Scala analysis: xen18-erlich-orwell-13
9L 4s MOS for Orwell, L=113.57, s=44.35
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 113.570 cents 113.570000 2: 157.920 cents 157.920000 3: 271.490 cents 271.490000 4: 385.060 cents 385.060000 5: 429.410 cents 429.410000 6: 542.980 cents 542.980000 7: 656.550 cents 656.550000 8: 770.120 cents 770.120000 9: 814.470 cents 814.470000 10: 928.040 cents 928.040000 11: 1041.610 cents 1041.610000 12: 1085.960 cents 1085.960000 13: 1199.530 cents 1199.530000
SHOW/INTERVAL
0: 113.5700 cents 113.5700 1: 113.5700 cents 113.5700 2: 44.3500 cents 44.3500 3: 113.5700 cents 113.5700 4: 113.5700 cents 113.5700 5: 44.3500 cents 44.3500 6: 113.5700 cents 113.5700 7: 113.5700 cents 113.5700 8: 113.5700 cents 113.5700 9: 44.3500 cents 44.3500 10: 113.5700 cents 113.5700 11: 113.5700 cents 113.5700 12: 44.3500 cents 44.3500 13: 113.5700 cents 113.5700
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 44.35000 cents 1: 9 113.57000 cents 2: 8 157.92000 cents 2: 5 227.14000 cents 3: 12 271.49000 cents 3: 1 340.71000 cents 4: 3 315.84000 cents 4: 10 385.06000 cents 5: 7 429.41000 cents 5: 6 498.63000 cents 6: 11 542.98000 cents 6: 2 612.20000 cents 7: 2 587.33000 cents 7: 11 656.55000 cents 8: 6 700.90000 cents 8: 7 770.12000 cents 9: 10 814.47000 cents 9: 3 883.69000 cents 10: 1 858.82000 cents 10: 12 928.04000 cents 11: 5 972.39000 cents 11: 8 1041.61000 cents 12: 9 1085.96000 cents 12: 4 1155.18000 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 : 113.6 157.9 271.5 385.1 429.4 543.0 656.5 770.1 814.5 928.0 1041.6 1086.0 1199.5 113.6 : 44.4 157.9 271.5 315.8 429.4 543.0 656.5 700.9 814.5 928.0 972.4 1086.0 1199.5 157.9 : 113.6 227.1 271.5 385.1 498.6 612.2 656.5 770.1 883.7 928.0 1041.6 1155.2 1199.5 271.5 : 113.6 157.9 271.5 385.1 498.6 543.0 656.5 770.1 814.5 928.0 1041.6 1086.0 1199.5 385.1 : 44.4 157.9 271.5 385.1 429.4 543.0 656.5 700.9 814.5 928.0 972.4 1086.0 1199.5 429.4 : 113.6 227.1 340.7 385.1 498.6 612.2 656.5 770.1 883.7 928.0 1041.6 1155.2 1199.5 543.0 : 113.6 227.1 271.5 385.1 498.6 543.0 656.5 770.1 814.5 928.0 1041.6 1086.0 1199.5 656.5 : 113.6 157.9 271.5 385.1 429.4 543.0 656.5 700.9 814.5 928.0 972.4 1086.0 1199.5 770.1 : 44.4 157.9 271.5 315.8 429.4 543.0 587.3 700.9 814.5 858.8 972.4 1086.0 1199.5 814.5 : 113.6 227.1 271.5 385.1 498.6 543.0 656.6 770.1 814.5 928.0 1041.6 1155.2 1199.5 928.0 : 113.6 157.9 271.5 385.1 429.4 543.0 656.6 700.9 814.5 928.0 1041.6 1086.0 1199.5 1041.6: 44.4 157.9 271.5 315.8 429.4 543.0 587.3 700.9 814.5 928.0 972.4 1086.0 1199.5 1086.0: 113.6 227.1 271.5 385.1 498.6 543.0 656.5 770.1 883.7 928.0 1041.6 1155.2 1199.5 1199.5
