Scala analysis: xen18-erlich-liese-09
2L 7s MOS for Liese, L=375.49, 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: 504.530 cents 504.530000 4: 569.050 cents 569.050000 5: 633.570 cents 633.570000 6: 698.090 cents 698.090000 7: 1073.580 cents 1073.580000 8: 1138.100 cents 1138.100000 9: 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: 375.4900 cents 375.4900 4: 64.5200 cents 64.5200 5: 64.5200 cents 64.5200 6: 64.5200 cents 64.5200 7: 375.4900 cents 375.4900 8: 64.5200 cents 64.5200 9: 64.5200 cents 64.5200
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 64.52000 cents 1: 2 375.49000 cents 2: 5 129.04000 cents 2: 4 440.01000 cents 3: 3 193.56000 cents 3: 6 504.53000 cents 4: 1 258.08000 cents 4: 8 569.05000 cents 5: 8 633.57000 cents 5: 1 944.54000 cents 6: 6 698.09000 cents 6: 3 1009.06000 cents 7: 4 762.61000 cents 7: 5 1073.58000 cents 8: 2 827.13000 cents 8: 7 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 0.0 : 64.5 129.0 504.5 569.0 633.6 698.1 1073.6 1138.1 1202.6 64.5 : 64.5 440.0 504.5 569.1 633.6 1009.1 1073.6 1138.1 1202.6 129.0 : 375.5 440.0 504.5 569.0 944.5 1009.1 1073.6 1138.1 1202.6 504.5 : 64.5 129.0 193.6 569.0 633.6 698.1 762.6 827.1 1202.6 569.0 : 64.5 129.0 504.5 569.1 633.6 698.1 762.6 1138.1 1202.6 633.6 : 64.5 440.0 504.5 569.0 633.6 698.1 1073.6 1138.1 1202.6 698.1 : 375.5 440.0 504.5 569.0 633.6 1009.1 1073.6 1138.1 1202.6 1073.6: 64.5 129.0 193.6 258.1 633.6 698.1 762.6 827.1 1202.6 1138.1: 64.5 129.0 193.6 569.1 633.6 698.1 762.6 1138.1 1202.6 1202.6
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 64.5200 .. 375.4900 cents 310.97000 cents 64.52000 cents 2: 129.0400 .. 440.0100 cents 310.97000 cents -246.45000 cents 3: 193.5600 .. 504.5300 cents 310.97000 cents -246.45000 cents 4: 258.0800 .. 569.0500 cents 310.97000 cents -246.45000 cents 5: 633.5700 .. 944.5400 cents 310.97000 cents 64.52000 cents 6: 698.0900 .. 1009.0600 cents 310.97000 cents -246.45000 cents 7: 762.6100 .. 1073.5800 cents 310.97000 cents -246.45000 cents 8: 827.1300 .. 1138.1000 cents 310.97000 cents -246.45000 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 64.52000 cents, class 1 Average step (divided formal octave): 133.6244 cents Largest one step interval : 375.49000 cents Average / Smallest step : 2.071055 Largest / Average step : 2.810040 Largest / Smallest step : 5.819746 Median interval of one step : 64.52000 cents, amount: 7 Most common interval of one step : 64.52000 cents, amount: 7 Least squares average step : 136.53411 cents, oct.: 1228.80695 cents Scale is not proper Scale has Myhill's property chromas: 310.97000 cents and 246.45000 cents, ratio: 1.261798 generators: 4 of 569.05000 cents and 5 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: 50 100 391 441 491 541 832 882 932 generators: 441 and 491 Number of contiguous 1-step segments: 0 Step pattern alph. order: AABAAABAA Step pattern size order : SSLSSSLSS Scale is a Constant Structure, by a margin of 64.52000 cents Scale diversity : 1.262036 Lumma stability : 0.160949 Lumma impropriety factor : 0.624453 Rothenberg efficiency : 0.740741 redundancy: 0.259259 Efficiency x scale size : 6.666667 Number of different interval sizes : 16 = 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 : 64.52000 cents Most common intervals : 569.05000 cents & inv., amount: 8 Scale is a chain of 4 triads 0.0 569.050 1138.100 cents Most common triad is 0.0 569.050 633.570 cents, amount: 7 Number of recognisable fifths : 6, average 698.0900 cents Number of recognisable fourths : 6, average 504.5300 cents Scale contains two identical disjunct tetrachords Formal octave complements present : 9 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 4-5 -- Rational properties --
FIT/MODE
9: 0 1 3 0 1 0 3 0 1 N SD: 38.2450 c. M: 69.1044 c. 10: 1 0 3 1 0 1 3 0 1 N I SD: 32.5793 c. M: 55.7420 c. 11: 1 0 4 0 1 0 4 0 1 N I SD: 32.2216 c. M:-44.8091 c. 12: 1 0 4 1 0 1 4 0 1 N I SD: 26.4894 c. M:-35.6983 c. 14: 1 0 5 0 1 1 4 1 1 N SD: 31.1960 c. M: 53.6414 c. 15: 1 1 4 1 1 1 4 1 1 N M DE I SD: 20.2101 c. M: 31.3093 c. 17: 1 1 5 1 1 1 5 1 1 N M DE I SD: 8.0330 c. M: 12.4447 c. 19: 1 1 6 1 1 1 6 1 1 N M DE I SD: 1.5804 c. M: 2.4484 c. 55: 3 3 17 3 3 3 17 3 3 N M DE I SD: 1.3910 c. M: 2.1549 c. 74: 4 4 23 4 4 4 23 4 4 N M DE I SD: 0.6281 c. M: 0.9730 c. 93: 5 5 29 5 5 5 29 5 5 N M DE I SD: 0.1769 c. M: 0.2740 c. 112: 6 6 35 6 6 6 35 6 6 N M DE I SD: 0.1213 c. M: 0.1879 c. 205: 11 11 64 11 11 11 64 11 11 N M DE I SD: 0.0140 c. M: 0.0217 c. 727: 39 39 227 39 39 39 227 39 39 N M DE I SD: 0.0069 c. M: 0.0106 c. 932: 50 50 291 50 50 50 291 50 50 N M DE I SD: 0.0023 c. M: 0.0035 c. 1137: 61 61 355 61 61 61 355 61 61 N M DE I SD: 0.0007 c. M: 0.0010 c.
