Scala analysis: orwell13eb
Equal beating version of Orwell[13], x^10 + 2x^3 - 8 generator
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 43.574 cents 43.573939 2: 157.541 cents 157.541077 3: 271.508 cents 271.508215 4: 315.082 cents 315.082155 5: 429.049 cents 429.049293 6: 543.016 cents 543.016431 7: 586.590 cents 586.590370 8: 700.558 cents 700.557508 9: 814.525 cents 814.524646 10: 858.099 cents 858.098585 11: 972.066 cents 972.065724 12: 1086.033 cents 1086.032862 13: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 113.9671 cents 113.9671 1: 43.5739 cents 43.5739 2: 113.9671 cents 113.9671 3: 113.9671 cents 113.9671 4: 43.5739 cents 43.5739 5: 113.9671 cents 113.9671 6: 113.9671 cents 113.9671 7: 43.5739 cents 43.5739 8: 113.9671 cents 113.9671 9: 113.9671 cents 113.9671 10: 43.5739 cents 43.5739 11: 113.9671 cents 113.9671 12: 113.9671 cents 113.9671 13: 113.9671 cents 113.9671
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 43.57394 cents 1: 9 113.96714 cents 2: 8 157.54108 cents 2: 5 227.93428 cents 3: 12 271.50822 cents 3: 1 341.90141 cents 4: 3 315.08215 cents 4: 10 385.47535 cents 5: 7 429.04929 cents 5: 6 499.44249 cents 6: 11 543.01643 cents 6: 2 613.40963 cents 7: 2 586.59037 cents 7: 11 656.98357 cents 8: 6 700.55751 cents 8: 7 770.95071 cents 9: 10 814.52465 cents 9: 3 884.91785 cents 10: 1 858.09859 cents 10: 12 928.49178 cents 11: 5 972.06572 cents 11: 8 1042.45892 cents 12: 9 1086.03286 cents 12: 4 1156.42606 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 : 43.6 157.5 271.5 315.1 429.0 543.0 586.6 700.6 814.5 858.1 972.1 1086.0 1200.0 43.6 : 114.0 227.9 271.5 385.5 499.4 543.0 657.0 771.0 814.5 928.5 1042.5 1156.4 1200.0 157.5 : 114.0 157.5 271.5 385.5 429.0 543.0 657.0 700.6 814.5 928.5 1042.5 1086.0 1200.0 271.5 : 43.6 157.5 271.5 315.1 429.0 543.0 586.6 700.6 814.5 928.5 972.1 1086.0 1200.0 315.1 : 114.0 227.9 271.5 385.5 499.4 543.0 657.0 771.0 884.9 928.5 1042.5 1156.4 1200.0 429.0 : 114.0 157.5 271.5 385.5 429.0 543.0 657.0 771.0 814.5 928.5 1042.5 1086.0 1200.0 543.0 : 43.6 157.5 271.5 315.1 429.0 543.0 657.0 700.6 814.5 928.5 972.1 1086.0 1200.0 586.6 : 114.0 227.9 271.5 385.5 499.4 613.4 657.0 771.0 884.9 928.5 1042.5 1156.4 1200.0 700.6 : 114.0 157.5 271.5 385.5 499.4 543.0 657.0 771.0 814.5 928.5 1042.5 1086.0 1200.0 814.5 : 43.6 157.5 271.5 385.5 429.0 543.0 657.0 700.6 814.5 928.5 972.1 1086.0 1200.0 858.1 : 114.0 227.9 341.9 385.5 499.4 613.4 657.0 771.0 884.9 928.5 1042.5 1156.4 1200.0 972.1 : 114.0 227.9 271.5 385.5 499.4 543.0 657.0 771.0 814.5 928.5 1042.5 1086.0 1200.0 1086.0: 114.0 157.5 271.5 385.5 429.0 543.0 657.0 700.6 814.5 928.5 972.1 1086.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.5739 .. 113.9671 cents 70.39320 cents 43.57394 cents 2: 157.5411 .. 227.9343 cents 70.39320 cents 43.57394 cents 3: 271.5082 .. 341.9014 cents 70.39320 cents 43.57394 cents 4: 315.0822 .. 385.4754 cents 70.39320 cents -26.81926 cents 5: 429.0493 .. 499.4425 cents 70.39320 cents 43.57394 cents 6: 543.0164 .. 613.4096 cents 70.39320 cents 43.57394 cents 7: 586.5904 .. 656.9836 cents 70.39320 cents -26.81926 cents 8: 700.5575 .. 770.9507 cents 70.39320 cents 43.57394 cents 9: 814.5246 .. 884.9178 cents 70.39320 cents 43.57394 cents 10: 858.0986 .. 928.4918 cents 70.39320 cents -26.81926 cents 11: 972.0657 .. 1042.4589 cents 70.39320 cents 43.57394 cents 12: 1086.0329 .. 1156.4261 cents 70.39320 cents 43.57394 cents
