Scala analysis: blackbeat15
Blackwood[15] with brats of -1
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 82.837 cents 82.836732 2: 157.163 cents 157.163268 3: 240.000 cents 240.000000 4: 322.837 cents 322.836732 5: 397.163 cents 397.163268 6: 480.000 cents 480.000000 7: 562.837 cents 562.836732 8: 637.163 cents 637.163268 9: 720.000 cents 720.000000 10: 802.837 cents 802.836732 11: 877.163 cents 877.163268 12: 960.000 cents 960.000000 13: 1042.837 cents 1042.836732 14: 1117.163 cents 1117.163268 15: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 82.8367 cents 82.8367 1: 82.8367 cents 82.8367 2: 74.3265 cents 74.3265 3: 82.8367 cents 82.8367 4: 82.8367 cents 82.8367 5: 74.3265 cents 74.3265 6: 82.8367 cents 82.8367 7: 82.8367 cents 82.8367 8: 74.3265 cents 74.3265 9: 82.8367 cents 82.8367 10: 82.8367 cents 82.8367 11: 74.3265 cents 74.3265 12: 82.8367 cents 82.8367 13: 82.8367 cents 82.8367 14: 74.3265 cents 74.3265 15: 82.8367 cents 82.8367
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 74.32654 cents 1: 10 82.83673 cents 2: 10 157.16327 cents 2: 5 165.67346 cents 3: 15 240.00000 cents 4: 5 314.32654 cents 4: 10 322.83673 cents 5: 10 397.16327 cents 5: 5 405.67346 cents 6: 15 480.00000 cents 7: 5 554.32654 cents 7: 10 562.83673 cents 8: 10 637.16327 cents 8: 5 645.67346 cents 9: 15 720.00000 cents 10: 5 794.32654 cents 10: 10 802.83673 cents 11: 10 877.16327 cents 11: 5 885.67346 cents 12: 15 960.00000 cents 13: 5 1034.32654 cents 13: 10 1042.83673 cents 14: 10 1117.16327 cents 14: 5 1125.67346 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.71429 = 12/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0.0 : 82.8 157.2 240.0 322.8 397.2 480.0 562.8 637.2 720.0 802.8 877.2 960.0 1042.8 1117.2 1200.0 82.8 : 74.3 157.2 240.0 314.3 397.2 480.0 554.3 637.2 720.0 794.3 877.2 960.0 1034.3 1117.2 1200.0 157.2 : 82.8 165.7 240.0 322.8 405.7 480.0 562.8 645.7 720.0 802.8 885.7 960.0 1042.8 1125.7 1200.0 240.0 : 82.8 157.2 240.0 322.8 397.2 480.0 562.8 637.2 720.0 802.8 877.2 960.0 1042.8 1117.2 1200.0 322.8 : 74.3 157.2 240.0 314.3 397.2 480.0 554.3 637.2 720.0 794.3 877.2 960.0 1034.3 1117.2 1200.0 397.2 : 82.8 165.7 240.0 322.8 405.7 480.0 562.8 645.7 720.0 802.8 885.7 960.0 1042.8 1125.7 1200.0 480.0 : 82.8 157.2 240.0 322.8 397.2 480.0 562.8 637.2 720.0 802.8 877.2 960.0 1042.8 1117.2 1200.0 562.8 : 74.3 157.2 240.0 314.3 397.2 480.0 554.3 637.2 720.0 794.3 877.2 960.0 1034.3 1117.2 1200.0 637.2 : 82.8 165.7 240.0 322.8 405.7 480.0 562.8 645.7 720.0 802.8 885.7 960.0 1042.8 1125.7 1200.0 720.0 : 82.8 157.2 240.0 322.8 397.2 480.0 562.8 637.2 720.0 802.8 877.2 960.0 1042.8 1117.2 1200.0 802.8 : 74.3 157.2 240.0 314.3 397.2 480.0 554.3 637.2 720.0 794.3 877.2 960.0 1034.3 1117.2 1200.0 877.2 : 82.8 165.7 240.0 322.8 405.7 480.0 562.8 645.7 720.0 802.8 885.7 960.0 1042.8 1125.7 1200.0 960.0 : 82.8 157.2 240.0 322.8 397.2 480.0 562.8 637.2 720.0 802.8 877.2 960.0 1042.8 1117.2 1200.0 1042.8: 74.3 157.2 240.0 314.3 397.2 480.0 554.3 637.2 720.0 794.3 877.2 960.0 1034.3 1117.2 1200.0 1117.2: 82.8 165.7 240.0 322.8 405.7 480.0 562.8 645.7 720.0 802.8 885.7 960.0 1042.8 1125.