Scala analysis: 12-of-blackjack
Paul Erlich's 12-tone proper Blackjack subset in 72-EDO
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: 200.000 cents 200.000000 3: 316.667 cents 316.666667 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: 966.667 cents 966.666667 11: 1083.333 cents 1083.333333 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 116.6667 cents 116.6667 1: 116.6667 cents 116.6667 2: 83.3333 cents 83.3333 3: 116.6667 cents 116.6667 4: 66.6667 cents 66.6667 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: 33.3333 cents 33.3333 11: 116.6667 cents 116.6667 12: 116.6667 cents 116.6667
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 33.33333 cents 1: 1 66.66667 cents 1: 2 83.33333 cents 1: 8 116.66667 cents 2: 2 150.00000 cents 2: 2 183.33333 cents 2: 4 200.00000 cents 2: 4 233.33333 cents 3: 5 266.66667 cents 3: 1 300.00000 cents 3: 4 316.66667 cents 3: 2 350.00000 cents 4: 8 383.33333 cents 4: 4 433.33333 cents 5: 3 466.66667 cents 5: 7 500.00000 cents 5: 2 550.00000 cents 6: 6 583.33333 cents 6: 6 616.66667 cents 7: 2 650.00000 cents 7: 7 700.00000 cents 7: 3 733.33333 cents 8: 4 766.66667 cents 8: 8 816.66667 cents 9: 2 850.00000 cents 9: 4 883.33333 cents 9: 1 900.00000 cents 9: 5 933.33333 cents 10: 4 966.66667 cents 10: 4 1000.00000 cents 10: 2 1016.66667 cents 10: 2 1050.00000 cents 11: 8 1083.33333 cents 11: 2 1116.66667 cents 11: 1 1133.33333 cents 11: 1 1166.66667 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.27273 = 36/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 116.7 200.0 316.7 383.3 500.0 583.3 700.0 816.7 933.3 966.7 1083.3 1200.0 116.7 : 83.3 200.0 266.7 383.3 466.7 583.3 700.0 816.7 850.0 966.7 1083.3 1200.0 200.0 : 116.7 183.3 300.0 383.3 500.0 616.7 733.3 766.7 883.3 1000.0 1116.7 1200.0 316.7 : 66.7 183.3 266.7 383.3 500.0 616.7 650.0 766.7 883.3 1000.0 1083.3 1200.0 383.3 : 116.7 200.0 316.7 433.3 550.0 583.3 700.0 816.7 933.3 1016.7 1133.3 1200.0 500.0 : 83.3 200.0 316.7 433.3 466.7 583.3 700.0 816.7 900.0 1016.7 1083.3 1200.0 583.3 : 116.7 233.3 350.0 383.3 500.0 616.7 733.3 816.7 933.3 1000.0 1116.7 1200.0 700.0 : 116.7 233.3 266.7 383.3 500.0 616.7 700.0 816.7 883.3 1000.0 1083.3 1200.0 816.7 : 116.7 150.0 266.7 383.3 500.0 583.3 700.0 766.7 883.3 966.7 1083.3 1200.0 933.3 : 33.3 150.0 266.7 383.3 466.7 583.3 650.0 766.7 850.0 966.7 1083.3 1200.0 966.7 : 116.7 233.3 350.0 433.3 550.0 616.7 733.3 816.7 933.3 1050.0 1166.7 1200.0 1083.3: 116.7 233.3 316.7 433.3 500.0 616.7 700.0 816.7 933.3 1050.0 1083.3 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: 266.6667 .. 350.0000 cents 83.33333 cents 33.33333 cents 4: 383.3333 .. 433.3333 cents 50.00000 cents 33.33333 cents 5: 466.6667 .. 550.0000 cents 83.33333 cents 33.33333 cents 6: 583.3333 .. 616.6667 cents 33.33333 cents 33.33333 cents 7: 650.0000 .. 733.3333 cents 83.33333 cents 33.33333 cents 8: 766.6667 .. 