Scala analysis: met24-bayyati9_fsharp
Set for Maqam Bayyati and Maqam Shuri
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 139.453 cents 139.453120 2: 289.453 cents 289.453120 3: 496.875 cents 496.875000 4: 577.734 cents 577.734370 5: 704.297 cents 704.296870 6: 785.156 cents 785.156240 7: 867.188 cents 867.187500 8: 992.578 cents 992.578120 9: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 207.4219 cents 207.4219 1: 139.4531 cents 139.4531 2: 150.0000 cents 150.0000 3: 207.4219 cents 207.4219 4: 80.8594 cents 80.8594 5: 126.5625 cents 126.5625 6: 80.8594 cents 80.8594 7: 82.0313 cents 82.0313 8: 125.3906 cents 125.3906 9: 207.4219 cents 207.4219
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 80.85937 cents 1: 1 82.03126 cents 1: 1 125.39062 cents 1: 1 126.56250 cents 1: 1 139.45312 cents 1: 1 150.00000 cents 1: 2 207.42188 cents 2: 1 162.89063 cents 2: 3 207.42187 cents 2: 1 288.28125 cents 2: 1 289.45312 cents 2: 1 332.81250 cents 2: 1 346.87500 cents 2: 1 357.42188 cents 3: 2 288.28124 cents 3: 1 289.45313 cents 3: 2 414.84375 cents 3: 1 438.28125 cents 3: 1 472.26562 cents 3: 2 496.87500 cents 4: 1 370.31250 cents 4: 1 414.84375 cents 4: 2 495.70312 cents 4: 1 554.29688 cents 4: 1 564.84375 cents 4: 1 577.73437 cents 4: 1 622.26562 cents 4: 1 704.29688 cents 5: 1 495.70312 cents 5: 1 577.73438 cents 5: 1 622.26563 cents 5: 1 635.15625 cents 5: 1 645.70312 cents 5: 2 704.29687 cents 5: 1 785.15625 cents 5: 1 829.68750 cents 6: 2 703.12500 cents 6: 1 727.73438 cents 6: 1 761.71875 cents 6: 2 785.15624 cents 6: 1 910.54687 cents 6: 2 911.71876 cents 7: 1 842.57812 cents 7: 1 853.12500 cents 7: 1 867.18750 cents 7: 1 910.54688 cents 7: 1 911.71875 cents 7: 3 992.57813 cents 7: 1 1037.10937 cents 8: 2 992.57812 cents 8: 1 1050.00000 cents 8: 1 1060.54688 cents 8: 1 1073.43750 cents 8: 1 1074.60938 cents 8: 1 1117.96874 cents 8: 2 1119.14063 cents Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 7.00000 = 7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 0.0 : 139.5 289.5 496.9 577.7 704.3 785.2 867.2 992.6 1200.0 139.5 : 150.0 357.4 438.3 564.8 645.7 727.7 853.1 1060.5 1200.0 289.5 : 207.4 288.3 414.8 495.7 577.7 703.1 910.5 1050.0 1200.0 496.9 : 80.9 207.4 288.3 370.3 495.7 703.1 842.6 992.6 1200.0 577.7 : 126.6 207.4 289.5 414.8 622.3 761.7 911.7 1119.1 1200.0 704.3 : 80.9 162.9 288.3 495.7 635.2 785.2 992.6 1073.4 1200.0 785.2 : 82.0 207.4 414.8 554.3 704.3 911.7 992.6 1119.1 1200.0 867.2 : 125.4 332.8 472.3 622.3 829.7 910.5 1037.1 1118.0 1200.0 992.6 : 207.4 346.9 496.9 704.3 785.2 911.7 992.6 1074.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.8594 .. 207.4219 cents 126.56251 cents 80.85937 cents 2: 162.8906 .. 357.4219 cents 194.53125 cents -44.53125 cents 3: 288.2812 .. 496.8750 cents 208.59376 cents -69.14064 cents 4: 370.3125 .. 704.2969 cents 333.98438 cents -126.56250 cents 5: 495.7031 .. 829.6875 cents 333.98438 cents -208.59376 cents 6: 703.1250 .. 911.7188 cents 208.59376 cents -126.56250 cents 7: 842.5781 .. 1037.1094 cents 194.53125 cents -69.14064 cents 8: 992.5781 .. 