Scala analysis: 12-of-blackjack-11
A 12-tone 11-limit subset of Blackjack
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 33.333 cents 33.333333 2: 150.000 cents 150.000000 3: 266.667 cents 266.666667 4: 383.333 cents 383.333333 5: 500.000 cents 500.000000 6: 583.333 cents 583.333333 7: 700.000 cents 700.000000 8: 816.667 cents 816.666667 9: 933.333 cents 933.333333 10: 1050.000 cents 1050.000000 11: 1083.333 cents 1083.333333 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 116.6667 cents 116.6667 1: 33.3333 cents 33.3333 2: 116.6667 cents 116.6667 3: 116.6667 cents 116.6667 4: 116.6667 cents 116.6667 5: 116.6667 cents 116.6667 6: 83.3333 cents 83.3333 7: 116.6667 cents 116.6667 8: 116.6667 cents 116.6667 9: 116.6667 cents 116.6667 10: 116.6667 cents 116.6667 11: 33.3333 cents 33.3333 12: 116.6667 cents 116.6667
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 33.33333 cents 1: 1 83.33333 cents 1: 9 116.66667 cents 2: 4 150.00000 cents 2: 2 200.00000 cents 2: 6 233.33333 cents 3: 1 183.33333 cents 3: 4 266.66667 cents 3: 3 316.66667 cents 3: 4 350.00000 cents 4: 2 300.00000 cents 4: 4 383.33333 cents 4: 4 433.33333 cents 4: 2 466.66667 cents 5: 3 416.66667 cents 5: 4 500.00000 cents 5: 5 550.00000 cents 6: 4 533.33333 cents 6: 2 583.33333 cents 6: 2 616.66667 cents 6: 4 666.66667 cents 7: 5 650.00000 cents 7: 4 700.00000 cents 7: 3 783.33333 cents 8: 2 733.33333 cents 8: 4 766.66667 cents 8: 4 816.66667 cents 8: 2 900.00000 cents 9: 4 850.00000 cents 9: 3 883.33333 cents 9: 4 933.33333 cents 9: 1 1016.66667 cents 10: 6 966.66667 cents 10: 2 1000.00000 cents 10: 4 1050.00000 cents 11: 9 1083.33333 cents 11: 1 1116.66667 cents 11: 2 1166.66667 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.45455 = 38/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 33.3 150.0 266.7 383.3 500.0 583.3 700.0 816.7 933.3 1050.0 1083.3 1200.0 33.3 : 116.7 233.3 350.0 466.7 550.0 666.7 783.3 900.0 1016.7 1050.0 1166.7 1200.0 150.0 : 116.7 233.3 350.0 433.3 550.0 666.7 783.3 900.0 933.3 1050.0 1083.3 1200.0 266.7 : 116.7 233.3 316.7 433.3 550.0 666.7 783.3 816.7 933.3 966.7 1083.3 1200.0 383.3 : 116.7 200.0 316.7 433.3 550.0 666.7 700.0 816.7 850.0 966.7 1083.3 1200.0 500.0 : 83.3 200.0 316.7 433.3 550.0 583.3 700.0 733.3 850.0 966.7 1083.3 1200.0 583.3 : 116.7 233.3 350.0 466.7 500.0 616.7 650.0 766.7 883.3 1000.0 1116.7 1200.0 700.0 : 116.7 233.3 350.0 383.3 500.0 533.3 650.0 766.7 883.3 1000.0 1083.3 1200.0 816.7 : 116.7 233.3 266.7 383.3 416.7 533.3 650.0 766.7 883.3 966.7 1083.3 1200.0 933.3 : 116.7 150.0 266.7 300.0 416.7 533.3 650.0 766.7 850.0 966.7 1083.3 1200.0 1050.0: 33.3 150.0 183.3 300.0 416.7 533.3 650.0 733.3 850.0 966.7 1083.3 1200.0 1083.3: 116.7 150.0 266.7 383.3 500.0 616.7 700.0 816.7 933.3 1050.0 1166.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.3333 .. 116.6667 cents 83.33333 cents 33.33333 cents 2: 150.0000 .. 233.3333 cents 83.33333 cents 33.33333 cents 3: 183.3333 .. 350.0000 cents 166.66667 cents -50.00000 cents 4: 300.0000 .. 466.6667 cents 166.66667 cents -50.00000 cents 5: 416.6667 .. 