Scala analysis: xen18-erlich-liese-15
2L 13s MOS for Liese, L=181.93, s=64.52
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 64.520 cents 64.520000 2: 129.040 cents 129.040000 3: 193.560 cents 193.560000 4: 375.490 cents 375.490000 5: 440.010 cents 440.010000 6: 504.530 cents 504.530000 7: 569.050 cents 569.050000 8: 633.570 cents 633.570000 9: 698.090 cents 698.090000 10: 762.610 cents 762.610000 11: 827.130 cents 827.130000 12: 1009.060 cents 1009.060000 13: 1073.580 cents 1073.580000 14: 1138.100 cents 1138.100000 15: 1202.620 cents 1202.620000
SHOW/INTERVAL
0: 64.5200 cents 64.5200 1: 64.5200 cents 64.5200 2: 64.5200 cents 64.5200 3: 64.5200 cents 64.5200 4: 181.9300 cents 181.9300 5: 64.5200 cents 64.5200 6: 64.5200 cents 64.5200 7: 64.5200 cents 64.5200 8: 64.5200 cents 64.5200 9: 64.5200 cents 64.5200 10: 64.5200 cents 64.5200 11: 64.5200 cents 64.5200 12: 181.9300 cents 181.9300 13: 64.5200 cents 64.5200 14: 64.5200 cents 64.5200 15: 64.5200 cents 64.5200
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 13 64.52000 cents 1: 2 181.93000 cents 2: 11 129.04000 cents 2: 4 246.45000 cents 3: 9 193.56000 cents 3: 6 310.97000 cents 4: 7 258.08000 cents 4: 8 375.49000 cents 5: 5 322.60000 cents 5: 10 440.01000 cents 6: 3 387.12000 cents 6: 12 504.53000 cents 7: 1 451.64000 cents 7: 14 569.05000 cents 8: 14 633.57000 cents 8: 1 750.98000 cents 9: 12 698.09000 cents 9: 3 815.50000 cents 10: 10 762.61000 cents 10: 5 880.02000 cents 11: 8 827.13000 cents 11: 7 944.54000 cents 12: 6 891.65000 cents 12: 9 1009.06000 cents 13: 4 956.17000 cents 13: 11 1073.58000 cents 14: 2 1020.69000 cents 14: 13 1138.10000 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 15 0.0 : 64.5 129.0 193.6 375.5 440.0 504.5 569.0 633.6 698.1 762.6 827.1 1009.1 1073.6 1138.1 1202.6 64.5 : 64.5 129.0 311.0 375.5 440.0 504.5 569.1 633.6 698.1 762.6 944.5 1009.1 1073.6 1138.1 1202.6 129.0 : 64.5 246.4 311.0 375.5 440.0 504.5 569.0 633.6 698.1 880.0 944.5 1009.1 1073.6 1138.1 1202.6 193.6 : 181.9 246.4 311.0 375.5 440.0 504.5 569.0 633.6 815.5 880.0 944.5 1009.1 1073.6 1138.1 1202.6 375.5 : 64.5 129.0 193.6 258.1 322.6 387.1 451.6 633.6 698.1 762.6 827.1 891.6 956.2 1020.7 1202.6 440.0 : 64.5 129.0 193.6 258.1 322.6 387.1 569.0 633.6 698.1 762.6 827.1 891.7 956.2 1138.1 1202.6 504.5 : 64.5 129.0 193.6 258.1 322.6 504.5 569.0 633.6 698.1 762.6 827.1 891.6 1073.6 1138.1 1202.6 569.0 : 64.5 129.0 193.6 258.1 440.0 504.5 569.1 633.6 698.1 762.6 827.1 1009.1 1073.6 1138.1 1202.6 633.6 : 64.5 129.0 193.6 375.5 440.0 504.5 569.0 633.6 698.1 762.6 944.5 1009.1 1073.6 1138.1 1202.6 698.1 : 64.5 129.0 311.0 375.5 440.0 504.5 569.0 633.6 698.1 880.0 944.5 1009.1 1073.6 1138.1 1202.6 762.6 : 64.5 246.4 311.0 375.5 440.0 504.5 569.1 633.6 815.5 880.0 944.5 1009.1 1073.6 1138.1 1202.6 827.1 : 181.9 246.4 311.0 375.5 440.0 504.5 569.1 751.0 815.5 880.0 944.5 1009.1 1073.6 1138.1 1202.6 1009.1: 64.5 129.0 193.6 258.1 322.6 387.1 569.1 633.6 698.1 762.6 827.1 891.7 956.2 1020.7 1202.6 1073.6: 64.5 129.0 193.6 258.1 322.6 504.5 569.0 633.6 698.1 762.6 827.1 891.7 956.2 1138.1 1202.6 1138.1: 64.5 129.0 193.6 258.1 440.0 504.5 569.1 633.6 698.1 762.6 827.1 891.7 1073.6 1138.1 1202.6 1202.6
