Scala analysis: xen18-erlich-liese-13
2L 11s MOS for Liese, L=246.45, 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: 440.010 cents 440.010000 5: 504.530 cents 504.530000 6: 569.050 cents 569.050000 7: 633.570 cents 633.570000 8: 698.090 cents 698.090000 9: 762.610 cents 762.610000 10: 1009.060 cents 1009.060000 11: 1073.580 cents 1073.580000 12: 1138.100 cents 1138.100000 13: 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: 246.4500 cents 246.4500 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: 246.4500 cents 246.4500 11: 64.5200 cents 64.5200 12: 64.5200 cents 64.5200 13: 64.5200 cents 64.5200
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 11 64.52000 cents 1: 2 246.45000 cents 2: 9 129.04000 cents 2: 4 310.97000 cents 3: 7 193.56000 cents 3: 6 375.49000 cents 4: 5 258.08000 cents 4: 8 440.01000 cents 5: 3 322.60000 cents 5: 10 504.53000 cents 6: 1 387.12000 cents 6: 12 569.05000 cents 7: 12 633.57000 cents 7: 1 815.50000 cents 8: 10 698.09000 cents 8: 3 880.02000 cents 9: 8 762.61000 cents 9: 5 944.54000 cents 10: 6 827.13000 cents 10: 7 1009.06000 cents 11: 4 891.65000 cents 11: 9 1073.58000 cents 12: 2 956.17000 cents 12: 11 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 0.0 : 64.5 129.0 193.6 440.0 504.5 569.0 633.6 698.1 762.6 1009.1 1073.6 1138.1 1202.6 64.5 : 64.5 129.0 375.5 440.0 504.5 569.1 633.6 698.1 944.5 1009.1 1073.6 1138.1 1202.6 129.0 : 64.5 311.0 375.5 440.0 504.5 569.0 633.6 880.0 944.5 1009.1 1073.6 1138.1 1202.6 193.6 : 246.4 311.0 375.5 440.0 504.5 569.0 815.5 880.0 944.5 1009.1 1073.6 1138.1 1202.6 440.0 : 64.5 129.0 193.6 258.1 322.6 569.0 633.6 698.1 762.6 827.1 891.7 956.2 1202.6 504.5 : 64.5 129.0 193.6 258.1 504.5 569.0 633.6 698.1 762.6 827.1 891.6 1138.1 1202.6 569.0 : 64.5 129.0 193.6 440.0 504.5 569.1 633.6 698.1 762.6 827.1 1073.6 1138.1 1202.6 633.6 : 64.5 129.0 375.5 440.0 504.5 569.0 633.6 698.1 762.6 1009.1 1073.6 1138.1 1202.6 698.1 : 64.5 311.0 375.5 440.0 504.5 569.0 633.6 698.1 944.5 1009.1 1073.6 1138.1 1202.6 762.6 : 246.4 311.0 375.5 440.0 504.5 569.1 633.6 880.0 944.5 1009.1 1073.6 1138.1 1202.6 1009.1: 64.5 129.0 193.6 258.1 322.6 387.1 633.6 698.1 762.6 827.1 891.7 956.2 1202.6 1073.6: 64.5 129.0 193.6 258.1 322.6 569.0 633.6 698.1 762.6 827.1 891.7 1138.1 1202.6 1138.1: 64.5 129.0 193.6 258.1 504.5 569.1 633.6 698.1 762.6 827.1 1073.6 1138.1 1202.6 1202.6
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 64.5200 .. 246.4500 cents 181.93000 cents 64.52000 cents 2: 129.0400 .. 310.9700 cents 181.93000 cents -117.41000 cents 3: 193.5600 .. 375.4900 cents 181.93000 cents -117.41000 cents 4: 258.0800 .. 440.0100 cents 181.93000 cents -117.41000 cents 5: 322.6000 .. 504.5300 cents 181.93000 cents -117.41000 cents 6: 387.1200 .. 569.0500 cents 181.93000 cents -117.41000 cents 7: 633.5700 .. 815.5000 cents 181.93000 cents 64.52000 cents 8: 698.0900 .. 880.0200 cents 181.93000 cents -117.41000 cents 9: 762.6100 .. 944.5400 cents 181.93000 cents -117.41000 cents 10: 827.1300 .. 1009.0600 cents 181.93000 cents -117.41000 cents 11: 891.6500 .. 1073.5800 cents 181.93000 cents -117.41000 cents 12: 956.1700 .. 1138.1000 cents 181.93000 cents -117.41000 cents