550.0000 cents 133.33333 cents -50.00000 cents 6: 533.3333 .. 666.6667 cents 133.33333 cents -16.66667 cents 7: 650.0000 .. 783.3333 cents 133.33333 cents -16.66667 cents 8: 733.3333 .. 900.0000 cents 166.66667 cents -50.00000 cents 9: 850.0000 .. 1016.6667 cents 166.66667 cents -50.00000 cents 10: 966.6667 .. 1050.0000 cents 83.33333 cents -50.00000 cents 11: 1083.3333 .. 1166.6667 cents 83.33333 cents 33.33333 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 33.33333 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 116.66667 cents Average / Smallest step : 3.000000 Largest / Average step : 1.166667 Largest / Smallest step : 3.500000 Median interval of one step : 116.66667 cents, amount: 9 Most common interval of one step : 116.66667 cents, amount: 9 Least squares average step : 100.48718 cents, oct.: 1205.84615 cents Scale is not proper Scale is a mode of a 72-tone equal temperament with octave 1200.000 cents degrees: 2 9 16 23 30 35 42 49 56 63 65 72 Least number of segments generator : 59 of 983.333 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 65 of 1083.333 cents and inv. generated superset size: 20 = 8 more = 166.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBBBCBBBBAB Step pattern size order : SLLLLMLLLLSL Interval vector is [ 0 2 0 0 1 0 9 0 4 0 1 2 0 6 0 4 0 2 3 0 4 0 4 0 3 4 0 2 0 4 0 4 5 0 2 0 ] Scale is a Constant Structure, by a margin of 16.66667 cents Scale diversity : 1.447743 Lumma stability : 0.111111 Lumma impropriety factor : 0.277778 Rothenberg efficiency : 0.405886 redundancy: 0.594114 Efficiency x scale size : 4.870635 Number of different interval sizes : 38 = 3.45455 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.45455 = 38/11 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 16.66667 cents Most common intervals : 116.66667 cents & inv., amount: 9 Most common triad is 0.0 116.667 1083.333 cents, amount: 6 Number of recognisable fifths : 4, average 700.0000 cents Formal octave complements present : 9 = 75.0000% Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 11-12 -- Rational properties --
FIT/MODE
12: 0 2 1 1 1 1 1 1 1 2 0 1 N T3 SD: 28.0542 c. M:-50.0000 c. 14: 0 2 1 1 2 1 1 2 1 1 1 1 N SD: 24.3781 c. M: 40.4762 c. 15: 0 2 1 2 1 1 2 1 2 1 1 1 N SD: 22.3192 c. M:-36.6667 c. 17: 0 2 2 1 2 1 2 1 2 2 0 2 N SD: 21.0461 c. M: 40.1961 c. 19: 1 1 2 2 2 1 2 2 2 2 0 2 N SD: 15.3153 c. M:-29.8246 c. 22: 1 2 2 2 2 2 2 2 2 2 1 2 P D3 SD: 10.8027 c. M:-21.2121 c. 24: 1 2 2 3 2 2 2 2 3 2 1 2 N SD: 12.7294 c. M:-16.6667 c. 29: 1 3 2 3 3 2 3 3 3 2 1 3 N SD: 11.3908 c. M:-18.3908 c. 31: 1 3 3 3 3 2 3 3 3 3 1 3 N SD: 3.7570 c. M:-5.3763 c. 41: 1 4 4 4 4 3 4 4 4 4 1 4 N SD: 2.8407 c. M: 4.0650 c. 72: 2 7 7 7 7 5 7 7 7 7 2 7 N SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 0.9775 cents 3 x x x x 4 x x x 5 x x 6 S SD: 16.3379 cents 4 x x x 5 x x 6 x 7 x x 8 S SD: 8.9178 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 11.7611 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 8.1762 cents 7 x x 8:9 x 10 x 