Scala analysis: 13-31a
31-tET Orwell[13]
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 38.710 cents 38.709680 2: 154.839 cents 154.838710 3: 270.968 cents 270.967740 4: 309.677 cents 309.677420 5: 425.806 cents 425.806450 6: 541.935 cents 541.935480 7: 580.645 cents 580.645160 8: 696.774 cents 696.774190 9: 812.903 cents 812.903230 10: 851.613 cents 851.612900 11: 967.742 cents 967.741940 12: 1083.871 cents 1083.870970 13: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 116.1290 cents 116.1290 1: 38.7097 cents 38.7097 2: 116.1290 cents 116.1290 3: 116.1290 cents 116.1290 4: 38.7097 cents 38.7097 5: 116.1290 cents 116.1290 6: 116.1290 cents 116.1290 7: 38.7097 cents 38.7097 8: 116.1290 cents 116.1290 9: 116.1290 cents 116.1290 10: 38.7097 cents 38.7097 11: 116.1290 cents 116.1290 12: 116.1290 cents 116.1290 13: 116.1290 cents 116.1290
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 38.70968 cents 1: 9 116.12903 cents 2: 8 154.83871 cents 2: 5 232.25806 cents 3: 12 270.96774 cents 3: 1 348.38710 cents 4: 3 309.67742 cents 4: 10 387.09677 cents 5: 7 425.80645 cents 5: 6 503.22580 cents 6: 11 541.93548 cents 6: 2 619.35484 cents 7: 2 580.64516 cents 7: 11 658.06451 cents 8: 6 696.77419 cents 8: 7 774.19355 cents 9: 10 812.90323 cents 9: 3 890.32258 cents 10: 1 851.61290 cents 10: 12 929.03226 cents 11: 5 967.74194 cents 11: 8 1045.16129 cents 12: 9 1083.87097 cents 12: 4 1161.29032 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 : 38.7 154.8 271.0 309.7 425.8 541.9 580.6 696.8 812.9 851.6 967.7 1083.9 1200.0 38.7 : 116.1 232.3 271.0 387.1 503.2 541.9 658.1 774.2 812.9 929.0 1045.2 1161.3 1200.0 154.8 : 116.1 154.8 271.0 387.1 425.8 541.9 658.1 696.8 812.9 929.0 1045.2 1083.9 1200.0 271.0 : 38.7 154.8 271.0 309.7 425.8 541.9 580.6 696.8 812.9 929.0 967.7 1083.9 1200.0 309.7 : 116.1 232.3 271.0 387.1 503.2 541.9 658.1 774.2 890.3 929.0 1045.2 1161.3 1200.0 425.8 : 116.1 154.8 271.0 387.1 425.8 541.9 658.1 774.2 812.9 929.0 1045.2 1083.9 1200.0 541.9 : 38.7 154.8 271.0 309.7 425.8 541.9 658.1 696.8 812.9 929.0 967.7 1083.9 1200.0 580.6 : 116.1 232.3 271.0 387.1 503.2 619.4 658.1 774.2 890.3 929.0 1045.2 1161.3 1200.0 696.8 : 116.1 154.8 271.0 387.1 503.2 541.9 658.1 774.2 812.9 929.0 1045.2 1083.9 1200.0 812.9 : 38.7 154.8 271.0 387.1 425.8 541.9 658.1 696.8 812.9 929.0 967.7 1083.9 1200.0 851.6 : 116.1 232.3 348.4 387.1 503.2 619.4 658.1 774.2 890.3 929.0 1045.2 1161.3 1200.0 967.7 : 116.1 232.3 271.0 387.1 503.2 541.9 658.1 774.2 812.9 929.0 1045.2 1083.9 1200.0 1083.9: 116.1 154.8 271.0 387.1 425.8 541.9 658.1 696.8 812.9 929.0 967.7 1083.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.7097 .. 116.1290 cents 77.41935 cents 38.70968 cents 2: 154.8387 .. 232.2581 cents 77.41935 cents 38.70968 cents 3: 270.9677 .. 348.3871 cents 77.41936 cents 38.70968 cents 4: 309.6774 .. 387.0968 cents 77.41935 cents -38.70968 cents 5: 425.8064 .. 503.2258 cents 77.41935 cents 38.70968 cents 6: 541.9355 .. 619.3548 cents 77.41936 cents 38.70968 cents 7: 580.6452 .. 658.0645 cents 77.41935 cents -38.70968 cents 8: 696.7742 .. 774.1936 cents 77.41936 cents 38.70968 cents 9: 812.9032 .. 890.3226 cents 77.41935 cents 38.70968 cents 10: 851.6129 .. 929.0323 cents 77.41936 cents -38.70968 cents 11: 967.7419 .. 1045.1613 cents 77.41935 cents 38.70968 cents 12: 1083.8710 .. 1161.2903 cents 77.41935 cents 38.70968 cents
SHOW DATA
