Scala analysis: met24-buzurg_al-erin10_Cup
Decatonic with septimal Buzurg & Rastlike modes
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 126.563 cents 126.562500 2: 232.031 cents 232.031250 3: 357.422 cents 357.421870 4: 496.875 cents 496.875000 5: 622.266 cents 622.265620 6: 704.297 cents 704.296870 7: 829.687 cents 829.687500 8: 935.156 cents 935.156250 9: 1061.719 cents 1061.718750 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 138.2813 cents 138.2813 1: 126.5625 cents 126.5625 2: 105.4687 cents 105.4687 3: 125.3906 cents 125.3906 4: 139.4531 cents 139.4531 5: 125.3906 cents 125.3906 6: 82.0312 cents 82.0312 7: 125.3906 cents 125.3906 8: 105.4687 cents 105.4687 9: 126.5625 cents 126.5625 10: 138.2813 cents 138.2813
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 82.03125 cents 1: 2 105.46875 cents 1: 3 125.39062 cents 1: 2 126.56250 cents 1: 1 138.28125 cents 1: 1 139.45313 cents 2: 2 207.42187 cents 2: 2 230.85937 cents 2: 2 232.03125 cents 2: 4 264.84375 cents 3: 1 312.89063 cents 3: 1 332.81250 cents 3: 1 346.87500 cents 3: 2 357.42187 cents 3: 3 370.31250 cents 3: 1 390.23437 cents 3: 1 391.40625 cents 4: 1 438.28125 cents 4: 1 439.45313 cents 4: 2 472.26562 cents 4: 3 495.70312 cents 4: 3 496.87500 cents 5: 1 564.84375 cents 5: 3 577.73437 cents 5: 1 597.65625 cents 5: 1 602.34375 cents 5: 3 622.26562 cents 5: 1 635.15625 cents 6: 3 703.12500 cents 6: 3 704.29687 cents 6: 2 727.73438 cents 6: 1 760.54687 cents 6: 1 761.71875 cents 7: 1 808.59375 cents 7: 1 809.76563 cents 7: 3 829.68750 cents 7: 2 842.57813 cents 7: 1 853.12500 cents 7: 1 867.18750 cents 7: 1 887.10937 cents 8: 4 935.15625 cents 8: 2 967.96875 cents 8: 2 969.14063 cents 8: 2 992.57813 cents 9: 1 1060.54687 cents 9: 1 1061.71875 cents 9: 2 1073.43750 cents 9: 3 1074.60938 cents 9: 2 1094.53125 cents 9: 1 1117.96875 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 5.55556 = 50/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 126.6 232.0 357.4 496.9 622.3 704.3 829.7 935.2 1061.7 1200.0 126.6 : 105.5 230.9 370.3 495.7 577.7 703.1 808.6 935.2 1073.4 1200.0 232.0 : 125.4 264.8 390.2 472.3 597.7 703.1 829.7 968.0 1094.5 1200.0 357.4 : 139.5 264.8 346.9 472.3 577.7 704.3 842.6 969.1 1074.6 1200.0 496.9 : 125.4 207.4 332.8 438.3 564.8 703.1 829.7 935.2 1060.5 1200.0 622.3 : 82.0 207.4 312.9 439.5 577.7 704.3 809.8 935.2 1074.6 1200.0 704.3 : 125.4 230.9 357.4 495.7 622.3 727.7 853.1 992.6 1118.0 1200.0 829.7 : 105.5 232.0 370.3 496.9 602.3 727.7 867.2 992.6 1074.6 1200.0 935.2 : 126.6 264.8 391.4 496.9 622.3 761.7 887.1 969.1 1094.5 1200.0 1061.7: 138.3 264.8 370.3 495.7 635.2 760.5 842.6 968.0 1073.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 82.0312 .. 139.4531 cents 57.42188 cents 82.03125 cents 2: 207.4219 .. 264.8438 cents 57.42188 cents 67.96874 cents 3: 312.8906 .. 391.4063 cents 78.51562 cents 48.04688 cents 4: 438.2813 .. 