SHOW DATA
Number of notes : 13 -- Interval properties -- Smallest interval : 64.52000 cents, class 1 Average step (divided formal octave): 92.5092 cents Largest one step interval : 246.45000 cents Average / Smallest step : 1.433807 Largest / Average step : 2.664058 Largest / Smallest step : 3.819746 Median interval of one step : 64.52000 cents, amount: 11 Most common interval of one step : 64.52000 cents, amount: 11 Least squares average step : 93.61991 cents, oct.: 1217.05889 cents Scale is not proper Scale has Myhill's property chromas: 181.93000 cents and 117.41000 cents, ratio: 1.549527 generators: 6 of 569.05000 cents and 7 of 633.57000 cents ET pair of linear temperament : 17&19 Scale is distributional even Scale is a mode of a 932-tone equal temperament with octave 1202.620 cents degrees: 50 100 150 341 391 441 491 541 591 782 832 882 932 generators: 441 and 491 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAABAAAAABAAA Step pattern size order : SSSLSSSSSLSSS Scale is a Constant Structure, by a margin of 11.63000 cents Scale diversity : 1.184399 Lumma stability : 0.160949 Lumma impropriety factor : 0.624453 Rothenberg efficiency : 0.717949 redundancy: 0.282051 Efficiency x scale size : 9.333333 Number of different interval sizes : 24 = 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: 12 Scale is a chain of 6 triads 0.0 569.050 1138.100 cents Most common triad is 0.0 569.050 633.570 cents, amount: 11 Number of recognisable fifths : 10, average 698.0900 cents Number of recognisable fourths : 10, average 504.5300 cents Scale contains two identical disjunct hexachords Formal octave complements present : 13 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 6-7 -- Rational properties --
FIT/MODE
13: 1 0 1 3 0 1 1 1 0 3 1 0 1 N I SD: 26.7674 c. M: 41.9838 c. 14: 1 1 0 3 1 1 0 1 1 3 0 1 1 N I SD: 24.8954 c. M: 42.7629 c. 16: 1 1 1 3 1 1 0 1 1 3 1 1 1 N I SD: 22.2379 c. M: 32.2600 c. 17: 1 1 1 3 1 1 1 1 1 3 1 1 1 N M DE I SD: 11.6410 c. M: 18.6671 c. 19: 1 1 1 4 1 1 1 1 1 4 1 1 1 N M DE I SD: 2.2903 c. M: 3.6726 c. 55: 3 3 3 11 3 3 3 3 3 11 3 3 3 N M DE I SD: 2.0157 c. M: 3.2324 c. 74: 4 4 4 15 4 4 4 4 4 15 4 4 4 N M DE I SD: 0.9101 c. M: 1.4595 c. 93: 5 5 5 19 5 5 5 5 5 19 5 5 5 N M DE I SD: 0.2563 c. M: 0.4110 c. 112: 6 6 6 23 6 6 6 6 6 23 6 6 6 N M DE I SD: 0.1757 c. M:-0.2818 c. 205: 11 11 11 42 11 11 11 11 11 42 11 11 11 N M DE I SD: 0.0203 c. M: 0.0325 c. 727: 39 39 39 149 39 39 39 39 39 149 39 39 39 N M DE I SD: 0.0099 c. M: 0.0159 c. 932: 50 50 50 191 50 50 50 50 50 191 50 50 50 N M DE I SD: 0.0033 c. M: 0.0053 c. 1137: 61 61 61 233 61 61 61 61 61 233 61 61 61 N M DE I SD: 0.0010 c. M: 0.0015 c.