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 74.3265 .. 82.8367 cents 8.51020 cents 74.32654 cents 2: 157.1633 .. 165.6735 cents 8.51020 cents 74.32654 cents 3: 240.0000 .. 240.0000 cents 1/1, 0.0000 cents 74.32654 cents 4: 314.3265 .. 322.8367 cents 8.51020 cents 74.32654 cents 5: 397.1633 .. 405.6735 cents 8.51020 cents 74.32654 cents 6: 480.0000 .. 480.0000 cents 1/1, 0.0000 cents 74.32654 cents 7: 554.3265 .. 562.8367 cents 8.51020 cents 74.32654 cents 8: 637.1633 .. 645.6735 cents 8.51020 cents 74.32654 cents 9: 720.0000 .. 720.0000 cents 1/1, 0.0000 cents 74.32654 cents 10: 794.3265 .. 802.8367 cents 8.51020 cents 74.32654 cents 11: 877.1633 .. 885.6735 cents 8.51020 cents 74.32654 cents 12: 960.0000 .. 960.0000 cents 1/1, 0.0000 cents 74.32654 cents 13: 1034.3265 .. 1042.8367 cents 8.51020 cents 74.32654 cents 14: 1117.1633 .. 1125.6735 cents 8.51020 cents 74.32654 cents
SHOW DATA
Number of notes : 15 -- Interval properties -- Smallest interval : 74.32654 cents, class 1 Average step (divided formal octave): 80.0000 cents Largest one step interval : 82.83673 cents Average / Smallest step : 1.076332 Largest / Average step : 1.035459 Largest / Smallest step : 1.114497 Median interval of one step : 82.83673 cents, amount: 10 Most common interval of one step : 82.83673 cents, amount: 10 Least squares average step : 79.98856 cents, oct.: 1199.82842 cents Scale is strictly proper Scale has 5 repeating blocks of 3 notes Blocks have Myhill's property chromas: 8.51020 cents and 65.81634 cents, ratio: 7.733822 generators: 1 of 82.83673 cents and 2 of 157.16327 cents ET pair of linear temperament : 130&145 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 565-tone equal temperament with octave 1200.000 cents degrees: 39 74 113 152 187 226 265 300 339 378 413 452 491 526 565 Least number of segments generator : 283 of 601.062 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 378 of 802.832 cents and inv. generated superset size: 455 = 440 more = 3033.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABAABAABAABA Step pattern size order : LSLLSLLSLLSLLSL Scale is a Constant Structure, by a margin of 74.32654 cents Scale diversity : 1.051113 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.929082 Number of different interval sizes : 24 = 1.71429 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.71429 = 12/7 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 8.51020 cents Most common triad is 0.0 240.000 480.000 cents, amount: 15 Number of recognisable fifths : 15, average 720.0000 cents Number of appreciable fifths : 0 Scale contains two identical disjunct heptachords Best minor thirds form a closed circle Formal octave complements present : 15 = 100.0000% Limited transpositions : 3 6 9 12 Limited inverse transpositions : 3 6 9 12 Inversional symmetry on degrees : 0 3 6 9 12 Inversional symmetry on intervals : 1-2 4-5 7-8 10-11 13-14 -- Rational properties --