496.8750 cents 58.59375 cents 46.87500 cents 5: 564.8437 .. 635.1563 cents 70.31250 cents 67.96875 cents 6: 703.1250 .. 761.7188 cents 58.59375 cents 67.96875 cents 7: 808.5937 .. 887.1094 cents 78.51562 cents 46.87500 cents 8: 935.1562 .. 992.5781 cents 57.42188 cents 48.04688 cents 9: 1060.5469 .. 1117.9688 cents 57.42188 cents 67.96874 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 82.03125 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 139.45313 cents Average / Smallest step : 1.462857 Largest / Average step : 1.162109 Largest / Smallest step : 1.700000 Median interval of one step : 125.39062 cents, amount: 3 Most common interval of one step : 125.39062 cents, amount: 3 Least squares average step : 119.04424 cents, oct.: 1190.44237 cents Scale is strictly proper Scale is a mode of a 1024-tone equal temperament with octave 2/1 degrees: 108 198 305 424 531 601 708 798 906 1024 Least number of segments generator : 513 of 601.172 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 663 of 776.953 cents and inv. generated superset size: 290 = 280 more = 2900.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDCECBAF Step pattern size order : DBCFCACBDE Scale is a Constant Structure, by a margin of 46.87500 cents Scale diversity : 1.431455 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.521484 Rothenberg efficiency : 0.289286 redundancy: 0.710714 Efficiency x scale size : 2.892857 Number of different interval sizes : 50 = 5.55556 / class Number of one step interval sizes : 6 Highest interval variety : 7 Mean interval variety : 5.55556 = 50/9 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 1.17187 cents Most common intervals : 264.84375 cents & inv., amount: 4 Most common triad is 0.0 577.734 935.156 cents, amount: 2 Number of recognisable fifths : 6, average 703.7109 cents Formal octave complements present : 1 = 10.0000% -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
10: 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 14.8260 c. M:-24.8438 c. 17: 2 1 2 2 2 1 2 1 2 2 P D3 SD: 12.0040 c. M: 20.2665 c. 19: 2 2 2 2 2 1 2 2 2 2 SP M ME SD: 12.2603 c. M:-21.5255 c. 26: 3 2 3 3 2 2 3 2 3 3 P D3 SD: 10.8915 c. M: 22.2656 c. 27: 3 2 3 3 3 2 3 2 3 3 SP D3 SD: 7.0805 c. M:-14.7569 c. 36: 4 3 4 4 4 2 4 3 4 4 SP SD: 5.6993 c. M:-11.0677 c. 41: 4 4 4 5 4 3 4 4 4 5 SP SD: 6.0473 c. M: 10.1753 c. 46: 5 4 5 5 5 3 5 4 5 5 SP SD: 4.5028 c. M:-7.8465 c. 58: 6 5 6 7 6 4 6 5 6 7 SP SD: 3.5450 c. M: 6.5463 c. 67: 7 6 7 8 7 4 7 6 7 8 SP SD: 3.8982 c. M: 5.8069 c. 68: 7 6 7 8 7 5 7 6 7 8 SP SD: 2.7580 c. M: 4.6186 c. 77: 8 7 8 9 8 5 8 7 8 9 SP SD: 1.9719 c. M: 3.7135 c. 87: 9 8 9 10 9 6 9 8 9 10 SP SD: 1.6992 c. M:-2.7748 c. 104: 11 9 11 12 11 7 11 9 11 12 SP SD: 0.6836 c. M: 1.2620 c. 191: 20 17 20 22 20 13 20 17 20 22 SP SD: 0.5776 c. M:-0.9694 c. 285: 30 25 30 33 30 19 30 25 30 33 SP SD: 0.5700 c. M: 1.1390 c. 295: 