Scala analysis: alabake
Baked alaska, with brats of 2 and 3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 102.565 cents 102.565223 2: 201.130 cents 201.130054 3: 299.695 cents 299.694886 4: 402.260 cents 402.260110 5: 500.825 cents 500.824942 6: 599.390 cents 599.389774 7: 701.955 cents 701.954998 8: 800.520 cents 800.519830 9: 899.085 cents 899.084662 10: 1001.650 cents 1001.649885 11: 1100.215 cents 1100.214717 12: 1198.780 cents 1198.779549
SHOW/INTERVAL
0: 98.5648 cents 98.5648 1: 102.5652 cents 102.5652 2: 98.5648 cents 98.5648 3: 98.5648 cents 98.5648 4: 102.5652 cents 102.5652 5: 98.5648 cents 98.5648 6: 98.5648 cents 98.5648 7: 102.5652 cents 102.5652 8: 98.5648 cents 98.5648 9: 98.5648 cents 98.5648 10: 102.5652 cents 102.5652 11: 98.5648 cents 98.5648 12: 98.5648 cents 98.5648
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 8 98.56483 cents 1: 4 102.56522 cents 2: 4 197.12966 cents 2: 8 201.13005 cents 3: 12 299.69489 cents 4: 8 398.25972 cents 4: 4 402.26011 cents 5: 4 496.82455 cents 5: 8 500.82494 cents 6: 12 599.38977 cents 7: 8 697.95461 cents 7: 4 701.95500 cents 8: 4 796.51944 cents 8: 8 800.51983 cents 9: 12 899.08466 cents 10: 8 997.64949 cents 10: 4 1001.64989 cents 11: 4 1096.21433 cents 11: 8 1100.21472 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.72727 = 19/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 102.6 201.1 299.7 402.3 500.8 599.4 702.0 800.5 899.1 1001.6 1100.2 1198.8 102.6 : 98.6 197.1 299.7 398.3 496.8 599.4 698.0 796.5 899.1 997.6 1096.2 1198.8 201.1 : 98.6 201.1 299.7 398.3 500.8 599.4 698.0 800.5 899.1 997.6 1100.2 1198.8 299.7 : 102.6 201.1 299.7 402.3 500.8 599.4 702.0 800.5 899.1 1001.6 1100.2 1198.8 402.3 : 98.6 197.1 299.7 398.3 496.8 599.4 698.0 796.5 899.1 997.6 1096.2 1198.8 500.8 : 98.6 201.1 299.7 398.3 500.8 599.4 698.0 800.5 899.1 997.6 1100.2 1198.8 599.4 : 102.6 201.1 299.7 402.3 500.8 599.4 702.0 800.5 899.1 1001.6 1100.2 1198.8 702.0 : 98.6 197.1 299.7 398.3 496.8 599.4 698.0 796.5 899.1 997.6 1096.2 1198.8 800.5 : 98.6 201.1 299.7 398.3 500.8 599.4 698.0 800.5 899.1 997.6 1100.2 1198.8 899.1 : 102.6 201.1 299.7 402.3 500.8 599.4 702.0 800.5 899.1 1001.6 1100.2 1198.8 1001.6: 98.6 197.1 299.7 398.3 496.8 599.4 698.0 796.5 899.1 997.6 1096.2 1198.8 1100.2: 98.6 201.1 299.7 398.3 500.8 599.4 698.0 800.5 899.1 997.6 1100.2 1198.8 1198.8
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 98.5648 .. 102.5652 cents 4.00039 cents 98.56483 cents 2: 197.1297 .. 201.1301 cents 4.00039 cents 94.56444 cents 3: 299.6949 .. 299.6949 cents 1/1, 0.0000 cents 98.56483 cents 4: 398.2597 .. 402.2601 cents 4.00039 cents 98.56483 cents 5: 496.8246 .. 500.8249 cents 4.00039 cents 94.56444 cents 6: 599.3898 .. 599.3898 cents 1/1, 0.0000 cents 98.56483 cents 7: 697.9546 .. 701.9550 cents 4.00039 cents 98.56483 cents 8: 796.5194 .. 800.5198 cents 4.00039 cents 94.56444 cents 9: 899.0847 .. 899.0847 cents 1/1, 0.0000 cents 98.56483 cents 10: 997.6495 .. 1001.6499 cents 4.00039 cents 98.56483 cents 11: 1096.2143 .. 