Scala analysis: 13-31-mean
13 out of 31 scale, a meantone analogue of Blackjack
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 154.839 cents 154.838710 2: 193.548 cents 193.548387 3: 348.387 cents 348.387097 4: 387.097 cents 387.096774 5: 541.935 cents 541.935484 6: 580.645 cents 580.645161 7: 735.484 cents 735.483871 8: 774.194 cents 774.193548 9: 929.032 cents 929.032258 10: 967.742 cents 967.741935 11: 1122.581 cents 1122.580645 12: 1161.290 cents 1161.290323 13: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 38.7097 cents 38.7097 1: 154.8387 cents 154.8387 2: 38.7097 cents 38.7097 3: 154.8387 cents 154.8387 4: 38.7097 cents 38.7097 5: 154.8387 cents 154.8387 6: 38.7097 cents 38.7097 7: 154.8387 cents 154.8387 8: 38.7097 cents 38.7097 9: 154.8387 cents 154.8387 10: 38.7097 cents 38.7097 11: 154.8387 cents 154.8387 12: 38.7097 cents 38.7097 13: 38.7097 cents 38.7097
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 38.70968 cents 1: 6 154.83871 cents 2: 1 77.41936 cents 2: 12 193.54839 cents 3: 8 232.25806 cents 3: 5 348.38710 cents 4: 2 270.96774 cents 4: 11 387.09677 cents 5: 9 425.80645 cents 5: 4 541.93548 cents 6: 3 464.51613 cents 6: 10 580.64516 cents 7: 10 619.35484 cents 7: 3 735.48387 cents 8: 4 658.06452 cents 8: 9 774.19355 cents 9: 11 812.90323 cents 9: 2 929.03226 cents 10: 5 851.61290 cents 10: 8 967.74194 cents 11: 12 1006.45161 cents 11: 1 1122.58065 cents 12: 6 1045.16129 cents 12: 7 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 : 154.8 193.5 348.4 387.1 541.9 580.6 735.5 774.2 929.0 967.7 1122.6 1161.3 1200.0 154.8 : 38.7 193.5 232.3 387.1 425.8 580.6 619.4 774.2 812.9 967.7 1006.5 1045.2 1200.0 193.5 : 154.8 193.5 348.4 387.1 541.9 580.6 735.5 774.2 929.0 967.7 1006.5 1161.3 1200.0 348.4 : 38.7 193.5 232.3 387.1 425.8 580.6 619.4 774.2 812.9 851.6 1006.5 1045.2 1200.0 387.1 : 154.8 193.5 348.4 387.1 541.9 580.6 735.5 774.2 812.9 967.7 1006.5 1161.3 1200.0 541.9 : 38.7 193.5 232.3 387.1 425.8 580.6 619.4 658.1 812.9 851.6 1006.5 1045.2 1200.0 580.6 : 154.8 193.5 348.4 387.1 541.9 580.6 619.4 774.2 812.9 967.7 1006.5 1161.3 1200.0 735.5 : 38.7 193.5 232.3 387.1 425.8 464.5 619.4 658.1 812.9 851.6 1006.5 1045.2 1200.0 774.2 : 154.8 193.5 348.4 387.1 425.8 580.6 619.4 774.2 812.9 967.7 1006.5 1161.3 1200.0 929.0 : 38.7 193.5 232.3 271.0 425.8 464.5 619.4 658.1 812.9 851.6 1006.5 1045.2 1200.0 967.7 : 154.8 193.5 232.3 387.1 425.8 580.6 619.4 774.2 812.9 967.7 1006.5 1161.3 1200.0 1122.6: 38.7 77.4 232.3 271.0 425.8 464.5 619.4 658.1 812.9 851.6 1006.5 1045.2 1200.0 1161.3: 38.7 193.5 232.3 387.1 425.8 580.6 619.4 774.2 812.9 967.7 1006.5 1161.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.7097 .. 154.8387 cents 116.12903 cents 38.70968 cents 2: 77.4194 .. 193.5484 cents 116.12903 cents -77.41935 cents 3: 232.2581 .. 348.3871 cents 116.12903 cents 38.70968 cents 4: 270.9677 .. 387.0968 cents 116.12903 cents -77.41935 cents 5: 425.8065 .. 541.9355 cents 116.12903 cents 38.70968 cents 6: 464.5161 .. 580.6452 cents 116.12903 cents -77.41935 cents 7: 619.3548 .. 735.4839 cents 116.12903 cents 38.70968 cents 8: 658.0645 .. 774.1935 cents 116.12903 cents -77.41935 cents 9: 812.9032 .. 929.0323 cents 116.12903 cents 38.70968 cents 10: 851.6129 .. 967.7419 cents 116.12903 cents -77.41935 cents 11: 1006.4516 .. 1122.5806 cents 116.12903 cents 38.70968 cents 12: 1045.1613 .. 1161.2903 cents 116.12903 cents -77.41935 cents
