Scala analysis: xen18-erlich-liese-11
2L 9s MOS for Liese, L=310.97, 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: 440.010 cents 440.010000 4: 504.530 cents 504.530000 5: 569.050 cents 569.050000 6: 633.570 cents 633.570000 7: 698.090 cents 698.090000 8: 762.610 cents 762.610000 9: 1073.580 cents 1073.580000 10: 1138.100 cents 1138.100000 11: 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: 310.9700 cents 310.9700 4: 64.5200 cents 64.5200 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: 310.9700 cents 310.9700 10: 64.5200 cents 64.5200 11: 64.5200 cents 64.5200
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 9 64.52000 cents 1: 2 310.97000 cents 2: 7 129.04000 cents 2: 4 375.49000 cents 3: 5 193.56000 cents 3: 6 440.01000 cents 4: 3 258.08000 cents 4: 8 504.53000 cents 5: 1 322.60000 cents 5: 10 569.05000 cents 6: 10 633.57000 cents 6: 1 880.02000 cents 7: 8 698.09000 cents 7: 3 944.54000 cents 8: 6 762.61000 cents 8: 5 1009.06000 cents 9: 4 827.13000 cents 9: 7 1073.58000 cents 10: 2 891.65000 cents 10: 9 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 0.0 : 64.5 129.0 440.0 504.5 569.0 633.6 698.1 762.6 1073.6 1138.1 1202.6 64.5 : 64.5 375.5 440.0 504.5 569.1 633.6 698.1 1009.1 1073.6 1138.1 1202.6 129.0 : 311.0 375.5 440.0 504.5 569.0 633.6 944.5 1009.1 1073.6 1138.1 1202.6 440.0 : 64.5 129.0 193.6 258.1 322.6 633.6 698.1 762.6 827.1 891.7 1202.6 504.5 : 64.5 129.0 193.6 258.1 569.0 633.6 698.1 762.6 827.1 1138.1 1202.6 569.0 : 64.5 129.0 193.6 504.5 569.1 633.6 698.1 762.6 1073.6 1138.1 1202.6 633.6 : 64.5 129.0 440.0 504.5 569.0 633.6 698.1 1009.1 1073.6 1138.1 1202.6 698.1 : 64.5 375.5 440.0 504.5 569.0 633.6 944.5 1009.1 1073.6 1138.1 1202.6 762.6 : 311.0 375.5 440.0 504.5 569.1 880.0 944.5 1009.1 1073.6 1138.1 1202.6 1073.6: 64.5 129.0 193.6 258.1 569.0 633.6 698.1 762.6 827.1 891.7 1202.6 1138.1: 64.5 129.0 193.6 504.5 569.1 633.6 698.1 762.6 827.1 1138.1 1202.6 1202.6
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 64.5200 .. 310.9700 cents 246.45000 cents 64.52000 cents 2: 129.0400 .. 375.4900 cents 246.45000 cents -181.93000 cents 3: 193.5600 .. 440.0100 cents 246.45000 cents -181.93000 cents 4: 258.0800 .. 504.5300 cents 246.45000 cents -181.93000 cents 5: 322.6000 .. 569.0500 cents 246.45000 cents -181.93000 cents 6: 633.5700 .. 880.0200 cents 246.45000 cents 64.52000 cents 7: 698.0900 .. 944.5400 cents 246.45000 cents -181.93000 cents 8: 762.6100 .. 1009.0600 cents 246.45000 cents -181.93000 cents 9: 827.1300 .. 1073.5800 cents 246.45000 cents -181.93000 cents 10: 891.6500 .. 