SHOW DATA
Number of notes : 13 -- Interval properties -- Smallest interval : 43.57394 cents, class 1 Average step (divided formal octave): 92.3077 cents Largest one step interval : 113.96714 cents Average / Smallest step : 2.118415 Largest / Average step : 1.234644 Largest / Smallest step : 2.615489 Median interval of one step : 113.96714 cents, amount: 9 Most common interval of one step : 113.96714 cents, amount: 9 Least squares average step : 88.86969 cents, oct.: 1155.30591 cents Scale is not proper Scale has Myhill's property chromas: 70.39320 cents and 26.81926 cents, ratio: 2.624726 generators: 3 of 271.50822 cents and 928.49178 cents ET pair of linear temperament : 22&31 Scale is distributional even Scale is a mode of a 358-tone equal temperament with octave 1200.000 cents degrees: 13 47 81 94 128 162 175 209 243 256 290 324 358 generators: 81 and 277 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBABBABBABBB Step pattern size order : SLLSLLSLLSLLL Scale is a Constant Structure, by a margin of 26.81926 cents Scale diversity : 1.224566 Lumma stability : 0.363116 Lumma impropriety factor : 0.067048 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 : 26.81926 cents Most common intervals : 271.50822 cents & inv., amount: 12 Scale is a chain of 6 triads 0.0 429.049 928.492 cents Most common triad is 0.0 271.508 928.492 cents, amount: 11 Number of recognisable fifths : 6, average 700.5575 cents Scale contains two identical conjunct heptachords Formal octave complements present : 1 = 7.6923% Limited inverse transpositions : 10 Inversional symmetry on degrees : 5 Inversional symmetry on intervals : 11-12 -- Rational properties --
FIT/MODE
13: 0 1 1 1 1 1 1 1 1 1 1 1 2 N T3 SD: 57.7348 c. M: 86.8928 c. 14: 1 1 1 1 1 1 1 1 2 0 1 2 1 N D3 SD: 24.2438 c. M:-42.6182 c. 15: 1 1 1 1 1 2 0 2 1 1 1 2 1 N D3 SD: 22.4589 c. M:-36.4261 c. 17: 0 2 2 0 2 1 1 2 1 1 2 1 2 N D3 SD: 26.1003 c. M: 48.8988 c. 19: 0 2 2 1 2 1 1 2 2 0 2 2 2 N T3 SD: 23.8065 c. M: 43.5739 c. 20: 0 2 2 1 2 2 0 2 2 1 2 2 2 N T3 SD: 27.9234 c. M: 46.5904 c. 21: 1 2 2 1 2 2 0 2 2 1 2 2 2 N T3 SD: 16.6625 c. M:-28.4121 c. 22: 1 2 2 1 2 2 1 2 2 1 2 2 2 P M ME S SD: 8.6200 c. M:-14.6287 c. Orwell-13 31: 1 3 3 1 3 3 1 3 3 1 3 3 3 N M DE S SD: 3.8217 c. M: 6.4857 c. Orwell-13 53: 2 5 5 2 5 5 2 5 5 2 5 5 5 N M DE S SD: 1.3428 c. M:-2.2788 c. Orwell-13 84: 3 8 8 3 8 8 3 8 8 3 8 8 8 N M DE S SD: 0.5632 c. M: 0.9557 c. Orwell-13 137: 5 13 13 5 13 13 5 13 13 5 13 13 13 N M DE S SD: 0.1742 c. M:-0.2956 c. Orwell-13 221: 8 21 21 8 21 21 8 21 21 8 21 21 21 N M DE S SD: 0.1061 c. M: 0.1800 c. 358: 13 34 34 13 34 34 13 34 34 13 34 34 34 N M DE S SD: 0.0012 c. M:-0.0020 c.
