Scala analysis: CD13_12_Iraq
Taqsîm mesuré, santûr - Ensemble de Muhammad Al-Qubbbânjî (sikah, hulaylawi, Iraq)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 82.388 cents 82.388179 2: 271.575 cents 271.574824 3: 497.027 cents 497.027236 4: 575.711 cents 575.710514 5: 652.580 cents 652.579562 6: 761.507 cents 761.507497 7: 979.000 cents 979.000477 8: 1065.014 cents 1065.013772 9: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 134.9862 cents 134.9862 1: 82.3882 cents 82.3882 2: 189.1866 cents 189.1866 3: 225.4524 cents 225.4524 4: 78.6833 cents 78.6833 5: 76.8690 cents 76.8690 6: 108.9279 cents 108.9279 7: 217.4930 cents 217.4930 8: 86.0133 cents 86.0133 9: 134.9862 cents 134.9862
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 76.86905 cents 1: 1 78.68328 cents 1: 1 82.38818 cents 1: 1 86.01329 cents 1: 1 108.92793 cents 1: 1 134.98623 cents 1: 1 189.18664 cents 1: 1 217.49298 cents 1: 1 225.45241 cents 2: 1 155.55233 cents 2: 1 185.79698 cents 2: 1 217.37441 cents 2: 1 220.99952 cents 2: 1 271.57482 cents 2: 1 303.50627 cents 2: 1 304.13569 cents 2: 1 326.42091 cents 2: 1 414.63906 cents 3: 1 264.48026 cents 3: 1 303.38770 cents 3: 1 381.00474 cents 3: 1 403.28996 cents 3: 1 406.56105 cents 3: 1 412.43421 cents 3: 1 438.49250 cents 3: 1 493.32233 cents 3: 1 497.02724 cents 4: 1 481.97324 cents 4: 1 489.30326 cents 4: 1 489.93267 cents 4: 1 492.57435 cents 4: 1 520.88068 cents 4: 1 547.42044 cents 4: 1 570.19138 cents 4: 1 575.71051 cents 4: 1 632.01346 cents 5: 1 567.98654 cents 5: 1 624.28949 cents 5: 1 629.80862 cents 5: 1 652.57956 cents 5: 1 679.11932 cents 5: 1 707.42565 cents 5: 1 710.06733 cents 5: 1 710.69674 cents 5: 1 718.02676 cents 6: 1 702.97276 cents 6: 1 706.67767 cents 6: 1 761.50750 cents 6: 1 787.56579 cents 6: 1 793.43895 cents 6: 1 796.71004 cents 6: 1 818.99526 cents 6: 1 896.61230 cents 6: 1 935.51974 cents 7: 1 785.36094 cents 7: 1 873.57909 cents 7: 1 895.86431 cents 7: 1 896.49372 cents 7: 1 928.42518 cents 7: 1 979.00048 cents 7: 1 982.62559 cents 7: 1 1014.20302 cents 7: 1 1044.44767 cents 8: 1 974.54759 cents 8: 1 982.50702 cents 8: 1 1010.81336 cents 8: 1 1065.01377 cents 8: 1 1091.07207 cents 8: 1 1113.98671 cents 8: 1 1117.61182 cents 8: 1 1121.31672 cents 8: 1 1123.13095 cents Highest number of different intervals for one interval class: 9 Average number of different intervals per interval class: 9.00000 = 9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 0.0 : 82.4 271.6 497.0 575.7 652.6 761.5 979.0 1065.0 1200.0 82.4 : 189.2 414.6 493.3 570.2 679.1 896.6 982.6 1117.6 1200.0 271.6 : 225.5 304.1 381.0 489.9 707.4 793.4 928.4 1010.8 1200.0 497.0 : 78.7 155.6 264.5 482.0 568.0 703.0 785.4 974.5 1200.0 575.7 : 76.9 185.8 403.3 489.3 624.3 706.7 895.9 1121.3 1200.0 652.6 : 108.9 326.4 412.4 547.4 629.8 819.0 1044.4 1123.1 1200.0 761.5 : 217.5 303.5 438.5 520.9 710.1 935.5 1014.2 1091.1 1200.0 979.0 : 86.0 221.0 303.4 492.6 718.0 796.7 873.6 982.5 1200.0 1065.0: 135.0 217.4 406.6 632.0 710.7 787.6 896.5 1114.