Scala analysis: orwell13
Orwell[13] in 115-et (7-limit poptimal)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 41.739 cents 41.739130 2: 156.522 cents 156.521739 3: 271.304 cents 271.304348 4: 313.043 cents 313.043478 5: 427.826 cents 427.826087 6: 542.609 cents 542.608696 7: 584.348 cents 584.347826 8: 699.130 cents 699.130435 9: 813.913 cents 813.913044 10: 855.652 cents 855.652174 11: 970.435 cents 970.434783 12: 1085.217 cents 1085.217391 13: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 114.7826 cents 114.7826 1: 41.7391 cents 41.7391 2: 114.7826 cents 114.7826 3: 114.7826 cents 114.7826 4: 41.7391 cents 41.7391 5: 114.7826 cents 114.7826 6: 114.7826 cents 114.7826 7: 41.7391 cents 41.7391 8: 114.7826 cents 114.7826 9: 114.7826 cents 114.7826 10: 41.7391 cents 41.7391 11: 114.7826 cents 114.7826 12: 114.7826 cents 114.7826 13: 114.7826 cents 114.7826
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 41.73913 cents 1: 9 114.78261 cents 2: 8 156.52174 cents 2: 5 229.56522 cents 3: 12 271.30435 cents 3: 1 344.34783 cents 4: 3 313.04348 cents 4: 10 386.08696 cents 5: 7 427.82609 cents 5: 6 500.86957 cents 6: 11 542.60870 cents 6: 2 615.65217 cents 7: 2 584.34783 cents 7: 11 657.39130 cents 8: 6 699.13044 cents 8: 7 772.17391 cents 9: 10 813.91304 cents 9: 3 886.95652 cents 10: 1 855.65217 cents 10: 12 928.69565 cents 11: 5 970.43478 cents 11: 8 1043.47826 cents 12: 9 1085.21739 cents 12: 4 1158.26087 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 : 41.7 156.5 271.3 313.0 427.8 542.6 584.3 699.1 813.9 855.7 970.4 1085.2 1200.0 41.7 : 114.8 229.6 271.3 386.1 500.9 542.6 657.4 772.2 813.9 928.7 1043.5 1158.3 1200.0 156.5 : 114.8 156.5 271.3 386.1 427.8 542.6 657.4 699.1 813.9 928.7 1043.5 1085.2 1200.0 271.3 : 41.7 156.5 271.3 313.0 427.8 542.6 584.3 699.1 813.9 928.7 970.4 1085.2 1200.0 313.0 : 114.8 229.6 271.3 386.1 500.9 542.6 657.4 772.2 887.0 928.7 1043.5 1158.3 1200.0 427.8 : 114.8 156.5 271.3 386.1 427.8 542.6 657.4 772.2 813.9 928.7 1043.5 1085.2 1200.0 542.6 : 41.7 156.5 271.3 313.0 427.8 542.6 657.4 699.1 813.9 928.7 970.4 1085.2 1200.0 584.3 : 114.8 229.6 271.3 386.1 500.9 615.7 657.4 772.2 887.0 928.7 1043.5 1158.3 1200.0 699.1 : 114.8 156.5 271.3 386.1 500.9 542.6 657.4 772.2 813.9 928.7 1043.5 1085.2 1200.0 813.9 : 41.7 156.5 271.3 386.1 427.8 542.6 657.4 699.1 813.9 928.7 970.4 1085.2 1200.0 855.7 : 114.8 229.6 344.3 386.1 500.9 615.7 657.4 772.2 887.0 928.7 1043.5 1158.3 1200.0 970.4 : 114.8 229.6 271.3 386.1 500.9 542.6 657.4 772.2 813.9 928.7 1043.5 1085.2 1200.0 1085.2: 114.8 156.5 271.3 386.1 427.8 542.6 657.4 699.1 813.9 928.7 970.4 1085.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 41.7391 .. 114.7826 cents 73.04348 cents 41.73913 cents 2: 156.5217 .. 229.5652 cents 73.04348 cents 41.73913 cents 3: 271.3043 .. 344.3478 cents 73.04348 cents 41.73913 cents 4: 313.0435 .. 386.0870 cents 73.04348 cents -31.30435 cents 5: 427.8261 .. 500.8696 cents 73.04348 cents 41.73913 cents 6: 542.6087 .. 615.6522 cents 73.04348 cents 41.73913 cents 7: 584.3478 .. 657.3913 cents 73.04348 cents -31.30435 cents 8: 699.1304 .. 772.1739 cents 73.04348 cents 41.73913 cents 9: 813.9130 .. 886.9565 cents 73.04348 cents 41.73913 cents 10: 855.6522 .. 928.6957 cents 73.04348 cents -31.30435 cents 11: 970.4348 .. 1043.4783 cents 73.04348 cents 41.73913 cents 12: 1085.2174 .. 1158.2609 cents 73.04348 cents 41.73913 cents