1119.1406 cents 126.56251 cents -44.53125 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 80.85937 cents, class 1 Average step (divided formal octave): 133.3333 cents Largest one step interval : 207.42188 cents Average / Smallest step : 1.648953 Largest / Average step : 1.555664 Largest / Smallest step : 2.565218 Median interval of one step : 126.56250 cents, amount: 1 Least squares average step : 131.80099 cents, oct.: 1186.20888 cents Scale is not proper Scale is a mode of a 1024-tone equal temperament with octave 2/1 degrees: 119 247 424 493 601 670 740 847 1024 Least number of segments generator : 513 of 601.172 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 673 of 788.672 cents and inv. generated superset size: 237 = 228 more = 2633.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEDFGC Step pattern size order : EFGADABCG Scale is not a Constant Structure Scale diversity : 1.468996 Lumma stability : 0.134766 Lumma impropriety factor : 0.572266 Rothenberg efficiency : 0.327160 redundancy: 0.672840 Efficiency x scale size : 2.944444 Number of different interval sizes : 44 = 5.50000 / class Number of one step interval sizes : 7 Highest interval variety : 8 Mean interval variety : 7.00000 = 7 Median interval variety : 6.5 Lowest interval variety : 6 Smallest interval difference : 1.17187 cents Most common intervals : 207.42188 cents & inv., amount: 5 Most common triad is 0.0 207.422 992.578 cents, amount: 3 Number of recognisable fifths : 5, average 703.8281 cents Formal octave complements present : 1 = 11.1111% -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
9: 1 1 1 1 1 1 0 1 2 N T3 SD: 48.9596 c. M: 96.8750 c. 10: 1 1 2 1 1 0 1 1 2 N S SD: 33.1612 c. M: 65.1562 c. 11: 1 1 2 1 1 1 1 1 2 N D3 S SD: 39.1434 c. M: 71.2713 c. 12: 1 2 2 1 1 1 1 1 2 N SD: 19.8434 c. M: 39.4531 c. 14: 2 1 3 1 1 1 1 2 2 N SD: 23.0831 c. M:-35.9933 c. 15: 2 2 2 1 2 1 1 1 3 N SD: 20.1301 c. M: 32.5781 c. 17: 2 2 3 1 2 1 1 2 3 N SD: 9.0228 c. M: 20.1287 c. 25: 3 3 4 2 3 1 2 3 4 N SD: 11.0528 c. M: 17.1562 c. 29: 3 4 5 2 3 2 2 3 5 N SD: 5.1902 c. M: 15.3152 c. 33: 4 4 6 2 3 3 2 3 6 N SD: 9.1292 c. M:-14.8438 c. 36: 4 5 6 2 4 3 2 4 6 N SD: 7.9938 c. M:-14.8438 c. 37: 4 5 6 3 4 2 3 4 6 N SD: 8.2495 c. M:-12.8273 c. 41: 5 5 7 3 4 3 3 4 7 N SD: 5.4809 c. M:-10.8613 c. 44: 5 6 7 3 5 3 3 4 8 N SD: 6.5319 c. M: 10.7599 c. 46: 5 6 8 3 5 3 3 5 8 N SD: 4.1055 c. M: 9.0183 c. 50: 6 6 9 3 5 4 3 5 9 N SD: 5.5375 c. M: 8.5781 c. 54: 6 7 9 4 6 3 4 6 9 N SD: 5.3519 c. M: 7.9861 c. 58: 7 7 10 4 6 4 4 6 10 N SD: 2.0214 c. M:-5.3745 c. 75: 9 9 13 5 8 5 5 8 13 N SD: 2.0677 c. M:-4.5469 c. 87: 10 11 15 6 9 6 6 9 15 N SD: 1.0650 c. M:-1.7780 c. 104: 12 13 18 7 11 7 7 11 18 N SD: 0.8796 c. M: 1.8029 c. 162: 19 20 28 11 17 11 11 17 28 N SD: 0.5713 c. M:-1.2876 c. 191: 22 24 33 13 20 13 13 20 33 N SD: 0.5334 c. M: 1.2332 c. 249: 29 31 43 17 26 17 17 26 43 N SD: 0.4066 c. M: 0.6824 c. 353: 41 44 61 24 37 24 24 37 61 N SD: 0.3496 c. M: 0.6142 c. 515: 60 64 89 35 54 35 35 54 89 N SD: 0.3746 c. M: 0.6075 c. 567: 66 71 98 38 60 38 39 59 98 N SD: 0.3390 c. M:-0.5374 c. 584: 68 73 101 39 62 39 40 61 101 N SD: 0.2840 