FIT/HARMONIC
1 x x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x x 3 x x x x 4 S SD: 0.6987 cents 3 x x x x x 4 x x x 5 x x 6 S SD: 17.3590 cents 4 x x x x 5 x x 6 x x 7 x 8 S SD: 10.7202 cents 5 x x x 6 x x 7 x 8 x 9 x 10 S SD: 9.1448 cents 6 x x 7 x x 8 x 9 x 10 x 11:12 S SD: 10.6460 cents 7 x x 8 x 9 x 10 x 11 x 12:13:14 S SD: 10.4642 cents 8 x 9 x x 10:11 x 12 x 13:14:15:16 S SD: 8.2647 cents 9 x 10 x 11 x 12:13 x 14:15:16:17:18 S SD: 11.1894 cents 10 x 11 x 12:13 x 14:15:16 x 18:19:20 S SD: 6.4931 cents 11 x 12:13 x 14:15 x 16 x 18:19:21:22 SD: 7.8875 cents 12 x 13:14 x 15:16:17:18:19:20:21:22:24 S SD: 7.5547 cents 13 x 14:15:16:17:18 x 19:21 x 23:24:26 SD: 8.9745 cents 14 x 15:16:17:18:19:20:21:22:23:25:26:28 SD: 6.9523 cents 15 x 16 x 18:19 x 21:22:24:25:26:28:30 SD: 7.0903 cents 16 x 18 x 19:21:22 x 24 x 26:28:30:32 SD: 7.5321 cents 17:18:19:20 x 22:23:24:25:27:28:30:32:34 SD: 6.8181 cents 18:19:20:21:22:23 x 25:27:29:30:32:34:36 SD: 6.5337 cents 19:20:21:22:23:24:26:27:28:30:31:33:36:38 SD: 6.0294 cents 20:21:22:23:24:26:27:28:30:32:33:35:37:40 SD: 5.0644 cents 21:22:23 x 25:27:29 x 31:34 x 37:39:42 SD: 5.6413 cents 22:23:24:26 x 28:30:31:33:35:36:39:41:44 SD: 3.9760 cents 24:25:26:28:29:31:33:34:36:38:39:42:45:48 SD: 3.8414 cents 25:26:27:29:30:32:34:35:37:40:41:44:47:50 SD: 3.5247 cents 26:27:28:30:31:33:36 x 39:42:43:46:49:52 SD: 4.9093 cents 27:28:30 x 32:35:37:38:40:43:44:47:51:54 SD: 4.4847 cents 28:29:31:33:34:36:38:39:42:45:46:49:52:56 SD: 3.3793 cents 29:30:32:34:35:37:40:41:43:46:48:51:54:58 SD: 3.3091 cents 30:31:33:35:36:38:41:42:45:48:49:53:56:60 SD: 2.3677 cents 40:41:44:47:48:51:55:56:60:64:66:70:75:80 SD: 1.4784 cents 64:66:70:75:77:82:88:90:96:102:105:112:120:128 SD: 1.3177 cents 65:67:71:76:78:83:89:91:97:104:107:114:122:130 SD: 1.2175 cents 70:72:77:82:84:90:96:98:105:112:115:123:131:140 SD: 1.0219 cents 81:83:89:95:97:104:111:114:121:130:133:142:152:162 SD: 1.0129 cents 82:84:90:96:98:105:112:115:123:131:135:144:154:164 SD: 0.9289 cents 95:97:104:111:114:122:130:133:142:152:156:167:178:190 SD: 0.9067 cents 106:109:116:124:127:136:145:149:159:170:174:186:198:212 SD: 0.6750 cents 117:120:128:137:140:150:160:164:175:187:192:205:219:234 SD: 0.5669 cents 125:128:137:146:150:160:171:175:187:200:205:219:234:250 SD: 0.5468 cents 146:150:160:171:175:187:200:205:219:234:240:256:273:292 SD: 0.4923 cents 166:170:182:194:199:213:227:233:249:266:273:291:311:332 SD: 0.4666 cents 171:175:187:200:205:219:234:240:256:274:281:300:320:342 SD: 0.4502 cents 188:193:206:220:226:241:257:264:282:301:309:330:352:376 SD: 0.4467 cents 189:194:207:221:227:242:259:265:283:303:310:331:354:378 SD: 0.4378 cents 190:195:208:222:228:243:260:267:285:304:312:333:356:380 SD: 0.3996 cents 195:200:214:228:234:250:267:274:292:312:320:342:365:390 SD: 0.3803 cents 196:201:215:229:235:251:268:275:294:314:322:344:367:392 SD: 0.3756 cents 206:211:226:241:247:264:282:289:309:330:338:361:386:412 SD: 0.3461 cents 230:236:252:269:276:295:315:323:345:368:378:403:431:460 SD: 0.3296 cents 231:237:253:270:277:296:316:324:346:370:379:405:433:462 SD: 0.2491 cents 271:278:297:317:325:347:371:380:406:434:445:475:507:542 SD: 0.2362 cents 305:313:334:357:366:391:417:428:457:488:501:535:571:610 SD: 0.2349 cents 345:354:378:404:414:442:472:484:517:552:566:605:646:690 SD: 0.2089 cents 355:364:389:415:426:455:486:498:532:568:583:622:665:710 SD: 0.1975 cents 377:387:413:441:452:483:516:529:565:603:619:661:706:754 SD: 0.1951 cents 391:401:428:457:469:501:535:549:586:626:642:686:732:782 SD: 0.1893 cents 399:409:437:467:479:511:546:560:598:639:655:700:747:798 SD: 0.1818 cents 401:411:439:469:481:514:549:563:601:642:658:703:751:802 SD: 0.1586 cents 431:442:472:504:517:552:590:605:646:690:708:756:807:862 SD: 0.1456 cents 441:452:483:516:529:565:603:619:661:706:724:773:826:882 SD: 0.1429 cents 511:524:560:598:613:655:699:717:766:818:839:896:957:1022 SD: 0.1267 cents 597:612:654:698:716:765:817:838:895:956:980:1047:1118:1194 SD: 0.1235 cents