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 76.8690 .. 225.4524 cents 148.58336 cents 76.86905 cents 2: 155.5523 .. 414.6391 cents 259.08673 cents -69.90009 cents 3: 264.4803 .. 497.0272 cents 232.54698 cents -150.15880 cents 4: 481.9732 .. 632.0135 cents 150.04022 cents -15.05400 cents 5: 567.9865 .. 718.0268 cents 150.04022 cents -64.02693 cents 6: 702.9728 .. 935.5197 cents 232.54698 cents -15.05400 cents 7: 785.3609 .. 1044.4477 cents 259.08673 cents -150.15880 cents 8: 974.5476 .. 1123.1310 cents 148.58336 cents -69.90009 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 76.86905 cents, class 1 Average step (divided formal octave): 133.3333 cents Largest one step interval : 225.45241 cents Average / Smallest step : 1.734552 Largest / Average step : 1.690893 Largest / Smallest step : 2.932941 Median interval of one step : 108.92793 cents, amount: 1 Least squares average step : 134.82287 cents, oct.: 1213.40583 cents Scale is not proper Step pattern alph. order: ABCDEFGHI Step pattern size order : CGIBAEHDF Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 0.11857 cents Scale diversity : 1.600685 Lumma stability : 0.128115 Lumma impropriety factor : 0.445211 Rothenberg efficiency : 0.222222 redundancy: 0.777778 Efficiency x scale size : 2.000000 Number of different interval sizes : 72 = 9.00000 / class Number of one step interval sizes : 9 Highest interval variety : 9 Mean interval variety : 9.00000 = 9 Median interval variety : 9 Lowest interval variety : 9 Smallest interval difference : 0.11857 cents Number of recognisable fifths : 6, average 709.3112 cents Number of appreciable fifths : 5, average 707.5680 cents Formal octave complements present : 1 = 11.1111% -- Rational properties --
FIT/MODE
9: 1 1 2 0 1 1 1 1 1 N T3 SD: 32.4924 c. M:-50.9452 c. 10: 1 1 2 1 0 1 2 1 1 N D3 I SD: 30.4861 c. M: 52.5796 c. 11: 1 2 2 0 1 1 2 1 1 N SD: 29.3690 c. M:-55.6979 c. 13: 1 2 2 1 1 1 3 1 1 N D3 S SD: 24.9046 c. M:-42.6785 c. 14: 1 2 3 1 1 1 2 1 2 N SD: 23.4234 c. M: 36.4423 c. 15: 1 2 3 1 1 1 3 1 2 N SD: 22.1290 c. M: 41.5075 c. 16: 1 3 3 1 1 1 3 1 2 N SD: 18.5937 c. M:-28.4252 c. 17: 1 3 3 1 1 2 3 1 2 N SD: 10.7044 c. M: 17.2854 c. 27: 2 4 5 2 2 2 5 2 3 N SD: 6.4546 c. M:-14.0871 c. 38: 3 6 7 2 3 3 7 3 4 N SD: 8.3882 c. M:-12.6357 c. 39: 3 6 7 3 2 4 7 3 4 N SD: 7.4749 c. M:-11.9093 c. 43: 3 7 8 3 2 4 8 3 5 N SD: 6.6487 c. M: 10.7191 c. 44: 3 7 8 3 3 4 8 3 5 N SD: 2.7125 c. M: 6.1181 c. 61: 4 10 11 4 4 6 11 4 7 N SD: 4.1585 c. M:-5.7056 c. 70: 5 11 13 5 4 6 13 5 8 N SD: 3.8163 c. M: 7.2218 c. 71: 5 11 13 5 5 6 13 5 8 N SD: 3.3365 c. M: 6.8864 c. 87: 6 14 16 6 5 8 16 6 10 N SD: 2.7351 c. M: 4.3037 c. 90: 6 14 17 6 6 8 16 7 10 N SD: 3.1052 c. M: 5.6671 c. 92: 6 15 17 6 6 8 17 7 10 N SD: 