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 64.5200 .. 181.9300 cents 117.41000 cents 64.52000 cents 2: 129.0400 .. 246.4500 cents 117.41000 cents -52.89000 cents 3: 193.5600 .. 310.9700 cents 117.41000 cents -52.89000 cents 4: 258.0800 .. 375.4900 cents 117.41000 cents -52.89000 cents 5: 322.6000 .. 440.0100 cents 117.41000 cents -52.89000 cents 6: 387.1200 .. 504.5300 cents 117.41000 cents -52.89000 cents 7: 451.6400 .. 569.0500 cents 117.41000 cents -52.89000 cents 8: 633.5700 .. 750.9800 cents 117.41000 cents 64.52000 cents 9: 698.0900 .. 815.5000 cents 117.41000 cents -52.89000 cents 10: 762.6100 .. 880.0200 cents 117.41000 cents -52.89000 cents 11: 827.1300 .. 944.5400 cents 117.41000 cents -52.89000 cents 12: 891.6500 .. 1009.0600 cents 117.41000 cents -52.89000 cents 13: 956.1700 .. 1073.5800 cents 117.41000 cents -52.89000 cents 14: 1020.6900 .. 1138.1000 cents 117.41000 cents -52.89000 cents
SHOW DATA
Number of notes : 15 -- Interval properties -- Smallest interval : 64.52000 cents, class 1 Average step (divided formal octave): 80.1747 cents Largest one step interval : 181.93000 cents Average / Smallest step : 1.242633 Largest / Average step : 2.269171 Largest / Smallest step : 2.819746 Median interval of one step : 64.52000 cents, amount: 13 Most common interval of one step : 64.52000 cents, amount: 13 Least squares average step : 80.42716 cents, oct.: 1206.40742 cents Scale is not proper Scale has Myhill's property chromas: 117.41000 cents and 52.89000 cents, ratio: 2.219890 generators: 7 of 569.05000 cents and 8 of 633.57000 cents ET pair of linear temperament : 17&19 Scale is distributional even Scale is a mode of a 1137-tone equal temperament with octave 1202.620 cents degrees: 61 122 183 355 416 477 538 599 660 721 782 954 1015 1076 1137 generators: 538 and 599 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAABAAAAAAABAAA Step pattern size order : SSSLSSSSSSSLSSS Scale is a Constant Structure, by a margin of 11.63000 cents Scale diversity : 1.149000 Lumma stability : 0.160949 Lumma impropriety factor : 0.527748 Rothenberg efficiency : 0.711111 redundancy: 0.288889 Efficiency x scale size : 10.666667 Number of different interval sizes : 28 = 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 : 11.63000 cents Most common intervals : 569.05000 cents & inv., amount: 14 Scale is a chain of 7 triads 0.0 569.050 1138.100 cents Most common triad is 0.0 569.050 633.570 cents, amount: 13 Number of recognisable fifths : 12, average 698.0900 cents Number of recognisable fourths : 12, average 504.5300 cents Scale contains two identical disjunct heptachords Formal octave complements present : 15 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 7-8 -- Rational properties --
