Scala analysis: met24-alternative12_Cup
Buzurg al-Erin 10 plus approx 13/11, 39/22
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: 289.453 cents 289.453120 4: 357.422 cents 357.421870 5: 496.875 cents 496.875000 6: 622.266 cents 622.265620 7: 704.297 cents 704.296870 8: 829.687 cents 829.687500 9: 935.156 cents 935.156250 10: 992.578 cents 992.578120 11: 1061.719 cents 1061.718750 12: 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: 57.4219 cents 57.4219 4: 67.9687 cents 67.9687 5: 139.4531 cents 139.4531 6: 125.3906 cents 125.3906 7: 82.0312 cents 82.0312 8: 125.3906 cents 125.3906 9: 105.4687 cents 105.4687 10: 57.4219 cents 57.4219 11: 69.1406 cents 69.1406 12: 138.2813 cents 138.2813
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 57.42187 cents 1: 1 67.96875 cents 1: 1 69.14063 cents 1: 1 82.03125 cents 1: 2 105.46875 cents 1: 2 125.39062 cents 1: 1 126.56250 cents 1: 1 138.28125 cents 1: 1 139.45313 cents 2: 1 125.39062 cents 2: 1 126.56250 cents 2: 2 162.89062 cents 2: 4 207.42188 cents 2: 1 230.85938 cents 2: 1 232.03125 cents 2: 2 264.84375 cents 3: 1 230.85937 cents 3: 1 232.03125 cents 3: 2 264.84375 cents 3: 1 288.28125 cents 3: 1 289.45312 cents 3: 1 312.89063 cents 3: 2 332.81250 cents 3: 1 333.98438 cents 3: 1 346.87500 cents 3: 1 370.31250 cents 4: 2 357.42187 cents 4: 3 370.31250 cents 4: 1 390.23437 cents 4: 1 391.40625 cents 4: 1 414.84375 cents 4: 1 427.73437 cents 4: 1 438.28125 cents 4: 1 439.45313 cents 4: 1 472.26563 cents 5: 1 439.45313 cents 5: 1 472.26562 cents 5: 4 495.70312 cents 5: 4 496.87500 cents 5: 1 540.23438 cents 5: 1 577.73438 cents 6: 1 554.29687 cents 6: 2 564.84375 cents 6: 2 577.73437 cents 6: 1 597.65625 cents 6: 1 602.34375 cents 6: 2 622.26562 cents 6: 2 635.15625 cents 6: 1 645.70313 cents 7: 1 622.26562 cents 7: 1 659.76562 cents 7: 4 703.12500 cents 7: 4 704.29687 cents 7: 1 727.73438 cents 7: 1 760.54687 cents 8: 1 727.73437 cents 8: 1 760.54687 cents 8: 1 761.71875 cents 8: 1 772.26563 cents 8: 1 785.15625 cents 8: 1 808.59375 cents 8: 1 809.76563 cents 8: 3 829.68750 cents 8: 2 842.57813 cents 9: 1 829.68750 cents 9: 1 853.12500 cents 9: 1 866.01562 cents 9: 2 867.18750 cents 9: 1 887.10937 cents 9: 1 910.54688 cents 9: 1 911.71875 cents 9: 2 935.15625 cents 9: 1 967.96875 cents 9: 1 969.14063 cents 10: 2 935.15625 cents 10: 1 967.96875 cents 10: 1 969.14062 cents 10: 4 992.57812 cents 10: 2 1037.10938 cents 10: 1 1073.43750 cents 10: 1 1074.60938 cents 11: 1 1060.54687 cents 11: 1 1061.71875 cents 11: 1 1073.43750 cents 11: 2 1074.60938 cents 11: 2 1094.53125 cents 11: 1 