Scala analysis: 13-84a
84-tET Orwell[13]
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 42.857 cents 42.857143 2: 157.143 cents 157.142857 3: 271.429 cents 271.428572 4: 314.286 cents 314.285714 5: 428.571 cents 428.571429 6: 542.857 cents 542.857143 7: 585.714 cents 585.714286 8: 700.000 cents 700.000000 9: 814.286 cents 814.285714 10: 857.143 cents 857.142857 11: 971.429 cents 971.428572 12: 1085.714 cents 1085.714286 13: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 114.2857 cents 114.2857 1: 42.8571 cents 42.8571 2: 114.2857 cents 114.2857 3: 114.2857 cents 114.2857 4: 42.8571 cents 42.8571 5: 114.2857 cents 114.2857 6: 114.2857 cents 114.2857 7: 42.8571 cents 42.8571 8: 114.2857 cents 114.2857 9: 114.2857 cents 114.2857 10: 42.8571 cents 42.8571 11: 114.2857 cents 114.2857 12: 114.2857 cents 114.2857 13: 114.2857 cents 114.2857
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 42.85714 cents 1: 9 114.28571 cents 2: 8 157.14286 cents 2: 5 228.57143 cents 3: 12 271.42857 cents 3: 1 342.85714 cents 4: 3 314.28571 cents 4: 10 385.71429 cents 5: 7 428.57143 cents 5: 6 500.00000 cents 6: 11 542.85714 cents 6: 2 614.28571 cents 7: 2 585.71429 cents 7: 11 657.14286 cents 8: 6 700.00000 cents 8: 7 771.42857 cents 9: 10 814.28571 cents 9: 3 885.71429 cents 10: 1 857.14286 cents 10: 12 928.57143 cents 11: 5 971.42857 cents 11: 8 1042.85714 cents 12: 9 1085.71429 cents 12: 4 1157.14286 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 : 42.9 157.1 271.4 314.3 428.6 542.9 585.7 700.0 814.3 857.1 971.4 1085.7 1200.0 42.9 : 114.3 228.6 271.4 385.7 500.0 542.9 657.1 771.4 814.3 928.6 1042.9 1157.1 1200.0 157.1 : 114.3 157.1 271.4 385.7 428.6 542.9 657.1 700.0 814.3 928.6 1042.9 1085.7 1200.0 271.4 : 42.9 157.1 271.4 314.3 428.6 542.9 585.7 700.0 814.3 928.6 971.4 1085.7 1200.0 314.3 : 114.3 228.6 271.4 385.7 500.0 542.9 657.1 771.4 885.7 928.6 1042.9 1157.1 1200.0 428.6 : 114.3 157.1 271.4 385.7 428.6 542.9 657.1 771.4 814.3 928.6 1042.9 1085.7 1200.0 542.9 : 42.9 157.1 271.4 314.3 428.6 542.9 657.1 700.0 814.3 928.6 971.4 1085.7 1200.0 585.7 : 114.3 228.6 271.4 385.7 500.0 614.3 657.1 771.4 885.7 928.6 1042.9 1157.1 1200.0 700.0 : 114.3 157.1 271.4 385.7 500.0 542.9 657.1 771.4 814.3 928.6 1042.9 1085.7 1200.0 814.3 : 42.9 157.1 271.4 385.7 428.6 542.9 657.1 700.0 814.3 928.6 971.4 1085.7 1200.0 857.1 : 114.3 228.6 342.9 385.7 500.0 614.3 657.1 771.4 885.7 928.6 1042.9 1157.1 1200.0 971.4 : 114.3 228.6 271.4 385.7 500.0 542.9 657.1 771.4 814.3 928.6 1042.9 1085.7 1200.0 1085.7: 114.3 157.1 271.4 385.7 428.6 542.9 657.1 700.0 814.3 928.6 971.4 1085.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 42.8571 .. 114.2857 cents 71.42857 cents 42.85714 cents 2: 157.1429 .. 228.5714 cents 71.42857 cents 42.85714 cents 3: 271.4286 .. 342.8571 cents 71.42857 cents 42.85714 cents 4: 314.2857 .. 385.7143 cents 71.42857 cents -28.57143 cents 5: 428.5714 .. 500.0000 cents 71.42857 cents 42.85714 cents 6: 542.8571 .. 614.2857 cents 71.42857 cents 42.85714 cents 7: 585.7143 .. 657.1429 cents 71.42857 cents -28.57143 cents 8: 700.0000 .. 771.4286 cents 71.42857 cents 42.85714 cents 9: 814.2857 .. 885.7143 cents 71.42857 cents 42.85714 cents 10: 857.1429 .. 928.5714 cents 71.42857 cents -28.57143 cents 11: 971.4286 .. 1042.8571 cents 71.42857 cents 42.85714 cents 12: 1085.7143 .. 1157.1429 cents 71.42857 cents 42.85714 cents