816.6667 cents 50.00000 cents 33.33333 cents 9: 850.0000 .. 933.3333 cents 83.33333 cents 33.33333 cents 10: 966.6667 .. 1050.0000 cents 83.33333 cents 33.33333 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: 8 Most common interval of one step : 116.66667 cents, amount: 8 Least squares average step : 99.71795 cents, oct.: 1196.61538 cents Scale is strictly proper Scale is a mode of a 72-tone equal temperament with octave 2/1 degrees: 7 12 19 23 30 35 42 49 56 58 65 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: 21 = 9 more = 175.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABACABAAADAA Step pattern size order : DCDBDCDDDADD Interval vector is [ 0 1 0 1 2 0 8 0 2 0 2 4 0 4 0 5 0 1 4 0 2 0 8 0 0 4 0 3 0 7 0 0 2 0 6 0 ] Scale is a Constant Structure, by a margin of 33.33333 cents Scale diversity : 1.425686 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.333333 Rothenberg efficiency : 0.395893 redundancy: 0.604107 Efficiency x scale size : 4.750722 Number of different interval sizes : 36 = 3.27273 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.27273 = 36/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 16.66667 cents Number of recognisable fifths : 7, average 700.0000 cents Best fifths form a closed circle Formal octave complements present : 7 = 58.3333% Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 9-10 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 18.0021 c. M:-33.3333 c. Twelve-tone Chromatic (1/11-comma) 18: 2 1 2 1 2 1 2 1 2 1 1 2 P D3 SD: 20.4124 c. M:-33.3333 c. 19: 2 1 2 1 2 1 2 2 2 0 2 2 P D3 SD: 9.9308 c. M: 19.2982 c. 22: 2 2 2 1 2 2 2 2 2 1 2 2 SP B ME SD: 10.2949 c. M:-18.1818 c. Pajara-12 24: 2 2 2 2 2 2 2 2 3 0 3 2 P T3 SD: 13.6083 c. M:-16.6667 c. 26: 3 1 3 1 3 2 2 3 2 1 2 3 N SD: 13.3337 c. M:-21.7949 c. 29: 3 2 3 1 3 2 3 3 3 0 3 3 P SD: 10.0232 c. M:-18.3908 c. 31: 3 2 3 2 3 2 3 3 3 1 3 3 SP D3 SD: 3.7313 c. M: 6.9892 c. Marvel-12 41: 4 3 4 2 4 3 4 4 4 1 4 4 SP SD: 2.8212 c. M:-5.2846 c. Marvel-12 72: 7 5 7 4 7 5 7 7 7 2 7 7 SP SD: 0.0000 c. M:-0.0000 c. Marvel-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 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 x 7 x 8 S SD: 1.0418 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 10.2067 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 12.9527 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 11.1755 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 5.0796 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 11.3060 cents 10 x 11:12 x 13:14:15:16:17 x 19:20 SD: 7.3096 cents 11:12 x 13:14:15 x 16:18:19 x 21:22 SD: 11.0197 cents 12:13 x 14:15:16:17:18:19 x 21:22:24 SD: 7.0477 cents 13:14:15 x 16:17:18:19:21:22:23:24:26 SD: 8.1892 cents 14:15:16:17 x 19:20:21:22:24 x 26:28 SD: 6.8227 cents 15:16:17:18:19:20:21:22:24 x 26:28:30 S SD: 4.6080 cents 18:19:20:22 x 24:25:27:29:31 x 34:36 SD: 4.9632 cents 19:20:21:23:24:25:27:28:30 x 33:36:38 SD: 6.7578 