SHOW DATA
Number of notes : 13 -- Interval properties -- Smallest interval : 41.73913 cents, class 1 Average step (divided formal octave): 92.3077 cents Largest one step interval : 114.78261 cents Average / Smallest step : 2.211538 Largest / Average step : 1.243478 Largest / Smallest step : 2.750000 Median interval of one step : 114.78261 cents, amount: 9 Most common interval of one step : 114.78261 cents, amount: 9 Least squares average step : 88.74025 cents, oct.: 1153.62319 cents Scale is not proper Scale has Myhill's property chromas: 73.04348 cents and 31.30435 cents, ratio: 2.333333 generators: 3 of 271.30435 cents and 928.69565 cents ET pair of linear temperament : 22&31 Scale is distributional even Scale is a mode of a 115-tone equal temperament with octave 1200.000 cents degrees: 4 15 26 30 41 52 56 67 78 82 93 104 115 generators: 26 and 89 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBABBABBABBB Step pattern size order : SLLSLLSLLSLLL Interval vector is [ 0 0 0 4 0 0 0 0 0 0 9 0 0 0 8 0 0 0 0 0 0 5 0 0 0 12 0 0 0 3 0 0 1 0 0 0 10 0 0 0 7 0 0 0 0 0 0 6 0 0 0 11 0 0 0 2 0 ] Scale is a Constant Structure, by a margin of 31.30435 cents Scale diversity : 1.221085 Lumma stability : 0.347826 Lumma impropriety factor : 0.078261 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 : 31.30435 cents Most common intervals : 271.30435 cents & inv., amount: 12 Scale is a chain of 6 triads 0.0 427.826 928.696 cents Most common triad is 0.0 271.304 928.696 cents, amount: 11 Number of recognisable fifths : 6, average 699.1304 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: 56.7446 c. M: 86.6890 c. 14: 0 2 1 1 1 1 1 1 1 1 1 2 1 N D3 SD: 24.3281 c. M: 42.4845 c. 15: 1 1 1 1 1 2 0 2 1 1 1 2 1 N D3 SD: 22.7267 c. M:-38.2609 c. 17: 1 1 2 0 2 2 0 2 2 0 2 1 2 N T3 SD: 20.1071 c. M:-33.1458 c. 18: 1 1 2 1 1 2 1 1 2 1 2 1 2 P D3 S SD: 20.1620 c. M: 32.4638 c. 19: 1 1 2 1 2 2 0 2 2 1 1 2 2 N D3 SD: 18.4018 c. M: 30.2059 c. 21: 1 2 2 0 2 2 1 2 2 1 2 2 2 N T3 SD: 16.4888 c. M: 28.3230 c. 22: 1 2 2 1 2 2 1 2 2 1 2 2 2 P M ME S SD: 10.0616 c. M:-17.0751 c. Orwell-13 28: 1 3 2 1 3 3 1 2 3 1 3 2 3 N S SD: 11.2895 c. M:-15.6522 c. 31: 1 3 3 1 3 3 1 3 3 1 3 3 3 N M DE S SD: 2.3802 c. M: 4.0393 c. Orwell-13 84: 3 8 8 3 8 8 3 8 8 3 8 8 8 N M DE S SD: 0.8784 c. M:-1.4907 c. Orwell-13 115: 4 11 11 4 11 11 4 11 11 4 11 11 11 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: 1.4123 cents 3 x x x x x 4 x x x 5 x x 6 S SD: 17.6698 cents 4 x x x x 5 x x 6 x x 7 x 8 S SD: 10.4099 cents 5 x x x 6 x x 7 x 8 x 9 x 10 S SD: 9.4538 cents 6 x x 7 x x 8 x 9 x 10 x 11:12 S SD: 10.7020 cents 7 x x 8 x 9 x 10 x 11 x 12:13:14 S SD: 10.4227 cents 8 x 9 x x 10:11 x 12 x 13:14:15:16 S SD: 8.1905 cents 9 x 10 x 11 x 12:13 x 14:15:16:17:18 