FIT/HARMONIC
1 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 3 x x x x 4 S SD: 2.3347 cents 3 x x x x 4 x x x 5 x x x 6 S SD: 40.6498 cents 4 x x x 5 x x x 6 x 7 x x 8 S SD: 16.8149 cents 5 x x 6 x x 7 x x 8:9 x x 10 S SD: 26.6635 cents 6 x x 7 x 8 x x 9 x x 11 x 12 SD: 15.5239 cents 7 x x 8:9 x x 10 x 11 x 13 x 14 SD: 7.6438 cents 8 x x 9:10 x 11 x 12 x 14:15 x 16 S SD: 10.2631 cents 9 x x 10 x 12 x 13 x 14:16:17 x 18 S SD: 4.7607 cents 10 x x 11:13 x 14 x 15:16:18 x 19:20 SD: 8.5014 cents 11 x 12 x 14 x 15:16 x 17:20 x 21:22 SD: 7.2229 cents 12 x 13 x 15:16 x 17:18:19:21:22:23:24 SD: 8.6036 cents 13 x 14:15:17 x 18:19 x 20:23:24:25:26 SD: 7.0997 cents 14 x 15:16:18:19 x 20:21:22:25:26:27:28 SD: 4.8300 cents 15 x 16:17:19:20:21:22 x 23:27:28:29:30 SD: 5.3959 cents 16 x 17:18:21 x 22:23:24:25:29:30:31:32 SD: 4.7962 cents 17 x 18:19:22:23:24 x 25:26:30:32:33:34 SD: 6.4101 cents 18:19 x 20:23:24:25:26:27:28:32:33:35:36 SD: 3.9270 cents 19:20 x 21 x 25:26:27:28:30:34:35:37:38 SD: 6.5562 cents 20:21 x 22:26:27:28:29:30:31:36:37:39:40 SD: 4.1039 cents 21:22:23 x 27:28:29:30:31:33:38:39:41:42 SD: 4.7064 cents 23:24:25:26:30:31:32:33:34:36:41:43:44:46 SD: 3.7058 cents 24:25:26:27:31:32:33:35:36:37:43:45:46:48 SD: 3.0166 cents 27:28:29:30:35:36:38:39:40:42:48:50:52:54 S SD: 2.8295 cents 34:35:37:38:44:46:47:49:51:53:61:63:66:68 SD: 2.6393 cents 36:37:39:40:46:48:50:52:54:56:64:67:69:72 SD: 2.5983 cents 38:39:41:42:49:51:53:55:57:59:68:71:73:76 SD: 2.5228 cents 41:43:44:46:53:55:57:59:61:64:73:76:79:82 SD: 2.1360 cents 48:50:52:54:62:64:67:69:72:75:86:89:93:96 SD: 1.8469 cents 49:51:53:55:63:66:68:71:73:76:88:91:95:98 SD: 1.7198 cents 51:53:55:57:66:68:71:74:76:79:91:95:98:102 SD: 1.5752 cents 52:54:56:58:67:70:72:75:78:81:93:97:100:104 SD: 1.2804 cents 74:77:80:83:95:99:103:107:111:115:133:138:143:148 SD: 1.2485 cents 75:78:81:84:97:100:104:108:112:117:134:139:145:150 SD: 1.2255 cents 76:79:82:85:98:102:106:110:114:118:136:141:147:152 SD: 1.0373 cents 77:80:83:86:99:103:107:111:115:120:138:143:149:154 SD: 0.8125 cents 100:104:108:112:129:134:139:144:150:155:179:186:193:200 SD: 0.7153 cents 101:105:109:113:130:135:140:146:151:157:181:188:195:202 SD: 0.6929 cents 127:132:137:142:164:170:176:183:190:197:227:236:245:254 SD: 0.6150 cents 129:134:139:144:166:173:179:186:193:200:231:240:249:258 SD: 0.5996 cents 154:160:166:172:199:206:214:222:230:239:276:286:297:308 SD: 0.5585 cents 159:165:171:178:205:213:221:229:238:247:285:296:307:318 SD: 0.4582 cents 177:184:191:198:228:237:246:255:265:275:317:329:342:355 SD: 0.4326 cents 183:190:197:205:236:245:254:264:274:284:328:340:353:367 SD: 0.3894 cents 210:218:226:235:271:281:292:303:314:326:376:390:405:421 SD: 0.3680 cents 211:219:227:236:272:282:293:304:316:328:378:392:407:423 SD: 0.3565 cents 231:240:249:258:298:309:321:333:346:359:414:429:446:463 SD: 0.3377 cents 242:251:261:271:312:324:336:349:362:376:433:450:467:485 SD: 0.3197 cents 260:270:280:291:335:348:361:375:389:404:466:483:502:521 SD: 0.2527 cents 287:298:309:321:370:384:399:414:430:446:514:534:554:575 SD: 0.2495 cents 296:307:319:331:382:396:411:427:443:460:530:550:571:593 SD: 0.2231 cents 322:334:347:360:415:431:447:464:482:500:577:599:621:645 SD: 0.2224 cents 339:352:365:379:437:454:471:489:507:527:607:630:654:679 SD: 0.2172 cents 349:362:376:390:450:467:485:503:522:542:625:649:673:699 SD: 0.2106 cents 363:377:391:406:468:486:504:523:543:564:650:675:701:727 SD: 0.2059 cents 373:387:402:417:481:499:518:538:558:579:668:693:720:747 SD: 0.1946 cents 398:413:429:445:513:533:553:574:596:618:713:740:768:797 SD: 0.1669 cents 455:472:490:509:587:609:632:656:681:707:815:846:878:911 SD: 0.1483 cents 532:552:573:595:686:712:739:767:796:826:953:989:1027:1066 SD: 0.1273 cents 556:577:599:622:717:744:772:802:832:864:996:1034:1073:1114 SD: 0.1263 cents 584:606:629:653:753:782:811:842:874:907:1046:1086:1127:1170 SD: 0.1153 cents