1138.1000 cents 246.45000 cents -181.93000 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 64.52000 cents, class 1 Average step (divided formal octave): 109.3291 cents Largest one step interval : 310.97000 cents Average / Smallest step : 1.694499 Largest / Average step : 2.844348 Largest / Smallest step : 4.819746 Median interval of one step : 64.52000 cents, amount: 9 Most common interval of one step : 64.52000 cents, amount: 9 Least squares average step : 109.81615 cents, oct.: 1207.97761 cents Scale is not proper Scale has Myhill's property chromas: 246.45000 cents and 181.93000 cents, ratio: 1.354642 generators: 5 of 569.05000 cents and 6 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: 50 100 341 391 441 491 541 591 832 882 932 generators: 441 and 491 Number of contiguous 1-step segments: 0 Step pattern alph. order: AABAAAAABAA Step pattern size order : SSLSSSSSLSS Scale is a Constant Structure, by a margin of 11.63000 cents Scale diversity : 1.238314 Lumma stability : 0.160949 Lumma impropriety factor : 0.624453 Rothenberg efficiency : 0.727273 redundancy: 0.272727 Efficiency x scale size : 8.000000 Number of different interval sizes : 20 = 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: 10 Scale is a chain of 5 triads 0.0 569.050 1138.100 cents Most common triad is 0.0 569.050 633.570 cents, amount: 9 Number of recognisable fifths : 8, average 698.0900 cents Number of recognisable fourths : 8, average 504.5300 cents Scale contains two identical disjunct pentachords Formal octave complements present : 11 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 5-6 -- Rational properties --
FIT/MODE
11: 1 0 3 1 0 1 0 1 3 0 1 N I SD: 29.1682 c. M:-44.8091 c. 12: 1 0 3 1 1 0 1 1 3 0 1 N I SD: 29.1992 c. M: 39.1367 c. 13: 1 0 4 0 1 1 1 0 4 0 1 N I SD: 28.8704 c. M: 41.9838 c. 14: 1 1 3 1 1 0 1 1 3 1 1 N I SD: 25.4244 c. M: 42.7629 c. 16: 1 1 4 1 1 0 1 1 4 1 1 N I SD: 19.9764 c. M: 32.2600 c. 17: 1 1 4 1 1 1 1 1 4 1 1 N M DE I SD: 9.8384 c. M: 15.5559 c. 19: 1 1 5 1 1 1 1 1 5 1 1 N M DE I SD: 1.9356 c. M: 3.0605 c. 55: 3 3 14 3 3 3 3 3 14 3 3 N M DE I SD: 1.7036 c. M: 2.6936 c. 74: 4 4 19 4 4 4 4 4 19 4 4 N M DE I SD: 0.7692 c. M: 1.2162 c. 93: 5 5 24 5 5 5 5 5 24 5 5 N M DE I SD: 0.2166 c. M: 0.3425 c. 112: 6 6 29 6 6 6 6 6 29 6 6 N M DE I SD: 0.1485 c. M:-0.2348 c. 205: 11 11 53 11 11 11 11 11 53 11 11 N M DE I SD: 0.0171 c. M: 0.0271 c. 727: 39 39 188 39 39 39 39 39 188 39 39 N M DE I SD: 0.0084 c. M: 0.0133 c. 932: 50 50 241 50 50 50 50 50 241 50 50 N M DE I SD: 0.0028 c. M: 0.0044 c. 1137: 61 61 294 61 61 61 61 61 294 61 61 N M DE I SD: 0.0008 c. M: 0.0013 c.