1117.96875 cents 11: 1 1130.85937 cents 11: 1 1132.03125 cents 11: 2 1142.57813 cents Highest number of different intervals for one interval class: 10 Average number of different intervals per interval class: 8.18182 = 90/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 126.6 232.0 289.5 357.4 496.9 622.3 704.3 829.7 935.2 992.6 1061.7 1200.0 126.6 : 105.5 162.9 230.9 370.3 495.7 577.7 703.1 808.6 866.0 935.2 1073.4 1200.0 232.0 : 57.4 125.4 264.8 390.2 472.3 597.7 703.1 760.5 829.7 968.0 1094.5 1200.0 289.5 : 68.0 207.4 332.8 414.8 540.2 645.7 703.1 772.3 910.5 1037.1 1142.6 1200.0 357.4 : 139.5 264.8 346.9 472.3 577.7 635.2 704.3 842.6 969.1 1074.6 1132.0 1200.0 496.9 : 125.4 207.4 332.8 438.3 495.7 564.8 703.1 829.7 935.2 992.6 1060.5 1200.0 622.3 : 82.0 207.4 312.9 370.3 439.5 577.7 704.3 809.8 867.2 935.2 1074.6 1200.0 704.3 : 125.4 230.9 288.3 357.4 495.7 622.3 727.7 785.2 853.1 992.6 1118.0 1200.0 829.7 : 105.5 162.9 232.0 370.3 496.9 602.3 659.8 727.7 867.2 992.6 1074.6 1200.0 935.2 : 57.4 126.6 264.8 391.4 496.9 554.3 622.3 761.7 887.1 969.1 1094.5 1200.0 992.6 : 69.1 207.4 334.0 439.5 496.9 564.8 704.3 829.7 911.7 1037.1 1142.6 1200.0 1061.7: 138.3 264.8 370.3 427.7 495.7 635.2 760.5 842.6 968.0 1073.4 1130.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 57.4219 .. 139.4531 cents 82.03126 cents 57.42187 cents 2: 125.3906 .. 264.8438 cents 139.45313 cents -14.06251 cents 3: 230.8594 .. 370.3125 cents 139.45313 cents -33.98438 cents 4: 357.4219 .. 472.2656 cents 114.84376 cents -12.89063 cents 5: 439.4531 .. 577.7344 cents 138.28125 cents -32.81250 cents 6: 554.2969 .. 645.7031 cents 91.40626 cents -23.43751 cents 7: 622.2656 .. 760.5469 cents 138.28125 cents -23.43751 cents 8: 727.7344 .. 842.5781 cents 114.84376 cents -32.81250 cents 9: 829.6875 .. 969.1406 cents 139.45313 cents -12.89063 cents 10: 935.1562 .. 1074.6094 cents 139.45313 cents -33.98438 cents 11: 1060.5469 .. 1142.5781 cents 82.03126 cents -14.06251 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 57.42187 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 139.45313 cents Average / Smallest step : 1.741497 Largest / Average step : 1.394531 Largest / Smallest step : 2.428572 Median interval of one step : 105.46875 cents, amount: 2 Least squares average step : 100.14663 cents, oct.: 1201.75961 cents Scale is not proper Scale is a mode of a 1024-tone equal temperament with octave 2/1 degrees: 108 198 247 305 424 531 601 708 798 847 906 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: 299 = 287 more = 2491.