1100.2147 cents 4.00039 cents 94.56444 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 98.56483 cents, class 1 Average step (divided formal octave): 99.8983 cents Largest one step interval : 102.56522 cents Average / Smallest step : 1.013529 Largest / Average step : 1.026696 Largest / Smallest step : 1.040586 Median interval of one step : 98.56483 cents, amount: 8 Most common interval of one step : 98.56483 cents, amount: 8 Least squares average step : 100.04190 cents, oct.: 1200.50279 cents Scale is strictly proper Scale has 4 repeating blocks of 3 notes Blocks have Myhill's property chromas: 4.00039 cents and 94.56444 cents, ratio: 23.638793 generators: 98.56483 cents and 2 of 201.13006 cents ET pair of linear temperament : 292&304 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 900-tone equal temperament with octave 1198.780 cents degrees: 77 151 225 302 376 450 527 601 675 752 826 900 Least number of segments generator : 451 of 600.722 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 601 of 800.518 cents and inv. generated superset size: 678 = 666 more = 5650.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBABBABBABB Step pattern size order : LSSLSSLSSLSS Scale is a Constant Structure, by a margin of 94.56444 cents Scale diversity : 1.022021 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.973304 Rothenberg efficiency (ambiguous key): 0.312963 redundancy: 0.687037 Efficiency x scale size : 3.755556 Number of different interval sizes : 19 = 1.72727 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.72727 = 19/11 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 4.00039 cents Most common triad is 0.0 299.695 599.390 cents, amount: 12 Number of recognisable fifths : 12, average 699.2881 cents Number of recognisable fourths : 12, average 499.4915 cents Scale contains two identical disjunct hexachords Best fifths form a closed circle Formal octave complements present : 4 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 3 6 9 Limited inverse transpositions : 1 4 7 10 Inversional symmetry on degrees : 2 5 8 11 Inversional symmetry on intervals : 0-1 3-4 6-7 9-10 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 1.7215 c. M: 2.6669 c. Twelve-tone Chromatic (1/11-comma) 160: 14 13 13 14 13 13 14 13 13 14 13 13 SP B ME S SD: 1.5027 c. M:-2.3280 c. 172: 15 14 14 15 14 14 15 14 14 15 14 14 SP B ME S SD: 1.2778 c. M:-1.9795 c. 184: 16 15 15 16 15 15 16 15 15 16 15 15 SP B ME S SD: 1.0822 c. M:-1.6765 c. 196: 17 16 16 17 16 16 17 16 16 17 16 16 SP B ME S SD: 0.9105 c. M:-1.4106 c. 208: 18 17 17 18 17 17 18 17 17 18 17 17 SP B ME S SD: 0.7587 c. M:-1.1753 c. 220: 19 18 18 19 18 18 19 18 18 19 18 18 SP B ME S SD: 0.6234 c. M:-0.9657 c. 232: 20 19 19 20 19 19 20 19 19 20 19 19 SP B ME S SD: 0.5021 c. M:-0.7778 c. 244: 21 20 20 21 20 20 21 20 20 21 20 20 SP B ME S SD: 0.3927 c. M:-0.6084 c. 256: 22 21 21 22 21 21 22 21 21 22 21 21 SP B ME S SD: 0.2936 c. M:-0.4549 c. 268: 23 22 22 23 22 22 23 22 22 23 22 22 SP B ME S SD: 0.2034 c. M:-0.3151 c. 280: 24 23 23 24 23 23 24 23 23 24 23 23 SP B ME S SD: 0.1209 c. M:-0.1873 c. 292: 25 24 24 25 24 24 25 24 24 25 24 24 SP B ME S SD: 0.0452 c. M:-0.0700 c. 304: 26 25 25 26 25 25 26 25 25 26 25 25 SP B ME S SD: 0.0245 c. M: 0.0380 c. 596: 51 49 49 51 49 49 51 49 49 51 49 49 SP B DE S SD: 0.0096 c. M:-0.0149 c. 900: 77 74 74 77 74 74 77 74 74 77 74 74 SP B DE S SD: 0.0019 c. M: 0.0030 c. 2396: 205 197 197 