S SD: 11.4947 cents 10 x 11 x 12:13 x 14:15:16 x 18:19:20 S SD: 6.7455 cents 11 x 12:13 x 14:15 x 16 x 18:19:21:22 SD: 7.7048 cents 12 x 13:14 x 15:16:17:18:19:20:21:22:24 S SD: 7.5274 cents 13 x 14:15:16:17:18 x 19:21 x 23:24:26 SD: 9.0485 cents 14 x 15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.0557 cents 15 x 16 x 18:19 x 21:22:24:25:26:28:30 SD: 6.9567 cents 16 x 18 x 19:20:22 x 24 x 26:28:30:32 S SD: 7.4822 cents 17:18:19:20 x 22:23:24:25:27:28:30:32:34 SD: 6.9909 cents 18:19:20:21:22:23 x 25:27:29:30:32:34:36 SD: 6.8188 cents 19:20:21:22:23:24:26:27:28:30:31:33:36:38 SD: 6.0952 cents 20:21:22:23:24:26:27:28:30:32:33:35:37:40 SD: 5.1846 cents 21:22:23 x 25:27:29 x 31:34 x 37:39:42 SD: 5.7104 cents 22:23:24:26 x 28:30:31:33:35:36:39:41:44 SD: 4.1050 cents 24:25:26:28:29:31:33:34:36:38:39:42:45:48 SD: 3.9475 cents 25:26:27:29:30:32:34:35:37:40:41:44:47:50 SD: 3.5191 cents 26:27:28:30:31:33:36 x 39:42:43:46:49:52 SD: 4.9946 cents 27:28:30 x 32:35:37:38:40:43:44:47:51:54 SD: 4.4781 cents 28:29:31:33:34:36:38:39:42:45:46:49:52:56 SD: 3.5076 cents 29:30:32:34:35:37:40:41:43:46:48:51:54:58 SD: 3.4858 cents 30:31:33:35:36:38:41:42:45:48:49:53:56:60 SD: 2.3887 cents 35:36:38:41:42:45:48:49:52:56:57:61:66:70 SD: 2.3031 cents 40:41:44:47:48:51:55:56:60:64:66:70:75:80 SD: 1.5787 cents 52:53:57:61:62:67:71:73:78:83:85:91:97:104 SD: 1.5566 cents 60:61:66:70:72:77:82:84:90:96:98:105:112:120 SD: 1.4701 cents 65:67:71:76:78:83:89:91:97:104:107:114:122:130 SD: 1.2878 cents 70:72:77:82:84:90:96:98:105:112:115:123:131:140 SD: 1.2424 cents 72:74:79:84:86:92:99:101:108:115:118:126:135:144 SD: 1.1393 cents 75:77:82:88:90:96:103:105:112:120:123:131:140:150 SD: 1.0108 cents 82:84:90:96:98:105:112:115:123:131:134:144:153:164 SD: 0.9347 cents 85:87:93:99:102:109:116:119:127:136:139:149:159:170 SD: 0.8737 cents 95:97:104:111:114:122:130:133:142:152:156:166:178:190 SD: 0.8214 cents 114:117:125:133:137:146:156:160:171:182:187:200:213:228 SD: 0.8209 cents 116:119:127:136:139:149:159:163:174:186:190:203:217:232 SD: 0.8112 cents 117:120:128:137:140:150:160:164:175:187:192:205:219:234 SD: 0.4412 cents 125:128:137:146:150:160:171:175:187:200:205:219:234:250 SD: 0.3898 cents 201:206:220:235:241:257:275:282:301:322:329:352:376:402 SD: 0.3684 cents 211:216:231:247:253:270:289:296:316:338:346:370:395:422 SD: 0.3447 cents 241:247:264:282:289:309:330:338:361:386:395:422:451:482 SD: 0.3247 cents 242:248:265:283:290:310:331:339:362:387:397:424:453:484 SD: 0.2391 cents 318:326:348:372:381:407:435:446:476:509:521:557:595:636 SD: 0.1891 cents 378:387:414:442:453:484:517:530:566:605:620:662:708:756 SD: 0.1870 cents 413:423:452:483:495:529:565:579:618:661:677:723:773:826 SD: 0.1603 cents 443:454:485:518:531:567:606:621:663:709:726:776:829:886 SD: 0.1420 cents 530:543:580:620:635:679:725:743:794:848:869:928:992:1060 SD: 0.1297 cents 535:548:586:626:641:685:732:750:801:856:877:937:1001:1070 SD: 0.1241 cents 560:574:613:655:671:717:766:785:839:896:918:981:1048:1120 SD: 0.1081 cents 571:585:625:668:684:731:781:800:855:914:936:1000:1069:1142 SD: 0.0919 cents