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 44.3500 .. 113.5700 cents 69.22000 cents 44.35000 cents 2: 157.9200 .. 227.1400 cents 69.22000 cents 44.35000 cents 3: 271.4900 .. 340.7100 cents 69.22000 cents 44.35000 cents 4: 315.8400 .. 385.0600 cents 69.22000 cents -24.87000 cents 5: 429.4100 .. 498.6300 cents 69.22000 cents 44.35000 cents 6: 542.9800 .. 612.2000 cents 69.22000 cents 44.35000 cents 7: 587.3300 .. 656.5500 cents 69.22000 cents -24.87000 cents 8: 700.9000 .. 770.1200 cents 69.22000 cents 44.35000 cents 9: 814.4700 .. 883.6900 cents 69.22000 cents 44.35000 cents 10: 858.8200 .. 928.0400 cents 69.22000 cents -24.87000 cents 11: 972.3900 .. 1041.6100 cents 69.22000 cents 44.35000 cents 12: 1085.9600 .. 1155.1800 cents 69.22000 cents 44.35000 cents
SHOW DATA
Number of notes : 13 -- Interval properties -- Smallest interval : 44.35000 cents, class 1 Average step (divided formal octave): 92.2715 cents Largest one step interval : 113.57000 cents Average / Smallest step : 2.080531 Largest / Average step : 1.230824 Largest / Smallest step : 2.560767 Median interval of one step : 113.57000 cents, amount: 9 Most common interval of one step : 113.57000 cents, amount: 9 Least squares average step : 92.35606 cents, oct.: 1200.62873 cents Scale is not proper Scale has Myhill's property chromas: 69.22000 cents and 24.87000 cents, ratio: 2.783273 generators: 3 of 271.49000 cents and 10 of 928.04000 cents ET pair of linear temperament : 22&31 Scale is distributional even Scale is a mode of a 1109-tone equal temperament with octave 1199.530 cents degrees: 105 146 251 356 397 502 607 712 753 858 963 1004 1109 generators: 251 and 858 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABAAABAABA Step pattern size order : LSLLSLLLSLLSL Scale is a Constant Structure, by a margin of 24.87000 cents Scale diversity : 1.225733 Lumma stability : 0.369728 Lumma impropriety factor : 0.062199 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 : 24.87000 cents Most common intervals : 271.49000 cents & inv., amount: 12 Scale is a chain of 6 triads 0.0 429.410 928.040 cents Most common triad is 0.0 271.490 928.040 cents, amount: 11 Number of recognisable fifths : 6, average 700.9000 cents Number of recognisable fourths : 6, average 498.6300 cents Scale contains two identical disjunct heptachords 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 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 19.9229 c. M: 31.9477 c. 18: 2 0 2 2 0 2 2 2 0 2 2 0 2 N M DE I SD: 18.4381 c. M: 29.5667 c. 20: 2 1 2 1 1 2 2 2 1 1 2 1 2 N D3 I SD: 17.8379 c. M:-28.3925 c. 21: 2 1 2 2 0 2 2 2 1 2 2 1 2 N T3 SD: 18.5279 c. M: 29.5667 c. 22: 2 1 2 2 1 2 2 2 1 2 2 1 2 P M ME I SD: 4.2298 c. M: 6.7827 c. 31: 3 1 3 3 1 3 3 3 1 3 3 1 3 N M DE I SD: 2.3512 c. M: 3.7703 c. 53: 5 2 5 5 2 5 5 5 2 5 5 2 5 N M DE I SD: 0.3805 c. M:-0.6102 c. 137: 13 5 13 13 5 13 13 13 5 13 13 5 13 N M DE I SD: 0.2376 c. M: 0.3810 c. 190: 18 7 18 18 7 18 18 18 7 18 18 7 18 N M DE I SD: 0.0652 c. M: 0.1045 c. 243: 23 9 23 23 9 23 23 23 9 23 23 9 23 N M DE I SD: 0.0320 c. M: 0.0514 c. 433: 41 16 41 41 16 41 41 41 16 41 41 16 41 N M DE I SD: 0.0106 c. M: 0.0170 c. 676: 64 25 64 64 25 64 64 64 25 64 64 25 64 N M DE I SD: 0.0047 c. M: 0.0075 c. 1109: 105 41 105 105 41 105 105 105 41 105 105 41 105 N M DE I SD: 0.0013 c. M: 0.0021 c. 1785: 169 66 169 169 66 169 169 169 66 169 169 66 169 N M DE I SD: 0.0010 c. M:-0.0016 c.