cents 20:21:22:24:25:27:28:30:32:34:35:37:40 SD: 4.7306 cents 22:24:25:26:27:29:31:33:35:38 x 41:44 SD: 5.8469 cents 23:25:26:28:29:31:32:34:37:39:40:43:46 SD: 4.7513 cents 24:26:27:29:30:32:34:36:38:41:42:45:48 SD: 3.2616 cents 25:27:28:30:31:33:35:37:40:43:44:47:50 SD: 3.2416 cents 26:28:29:31:32:35:36:39:42:45 x 49:52 SD: 4.2933 cents 27:29:30:32:34:36:38:40:43:46:47:50:54 SD: 3.8505 cents 28:30:31:34:35:37:39:42:45:48:49:52:56 SD: 3.2562 cents 30:32:34:36:37:40:42:45:48:51:52:56:60 SD: 2.8414 cents 32:34:36:38:40:43:45:48:51:55:56:60:64 SD: 2.4364 cents 40:43:45:48:50:53:56:60:64:69:70:75:80 SD: 1.7008 cents 48:51:54:58:60:64:67:72:77:82:84:90:96 SD: 1.6559 cents 55:59:62:66:69:73:77:82:88:94:96:103:110 SD: 1.6428 cents 56:60:63:67:70:75:78:84:90:96:98:105:112 SD: 1.3233 cents 60:64:67:72:75:80:84:90:96:103:105:112:120 SD: 1.0172 cents 84:90:94:101:105:112:118:126:135:144:147:157:168 SD: 0.8773 cents 90:96:101:108:112:120:126:135:144:154:157:168:180 SD: 0.8151 cents 98:105:110:118:122:131:137:147:157:168:171:183:196 SD: 0.7581 cents 113:121:127:136:141:151:158:169:181:194:198:211:226 SD: 0.7341 cents 114:122:128:137:142:152:160:171:183:195:199:213:228 SD: 0.6571 cents 129:138:145:155:161:172:181:193:207:221:225:241:258 SD: 0.5734 cents 130:139:146:156:162:174:182:195:208:223:227:243:260 SD: 0.5724 cents 140:150:157:168:175:187:196:210:224:240:245:262:280 SD: 0.5415 cents 154:165:173:185:192:206:216:231:247:264:269:288:308 SD: 0.5170 cents 155:166:174:186:193:207:217:232:248:266:271:290:310 SD: 0.5074 cents 170:182:191:204:212:227:238:255:272:291:297:318:340 SD: 0.4532 cents 174:186:195:209:217:232:244:261:279:298:304:325:348 SD: 0.4526 cents 185:198:208:222:231:247:259:277:297:317:323:346:370 SD: 0.4283 cents 189:202:212:227:236:252:265:283:303:324:330:353:378 SD: 0.3735 cents 214:229:240:257:267:286:300:321:343:367:374:400:428 SD: 0.3076 cents 229:245:257:275:286:306:321:343:367:393:400:428:458 SD: 0.2911 cents 230:246:258:276:287:307:322:345:369:394:402:430:460 SD: 0.2880 cents 245:262:275:294:306:327:343:367:393:420:428:458:490 SD: 0.2292 cents 319:341:358:383:398:426:447:478:511:547:558:596:638 SD: 0.2229 cents 343:367:385:412:428:458:480:514:550:588:600:641:686 SD: 0.2168 cents 344:368:386:413:429:459:482:515:551:590:601:643:688 SD: 0.2144 cents 359:384:403:431:448:479:503:538:575:616:627:671:718 SD: 0.2105 cents 375:401:421:450:468:501:525:562:601:643:655:701:750 SD: 0.2061 cents 385:412:432:462:480:514:539:577:617:660:673:720:770 SD: 0.1947 cents 400:428:449:480:499:534:560:599:641:686:699:748:800 SD: 0.1589 cents 459:491:515:551:573:613:643:688:736:787:802:858:918 SD: 0.1565 cents 484:518:543:581:604:646:678:725:776:830:846:905:968 SD: 0.1317 cents 504:539:566:605:629:673:706:755:808:864:881:942:1008 SD: 0.1265 cents 532:569:597:639:664:710:745:797:853:912:930:995:1064 SD: 0.1173 cents 574:614:644:689:716:766:804:860:920:984:1003:1073:1148 SD: 0.1127 cents