Scala analysis: 12-of-blackjack-7-9-11
A 12-tone subset of Blackjack with six 4-7-9-11 tetrads
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 116.667 cents 116.666667 2: 233.333 cents 233.333333 3: 350.000 cents 350.000000 4: 433.333 cents 433.333333 5: 466.667 cents 466.666667 6: 550.000 cents 550.000000 7: 583.333 cents 583.333333 8: 666.667 cents 666.666667 9: 783.333 cents 783.333333 10: 900.000 cents 900.000000 11: 1016.667 cents 1016.666667 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 183.3333 cents 183.3333 1: 116.6667 cents 116.6667 2: 116.6667 cents 116.6667 3: 116.6667 cents 116.6667 4: 83.3333 cents 83.3333 5: 33.3333 cents 33.3333 6: 83.3333 cents 83.3333 7: 33.3333 cents 33.3333 8: 83.3333 cents 83.3333 9: 116.6667 cents 116.6667 10: 116.6667 cents 116.6667 11: 116.6667 cents 116.6667 12: 183.3333 cents 183.3333
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 33.33333 cents 1: 3 83.33333 cents 1: 6 116.66667 cents 1: 1 183.33333 cents 2: 4 116.66667 cents 2: 2 200.00000 cents 2: 4 233.33333 cents 2: 2 300.00000 cents 3: 1 150.00000 cents 3: 2 200.00000 cents 3: 2 233.33333 cents 3: 2 316.66667 cents 3: 2 350.00000 cents 3: 3 416.66667 cents 4: 2 233.33333 cents 4: 2 316.66667 cents 4: 2 350.00000 cents 4: 2 433.33333 cents 4: 4 533.33333 cents 5: 1 316.66667 cents 5: 2 350.00000 cents 5: 2 433.33333 cents 5: 2 466.66667 cents 5: 2 616.66667 cents 5: 3 650.00000 cents 6: 2 433.33333 cents 6: 2 466.66667 cents 6: 2 550.00000 cents 6: 2 650.00000 cents 6: 2 733.33333 cents 6: 2 766.66667 cents 7: 3 550.00000 cents 7: 2 583.33333 cents 7: 2 733.33333 cents 7: 2 766.66667 cents 7: 2 850.00000 cents 7: 1 883.33333 cents 8: 4 666.66667 cents 8: 2 766.66667 cents 8: 2 850.00000 cents 8: 2 883.33333 cents 8: 2 966.66667 cents 9: 3 783.33333 cents 9: 2 850.00000 cents 9: 2 883.33333 cents 9: 2 966.66667 cents 9: 2 1000.00000 cents 9: 1 1050.00000 cents 10: 2 900.00000 cents 10: 4 966.66667 cents 10: 2 1000.00000 cents 10: 4 1083.33333 cents 11: 1 1016.66667 cents 11: 6 1083.33333 cents 11: 3 1116.66667 cents 11: 2 1166.66667 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.09091 = 56/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 116.7 233.3 350.0 433.3 466.7 550.0 583.3 666.7 783.3 900.0 1016.7 1200.0 116.7 : 116.7 233.3 316.7 350.0 433.3 466.7 550.0 666.7 783.3 900.0 1083.3 1200.0 233.3 : 116.7 200.0 233.3 316.7 350.0 433.3 550.0 666.7 783.3 966.7 1083.3 1200.0 350.0 : 83.3 116.7 200.0 233.3 316.7 433.3 550.0 666.7 850.0 966.7 1083.3 1200.0 433.3 : 33.3 116.7 150.0 233.3 350.0 466.7 583.3 766.7 883.3 1000.0 1116.7 1200.0 466.7 : 83.3 116.7 200.0 316.7 