FIT/HARMONIC
1 x x x x x x x x x x 2 S SD: 2.6200 cents 2 x x x x x x 3 x x x 4 S SD: 2.3347 cents 3 x x x 4 x x x 5 x x 6 S SD: 40.6498 cents 4 x x 5 x x x 6 x 7 x 8 S SD: 29.4518 cents 5 x x 6 x 7 x x 8:9 x 10 S SD: 29.2565 cents 6 x 7 x 8 x x 9 x 11 x 12 SD: 28.0340 cents 7 x 8:9 x x 10 x 11:13 x 14 SD: 17.5752 cents 8 x 9:10 x 11 x 12 x 15 x 16 S SD: 15.8472 cents 9 x 10 x 12 x 13 x 14:17 x 18 SD: 10.0906 cents 10 x 11:13 x 14 x 15:16 x 19:20 SD: 10.1324 cents 11 x 12:14 x 15:16 x 17:20:21:22 SD: 8.0574 cents 12 x 13:15:16 x 17:18:19:22:23:24 SD: 8.4498 cents 13 x 14:17 x 18:19 x 20:24:25:26 SD: 5.0787 cents 14 x 15:18:19 x 20:21:22:26:27:28 SD: 4.1281 cents 15 x 16:19:20:21:22 x 23:28:29:30 SD: 5.9992 cents 16 x 17:21 x 22:23:24:25:30:31:32 SD: 5.2768 cents 17 x 18:22:23:24 x 25:26:32:33:34 SD: 7.2928 cents 18:19 x 23:24:25:26:27:28:33:35:36 SD: 4.3909 cents 19:20 x x 25:26:27:28:30:35:37:38 SD: 7.6873 cents 20:21:22:26:27:28:29:30:31:37:39:40 SD: 4.8365 cents 23:24:25:30:31:32:33:34:36:43:44:46 SD: 3.9657 cents 24:25:26:31:32:33:35:36:37:45:46:48 SD: 3.4384 cents 27:28:29:35:36:38:39:40:42:50:52:54 SD: 2.9603 cents 36:37:39:46:48:50:52:54:56:67:69:72 SD: 2.6477 cents 38:39:41:49:51:53:55:57:59:71:73:76 SD: 2.3377 cents 41:43:44:53:55:57:59:61:64:76:79:82 SD: 2.2860 cents 47:49:51:61:63:65:68:70:73:87:91:94 SD: 2.2457 cents 48:50:52:62:64:67:69:72:75:89:93:96 SD: 1.9690 cents 49:51:53:63:66:68:71:73:76:91:95:98 SD: 1.9013 cents 51:53:55:66:68:71:74:76:79:95:98:102 SD: 1.7594 cents 52:54:56:67:70:72:75:78:81:97:100:104 SD: 1.4373 cents 56:58:60:72:75:78:81:84:87:104:108:112 SD: 1.3148 cents 74:77:80:95:99:103:107:111:115:138:143:148 SD: 1.2913 cents 76:79:82:98:102:106:110:114:118:141:147:152 SD: 1.2169 cents 77:80:83:99:103:107:111:115:120:143:149:154 SD: 0.9348 cents 100:104:108:129:134:139:144:150:155:186:193:200 SD: 0.8044 cents 115:119:124:148:154:160:166:172:179:214:222:230 SD: 0.7887 cents 127:132:137:164:170:176:183:190:197:236:245:254 SD: 0.6474 cents 141:146:152:182:189:196:203:211:219:262:272:282 SD: 0.6159 cents 156:162:168:201:209:217:225:233:242:290:301:312 SD: 0.5551 cents 157:163:169:202:210:218:226:235:244:292:303:314 SD: 0.5307 cents 159:165:171:205:213:221:229:238:247:296:307:318 SD: 0.5014 cents 183:190:197:236:245:254:264:274:284:340:353:367 SD: 0.3570 cents 231:240:249:298:309:321:333:346:359:429:446:463 SD: 0.3333 cents 242:251:261:312:324:336:349:362:376:450:467:485 SD: 0.2611 cents 260:270:280:335:348:361:375:389:404:483:502:521 SD: 0.2479 cents 298:309:321:384:399:414:430:446:463:554:575:597 SD: 0.2355 cents 314:326:338:405:420:436:453:470:488:584:606:629 SD: 0.2284 cents 349:362:376:450:467:485:503:522:542:649:673:699 SD: 0.2191 cents 390:405:420:503:522:542:562:584:606:725:753:781 SD: 0.2060 cents 398:413:429:513:533:553:574:596:618:740:768:797 SD: 0.1932 cents 401:416:432:517:537:557:578:600:623:746:774:803 SD: 0.1873 cents 414:430:446:534:554:575:597:620:643:770:799:829 SD: 0.1814 cents 425:441:458:548:569:590:613:636:660:790:820:851 SD: 0.1682 cents 453:470:488:584:606:629:653:678:704:842:874:907 SD: 0.1661 cents 529:549:570:682:708:735:763:792:822:983:1021:1060 SD: 0.1388 cents 553:574:596:713:740:768:797:828:859:1028:1067:1108 SD: 0.1349 cents 580:602:625:748:776:806:836:868:901:1078:1119:1162 SD: 0.1242 cents