FIT/MODE
15: 0 1 1 2 1 1 1 1 0 1 1 2 1 1 1 N T3 SD: 38.1530 c. M: 64.5200 c. 16: 1 1 1 2 1 1 1 0 1 1 1 2 1 1 1 N T3 I SD: 20.7027 c. M: 32.2600 c. 17: 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 P M ME I SD: 13.4418 c. M: 21.7782 c. 19: 1 1 1 3 1 1 1 1 1 1 1 3 1 1 1 N M DE I SD: 2.6446 c. M: 4.2847 c. 55: 3 3 3 8 3 3 3 3 3 3 3 8 3 3 3 N M DE I SD: 2.3276 c. M: 3.7711 c. 74: 4 4 4 11 4 4 4 4 4 4 4 11 4 4 4 N M DE I SD: 1.0509 c. M: 1.7027 c. 93: 5 5 5 14 5 5 5 5 5 5 5 14 5 5 5 N M DE I SD: 0.2959 c. M: 0.4795 c. 112: 6 6 6 17 6 6 6 6 6 6 6 17 6 6 6 N M DE I SD: 0.2029 c. M: 0.3287 c. 205: 11 11 11 31 11 11 11 11 11 11 11 31 11 11 11 N M DE I SD: 0.0234 c. M: 0.0379 c. 727: 39 39 39 110 39 39 39 39 39 39 39 110 39 39 39 N M DE I SD: 0.0115 c. M: 0.0186 c. 932: 50 50 50 141 50 50 50 50 50 50 50 141 50 50 50 N M DE I SD: 0.0038 c. M: 0.0062 c. 1137: 61 61 61 172 61 61 61 61 61 61 61 172 61 61 61 N M DE I SD: 0.0011 c. M: 0.0018 c.
FIT/HARMONIC
1 x x x x x x x x x x x x x x 2 S SD: 2.6200 cents 2 x x x x x x x x 3 x x x x x 4 S SD: 2.3347 cents 3 x x x x x 4 x x x x 5 x x x 6 S SD: 19.2182 cents 4 x x x 5 x x x x 6 x x 7 x x 8 S SD: 10.4813 cents 5 x x x 6 x x 7 x x x 8:9 x x 10 S SD: 12.6863 cents 6 x x 7 x x 8 x x 9 x 10 x 11 x 12 S SD: 16.0727 cents 7 x x 8 x 9 x x 10 x 11 x x 13 x 14 SD: 7.6438 cents 8 x x 9:10 x x 11 x 12 x 13:14:15 x 16 S SD: 6.3425 cents 9 x x 10:11 x 12 x 13 x 14:15:16:17 x 18 S SD: 7.9925 cents 10 x x 11:12:13 x 14 x 15 x 16:18 x 19:20 S SD: 8.4469 cents 11 x 12 x x 14 x 15:16 x 17:18:20 x 21:22 S SD: 7.0160 cents 12 x 13 x 15 x 16 x 17:18 x 19:21:22:23:24 SD: 6.7433 cents 13 x 14:15:16:17 x 18:19 x 20:21:23:24:25:26 SD: 6.0707 cents 14 x 15:16:17:18:19 x 20:21:22:23:25:26:27:28 SD: 5.6613 cents 15 x 16:17 x 19:20:21:22 x 23:24:27:28:29:30 SD: 5.0715 cents 16 x 17:18:20:21 x 22:23:24:25:26:29:30:31:32 SD: 4.2691 cents 17 x 18:19:21:22:23:24 x 25:26:27:30:32:33:34 SD: 5.8344 cents 18:19 x 20:22:23:24:25:26:27:28:29:32:33:35:36 SD: 3.9198 cents 19:20 x 21:24 x 25:26:27:28:30:31:34:35:37:38 SD: 6.1803 cents 20:21 x 22:25:26:27:28:29:30:31:32:36:37:39:40 SD: 3.7274 cents 21:22:23 x 26:27:28:29:30:31:33:34:38:39:41:42 SD: 4.0860 cents 23:24:25:26:29:30:31:32:33:34:36:37:41:43:44:46 SD: 3.6537 cents 24:25:26:27:30:31:32:33:35:36:37:39:43:45:46:48 SD: 2.8554 cents 28:29:30:31:35:36:37:39:40:42:44:45:50:52:54:56 SD: 2.8248 cents 29:30:31:32:36:37:39:40:42:43:45:47:52:54:56:58 SD: 2.7722 cents 34:35:37:38:42:44:46:47:49:51:53:55:61:63:66:68 