433.3 550.0 733.3 850.0 966.7 1083.3 1166.7 1200.0 550.0 : 33.3 116.7 233.3 350.0 466.7 650.0 766.7 883.3 1000.0 1083.3 1116.7 1200.0 583.3 : 83.3 200.0 316.7 433.3 616.7 733.3 850.0 966.7 1050.0 1083.3 1166.7 1200.0 666.7 : 116.7 233.3 350.0 533.3 650.0 766.7 883.3 966.7 1000.0 1083.3 1116.7 1200.0 783.3 : 116.7 233.3 416.7 533.3 650.0 766.7 850.0 883.3 966.7 1000.0 1083.3 1200.0 900.0 : 116.7 300.0 416.7 533.3 650.0 733.3 766.7 850.0 883.3 966.7 1083.3 1200.0 1016.7: 183.3 300.0 416.7 533.3 616.7 650.0 733.3 766.7 850.0 966.7 1083.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.3333 .. 183.3333 cents 150.00000 cents 33.33333 cents 2: 116.6667 .. 300.0000 cents 183.33333 cents -66.66667 cents 3: 150.0000 .. 416.6667 cents 266.66667 cents -150.00000 cents 4: 233.3333 .. 533.3333 cents 300.00000 cents -183.33333 cents 5: 316.6667 .. 650.0000 cents 333.33333 cents -216.66667 cents 6: 433.3333 .. 766.6667 cents 333.33333 cents -216.66667 cents 7: 550.0000 .. 883.3333 cents 333.33333 cents -216.66667 cents 8: 666.6667 .. 966.6667 cents 300.00000 cents -216.66667 cents 9: 783.3333 .. 1050.0000 cents 266.66667 cents -183.33333 cents 10: 900.0000 .. 1083.3333 cents 183.33333 cents -150.00000 cents 11: 1016.6667 .. 1166.6667 cents 150.00000 cents -66.66667 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 : 183.33333 cents Average / Smallest step : 3.000000 Largest / Average step : 1.833333 Largest / Smallest step : 5.500000 Median interval of one step : 116.66667 cents, amount: 6 Most common interval of one step : 116.66667 cents, amount: 6 Least squares average step : 92.38462 cents, oct.: 1108.61538 cents Scale is not proper Scale is a mode of a 72-tone equal temperament with octave 2/1 degrees: 7 14 21 26 28 33 35 40 47 54 61 72 Least number of segments generator : 37 of 616.667 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: AAABCBCBAAAD Step pattern size order : CCCBABABCCCD Interval vector is [ 0 2 0 0 3 0 10 0 1 0 1 4 0 8 0 0 0 2 5 0 6 0 0 0 3 6 0 4 0 0 0 4 5 0 2 0 ] Scale is not a Constant Structure Scale diversity : 1.330556 Lumma stability : 0.055556 Lumma impropriety factor : 0.805556 Rothenberg efficiency : 0.514153 redundancy: 0.485847 Efficiency x scale size : 6.169841 Number of different interval sizes : 32 = 2.90909 / class Number of one step interval sizes : 4 Highest interval variety : 6 Mean interval variety : 5.09091 = 56/11 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 16.66667 cents Most common intervals : 116.66667 cents & inv., amount: 10 Most common triad is 0.0 116.667 1083.333 cents, amount: 8 Number of recognisable fifths : 0 Formal octave complements present : 1 = 8.3333% Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 11-12 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