SHOW DATA
Number of notes : 13 -- Interval properties -- Smallest interval : 38.70968 cents, class 1 Average step (divided formal octave): 92.3077 cents Largest one step interval : 154.83871 cents Average / Smallest step : 2.384615 Largest / Average step : 1.677419 Largest / Smallest step : 4.000000 Median interval of one step : 38.70968 cents, amount: 7 Most common interval of one step : 38.70968 cents, amount: 7 Least squares average step : 98.40482 cents, oct.: 1279.26267 cents Scale is not proper Scale has Myhill's property chromas: 116.12903 cents and 77.41935 cents, ratio: 1.500000 generators: 2 of 193.54839 cents and 1006.45161 cents ET pair of linear temperament : 31&31 Scale is distributional even Scale is a mode of a 31-tone equal temperament with octave 2/1 degrees: 4 5 9 10 14 15 19 20 24 25 29 30 31 generators: 5 and 26 Number of contiguous 1-step segments: 6 Step pattern alph. order: ABABABABABABB Step pattern size order : LSLSLSLSLSLSS Interval vector is [ 7 1 0 6 12 8 2 0 5 11 9 3 0 4 10 ] Scale is a Constant Structure, by a margin of 38.70968 cents Scale diversity : 1.211242 Lumma stability : 0.225806 Lumma impropriety factor : 0.387097 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 : 38.70968 cents Most common intervals : 193.54839 cents & inv., amount: 12 Scale is a chain of 6 triads 0.0 193.548 387.097 cents Most common triad is 0.0 193.548 1006.452 cents, amount: 11 Number of recognisable fifths : 0 Scale contains two identical disjunct hexachords Formal octave complements present : 1 = 7.6923% Limited inverse transpositions : 11 Inversional symmetry on degrees : 12 Inversional symmetry on intervals : 5-6 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
13: 2 0 2 0 2 0 2 0 2 0 2 1 0 N T3 SD: 24.2048 c. M: 44.6650 c. 14: 2 0 2 1 1 1 2 0 2 0 2 1 0 N T3 SD: 23.7481 c. M:-41.4747 c. 15: 2 0 2 1 2 0 2 1 2 0 2 1 0 N SD: 22.0258 c. M:-38.7097 c. 16: 2 1 2 0 2 1 2 0 2 1 2 0 1 N T3 SD: 20.6492 c. M: 36.2903 c. 17: 2 1 2 0 3 0 2 1 2 1 2 0 1 N SD: 19.5573 c. M: 34.1556 c. 18: 2 1 2 1 2 1 2 1 2 1 2 0 1 N T3 SD: 17.4812 c. M:-32.2581 c. 19: 2 1 3 0 3 0 3 0 3 0 3 0 1 N SD: 19.6150 c. M:-30.5603 c. 21: 3 0 3 1 2 1 3 1 2 1 3 0 1 N SD: 16.4395 c. M: 27.6498 c. 22: 3 1 2 1 3 1 3 0 3 1 3 0 1 N SD: 16.2294 c. M:-28.1525 c. 23: 3 1 3 0 3 1 3 1 3 1 3 0 1 N SD: 15.2405 c. M:-25.2454 c. 25: 3 1 3 1 3 1 3 1 3 1 3 1 1 N M DE S SD: 10.9488 c. M: 18.5806 c. Hemithirds-13, Spell-13 31: 4 1 4 1 4 1 4 1 4 1 4 1 1 N M DE S SD: 0.0000 c. M: 0.0000 c. Hemithirds-13, Roulette-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 3 x x x x x 4 S SD: 16.7644 cents 3 x x x x 4 x x x 5 x x x 6 S SD: 20.8756 cents 4 x x x 5 x x 6 x x 7 x x 8 S SD: 8.3889 cents 5 x x 6 x x 7 x 8 x 9 x x 10 S SD: 14.3121 cents 6 x 7 x x 8 x 9 x 10 x 11 x 12 S SD: 20.9386 cents 7 x 8 x 9 x 10 x 11:12 x 13 x 14 S SD: 12.5764 cents 8 x 9 x 10:11 x 12:13 x 14:15 x 16 S SD: 10.3824 cents 9 x 10:11 x 12:13 x 14:15:16:17 x 18 S SD: 10.2642 cents 10:11 x 12:13 x 14:15:16:17 x 19 x 20 SD: 10.3071 cents 11:12 x 13:14:15 x 17 x 19 x 21 x 22 SD: 8.9295 cents 12:13 x x 15:16:17:18:19 x 21:23 x 24 SD: 7.2751 cents 13:14:15:16 x x 18:20 x 22:23:25 x 26 SD: 7.8503 cents 14:15:16:17:18:19:20:21:22:24 x 27 x 28 S SD: 8.1684 cents 15:16:17:18:19 x 21:23 x x 26:29 x 30 SD: 7.5120 cents 