SD: 2.4050 cents 36:37:39:40:45:46:48:50:52:54:56:58:64:67:69:72 SD: 2.3666 cents 38:39:41:42:47:49:51:53:55:57:59:61:68:71:73:76 SD: 2.3017 cents 41:43:44:46:51:53:55:57:59:61:64:66:73:76:79:82 SD: 1.8680 cents 48:50:52:54:60:62:64:67:69:72:75:77:86:89:93:96 SD: 1.8542 cents 49:51:53:55:61:63:66:68:71:73:76:79:88:91:95:98 SD: 1.5113 cents 52:54:56:58:65:67:70:72:75:78:81:84:93:97:100:104 SD: 1.3399 cents 59:61:64:66:73:76:79:82:85:88:92:95:106:110:114:118 SD: 1.3099 cents 62:64:67:69:77:80:83:86:89:93:96:100:111:115:120:124 SD: 1.2553 cents 70:73:75:78:87:90:94:97:101:105:109:113:125:130:135:140 SD: 1.2476 cents 74:77:80:83:92:95:99:103:107:111:115:119:133:138:143:148 SD: 1.1305 cents 75:78:81:84:93:97:100:104:108:112:117:121:134:139:145:150 SD: 1.0836 cents 77:80:83:86:96:99:103:107:111:115:120:124:138:143:149:154 SD: 0.8341 cents 100:104:108:112:124:129:134:139:144:150:155:161:179:186:193:200 SD: 0.6767 cents 127:132:137:142:158:164:170:176:183:190:197:205:227:236:245:254 SD: 0.5740 cents 129:134:139:144:160:166:173:179:186:193:200:208:231:240:249:258 SD: 0.5488 cents 152:158:164:170:189:196:203:211:219:227:236:245:272:283:293:304 SD: 0.5448 cents 154:160:166:172:191:199:206:214:222:230:239:248:276:286:297:308 SD: 0.5379 cents 157:163:169:176:195:202:210:218:226:235:244:253:281:292:303:314 SD: 0.4932 cents 177:184:191:198:220:228:237:246:255:265:275:285:317:329:342:355 SD: 0.4152 cents 183:190:197:205:227:236:245:254:264:274:284:295:328:340:353:367 SD: 0.3770 cents 210:218:226:235:261:271:281:292:303:314:326:339:376:390:405:421 SD: 0.3495 cents 211:219:227:236:262:272:282:293:304:316:328:340:378:392:407:423 SD: 0.3223 cents 242:251:261:271:301:312:324:336:349:362:376:390:433:450:467:485 SD: 0.3206 cents 255:265:275:285:317:329:341:354:368:382:396:411:457:474:492:511 SD: 0.3108 cents 260:270:280:291:323:335:348:361:375:389:404:419:466:483:502:521 SD: 0.2292 cents 296:307:319:331:368:382:396:411:427:443:460:477:530:550:571:593 SD: 0.2271 cents 314:326:338:351:390:405:420:436:453:470:488:506:562:584:606:629 SD: 0.2079 cents 322:334:347:360:400:415:431:447:464:482:500:519:577:599:621:645 SD: 0.1987 cents 346:359:373:387:430:446:463:481:499:518:538:558:620:643:668:693 SD: 0.1984 cents 363:377:391:406:451:468:486:504:523:543:564:585:650:675:701:727 SD: 0.1908 cents 372:386:401:416:462:480:498:517:536:557:578:600:666:692:718:745 SD: 0.1887 cents 387:402:417:433:481:499:518:538:558:579:601:624:693:719:747:775 SD: 0.1860 cents 398:413:429:445:494:513:533:553:574:596:618:642:713:740:768:797 SD: 0.1772 cents 425:441:458:475:528:548:569:590:613:636:660:685:761:790:820:851 SD: 0.1540 cents 455:472:490:509:565:587:609:632:656:681:707:734:815:846:878:911 SD: 0.1445 cents 532:552:573:595:661:686:712:739:767:796:826:858:953:989:1027:1066 SD: 0.1154 cents