12: 1 1 1 1 0 1 0 1 1 2 1 2 N SD: 50.4608 c. M: 83.3333 c. 13: 1 2 1 1 0 1 0 1 1 2 1 2 N SD: 25.0629 c. M: 44.8718 c. 14: 1 2 1 1 0 1 1 1 1 1 2 2 N SD: 24.3005 c. M: 42.8571 c. 15: 1 2 1 1 1 1 0 1 2 1 2 2 N SD: 22.6487 c. M: 36.6667 c. 16: 2 1 2 1 0 1 1 1 1 2 2 2 N SD: 21.5166 c. M: 33.3333 c. 17: 2 1 2 1 1 1 0 1 2 2 1 3 N SD: 19.6609 c. M: 31.3725 c. 20: 2 2 2 1 1 1 1 1 2 2 2 3 N SD: 8.9235 c. M:-16.6667 c. 31: 3 3 3 2 1 2 1 2 3 3 3 5 N SD: 6.4104 c. M: 10.2151 c. 41: 4 4 4 3 1 3 1 3 4 4 4 6 N SD: 4.8469 c. M:-7.7236 c. 52: 5 5 5 4 1 4 1 4 5 5 5 8 N SD: 3.4321 c. M: 6.4103 c. 61: 6 6 6 4 2 4 2 4 6 6 6 9 N SD: 3.9231 c. M:-6.8306 c. 72: 7 7 7 5 2 5 2 5 7 7 7 11 N SD: 0.0000 c. M: 0.0000 c. Blackjack-12
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 x 3 x x x 4 S SD: 17.6442 cents 3 x x x x 4 x x x x 5 x 6 S SD: 11.6869 cents 4 x x 5 x x x x 6 x x 7:8 S SD: 17.4153 cents 5 x x 6 x x x 7 x 8 x 9:10 S SD: 9.1725 cents 6 x 7 x x 8 x x 9 x 10:11:12 S SD: 11.3875 cents 7 x 8 x 9 x x 10 x 11:12:13:14 S SD: 10.4015 cents 8 x 9:10 x x 11 x 12:13 x 14:16 S SD: 13.5461 cents 9 x 10:11 x 12 x x 13:14:15:16:18 S SD: 9.2663 cents 10:11 x 12 x 13 x 14:15:16:17:18:20 S SD: 8.7402 cents 11:12:13 x 14 x 15 x 16:17:19:20:22 SD: 10.1666 cents 12:13:14:15 x 16 x 17:18:19:20:22:24 S SD: 8.3685 cents 13:14:15:16 x 17:18 x 19:20:22:23:26 SD: 5.5435 cents 14:15:16:17:18 x 19:20:21:22:24:25:28 SD: 5.9873 cents 15:16:17:18:19:20 x 21:22:24:25:27:30 SD: 5.9108 cents 16:17:18:20 x 21:22 x 24:25:27:29:32 SD: 6.2460 cents 17:18:19:21:22 x 23:24:25:27:29:31:34 SD: 6.2718 cents 18:19:21:22:23:24 x 25:26:28:30:32:36 SD: 6.3326 cents 19:20:22:23:24:25:26:27:28:30:32:34:38 SD: 4.7976 cents 20:21:23:24 x 26:27:28:29:31:34:36:40 SD: 6.3483 cents 21:22:24:26:27:28:29 x 31:33:35:38:42 SD: 5.1178 cents 22:24:25:27:28:29:30:31:32:35:37:40:44 SD: 4.6108 cents 23:25:26:28 x 30 x 32:34:36:39:41:46 SD: 4.5749 cents 24:26:27:29:31 x 33:34:35:38:40:43:48 SD: 4.9428 cents 25:27:29:31:32:33:34:35:37:39:42:45:50 SD: 3.9171 cents 26:28:30:32:33:34:36 x 38:41:44:47:52 SD: 3.3363 cents 27:29:31:33:35 x 37:38:40:42:45:49:54 SD: 3.4456 cents 28:30:32:34:36:37:38:39:41:44:47:50:56 SD: 2.9173 cents 30:32:34:37 x 39:41:42:44:47:50:54:60 SD: 2.8873 cents 31:33:35:38:40:41:43 x 46:49:52:56:62 SD: 3.7315 cents 32:34:37:39:41:42:44:45:47:50:54:58:64 SD: 2.5269 cents 35:37:40:43:45:46:48:49:51:55:59:63:70 SD: 2.2966 cents 37:40:42:45 x 48:51:52:54:58:62:67:74 SD: 3.2975 cents 38:41:43:47:49:50:52:53:56:60:64:68:76 