SHOW DATA
Number of notes : 13 -- Interval properties -- Smallest interval : 42.85714 cents, class 1 Average step (divided formal octave): 92.3077 cents Largest one step interval : 114.28571 cents Average / Smallest step : 2.153846 Largest / Average step : 1.238095 Largest / Smallest step : 2.666667 Median interval of one step : 114.28571 cents, amount: 9 Most common interval of one step : 114.28571 cents, amount: 9 Least squares average step : 88.81912 cents, oct.: 1154.64853 cents Scale is not proper Scale has Myhill's property chromas: 71.42857 cents and 28.57143 cents, ratio: 2.500000 generators: 3 of 271.42857 cents and 928.57143 cents ET pair of linear temperament : 22&31 Scale is distributional even Scale is a mode of a 84-tone equal temperament with octave 2/1 degrees: 3 11 19 22 30 38 41 49 57 60 68 76 84 generators: 19 and 65 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBABBABBABBB Step pattern size order : SLLSLLSLLSLLL Interval vector is [ 0 0 4 0 0 0 0 9 0 0 8 0 0 0 0 5 0 0 12 0 0 3 0 1 0 0 10 0 0 7 0 0 0 0 6 0 0 11 0 0 2 0 ] Scale is a Constant Structure, by a margin of 28.57143 cents Scale diversity : 1.223435 Lumma stability : 0.357143 Lumma impropriety factor : 0.071429 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 : 28.57143 cents Most common intervals : 271.42857 cents & inv., amount: 12 Scale is a chain of 6 triads 0.0 428.571 928.571 cents Most common triad is 0.0 271.429 928.571 cents, amount: 11 Number of recognisable fifths : 6, average 700.0000 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 -- Prime limit : 2 (not all pitches rational)
FIT/MODE
13: 0 1 1 1 1 1 1 1 1 1 1 1 2 N T3 SD: 57.3457 c. M: 86.8132 c. 14: 1 1 1 1 1 1 1 1 2 0 1 2 1 N D3 SD: 24.4243 c. M:-42.8571 c. 15: 1 1 1 1 1 2 0 2 1 1 1 2 1 N D3 SD: 22.5529 c. M:-37.1429 c. 17: 1 1 2 0 2 2 0 2 2 0 2 1 2 N T3 SD: 20.2353 c. M:-32.7731 c. 19: 0 2 2 1 2 1 1 2 2 0 2 2 2 N T3 SD: 23.4320 c. M: 42.8571 c. 20: 0 2 2 1 2 2 0 2 2 1 2 2 2 N T3 SD: 27.4734 c. M: 45.7143 c. 21: 1 2 2 1 2 2 0 2 2 1 2 2 2 N T3 SD: 16.8100 c. M:-28.5714 c. 22: 1 2 2 1 2 2 1 2 2 1 2 2 2 P M ME S SD: 9.1832 c. M:-15.5844 c. Orwell-13 28: 1 3 2 1 3 3 1 2 3 1 3 2 3 N S SD: 11.2066 c. M: 14.2857 c. 31: 1 3 3 1 3 3 1 3 3 1 3 3 3 N M DE S SD: 3.2586 c. M: 5.5300 c. Orwell-13 53: 2 5 5 2 5 5 2 5 5 2 5 5 5 N M DE S SD: 1.9059 c. M:-3.2345 c. Orwell-13 84: 3 8 8 3 8 8 3 8 8 3 8 8 8 N M DE S SD: 0.0000 c. M: 0.0000 c. Orwell-13