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEFGFBCHI Step pattern size order : GEABIFDFEACH Scale is not a Constant Structure Scale diversity : 1.522453 Lumma stability : 0.095703 Lumma impropriety factor : 0.195313 Rothenberg efficiency : 0.245623 redundancy: 0.754377 Efficiency x scale size : 2.947475 Number of different interval sizes : 72 = 6.54545 / class Number of one step interval sizes : 9 Highest interval variety : 10 Mean interval variety : 8.18182 = 90/11 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 1.17187 cents Number of recognisable fifths : 8, average 703.7109 cents Formal octave complements present : 1 = 8.3333% -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
12: 1 1 1 0 2 1 1 1 1 1 0 2 N T3 SD: 31.1524 c. M: 61.7188 c. 14: 1 2 0 1 2 1 1 2 1 1 0 2 N SD: 25.6691 c. M: 40.8482 c. 15: 2 1 1 0 2 2 1 1 2 0 1 2 N SD: 24.8202 c. M: 37.4219 c. 16: 2 1 1 1 2 1 1 2 1 1 1 2 N D3 I SD: 20.1418 c. M: 35.1562 c. 17: 2 1 1 1 2 2 1 2 1 1 1 2 N D3 SD: 11.2184 c. M: 20.2665 c. 27: 3 2 2 1 3 3 2 3 2 1 2 3 N SD: 9.9559 c. M:-21.6580 c. 29: 3 3 1 2 3 3 2 3 3 1 2 3 N SD: 9.0235 c. M:-16.5679 c. 36: 4 3 2 2 4 4 2 4 3 2 2 4 N SD: 6.3976 c. M:-11.0677 c. 41: 4 4 2 2 5 4 3 4 4 2 2 5 N SD: 5.6465 c. M: 10.1753 c. 46: 5 4 2 3 5 5 3 5 4 2 3 5 N SD: 4.1894 c. M:-7.8465 c. 58: 6 5 3 3 7 6 4 6 5 3 3 7 N SD: 3.2402 c. M: 6.5463 c. 77: 8 7 4 4 9 8 5 8 7 4 4 9 N SD: 2.9776 c. M:-6.6508 c. 83: 9 7 4 5 9 9 6 8 8 4 4 10 N SD: 4.0030 c. M: 6.2971 c. 85: 9 7 4 5 10 9 6 9 7 4 5 10 N SD: 3.7548 c. M: 7.1002 c. 87: 9 8 4 5 10 9 6 9 8 4 5 10 N SD: 1.5596 c. M:-2.7748 c. 104: 11 9 5 6 12 11 7 11 9 5 6 12 N SD: 0.6909 c. M: 1.2620 c. 191: 20 17 9 11 22 20 13 20 17 9 11 22 N SD: 0.5435 c. M:-0.9694 c. 295: 31 26 14 17 34 31 20 31 26 14 17 34 N SD: 0.3934 c. M: 0.6396 c. 538: 57 47 26 30 63 56 37 56 47 26 31 62 N SD: 0.3869 c. M: 0.5838 c. 544: 57 48 26 31 63 57 37 57 48 26 31 63 N SD: 0.4472 c. M: 0.8272 c. 548: 58 48 26 31 64 57 38 57 48 26 32 63 N SD: 0.4071 c. M:-0.8126 c. 567: 60 50 27 32 66 59 39 59 50 27 33 65 N SD: 0.4214 c. M:-0.7730 c. 580: 61 51 28 33 67 61 39 61 51 28 33 67 N SD: 0.4063 c. M: 0.8486 c. 584: 62 51 28 33 68 61 40 61 51 28 34 67 N SD: 0.4038 c. M:-0.8348 c. 625: 66 55 30 35 73 65 43 65 55 30 36 72 N SD: 0.2604 c. M:-0.4669 c. 671: 71 59 32 38 78 70 46 70 59 32 39 77 N SD: 0.3008 c. M:-0.5763 c. 729: 77 64 35 41 85 76 50 76 64 35 42 84 N SD: 0.1592 c. M:-0.2588 c. 833: 88 73 40 47 97 87 57 87 73 40 48 96 N SD: 0.1246 c. M: 0.2223 c. 920: 97 81 44 52 107 96 63 96 81 44 53 106 N SD: 0.0781 c. M:-0.1427 c. 1024: 108 90 49 58 119 107 70 107 90 49 59 118 N SD: 0.0000 c. M:-0.0000 c.