SD: 3.0129 cents 39:42:45:48:50:51:54:55:57:61:66:70:78 SD: 2.7291 cents 40:43:46:49:51:52:55:56:59:63:67:72:80 SD: 1.9837 cents 42:45:48:51:54:55:58:59:62:66:71:76:84 SD: 1.9542 cents 45:48:51:55:58:59:62:63:66:71:76:81:90 SD: 1.8224 cents 49:52:56:60:63:64:67:69:72:77:82:88:98 SD: 1.7789 cents 53:57:61:65:68:69:73:74:78:83:89:95:106 SD: 1.7639 cents 54:58:62:66:69:71:74:76:79:85:91:97:108 SD: 1.6648 cents 56:60:64:69:72:73:77:78:82:88:94:101:112 SD: 1.6079 cents 57:61:65:70:73:75:78:80:84:90:96:103:114 SD: 1.5975 cents 62:66:71:76:80:81:85:87:91:97:104:112:124 SD: 1.5132 cents 67:72:77:82:86:88:92:94:98:105:113:121:134 SD: 1.5068 cents 68:73:78:83:87:89:93:95:100:107:114:122:136 SD: 1.3566 cents 70:75:80:86:90:92:96:98:103:110:118:126:140 SD: 0.9522 cents 75:80:86:92:96:98:103:105:110:118:126:135:150 SD: 0.9116 cents 85:91:97:104:109:111:117:119:125:134:143:153:170 SD: 0.7862 cents 98:105:112:120:126:128:135:137:144:154:165:176:196 SD: 0.7443 cents 110:118:126:135:141:144:151:154:162:173:185:198:220 SD: 0.7296 cents 113:121:129:138:145:148:155:158:166:178:190:203:226 SD: 0.7164 cents 117:125:134:143:150:153:161:164:172:184:197:210:234 SD: 0.6363 cents 126:135:144:154:162:165:173:176:185:198:212:227:252 SD: 0.6266 cents 130:139:149:159:167:170:179:182:191:204:219:234:260 SD: 0.5924 cents 145:155:166:177:186:190:199:203:213:228:244:261:290 SD: 0.5178 cents 155:166:177:190:199:203:213:217:228:244:261:279:310 SD: 0.5052 cents 173:185:198:212:222:227:238:242:254:272:291:311:346 SD: 0.4932 cents 175:187:200:214:225:229:240:245:257:275:294:315:350 SD: 0.4775 cents 187:200:214:229:240:245:257:262:275:294:314:336:374 SD: 0.3451 cents 200:214:229:245:257:262:275:280:294:314:336:360:400 SD: 0.3445 cents 229:245:262:280:294:300:315:321:337:360:385:412:458 SD: 0.3355 cents 243:260:278:297:312:318:334:340:357:382:409:437:486 SD: 0.3234 cents 264:282:302:323:339:346:363:370:388:415:444:475:528 SD: 0.2982 cents 285:305:326:349:366:373:392:399:419:448:479:513:570 SD: 0.2482 cents 313:335:358:383:402:410:430:438:460:492:526:563:626 SD: 0.2186 cents 334:357:382:409:429:437:459:468:491:525:562:601:668 SD: 0.2145 cents 362:387:414:443:465:474:497:507:532:569:609:651:724 SD: 0.1836 cents 402:430:460:492:516:526:552:563:591:632:676:723:804 SD: 0.1764 cents 430:460:492:526:552:563:591:602:632:676:723:774:860 SD: 0.1719 cents 472:505:540:578:606:618:649:661:694:742:794:849:944 SD: 0.1641 cents 500:535:572:612:642:655:687:700:735:786:841:900:1000 SD: 0.1470 cents 549:587:628:672:705:719:754:769:807:863:923:988:1098 SD: 0.1320 cents 562:601:643:688:722:736:772:787:826:884:945:1011:1124 SD: 0.1079 cents