FIT/MODE
15: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 2.3162 c. M:-2.8367 c. 85: 6 5 6 6 5 6 6 5 6 6 5 6 6 5 6 SP B ME I SD: 1.5262 c. M:-1.8692 c. 100: 7 6 7 7 6 7 7 6 7 7 6 7 7 6 7 SP B ME I SD: 0.9498 c. M:-1.1633 c. Blackwood-15 115: 8 7 8 8 7 8 8 7 8 8 7 8 8 7 8 SP B ME I SD: 0.5238 c. M:-0.6415 c. 130: 9 8 9 9 8 9 9 8 9 9 8 9 9 8 9 SP B ME I SD: 0.1961 c. M:-0.2402 c. 145: 10 9 10 10 9 10 10 9 10 10 9 10 10 9 10 SP B ME I SD: 0.0638 c. M:-0.0781 c. 275: 19 17 19 19 17 19 19 17 19 19 17 19 19 17 19 SP B DE I SD: 0.0591 c. M:-0.0724 c. 420: 29 26 29 29 26 29 29 26 29 29 26 29 29 26 29 SP B DE I SD: 0.0167 c. M:-0.0204 c. 565: 39 35 39 39 35 39 39 35 39 39 35 39 39 35 39 SP B DE I SD: 0.0040 c. M:-0.0049 c. 1550: 107 96 107 107 96 107 107 96 107 107 96 107 107 96 107 SP B DE I SD: 0.0016 c. M:-0.0020 c. 2115: 146 131 146 146 131 146 146 131 146 146 131 146 146 131 146 SP B DE I SD: 0.0001 c. M:-0.0001 c.
FIT/HARMONIC
1 x x 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 x 3 x x x x x 4 S SD: 9.0225 cents 3 x x x x x 4 x x x x 5 x x x 6 S SD: 6.4756 cents 4 x x x x 5 x x x 6 x x 7 x x 8 S SD: 5.7076 cents 5 x x x 6 x x 7 x x 8 x x 9 x 10 S SD: 6.9100 cents 6 x x 7 x x 8 x x 9 x 10 x 11 x 12 S SD: 6.3850 cents 7 x x 8 x 9 x x 10 x 11 x 12:13 x 14 S SD: 8.8895 cents 8 x x 9 x 10 x 11 x 12 x 13:14 x 15:16 S SD: 8.0365 cents 9 x 10 x 11 x 12 x 13 x 14:15:16 x 17:18 S SD: 7.5513 cents 10 x 11 x 12 x 13:14 x 15:16 x 17:18:19:20 S SD: 6.3181 cents 11 x 12 x 13:14 x 15:16:17 x 18:19:20:21:22 S SD: 6.0183 cents 12 x 13:14 x 15:16 x 17:18:19:20:21:22:23:24 S SD: 4.7964 cents 13 x 14:15:16 x 17:18:19:20:21:22:23:24:25:26 S SD: 6.3231 cents 14:15 x 16:17:18 x 19:20:21:22:23:24:26:27:28 S SD: 6.7014 cents 15:16 x 17:18:19:20:21:22:23:24:25:26:27:29:30 SD: 4.9532 cents 16:17 x 18:19:20:21:22:23:24:25:27:28:29:31:32 SD: 5.5051 cents 17:18:19:20 x 21:22:24:25:26:27:28:30:31:32:34 S SD: 6.7377 cents 18:19:20:21:22:23:24:25:26:27:29:30:31:33:34:36 SD: 4.5881 cents 19:20:21:22:23:24:25:26:27:29:30:32:33:35:36:38 SD: 3.7319 cents 20:21:22:23:24:25:26:28:29:30:32:33:35:37:38:40 SD: 3.3201 cents 29:30:32:33:35:36:38:40:42:44:46:48:50:53:55:58 SD: 3.1033 cents 31:33:34:36:37:39:41:43:45:47:49:51:54:57:59:62 SD: 2.8744 cents 34:36:37:39:41:43:45:47:49:52:54:56:59:62:65:68 SD: 2.1199 cents 39:41:43:45:47:49:51:54:56:59:62:65:68:71:74:78 SD: 1.8236 cents 41:43:45:47:49:52:54:57:59:62:65:68:71:75:78:82 SD: 1.7713 cents 