FIT/HARMONIC
1 x x x x x x x x 2 S SD: 2.6200 cents 2 x x x x x 3 x x 4 S SD: 2.3347 cents 3 x x 4 x x 5 x x 6 S SD: 62.1333 cents 4 x x 5 x x 6:7 x 8 S SD: 39.5050 cents 5 x 6 x 7 x x 9 x 10 SD: 48.8251 cents 6 x 7:8 x x 9:11 x 12 SD: 28.0340 cents 7 x 8:9 x 10 x 13 x 14 SD: 24.9184 cents 8 x 9 x 11 x 12:15 x 16 SD: 15.6940 cents 9 x 10:12 x 13 x 17 x 18 SD: 12.1000 cents 10 x 11:13:14 x 15 x 19:20 SD: 11.4889 cents 11 x 12 x 15:16 x 20:21:22 S SD: 9.9556 cents 12 x 13:16 x 17:18:22:23:24 SD: 6.0852 cents 13 x 14:17:18:19 x 24:25:26 SD: 6.9689 cents 14 x 15:19 x 20:21:26:27:28 SD: 4.4280 cents 15 x 16:20:21:22 x 28:29:30 SD: 5.4543 cents 16 x 17:21:22:23:24:30:31:32 SD: 6.0560 cents 17 x 18:23:24 x 25:32:33:34 SD: 8.4956 cents 18:19 x 24:25:26:27:33:35:36 SD: 5.1203 cents 19:20 x 25:26:27:28:35:37:38 SD: 7.9002 cents 20:21:22:27:28:29:30:37:39:40 SD: 5.6803 cents 21:22:23:28:29:30:31:39:41:42 SD: 5.5084 cents 23:24:25:31:32:33:34:43:44:46 SD: 4.0581 cents 24:25:26:32:33:35:36:45:46:48 SD: 3.9225 cents 26:27:28:35:36:37:39:48:50:52 SD: 3.2550 cents 29:30:31:39:40:42:43:54:56:58 SD: 3.0928 cents 30:31:32:40:42:43:45:56:58:60 SD: 3.0838 cents 36:37:39:48:50:52:54:67:69:72 SD: 2.7174 cents 41:43:44:55:57:59:61:76:79:82 SD: 2.5899 cents 47:49:51:63:65:68:70:87:91:94 SD: 2.4365 cents 48:50:52:64:67:69:72:89:93:96 SD: 2.1062 cents 50:52:54:67:69:72:75:93:96:100 SD: 1.8235 cents 52:54:56:70:72:75:78:97:100:104 SD: 1.6723 cents 54:56:58:72:75:78:81:100:104:108 SD: 1.4158 cents 74:77:80:99:103:107:111:138:143:148 SD: 1.3366 cents 77:80:83:103:107:111:115:143:149:154 SD: 0.7939 cents 113:117:122:151:157:163:169:210:218:226 SD: 0.7732 cents 127:132:137:170:176:183:190:236:245:254 SD: 0.6776 cents 129:134:139:173:179:186:193:240:249:258 SD: 0.5781 cents 157:163:169:210:218:226:235:292:303:314 SD: 0.4950 cents 183:190:197:245:254:264:274:340:353:367 SD: 0.3887 cents 231:240:249:309:321:333:346:429:446:463 SD: 0.3873 cents 233:242:251:312:324:336:349:433:450:467 SD: 0.3658 cents 242:251:261:324:336:349:362:450:467:485 SD: 0.3173 cents 260:270:280:348:361:375:389:483:502:521 SD: 0.2666 cents 296:307:319:396:411:427:443:550:571:593 SD: 0.2539 cents 340:353:366:455:472:490:509:632:656:681 SD: 0.2451 cents 346:359:373:463:481:499:518:643:668:693 SD: 0.2425 cents 373:387:402:499:518:538:558:693:720:747 SD: 0.2282 cents 375:389:404:502:521:541:561:697:724:751 SD: 0.2155 cents 398:413:429:533:553:574:596:740:768:797 SD: 0.2089 cents 399:414:430:534:554:575:597:742:770:799 SD: 0.1907 cents 453:470:488:606:629:653:678:842:874:907 SD: 0.1868 cents 455:472:490:609:632:656:681:846:878:911 SD: 0.1657 cents 527:547:568:705:732:760:789:980:1017:1056 SD: 0.1587 cents 532:552:573:712:739:767:796:989:1027:1066 SD: 0.1466 cents 555:576:598:743:771:800:831:1032:1071:1112 SD: 0.1374 cents