2.8657 c. M: 4.9858 c. 98: 7 15 19 6 6 9 18 7 11 N SD: 2.5781 c. M:-5.0136 c. 107: 7 17 20 7 7 10 19 8 12 N SD: 2.6760 c. M: 3.8835 c. 114: 8 18 21 8 7 10 21 8 13 N SD: 2.1081 c. M: 3.6128 c. 123: 8 20 23 8 8 11 22 9 14 N SD: 2.0323 c. M: 4.3394 c. 131: 9 21 24 9 8 12 24 9 15 N SD: 1.8698 c. M:-3.2343 c. 132: 9 21 25 8 9 12 24 9 15 N SD: 2.0446 c. M: 2.9832 c. 136: 9 22 25 9 9 12 25 10 15 N SD: 2.1171 c. M: 2.9764 c. 140: 10 22 26 9 9 13 25 10 16 N SD: 1.8769 c. M:-3.3261 c. 142: 10 22 27 9 9 13 26 10 16 N SD: 1.3121 c. M:-2.1189 c. 177: 12 28 33 12 11 16 32 13 20 N SD: 1.5487 c. M: 2.7293 c. 178: 12 28 34 11 12 16 32 13 20 N SD: 1.5116 c. M: 2.6768 c. 186: 13 29 35 12 12 17 34 13 21 N SD: 0.9926 c. M:-1.6447 c. 217: 15 34 41 14 14 20 39 16 24 N SD: 1.0172 c. M:-2.2673 c. 246: 17 39 46 16 16 22 45 17 28 N SD: 1.0192 c. M: 1.5991 c. 248: 17 39 47 16 16 22 45 18 28 N SD: 0.9865 c. M: 1.8301 c. 261: 18 41 49 17 17 24 47 19 29 N SD: 0.9004 c. M:-1.7109 c. 265: 18 42 50 17 17 24 48 19 30 N SD: 0.7226 c. M:-1.0860 c. 292: 20 46 55 19 19 26 53 21 33 N SD: 0.6516 c. M: 1.2335 c. 304: 21 48 57 20 19 28 55 22 34 N SD: 0.6397 c. M: 1.2638 c. 309: 21 49 58 20 20 28 56 22 35 N SD: 0.5606 c. M: 0.9532 c. 331: 23 52 62 22 21 30 60 24 37 N SD: 0.5290 c. M:-0.9955 c. 348: 24 55 65 23 22 32 63 25 39 N SD: 0.5256 c. M: 0.8554 c. 375: 26 59 70 25 24 34 68 27 42 N SD: 0.5185 c. M: 1.0272 c. 381: 26 60 72 25 24 35 69 27 43 N SD: 0.5682 c. M: 0.7087 c. 408: 28 64 77 27 26 37 74 29 46 N SD: 0.4731 c. M: 0.9866 c. 463: 32 73 87 30 30 42 84 33 52 N SD: 0.4890 c. M:-0.6971 c. 478: 33 75 90 31 31 43 87 34 54 N SD: 0.4872 c. M: 0.8380 c. 482: 33 76 91 31 31 44 87 35 54 N SD: 0.4821 c. M:-0.8981 c. 498: 34 79 93 33 32 45 90 36 56 N SD: 0.4517 c. M:-0.7143 c. 500: 34 79 94 33 32 45 91 36 56 N SD: 0.4509 c. M: 0.7882 c. 509: 35 80 96 33 33 46 92 37 57 N SD: 0.4179 c. M: 0.6115 c. 526: 36 83 99 34 34 48 95 38 59 N SD: 0.3783 c. M: 0.8056 c. 553: 38 87 104 36 36 50 100 40 62 N SD: 0.3721 c. M: 0.6653 c. 596: 41 94 112 39 38 54 108 43 67 N SD: 0.2705 c. M: 0.4770 c. 640: 44 101 120 42 41 58 116 46 72 N SD: 0.1728 c. M:-0.3002 c. 1021: 70 161 192 67 65 93 185 73 115 N SD: 0.1469 c. M: 0.2779 c. 1048: 72 165 197 69 67 95 190 75 118 N SD: 0.1236 c. M:-0.2437 c. 1065: 73 168 200 70 68 97 193 76 120 N SD: 0.1418 c. M: 0.2250 c. 1357: 93 214 255 89 87 123 246 97 153 N SD: 0.1306 c. M: 0.3122 c. 1396: 96 220 262 92 89 127 253 100 157 N SD: 0.1246 c. M:-0.2207 c. 1511: 104 238 284 99 97 137 274 108 170 N SD: 0.1408 c. M:-0.2331 c. 1530: 105 241 288 100 98 139 277 110 172 N SD: 0.1237 c. M:-0.2277 c. 1574: 108 248 296 103 101 143 285 113 177 N SD: 0.0875 c. M: 0.1644 c. 1661: 114 262 312 109 106 151 301 119 187 N SD: 0.0905 c. M: 0.2015 c. 1688: 116 266 317 111 108 153 306 121 190 N SD: 0.0853 c. M: 0.1331 c. 1705: 117 269 320 112 109 155 309 122 192 N SD: 0.0897 c. M: 0.1457 