16 x 18 x 20:22 x 24:25:27:28 x 31:32 SD: 5.1217 cents 17 x 19:21 x 23:24:26:27:29:30 x 33:34 SD: 4.5421 cents 18 x 20:22:23 x 25 x 28:31 x 34:35:36 SD: 5.5038 cents 19:21 x 23:24:26:27:29:30:32:33:36:37:38 SD: 4.6932 cents 20:22 x 24:25:27:28 x 31:34:35:38:39:40 SD: 4.2495 cents 21:23 x x 26:29 x 32:33:36:37:40:41:42 SD: 3.0665 cents 22:24:25:27:28:30:31:34 x 38 x 42:43:44 SD: 4.6193 cents 23:25:26:28:29:31:32:35:36:39:40:44:45:46 SD: 3.2882 cents 25:27:28 x 31:34:35:38:39:43:44:48:49:50 SD: 2.8781 cents 26:28:29:32:33 x 36:40:41:44:45:50:51:52 SD: 4.4800 cents 27 x 30:33:34:37:38:41:42:46:47:52:53:54 SD: 2.5487 cents 28 x 31:34:35:38:39:43:44:48:49:54:55:56 SD: 2.7388 cents 29:32 x 35:36:40:41:44:45:50:51:55:57:58 SD: 4.1220 cents 30:33:34:37:38:41:42:46:47:51:52:57:59:60 SD: 3.3961 cents 31:34:35:38:39:42:43:47:48:53:54:59:61:62 SD: 3.1162 cents 32:35:36:39:40:44:45:49:50:55:56:61:63:64 SD: 1.8340 cents 38:42 x 46:48:52:53:58:59:65:66:73:74:76 SD: 3.1195 cents 39:43:44:48:49:53:55:60:61:67:68:75:76:78 SD: 2.7491 cents 40:44:45:49:50:55:56:61:63:68:70:77:78:80 SD: 2.1026 cents 41:45:46:50:51:56:57:63:64:70:72:78:80:82 SD: 1.7668 cents 44:48:49:54:55:60:62:67:69:75:77:84:86:88 SD: 1.5910 cents 55:60:62:67:69:75:77:84:86:94:96:105:108:110 SD: 1.5187 cents 60:66:67:73:75:82:84:92:94:103:105:115:117:120 SD: 1.3478 cents 66:72:74:81:83:90:92:101:103:113:115:126:129:132 SD: 1.3255 cents 67:73:75:82:84:92:94:102:105:115:117:128:131:134 SD: 1.2626 cents 68:74:76:83:85:93:95:104:106:116:119:130:133:136 SD: 0.9102 cents 76:83:85:93:95:104:106:116:119:130:133:145:149:152 SD: 0.6988 cents 108:118:121:132:135:148:151:165:169:185:189:207:211:216 SD: 0.5822 cents 117:128:131:143:146:160:164:179:183:200:205:224:229:234 SD: 0.5560 cents 128:140:143:157:160:175:179:196:200:219:224:245:250:256 SD: 0.5258 cents 136:149:152:166:170:186:190:208:213:233:238:260:266:272 SD: 0.5047 cents 160:175:179:196:200:219:224:245:250:274:280:306:313:320 SD: 0.4171 cents 179:196:200:219:224:245:250:274:280:306:313:342:350:358 SD: 0.3684 cents 183:200:205:224:229:250:256:280:286:313:320:350:358:366 SD: 0.3425 cents 204:223:228:249:255:279:285:312:319:349:357:390:399:408 SD: 0.3271 cents 228:249:255:279:285:312:319:349:357:390:399:436:446:456 SD: 0.3176 cents 247:270:276:302:309:338:345:378:386:422:432:472:483:494 SD: 0.3159 cents 248:271:277:303:310:339:347:379:388:424:434:474:485:496 SD: 0.3025 cents 255:279:285:312:319:349:357:390:399:436:446:488:499:510 SD: 0.2574 cents 287:314:321:351:359:392:401:439:449:491:502:549:561:574 SD: 0.2435 cents 296:324:331:362:370:405:414:453:463:506:518:566:579:592 SD: 0.2122 cents 319:349:357:390:399:436:446:488:499:546:558:610:624:638 SD: 0.1944 cents 331:362:370:405:414:453:463:506:518:566:579:633:647:662 SD: 0.1917 cents 363:397:406:444:454:496:508:555:568:621:635:694:710:726 SD: 0.1842 cents 387:423:433:473:484:529:541:592:605:662:677:740:757:774 SD: 0.1684 cents 431:471:482:527:539:589:603:659:674:737:754:824:843:862 SD: 0.1621 cents 449:491:502:549:562:614:628:687:702:768:785:859:878:898 SD: 0.1597 cents 459:502:513:561:574:628:642:702:718:785:803:878:898:918 SD: 0.1447 cents 490:536:548:599:613:670:685:749:766:838:857:937:958:980 SD: 0.1398 cents 514:562:575:629:643:703:719:786:804:879:899:983:1005:1028 SD: 0.1264 cents 525:574:587:642:657:718:734:803:821:898:918:1004:1027:1050 SD: 0.1160 cents