c. M:-0.4977 c. 613: 71 77 106 41 65 41 42 64 106 N SD: 0.2780 c. M: 0.4645 c. 671: 78 84 116 45 71 45 46 70 116 N SD: 0.1839 c. M:-0.3231 c. 758: 88 95 131 51 80 51 52 79 131 N SD: 0.1871 c. M:-0.3587 c. 775: 90 97 134 52 82 52 53 81 134 N SD: 0.1306 c. M:-0.2193 c. 833: 97 104 144 56 88 56 57 87 144 N SD: 0.1223 c. M:-0.2828 c. 862: 100 108 149 58 91 58 59 90 149 N SD: 0.1074 c. M: 0.2420 c. 920: 107 115 159 62 97 62 63 96 159 N SD: 0.0994 c. M:-0.2038 c. 937: 109 117 162 63 99 63 64 98 162 N SD: 0.0989 c. M: 0.1651 c. 1024: 119 128 177 69 108 69 70 107 177 N SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x x 4 S SD: 1.1709 cents 3 x x 4 x x x 5 x 6 S SD: 5.7370 cents 4 x 5 x x 6 x x 7:8 S SD: 24.9395 cents 5 x 6 x 7 x 8 x 9:10 S SD: 9.2704 cents 6 x 7:8 x 9 x 10:11:12 S SD: 10.5885 cents 7 x 8:9:10 x 11 x 12:14 S SD: 18.5114 cents 8:9 x x 11:12 x 13:14:16 SD: 13.0522 cents 9:10:11:12:13 x 14:15:16:18 S SD: 12.1121 cents 10:11:12:13:14:15:16:17:18:20 S SD: 9.4767 cents 11:12:13:15 x x 17:18:20:22 SD: 9.8322 cents 12:13:14:16:17:18:19:20:21:24 S SD: 5.1198 cents 13:14:15:17:18 x 20:21:23:26 SD: 9.7313 cents 14:15:17:19:20:21:22:23:25:28 SD: 8.1422 cents 15:16:18:20:21:23:24:25:27:30 SD: 7.4439 cents 16:17:19:21:22:24:25:26:28:32 SD: 7.0895 cents 18:20:21:24:25:27:28:30:32:36 SD: 6.2457 cents 20:22:24:27:28:30:31:33:35:40 SD: 6.2304 cents 21:23:25:28:29:32:33:35:37:42 SD: 4.8515 cents 22:24:26:29:31:33:35:36:39:44 SD: 4.0001 cents 23:25:27:31:32:35:36:38:41:46 SD: 3.9564 cents 26:28:31:35:36:39:41:43:46:52 SD: 3.3818 cents 28:30:33:37:39:42:44:46:50:56 SD: 3.2330 cents 33:36:39:44:46:50:52:54:59:66 SD: 3.0542 cents 35:38:41:47:49:53:55:58:62:70 SD: 2.9801 cents 36:39:43:48:50:54:57:59:64:72 SD: 2.9001 cents 38:41:45:51:53:57:60:63:67:76 SD: 2.3587 cents 40:43:47:53:56:60:63:66:71:80 SD: 2.3113 cents 45:49:53:60:63:68:71:74:80:90 SD: 1.9327 cents 48:52:57:64:67:72:76:79:85:96 SD: 1.6208 cents 60:65:71:80:84:90:94:99:106:120 SD: 1.3654 cents 66:72:78:88:92:99:104:109:117:132 SD: 1.3504 cents 71:77:84:95:99:107:112:117:126:142 SD: 1.1987 cents 83:90:98:111:116:125:131:137:147:166 SD: 1.1237 cents 84:91:99:112:117:126:132:139:149:168 SD: 0.9889 cents 94:102:111:125:131:141:148:155:167:188 SD: 0.7162 cents 106:115:125:141:148:159:167:175:188:212 SD: 0.6749 cents 120:130:142:160:168:180:189:198:213:240 SD: 0.6727 cents 132:143:156:176:184:198:208:218:234:264 SD: 0.5376 cents 154:167:182:205:215:231:242:254:273:308 SD: 0.4829 cents 169:183:200:225:236:254:266:279:300:338 SD: 0.3835 cents 225:244:266:300:314:338:354:371:399:450 SD: 0.2678 cents 265:287:313:353:370:398:417:437:470:530 SD: 0.2636 cents 275:298:325:366:384:413:433:454:488:550 SD: 0.2610 cents 298:323:352:397:416:448:469:492:529:596 SD: 0.2575 cents 323:350:382:430:451:485:508:533:573:646 SD: 0.2562 cents 331:359:391:441:462:497:521:546:587:662 SD: 0.2236 cents 346:375:409:461:483:520:545:571:614:692 SD: 0.2005 cents 394:427:466:525:550:592:620:650:699:788 SD: 0.1572 cents 406:440:480:541:567:610:639:670:720:812 SD: 0.1274 cents 500:542:591:666:698:751:787:825:887:1000 SD: 0.0779 cents