Number of notes : 13 -- Interval properties -- Smallest interval : 38.70967 cents, class 1 Average step (divided formal octave): 92.3077 cents Largest one step interval : 116.12903 cents Average / Smallest step : 2.384616 Largest / Average step : 1.258064 Largest / Smallest step : 3.000001 Median interval of one step : 116.12903 cents, amount: 9 Most common interval of one step : 116.12903 cents, amount: 9 Least squares average step : 88.52653 cents, oct.: 1150.84485 cents Scale is not proper Scale has Myhill's property chromas: 77.41935 cents and 38.70967 cents, ratio: 2.000000 generators: 3 of 270.96774 cents and 929.03226 cents ET pair of linear temperament : 31&19999969 Scale is distributional even Scale is a mode of a 31-tone equal temperament with octave 2/1 degrees: 1 4 7 8 11 14 15 18 21 22 25 28 31 generators: 7 and 24 Number of contiguous 1-step segments: 4 Step pattern alph. order: ABBABBABBABBB Step pattern size order : SLLSLLSLLSLLL Interval vector is [ 4 0 9 8 0 5 12 3 1 10 7 0 6 11 2 ] Scale is a Constant Structure, by a margin of 38.70967 cents Scale diversity : 1.211242 Lumma stability : 0.322581 Lumma impropriety factor : 0.096774 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 : 38.70967 cents Most common intervals : 270.96774 cents & inv., amount: 12 Scale is a chain of 6 triads 0.0 425.806 929.032 cents Most common triad is 0.0 270.968 929.032 cents, amount: 11 Number of recognisable fifths : 6, average 696.7742 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: 55.1534 c. M: 86.3524 c. 14: 0 2 1 1 1 1 1 1 1 1 1 2 1 N D3 SD: 24.2262 c. M: 41.4747 c. 15: 0 2 1 1 1 2 0 2 1 1 1 2 1 N D3 SD: 23.0153 c. M: 38.7097 c. 17: 1 1 2 0 2 2 0 2 2 0 2 1 2 N T3 SD: 19.9510 c. M:-34.1556 c. 18: 1 1 2 1 1 2 1 1 2 1 2 1 2 P D3 S SD: 20.7047 c. M:-32.2581 c. 19: 0 2 2 1 1 2 1 2 2 0 2 2 2 N T3 SD: 24.6498 c. M: 46.8591 c. 20: 0 2 2 1 2 2 0 2 2 1 2 2 2 N T3 SD: 24.9601 c. M: 40.6452 c. 21: 1 2 2 0 2 2 1 2 2 1 2 2 2 N T3 SD: 15.8321 c. M: 27.6498 c. 22: 1 2 2 1 2 2 1 2 2 1 2 2 2 P M ME S SD: 12.4418 c. M:-21.1144 c. Orwell-13 27: 1 2 3 1 3 2 1 3 2 1 3 2 3 N T3 SD: 11.6542 c. M: 21.5054 c. 28: 1 3 2 1 3 3 1 2 3 1 3 2 3 N S SD: 11.8431 c. M:-19.3548 c. 31: 1 3 3 1 3 3 1 3 3 1 3 3 3 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: 2.5904 cents 3 x x x x x 4 x x x 5 x x 6 S SD: 18.2533 cents 4 x x x x 5 x x 6 x x 7 x 8 S SD: 9.9615 cents 5 x x x 6 x x 7 x 8 x 9 x 10 S SD: 10.0501 cents 6 x x 7 x x 8 x 9 x 10 x 11:12 S SD: 10.8437 cents 7 x x 8 x 9 x 10 x 11 x 12:13:14 S SD: 10.3982 cents 8 x 9 x x 10:11 x 12 x 13:14:15:16 S SD: 8.1259 cents 9 x 10 x 11 x 12:13 x 14:15:16:17:18 S SD: 12.0269 cents 10 x 11 x 12:13 x 14:15:16 x 17:19:20 SD: 7.1445 cents 11 x 12:13 x 14:15 x 16 x 18:19:21:22 SD: 7.4444 cents 12 x 13:14 x 15:16:17:18:19:20:21:22:24 S SD: 7.5291 cents 13 x 14:15:16:17 x 18:19:21 x 23:24:26 SD: 9.1110 cents 14 x 15:16:17:18:19:20:21:22:23:24:26:28 S SD: 7.2238 cents 15 x 16 x 18:19 x 21:22:24:25:26:28:30 SD: 6.8063 cents 16 x 18 x 19:20:22 x 24 x 26:28:30:32 S SD: 7.3484 cents 17 x 19:20 x 22:23:24:25:27:28:30:32:34 SD: 5.8037 cents 18:19:20:21:22:23 x 25:27:29 x 31:34:36 SD: 7.3580 cents 19:20:21:22:23:24:26:27:28:30:31:33:36:38 SD: 6.2585 cents 20:21:22:23:24:26:27:28:30:32:33:35:37:40 SD: 5.4418 cents 21:22:23 x 25:27:29 x 31 x 34:37:39:42 SD: 5.7550 cents 22:23:24:26 x 28:30:31:33:35:36:38:41:44 SD: 4.3220 cents 24:25:26:28:29:31:33:34:36:38:39:42:45:48 