47:49:51:54:57:59:62:65:68:71:75:78:82:86:90:94 SD: 1.7114 cents 53:56:58:61:64:67:70:73:77:80:84:88:92:97:101:106 SD: 1.5575 cents 54:57:59:62:65:68:71:75:78:82:86:90:94:99:103:108 SD: 1.2015 cents 62:65:68:71:75:78:82:86:90:94:99:103:108:113:118:124 SD: 1.0673 cents 74:78:81:85:89:93:98:102:107:112:118:123:129:135:141:148 SD: 0.9978 cents 81:85:89:93:98:102:107:112:117:123:129:134:141:148:154:162 SD: 0.8700 cents 85:89:93:98:102:107:112:118:123:129:135:141:148:155:162:170 SD: 0.8500 cents 93:98:102:107:112:117:123:129:134:141:148:154:162:170:177:186 SD: 0.8462 cents 97:102:106:111:117:122:128:134:140:147:154:161:169:177:185:194 SD: 0.6767 cents 117:123:128:134:141:147:154:162:169:177:186:194:204:214:223:234 SD: 0.6410 cents 127:133:139:146:153:160:168:176:184:192:202:211:221:232:242:254 SD: 0.6295 cents 128:134:140:147:154:161:169:177:185:194:204:212:223:234:244:256 SD: 0.5251 cents 146:153:160:168:176:184:193:202:211:221:232:242:254:267:278:292 SD: 0.5147 cents 147:154:161:169:177:185:194:203:212:223:234:244:256:268:280:294 SD: 0.4984 cents 159:167:174:183:192:200:210:220:230:241:253:264:277:290:303:318 SD: 0.4581 cents 166:174:182:191:200:209:219:230:240:252:264:276:289:303:316:332 SD: 0.4534 cents 167:175:183:192:201:210:220:231:241:253:266:277:291:305:318:334 SD: 0.4387 cents 182:191:199:209:219:229:240:252:263:276:289:302:317:332:347:364 SD: 0.3421 cents 200:210:219:230:241:252:264:277:289:303:318:332:348:365:381:400 SD: 0.3159 cents 209:219:229:240:252:263:276:289:302:317:332:347:364:382:398:418 SD: 0.3137 cents 229:240:251:263:276:288:302:317:331:347:364:380:399:418:437:458 SD: 0.2383 cents 263:276:288:302:317:331:347:364:380:399:418:437:458:480:501:526 SD: 0.2372 cents 283:297:310:325:341:356:373:392:409:429:450:470:493:517:540:566 SD: 0.2199 cents 341:358:373:392:411:429:450:472:493:517:542:566:594:623:650:682 SD: 0.2123 cents 364:382:399:418:439:458:480:504:526:552:579:604:634:665:694:728 SD: 0.2119 cents 369:387:404:424:445:464:487:511:533:559:587:612:642:674:704:738 SD: 0.2109 cents 370:388:405:425:446:465:488:512:535:561:588:614:644:676:705:740 SD: 0.1980 cents 388:407:425:446:468:488:512:537:561:588:617:644:676:709:740:776 SD: 0.1953 cents 391:410:428:449:471:492:516:541:565:593:622:649:681:714:745:782 SD: 0.1614 cents 429:450:470:493:517:540:566:594:620:650:682:712:747:784:818:858 SD: 0.1472 cents 473:496:518:543:570:595:624:655:683:717:752:785:824:864:902:946 SD: 0.1444 cents 492:516:539:565:593:619:649:681:711:746:782:817:857:899:938:984 SD: 0.1387 cents 526:552:576:604:634:662:694:728:760:797:836:873:916:961:1003:1052 SD: 0.1223 cents 547:574:599:628:659:688:722:757:790:829:870:908:952:999:1043:1094 SD: 0.1207 cents 570:598:624:655:687:717:752:789:824:864:906:946:992:1041:1087:1140 SD: 0.1098 cents 591:620:647:679:712:743:780:818:854:896:940:981:1029:1079:1127:1182 SD: 0.1062 cents