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: 1.1709 cents 3 x x x x 4 x x x 5 x x 6 S SD: 16.9370 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 9.3688 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 11.2216 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.5013 cents 7 x 8 x x 9:10 x 11:12 x 13:14 S SD: 11.2239 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 9.6676 cents 9 x 10 x 11:12:13:14 x 15:16:17:18 S SD: 11.4312 cents 10:11 x 12 x 13:14:15:16:17:18 x 20 S SD: 9.1111 cents 11:12 x 13:14:15:16:17:18:19 x 20:22 S SD: 10.1435 cents 12:13 x 14:15:16:17:18:19 x 21:22:24 SD: 6.1226 cents 13:14:15 x 16:17:19:20:21:22:23:24:26 SD: 6.3318 cents 14:15:16 x 17:19:20:21:23:24:25:26:28 SD: 4.6891 cents 15:16:17:18 x 20:21:23:24:26:27:28:30 SD: 6.7588 cents 16:17:18:19:20:21:23:24:26:27:28:30:32 SD: 5.9654 cents 18:19 x 21:22:24:26:27:29:31:32:33:36 SD: 4.1919 cents 19:20:22 x 23:25:27:29:31:33:34:35:38 SD: 6.4470 cents 20:22:23:24:25:27:29:30:32:34:35:37:40 SD: 5.9869 cents 21:23:24:25:26:28:30:32:34:36:37:39:42 SD: 3.8878 cents 26:28:30:31:32:35:37:39:42:45:46:48:52 SD: 2.8468 cents 28:30:32:33:34:37:40:42:45:48:50:52:56 SD: 2.7166 cents 34:37:39:40:42:45:49:51:55:58:60:63:68 SD: 2.7015 cents 39:42:45:46:48:52:56:59:63:67:69:72:78 SD: 1.7980 cents 49:53:56:58:60:65:70:74:79:84:87:90:98 SD: 1.6811 cents 54:58:62:64:66:72:77:81:87:93:96:100:108 SD: 1.5400 cents 62:67:71:73:76:83:89:93:100:106:110:114:124 SD: 1.4962 cents 64:69:73:76:79:85:92:96:103:110:114:118:128 SD: 1.4785 cents 65:70:74:77:80:87:93:98:105:112:115:120:130 SD: 1.3361 cents 67:72:77:79:82:89:96:101:108:115:119:124:134 SD: 1.3302 cents 70:75:80:83:86:93:100:105:113:120:124:129:140 SD: 1.0507 cents 78:84:89:92:96:104:112:117:126:134:138:144:156 SD: 0.7630 cents 105:113:120:124:129:140:150:158:170:180:186:194:210 SD: 0.7028 cents 106:114:121:125:130:141:152:159:171:182:188:196:212 SD: 0.6895 cents 120:129:137:142:148:160:172:180:194:206:213:222:240 SD: 0.6878 cents 127:137:145:150:156:169:182:191:205:218:225:235:254 SD: 0.6574 cents 130:140:149:154:160:173:186:195:210:223:231:240:260 SD: 0.6570 cents 132:142:151:156:162:176:189:198:213:227:234:244:264 SD: 0.4971 cents 148:159:169:175:182:197:212:222:239:254:263:273:296 SD: 0.4680 cents 169:182:193:200:208:225:242:254:273:290:300:312:338 SD: 0.3841 cents 187:201:214:221:230:249:268:281:302:321:332:345:374 SD: 0.2830 cents 265:285:303:313:326:353:380:398:428:455:470:489:530 SD: 0.2476 cents 301:324:344:356:370:401:431:452:486:517:534:556:602 SD: 0.2016 cents 384:413:439:454:472:512:550:577:620:659:681:709:768 SD: 0.1472 cents 462:497:528:546:568:616:662:694:746:793:820:853:924 SD: 0.1444 cents 488:525:558:577:600:650:699:733:788:838:866:901:976 SD: 0.1137 cents 566:609:647:669:696:754:811:850:914:971:1004:1045:1132 SD: 0.1063 cents 592:637:677:700:728:789:848:889:956:1016:1050:1093:1184 SD: 0.1042 cents