SD: 4.2008 cents 25:26:27:29:30:32:34:35:37:40:41:44:47:50 SD: 3.6080 cents 26:27:28:30:31:33 x 36:39:42:43:45:49:52 SD: 5.0366 cents 27:28:30 x 32:35:37:38:40:43:44:47:50:54 SD: 4.5562 cents 28:29:31:33 x 36:38:39:42:45:46:49:52:56 SD: 3.4804 cents 30:31:33:35:36:38:41:42:45:48:49:52:56:60 SD: 2.4854 cents 33:34:36:39 x 42:45:46:49:53:54:58:62:66 SD: 2.6196 cents 35:36:38:41:42:45:48:49:52:56:57:61:65:70 SD: 2.1506 cents 40:41:44:47:48:51:55:56:60:64:65:70:75:80 SD: 1.7412 cents 47:48:51:55:56:60:64:66:70:75:77:82:88:94 SD: 1.6114 cents 52:53:57:61:62:67:71:73:78:83:85:91:97:104 SD: 1.5107 cents 55:56:60:64:66:70:75:77:82:88:90:96:103:110 SD: 1.3930 cents 65:66:71:76:78:83:89:91:97:104:106:114:122:130 SD: 1.3454 cents 71:73:78:83:85:91:97:99:106:114:116:124:133:142 SD: 1.2677 cents 75:77:82:88:90:96:103:105:112:120:123:131:140:150 SD: 1.1437 cents 76:78:83:89:91:97:104:106:114:122:124:133:142:152 SD: 1.0289 cents 82:84:90:96:98:105:112:115:123:131:134:143:153:164 SD: 0.9752 cents 83:85:91:97:99:106:114:116:124:133:136:145:155:166 SD: 0.9303 cents 87:89:95:102:104:111:119:122:130:139:142:152:163:174 SD: 0.7492 cents 93:95:102:109:111:119:127:130:139:149:152:163:174:186 SD: 0.7291 cents 107:109:117:125:128:137:146:150:160:171:175:187:200:214 SD: 0.7251 cents 118:121:129:138:141:151:161:165:176:189:193:206:221:236 SD: 0.7138 cents 123:126:135:144:147:157:168:172:184:197:201:215:230:246 SD: 0.6834 cents 128:131:140:150:153:164:175:179:191:205:209:224:239:256 SD: 0.6180 cents 137:140:150:160:164:175:187:192:205:219:224:240:256:274 SD: 0.5700 cents 147:150:161:172:176:188:201:206:220:235:240:257:275:294 SD: 0.5441 cents 168:172:184:196:201:215:230:235:251:269:275:294:314:336 SD: 0.5205 cents 169:173:185:198:202:216:231:236:253:270:276:296:316:338 SD: 0.5126 cents 172:176:188:201:206:220:235:241:257:275:281:301:322:344 SD: 0.4478 cents 179:183:196:209:214:229:245:250:268:286:293:313:335:358 SD: 0.4271 cents 183:187:200:214:219:234:250:256:274:293:299:320:342:366 SD: 0.3468 cents 214:219:234:250:256:274:293:299:320:342:350:374:400:428 SD: 0.3456 cents 224:229:245:262:268:286:306:313:335:358:366:392:419:448 SD: 0.3411 cents 226:231:247:264:270:289:309:316:338:361:370:395:423:452 SD: 0.3378 cents 236:241:258:276:282:302:323:330:353:377:386:413:441:472 SD: 0.3312 cents 254:260:278:297:304:325:347:355:380:406:415:444:475:508 SD: 0.3189 cents 255:261:279:298:305:326:349:357:381:408:417:446:477:510 SD: 0.2844 cents 266:272:291:311:318:340:364:372:398:425:435:465:497:532 SD: 0.2404 cents 301:308:329:352:360:385:412:421:450:481:492:526:563:602 SD: 0.2366 cents 302:309:330:353:361:386:413:422:452:483:494:528:565:604 SD: 0.2360 cents 307:314:336:359:367:393:420:429:459:491:502:537:574:614 SD: 0.2238 cents 354:362:387:414:423:453:484:495:529:566:579:619:662:708 SD: 0.1862 cents 362:370:396:423:433:463:495:506:541:579:592:633:677:724 SD: 0.1807 cents 384:393:420:449:459:491:525:537:574:614:628:672:718:768 SD: 0.1761 cents 394:403:431:461:471:504:539:551:589:630:644:689:737:788 SD: 0.1518 cents 449:459:491:525:537:574:614:628:671:718:734:785:840:898 SD: 0.1462 cents 525:537:574:614:628:671:718:734:785:840:859:918:982:1050 SD: 0.1399 cents 537:549:587:628:642:687:734:751:803:859:878:939:1004:1074 SD: 0.1332 cents 567:580:620:663:678:725:775:793:848:907:927:992:1060:1134 SD: 0.1253 cents 577:590:631:675:690:738:789:807:863:923:944:1009:1079:1154 SD: 0.0849 cents