 cents 13 x 14:15 x 16:17:18:19:20:21:22:23:24:25:26 S SD: 6.7308 cents 14:15 x 16:17:18 x 19:20:21:22:23:24:26:27:28 S SD: 6.6537 cents 15:16 x 17:18:19:20:21:22:23:24:25:26:27:29:30 SD: 5.2600 cents 16:17 x 18:19:20:21:22:23:24:25:26:28:29:30:32 S SD: 5.3355 cents 17:18:19 x 20:21:22:24:25:26:27:28:30:31:32:34 S SD: 6.7694 cents 18:19:20:21:22:23:24:25:26:27:29:30:31:33:34:36 SD: 4.6867 cents 19:20:21:22:23:24:25:26:27:29:30:31:33:35:36:38 SD: 3.6805 cents 20:21:22:23:24:25:26:28:29:30:32:33:35:36:38:40 SD: 3.2871 cents 29:30:32:33:35:36:38:40:42:44:46:48:50:53:55:58 SD: 2.9546 cents 31:33:34:36:37:39:41:43:45:47:49:51:54:57:59:62 SD: 2.9147 cents 32:34:35:37:39:40:42:44:46:48:51:53:56:58:61:64 SD: 2.8496 cents 34:36:37:39:41:43:45:47:49:51:54:56:59:62:65:68 SD: 2.0584 cents 39:41:43:45:47:49:51:54:56:59:62:65:68:71:74:78 SD: 1.7930 cents 41:43:45:47:49:51:54:57:59:62:65:68:71:75:78:82 SD: 1.7851 cents 47:49:51:54:57:59:62:65:68:71:75:78:82:86:89:94 SD: 1.7809 cents 53:56:58:61:64:67:70:73:76:80:84:88:92:97:101:106 SD: 1.6237 cents 54:57:59:62:65:68:71:75:78:82:86:89:94:98:103:108 SD: 1.4065 cents 62:65:68:71:75:78:82:86:89:94:98:103:108:113:118:124 SD: 1.2800 cents 63:66:69:72:76:79:83:87:91:95:100:104:109:115:120:126 SD: 1.0949 cents 73:77:80:84:88:92:96:101:105:110:116:121:127:133:139:146 SD: 1.0872 cents 78:82:85:90:94:98:103:108:112:118:124:129:136:142:148:156 SD: 1.0870 cents 81:85:89:93:98:102:107:112:117:123:129:134:141:148:154:162 SD: 1.0245 cents 82:86:90:94:99:103:108:113:118:124:130:136:143:150:156:164 SD: 0.9945 cents 88:92:96:101:106:111:116:122:127:133:140:146:153:161:167:176 SD: 0.9846 cents 93:98:102:107:112:117:123:129:134:141:148:154:162:170:177:186 SD: 0.9712 cents 94:99:103:108:113:118:124:130:136:142:149:156:163:171:179:188 SD: 0.9507 cents 97:102:106:111:117:122:128:134:140:147:154:161:169:177:184:194 SD: 0.7979 cents 102:107:112:117:123:128:134:141:147:154:162:169:177:186:194:204 SD: 0.7712 cents 107:112:117:123:129:134:141:148:154:162:170:177:186:195:203:213 SD: 0.6588 cents 117:123:128:134:141:147:154:162:169:177:186:194:203:213:222:233 SD: 0.6402 cents 122:128:133:140:147:153:161:169:176:185:194:202:212:223:232:243 SD: 0.6200 cents 136:143:149:156:164:171:179:188:196:206:216:225:236:248:259:271 SD: 0.5195 cents 141:148:154:162:170:177:186:195:203:213:224:233:245:257:268:281 SD: 0.4611 cents 160:168:175:184:193:201:211:221:231:242:254:265:278:292:304:319 SD: 0.3756 cents 183:192:200:210:221:230:241:253:264:277:291:303:318:334:348:365 SD: 0.3572 cents 195:205:213:224:235:245:257:270:281:295:310:323:339:356:371:389 SD: 0.3380 cents 204:214:223:234:246:256:269:282:294:309:324:338:355:372:388:407 SD: 0.3165 cents 224:235:245:257:270:281:295:310:323:339:356:371:389:409:426:447 SD: 0.2642 cents 263:276:288:302:317:330:347:364:379:398:418:435:457:480:500:525 SD: 0.2631 cents 302:317:330:347:364:379:398:418:435:457:480:500:525:551:574:603 SD: 0.2519 cents 308:323:337:354:371:387:406:426:444:466:489:510:535:562:585:615 SD: 0.2511 cents 317:333:347:364:382:398:418:439:457:480:504:525:551:578:603:633 SD: 0.2387 cents 323:339:353:371:389:406:426:447:466:489:513:535:561:589:614:644 SD: 0.2249 cents 343:360:375:394:413:431:452:475:495:519:545:568:596:626:652:684 SD: 0.2235 cents 351:368:384:403:423:441:463:486:506:531:558:581:610:640:667:700 SD: 0.2200 cents 352:369:385:404:424:442:464:487:508:533:559:583:612:642:669:702 SD: 0.2194 cents 360:378:394:413:434:452:475:498:519:545:572:596:626:657:684:718 SD: 0.2122 cents 362:380:396:416:436:455:477:501:522:548:575:599:629:660:688:722 SD: 0.1924 cents 364:382:398:418:439:457:480:504:525:551:578:603:633:664:692:726 SD: 0.1920 cents 380:399:416:436:458:477:501:526:548:575:604:629:660:693:722:758 SD: 0.1917 cents 384:403:420:441:463:482:506:531:554:581:610:636:667:700:730:766 SD: 0.1784 cents 386:405:422:443:465:485:509:534:557:584:613:639:671:704:734:770 SD: 0.1678 cents 425:446:465:488:512:534:560:588:613:643:675:704:739:775:808:848 SD: 0.1444 cents 477:501:522:548:575:599:629:660:688:722:758:790:829:870:907:952 SD: 0.1441 cents 500:525:547:574:603:628:659:692:721:757:794:828:869:912:950:998 SD: 0.1411 cents 547:574:598:628:659:687:721:757:789:828:869:906:951:998:1040:1091 SD: 0.1276 cents 566:594:619:650:682:711:746:783:816:857:899:937:984:1032:1076:1129 SD: 0.1088 cents 586:615:641:673:706:736:772:811:845:887:931:970:1018:1069:1114:1169 SD: 0.1072 cents