c. 2107: 145 332 396 138 135 191 382 151 237 N SD: 0.1031 c. M:-0.1937 c. 2113: 145 333 397 139 135 192 383 151 238 N SD: 0.1015 c. M: 0.1770 c. 2124: 146 335 399 139 136 193 385 152 239 N SD: 0.0945 c. M:-0.1766 c. 2151: 148 339 404 141 138 195 390 154 242 N SD: 0.0901 c. M:-0.1781 c. 2170: 149 342 408 142 139 197 393 156 244 N SD: 0.0842 c. M: 0.1986 c. 2214: 152 349 416 145 142 201 401 159 249 N SD: 0.0589 c. M: 0.1387 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: 24.6877 cents 3 x x 4 x x x 5 x 6 S SD: 31.5491 cents 4 x x 5 x 6 x 7 x 8 S SD: 30.4127 cents 5 x 6 x 7 x 8:9 x 10 S SD: 15.7485 cents 6 x 7:8 x 9 x x 11:12 SD: 10.4039 cents 7 x 8:9 x 10:11:12:13:14 S SD: 13.7691 cents 8 x 9 x 11:12 x 14:15:16 SD: 15.1435 cents 9 x 11:12 x 13:14:16:17:18 SD: 12.4609 cents 11:12:13 x 15:16:17:19:20:22 SD: 11.5418 cents 12:13:14:16:17:18:19:21:22:24 SD: 9.8573 cents 13:14:15:17:18:19:20:23:24:26 SD: 7.2405 cents 14:15:16:19 x 20:22:25:26:28 SD: 9.9524 cents 15:16:18:20:21:22:23:26:28:30 SD: 7.3525 cents 16:17:19:21:22:23:25:28:30:32 SD: 6.8715 cents 17:18:20:23:24:25:26:30:31:34 SD: 6.1417 cents 18:19:21:24:25:26:28:32:33:36 SD: 3.5158 cents 33:35:39:44:46:48:51:58:61:66 SD: 3.0998 cents 35:37:41:47:49:51:54:62:65:70 SD: 2.9417 cents 36:38:42:48:50:52:56:63:67:72 SD: 2.8880 cents 39:41:46:52:54:57:61:69:72:78 SD: 2.8279 cents 40:42:47:53:56:58:62:70:74:80 SD: 2.2318 cents 41:43:48:55:57:60:64:72:76:82 SD: 2.0031 cents 42:44:49:56:59:61:65:74:78:84 SD: 1.9441 cents 54:57:63:72:75:79:84:95:100:108 SD: 1.7593 cents 58:61:68:77:81:85:90:102:107:116 SD: 1.5584 cents 59:62:69:79:82:86:92:104:109:118 SD: 1.5097 cents 63:66:74:84:88:92:98:111:117:126 SD: 1.2655 cents 76:80:89:101:106:111:118:134:141:152 SD: 1.1592 cents 78:82:91:104:109:114:121:137:144:156 SD: 1.1265 cents 81:85:95:108:113:118:126:143:150:162 SD: 0.8868 cents 99:104:116:132:138:144:154:174:183:198 SD: 0.8146 cents 105:110:123:140:146:153:163:185:194:210 SD: 0.7298 cents 129:135:151:172:180:188:200:227:239:258 SD: 0.6034 cents 142:149:166:189:198:207:220:250:263:284 SD: 0.5364 cents 147:154:172:196:205:214:228:259:272:294 SD: 0.4407 cents 183:192:214:244:255:267:284:322:339:366 SD: 0.3864 cents 201:211:235:268:280:293:312:354:372:402 SD: 0.3438 cents 205:215:240:273:286:299:318:361:379:410 SD: 0.3132 cents 246:258:288:328:343:359:382:433:455:492 SD: 0.2817 cents 271:284:317:361:378:395:421:477:501:542 SD: 0.2470 cents 306:321:358:408:427:446:475:539:566:612 SD: 0.2235 cents 347:364:406:462:484:506:539:611:642:694 SD: 0.2188 cents 367:385:429:489:512:535:570:646:679:734 SD: 0.1968 cents 388:407:454:517:541:566:602:683:718:776 SD: 0.1914 cents 393:412:460:524:548:573:610:692:727:786 SD: 0.1866 cents 406:426:475:541:566:592:630:715:751:812 SD: 0.1768 cents 413:433:483:550:576:602:641:727:764:826 SD: 0.1589 cents 454:476:531:605:633:662:705:799:840:908 SD: 0.1086 cents