31 26 31 34 31 20 31 26 31 34 SP SD: 0.3804 c. M: 0.6038 c. 538: 57 47 56 63 56 37 56 47 57 62 SP SD: 0.3920 c. M: 0.5838 c. 544: 57 48 57 63 57 37 57 48 57 63 SP SD: 0.4650 c. M: 0.8272 c. 548: 58 48 57 64 57 38 57 48 58 63 SP SD: 0.3818 c. M:-0.8126 c. 567: 60 50 59 66 59 39 59 50 60 65 SP SD: 0.4344 c. M:-0.7730 c. 580: 61 51 61 67 61 39 61 51 61 67 SP SD: 0.4079 c. M: 0.8486 c. 615: 65 54 64 72 64 42 64 54 65 71 SP SD: 0.3525 c. M:-0.6860 c. 625: 66 55 65 73 65 43 65 55 66 72 SP SD: 0.2433 c. M:-0.4050 c. 729: 77 64 76 85 76 50 76 64 77 84 SP SD: 0.1539 c. M:-0.2443 c. 833: 88 73 87 97 87 57 87 73 88 96 SP SD: 0.1324 c. M: 0.2223 c. 920: 97 81 96 107 96 63 96 81 97 106 SP SD: 0.0773 c. M:-0.1427 c. 1024: 108 90 107 119 107 70 107 90 108 118 SP SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x x 4 S SD: 1.1709 cents 3 x x x 4 x x x 5 x 6 S SD: 16.9370 cents 4 x x 5 x x 6 x 7 x 8 S SD: 11.1071 cents 5 x x 6 x 7 x 8 x 9:10 S SD: 14.8712 cents 6 x 7 x 8 x 9 x 10:11:12 S SD: 10.4798 cents 7 x 8 x 9:10 x 11:12:13:14 S SD: 11.2239 cents 8 x 9:10:11 x 12:13:14:15:16 S SD: 10.1174 cents 9 x 10:11:12:13:14 x 15:17:18 SD: 12.8526 cents 10:11 x 12:13:14:15:16:17:18:20 S SD: 10.6021 cents 12:13:14:15:16:17:18:19:21:22:24 SD: 7.0866 cents 13:14:15:16:17:19:20:21:22:24:26 SD: 6.9482 cents 14:15:16:17:19:20:21:23:24:26:28 SD: 5.0345 cents 21:23:24:26:28:30:32:34:36:39:42 SD: 4.3343 cents 26:28:30:32:35:37:39:42:45:48:52 SD: 3.0282 cents 28:30:32:34:37:40:42:45:48:52:56 SD: 3.0195 cents 34:37:39:42:45:49:51:55:58:63:68 SD: 2.9993 cents 36:39:41:44:48:52:54:58:62:66:72 SD: 2.6630 cents 39:42:45:48:52:56:59:63:67:72:78 SD: 2.0707 cents 42:45:48:52:56:60:63:68:72:78:84 SD: 1.8892 cents 54:58:62:66:72:77:81:87:93:100:108 SD: 1.7529 cents 56:60:64:69:75:80:84:90:96:103:112 SD: 1.7111 cents 57:61:65:70:76:82:86:92:98:105:114 SD: 1.5820 cents 64:69:73:79:85:92:96:103:110:118:128 SD: 1.4225 cents 70:75:80:86:93:100:105:113:120:129:140 SD: 1.1046 cents 78:84:89:96:104:112:117:126:134:144:156 SD: 0.6862 cents 117:126:134:144:156:168:176:189:201:216:234 SD: 0.6567 cents 130:140:149:160:173:186:195:210:223:240:260 SD: 0.6337 cents 132:142:151:162:176:189:198:213:227:244:264 SD: 0.5790 cents 145:156:166:178:193:208:218:234:249:268:290 SD: 0.5208 cents 148:159:169:182:197:212:222:239:254:273:296 SD: 0.4835 cents 169:182:193:208:225:242:254:273:290:312:338 SD: 0.3981 cents 187:201:214:230:249:268:281:302:321:345:374 SD: 0.3169 cents 265:285:303:326:353:380:398:428:455:489:530 SD: 0.2634 cents 301:324:344:370:401:431:452:486:517:556:602 SD: 0.2162 cents 370:398:423:455:493:530:556:597:635:683:740 SD: 0.1850 cents 384:413:439:472:512:550:577:620:659:709:768 SD: 0.1549 cents 476:512:544:585:634:682:715:769:817:879:952 SD: 0.1470 cents 488:525:558:600:650:699:733:788:838:901:976 SD: 0.1169 cents 592:637:677:728:789:848:889:956:1016:1093:1184 SD: 0.0933 cents