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: 0.9775 cents 3 x x x x x 4 x x x 5 x x 6 S SD: 17.4764 cents 4 x x x x 5 x x 6 x x 7 x 8 S SD: 10.5957 cents 5 x x x 6 x x 7 x 8 x 9 x 10 S SD: 9.2605 cents 6 x x 7 x x 8 x 9 x 10 x 11:12 S SD: 10.6652 cents 7 x x 8 x 9 x 10 x 11 x 12:13:14 S SD: 10.4456 cents 8 x 9 x x 10:11 x 12 x 13:14:15:16 S SD: 8.2326 cents 9 x 10 x 11 x 12:13 x 14:15:16:17:18 S SD: 11.3070 cents 10 x 11 x 12:13 x 14:15:16 x 18:19:20 S SD: 6.5890 cents 11 x 12:13 x 14:15 x 16 x 18:19:21:22 SD: 7.8140 cents 12 x 13:14 x 15:16:17:18:19:20:21:22:24 S SD: 7.5415 cents 13 x 14:15:16:17:18 x 19:21 x 23:24:26 SD: 9.0018 cents 14 x 15:16:17:18:19:20:21:22:23:25:26:28 SD: 6.9901 cents 15 x 16 x 18:19 x 21:22:24:25:26:28:30 SD: 7.0344 cents 16 x 18 x 19:21:22 x 24 x 26:28:30:32 SD: 7.5481 cents 17:18:19:20 x 22:23:24:25:27:28:30:32:34 SD: 6.8834 cents 18:19:20:21:22:23 x 25:27:29:30:32:34:36 SD: 6.6432 cents 19:20:21:22:23:24:26:27:28:30:31:33:36:38 SD: 6.0521 cents 20:21:22:23:24:26:27:28:30:32:33:35:37:40 SD: 5.1080 cents 21:22:23 x 25:27:29 x 31:34 x 37:39:42 SD: 5.6651 cents 22:23:24:26 x 28:30:31:33:35:36:39:41:44 SD: 4.0222 cents 24:25:26:28:29:31:33:34:36:38:39:42:45:48 SD: 3.8783 cents 25:26:27:29:30:32:34:35:37:40:41:44:47:50 SD: 3.5171 cents 26:27:28:30:31:33:36 x 39:42:43:46:49:52 SD: 4.9391 cents 27:28:30 x 32:35:37:38:40:43:44:47:51:54 SD: 4.4771 cents 28:29:31:33:34:36:38:39:42:45:46:49:52:56 SD: 3.4244 cents 29:30:32:34:35:37:40:41:43:46:48:51:54:58 SD: 3.3736 cents 30:31:33:35:36:38:41:42:45:48:49:53:56:60 SD: 2.3679 cents 40:41:44:47:48:51:55:56:60:64:66:70:75:80 SD: 1.5058 cents 64:66:70:75:77:82:88:90:96:102:105:112:120:128 SD: 1.3770 cents 65:67:71:76:78:83:89:91:97:104:107:114:122:130 SD: 1.2301 cents 70:72:77:82:84:90:96:98:105:112:115:123:131:140 SD: 1.0960 cents 75:77:82:88:90:96:103:105:112:120:123:131:140:150 SD: 1.0659 cents 76:78:83:89:91:97:104:107:114:122:125:133:142:152 SD: 1.0427 cents 82:84:90:96:98:105:112:115:123:131:135:144:154:164 SD: 0.9497 cents 92:94:101:108:110:118:126:129:138:147:151:161:172:184 SD: 0.9349 cents 95:97:104:111:114:122:130:133:142:152:156:167:178:190 SD: 0.8797 cents 106:109:116:124:127:136:145:149:159:170:174:186:198:212 SD: 0.7399 cents 114:117:125:133:137:146:156:160:171:182:187:200:213:228 SD: 0.7129 cents 117:120:128:137:140:150:160:164:175:187:192:205:219:234 SD: 0.4835 cents 125:128:137:146:150:160:171:175:187:200:205:219:234:250 SD: 0.4511 cents 171:175:187:200:205:219:234:240:256:274:281:300:320:342 SD: 0.4333 cents 200:205:219:234:240:256:274:281:300:320:328:351:374:400 SD: 0.4304 cents 201:206:220:235:241:257:275:282:301:322:330:352:376:402 SD: 0.3434 cents 211:216:231:247:253:270:289:296:316:338:346:370:395:422 SD: 0.3226 cents 231:237:253:270:277:296:316:324:346:370:379:405:432:462 SD: 0.2554 cents 271:278:297:317:325:347:371:380:406:434:445:475:507:542 SD: 0.2448 cents 323:331:354:378:387:414:442:453:484:517:530:566:605:646 SD: 0.2042 cents 367:376:402:429:440:470:502:515:550:587:602:643:687:734 SD: 0.1859 cents 431:442:472:504:517:552:590:605:646:690:707:755:807:862 SD: 0.1786 cents 432:443:473:505:518:553:591:606:647:691:709:757:809:864 SD: 0.1782 cents 442:453:484:517:530:566:605:620:662:707:725:775:828:884 SD: 0.1547 cents 484:496:530:566:580:620:662:679:725:775:794:848:906:968 SD: 0.1393 cents 524:537:574:613:628:671:717:735:785:839:860:918:981:1048 SD: 0.1311 cents 548:562:600:641:657:702:750:769:821:877:899:960:1026:1096 SD: 0.1195 cents