11:12 x 13:14 S SD: 11.4354 cents 8 x 9 x 10 x 11:12:13:14 x 15:16 S SD: 9.5176 cents 9 x 10 x 11:12:13 x 14:15 x 17:18 SD: 12.8538 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 8.2315 cents 11 x 12:13:14:15 x 16:18:19:20:21:22 S SD: 9.3069 cents 12 x 13:14:15:16:17:18:19:21:22 x 24 SD: 4.7325 cents 13 x 14:15:16:17:18:19:21:22:24 x 26 SD: 7.5733 cents 14 x 15:16:17:19:20:21:22:24 x 26:28 SD: 8.7853 cents 15 x 16:18:19:20:21:22:24:26 x 28:30 S SD: 7.9240 cents 16 x 17:19:20:21:22:24:26:27:29:30:32 SD: 7.4063 cents 17 x 19:20:21:23:24:25:27:29:31:32:34 SD: 6.2118 cents 18 x 20:21:22:24:25:27:29:31:33:34:36 SD: 4.9940 cents 20:21:22:23:25:27:28:30:32:34:37 x 40 SD: 5.9589 cents 21:22:23:25:26:28:29:31:34:36 x 39:42 SD: 6.6910 cents 22:23:24:26:27:29:31:33:35:38:40:41:44 SD: 5.5348 cents 23:24:25:27:29:31:32:34:37:39:42:43:46 SD: 4.9472 cents 24:25:26:28:30:32:34:36:38:41:44:45:48 SD: 4.1140 cents 27:28:29:32:34:36:38:40:43:46 x 50:54 SD: 5.4105 cents 28:29:31:33:35:37:39:42:45:48:51:52:56 SD: 4.1386 cents 30:31:33:35:37:40:42:45:48:51:55:56:60 SD: 3.1467 cents 32:33:35:37:40:43:45:48:51:55:59:60:64 SD: 2.7307 cents 35:36:38:41:44:47:49:52:56:60:64:65:70 SD: 2.6437 cents 36:37:39:42:45:48:50:54:58:62:66:67:72 SD: 2.3045 cents 42:43:46:49:52:56:59:63:67:72:77:79:84 SD: 1.8711 cents 48:49:52:56:60:64:67:72:77:82:88:90:96 SD: 1.3290 cents 53:54:58:62:66:71:74:79:85:91:97:99:106 SD: 1.3078 cents 60:61:65:70:75:80:84:90:96:103:110:112:120 SD: 1.1544 cents 78:80:85:91:97:104:109:117:125:134:143:146:156 SD: 1.1393 cents 84:86:92:98:105:112:118:126:135:144:154:157:168 SD: 1.1064 cents 89:91:97:104:111:119:125:133:143:153:163:166:178 SD: 1.0266 cents 90:92:98:105:112:120:126:135:144:154:165:168:180 SD: 0.7829 cents 98:100:107:114:122:131:137:147:157:168:180:183:196 SD: 0.7472 cents 101:103:110:118:126:135:141:151:162:173:185:189:202 SD: 0.7283 cents 102:104:111:119:127:136:143:153:163:175:187:191:204 SD: 0.7121 cents 108:110:118:126:135:144:151:162:173:185:198:202:216 SD: 0.5516 cents 144:147:157:168:180:192:202:216:231:247:264:269:288 SD: 0.4907 cents 162:165:177:189:202:216:227:243:260:278:297:303:324 SD: 0.4723 cents 197:201:215:230:246:263:276:295:316:338:361:368:394 SD: 0.3415 cents 209:213:228:244:261:279:293:313:335:358:383:391:418 SD: 0.3003 cents 245:250:267:286:306:327:343:367:393:420:449:458:490 SD: 0.2954 cents 265:270:289:309:331:354:371:397:425:454:486:495:530 SD: 0.2910 cents 277:282:302:323:346:370:388:415:444:475:508:518:554 SD: 0.2744 cents 295:301:322:344:368:394:413:442:473:506:541:552:590 SD: 0.2678 cents 299:305:326:349:373:399:419:448:479:513:548:559:598 SD: 0.2215 cents 307:313:335:358:383:410:430:460:492:526:563:574:614 SD: 0.1643 cents 355:362:387:414:443:474:497:532:569:609:651:664:710 SD: 0.1534 cents 367:374:400:428:458:490:514:550:588:629:673:686:734 SD: 0.1395 cents 516:526:563:602:644:689:723:773:827:885:946:965:1032 SD: 0.1387 cents 529:539:577:617:660:706:741:793:848:907:970:989:1058 SD: 0.1234 cents 564:575:615:658:704:753:790:845:904:967:1034:1054:1128 SD: 0.1033 cents