205 197 197 205 197 197 205 197 197 SP B DE S SD: 0.0010 c. M:-0.0015 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 1.2205 cents 2 x x x x x x 3 x x x x 4 S SD: 0.6102 cents 3 x x x x 4 x x x 5 x x 6 S SD: 5.0119 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 9.1282 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 6.2234 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 9.9722 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 9.6955 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 9.1815 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.2690 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.0350 cents 11:12 x 13:14:15:16 x 17:18:20:21:22 S SD: 11.0597 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.1997 cents 13:14:15 x 16:17:18:20:21:22:23:25:26 SD: 9.7237 cents 14:15:16:17:18:19:20:21:22:24:25:26:28 S SD: 6.9719 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 4.8605 cents 22:23:25:26:28:29:31:33:35:37:39:42:44 SD: 4.1168 cents 26:28:29:31:33:35:37:39:41:44:46:49:52 SD: 3.4830 cents 27:29:30:32:34:36:38:41:43:45:48:51:54 SD: 3.3686 cents 31:33:35:37:39:41:44:47:49:52:55:59:62 SD: 2.8925 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.2152 cents 42:45:47:50:53:56:59:63:67:71:75:79:84 SD: 2.1538 cents 46:49:52:55:58:61:65:69:73:77:82:87:92 SD: 1.8235 cents 48:51:54:57:61:64:68:72:76:81:86:91:96 SD: 1.6368 cents 54:57:61:64:68:72:76:81:86:91:96:102:108 SD: 1.5934 cents 63:67:71:75:79:84:89:95:100:106:112:119:126 SD: 1.4268 cents 65:69:73:77:82:87:92:98:103:109:116:123:130 SD: 1.1396 cents 80:85:90:95:101:107:113:120:127:134:143:151:160 SD: 0.7590 cents 114:121:128:136:144:152:161:171:181:192:203:215:228 SD: 0.7156 cents 116:123:130:138:146:155:164:174:184:195:207:219:232 SD: 0.5281 cents 148:157:166:176:187:198:209:222:235:249:264:279:296 SD: 0.5074 cents 160:170:180:190:202:214:226:240:254:269:285:302:320 SD: 0.4977 cents 164:174:184:195:207:219:232:246:260:276:292:310:328 SD: 0.4706 cents 179:190:201:213:226:239:253:269:284:301:319:338:358 SD: 0.3807 cents 194:206:218:231:245:259:274:291:308:326:346:366:388 SD: 0.3579 cents 242:257:272:288:305:323:342:363:384:407:432:457:484 SD: 0.3437 cents 244:259:274:290:308:326:345:366:387:410:435:461:488 SD: 0.2709 cents 260:276:292:309:328:347:368:390:413:437:464:491:520 SD: 0.2639 cents 310:329:348:369:391:414:438:465:492:521:553:585:620 SD: 0.2500 cents 348:369:391:414:439:465:492:522:553:585:621:657:696 SD: 0.2292 cents 360:382:404:428:454:481:509:540:572:605:642:680:719 SD: 0.2184 cents 364:386:409:433:459:486:515:546:578:612:649:687:727 SD: 0.2180 cents 382:405:429:454:482:510:540:573:607:642:681:721:763 SD: 0.2093 cents 408:433:458:485:515:545:577:612:648:686:728:770:815 SD: 0.1864 cents 444:471:499:528:560:593:628:666:705:746:792:838:887 SD: 0.1603 cents 486:516:546:578:613:649:687:729:772:817:867:918:971 SD: 0.1549 cents 512:543:575:609:646:684:724:768:813:861:913:967:1023 SD: 0.1440 cents 536:569:602:637:676:716:758:804:851:901:956:1012:1071 SD: 0.1302 cents 554:588:622:659:699:740:783:831:880:931:988:1046:1107 SD: 0.1302 cents 570:605:640:678:719:761:806:855:905:958:1017:1076:1139 SD: 0.1280 cents 592:628:665:704:747:791:837:888:940:995:1056:1118:1183 SD: 0.1040 cents