FIT/HARMONIC
1 x x x x x x x x x x x x 2 S SD: 0.4700 cents 2 x x x x x x 3 x x x x x 4 S SD: 22.7037 cents 3 x x x x x 4 x x x 5 x x 6 S SD: 20.8897 cents 4 x x x 5 x x 6 x x 7 x x 8 S SD: 15.2621 cents 5 x x 6 x x 7 x x 8 x 9 x 10 S SD: 12.7900 cents 6 x x 7 x x 8:9 x x 10:11 x 12 S SD: 12.9856 cents 7 x x 8 x 9 x 10:11 x 12 x 13:14 S SD: 8.5307 cents 8 x 9 x 10 x 11:12 x 13:14 x 15:16 S SD: 10.1518 cents 9 x 10 x 11 x 12:13:14 x 15:16:17:18 S SD: 10.3450 cents 10 x 11:12 x 13:14:15 x 16:17:18:19:20 S SD: 8.6845 cents 11 x 12:13 x 14:15:16:17:18:19:20:21:22 S SD: 5.6246 cents 12 x 13:14:15 x 16:18 x 19:21:22 x 24 SD: 8.9990 cents 13:14 x 15:16:17:18:19:20:21:22:24 x 26 S SD: 6.1725 cents 14:15 x 16:17:18:19:20:22 x 24 x 26:28 S SD: 7.8733 cents 15:16 x 18 x 19:21:22:23:24:26:27:28:30 SD: 7.0795 cents 16:17:18:19:20:21:22:23:25:26:27:29:30:32 SD: 6.3320 cents 17:18:19:20:21:22:23:25 x 27:29:31:32:34 SD: 4.5331 cents 19:20:21:22:24 x 26:28:30 x 32:35:36:38 SD: 5.3849 cents 20:21:22:23:25:26:27:29:31:32:34 x 37:40 SD: 5.1157 cents 21:22:23:25:26:27:29:31:33:34:36:38:39:42 SD: 4.7638 cents 22:23:24:26:27:28:30:32:34:35:38:40:41:44 SD: 4.6820 cents 23 x 25:27:29 x 31:34:36:37:39:42:43:46 SD: 3.9437 cents 24 x 26:28:30:31:33:35:37:38:41:44:45:48 SD: 3.2478 cents 25:27 x 29:31:32:34:37:39:40:43:46:47:50 SD: 3.4669 cents 26:28 x 30:32:33:36:38:41:42:44:47:49:52 SD: 4.8713 cents 27:29:30:32:34:35:37:39:42:43:46:49:51:54 SD: 3.9755 cents 28:30:31:33:35:36:38:41:44:45:48:51:52:56 SD: 2.6994 cents 32:34:35:37:40:41:44:47:50:51:55:58:60:64 SD: 2.3647 cents 40:43:44:47:50:51:55:58:62:64:68:73:75:80 SD: 2.1684 cents 41:44:45:48:51:53:56:60:64:66:70:75:77:82 SD: 1.7616 cents 52:56:57:61:65:67:71:76:81:83:89:95:97:104 SD: 1.5953 cents 57:61:62:67:71:73:78:83:89:91:97:104:107:114 SD: 1.5331 cents 60:64:66:70:75:77:82:88:94:96:103:110:112:120 SD: 1.3899 cents 63:67:69:74:79:81:86:92:98:101:108:115:118:126 SD: 1.2323 cents 71:76:78:83:89:91:97:104:111:114:121:130:133:142 SD: 1.0992 cents 75:80:82:88:94:96:103:110:117:120:128:137:140:150 SD: 1.0919 cents 76:81:83:89:95:97:104:111:119:122:130:139:142:152 SD: 1.0482 cents 85:91:93:99:106:109:116:124:133:136:145:155:159:170 SD: 0.9829 cents 92:98:101:108:115:118:126:134:144:147:157:168:172:184 SD: 0.9759 cents 93:99:102:109:116:119:127:136:145:149:159:170:174:186 SD: 0.7074 cents 117:125:128:137:146:150:160:171:183:187:200:214:219:234 SD: 0.5650 cents 136:145:149:159:170:174:186:199:212:218:232:248:255:272 SD: 0.5556 cents 148:158:162:173:185:190:203:216:231:237:253:270:277:296 SD: 0.4743 cents 165:176:181:193:206:211:226:241:257:264:282:301:309:330 SD: 0.4648 cents 177:189:194:207:221:227:242:259:276:283:303:323:331:354 SD: 0.4141 cents 188:201:206:220:235:241:257:275:293:301:321:343:352:376 SD: 0.3575 cents 189:202:207:221:236:242:259:276:295:303:323:345:354:378 SD: 0.3525 cents 206:220:226:241:257:264:282:301:321:330:352:376:386:412 SD: 0.3419 cents 234:250:256:274:292:300:320:342:365:375:400:427:438:468 SD: 0.3368 cents 241:257:264:282:301:309:330:352:376:386:412:440:451:482 SD: 0.2532 cents 252:269:276:295:315:323:345:368:393:403:431:460:472:504 SD: 0.2486 cents 282:301:309:330:352:361:386:412:440:451:482:515:528:564 SD: 0.2422 cents 313:334:343:366:391:401:428:457:488:501:535:571:586:626 SD: 0.2193 cents 323:345:354:378:403:414:442:472:504:517:552:590:605:646 SD: 0.2162 cents 337:360:369:394:421:432:461:492:526:539:576:615:631:674 SD: 0.2136 cents 353:377:387:413:441:452:483:516:551:565:603:644:661:706 SD: 0.2016 cents 366:391:401:428:457:469:501:535:571:586:626:668:685:732 SD: 0.1665 cents 429:458:470:502:536:550:587:627:669:687:733:783:803:858 SD: 0.1489 cents 501:535:549:586:626:642:686:732:782:802:856:914:938:1002 SD: 0.1463 cents 543:580:595:635:678:696:743:793:847:869:928:991:1017:1086 SD: 0.1311 cents 578:617:633:676:722:741:791:845:902:925:988:1055:1082:1156 SD: 0.1284 cents 589:629:645:689:736:755:806:861:919:943:1007:1075:1103:1178 SD: 0.1147 cents