Scala analysis: CD13_11_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: 171.568 cents 171.567742 2: 275.421 cents 275.421214 3: 359.651 cents 359.651335 4: 610.659 cents 610.659149 5: 742.678 cents 742.677758 6: 844.483 cents 844.483012 7: 1065.376 cents 1065.376481 8: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 134.6235 cents 134.6235 1: 171.5677 cents 171.5677 2: 103.8535 cents 103.8535 3: 84.2301 cents 84.2301 4: 251.0078 cents 251.0078 5: 132.0186 cents 132.0186 6: 101.8053 cents 101.8053 7: 220.8935 cents 220.8935 8: 134.6235 cents 134.6235
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 84.23012 cents 1: 1 101.80525 cents 1: 1 103.85347 cents 1: 1 132.01861 cents 1: 1 134.62352 cents 1: 1 171.56774 cents 1: 1 220.89347 cents 1: 1 251.00781 cents 2: 1 188.08359 cents 2: 1 233.82386 cents 2: 1 275.42121 cents 2: 1 306.19126 cents 2: 1 322.69872 cents 2: 1 335.23793 cents 2: 1 355.51699 cents 2: 1 383.02642 cents 3: 1 359.65133 cents 3: 1 410.04473 cents 3: 1 439.09141 cents 3: 1 454.71733 cents 3: 1 457.32224 cents 3: 1 467.25654 cents 3: 1 484.83168 cents 3: 1 527.08473 cents 4: 1 494.27485 cents 4: 1 569.06180 cents 4: 1 571.11002 cents 4: 1 589.34085 cents 4: 1 610.65915 cents 4: 1 628.88998 cents 4: 1 630.93820 cents 4: 1 705.72515 cents 5: 1 672.91527 cents 5: 1 715.16832 cents 5: 1 732.74346 cents 5: 1 742.67776 cents 5: 1 745.28267 cents 5: 1 760.90859 cents 5: 1 789.95527 cents 5: 1 840.34867 cents 6: 1 816.97358 cents 6: 1 844.48301 cents 6: 1 864.76207 cents 6: 1 877.30128 cents 6: 1 893.80874 cents 6: 1 924.57879 cents 6: 1 966.17614 cents 6: 1 1011.91641 cents 7: 1 948.99219 cents 7: 1 979.10653 cents 7: 1 1028.43226 cents 7: 1 1065.37648 cents 7: 1 1067.98139 cents 7: 1 1096.14653 cents 7: 1 1098.19475 cents 7: 1 1115.76988 cents Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 8.00000 = 8
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 171.6 275.4 359.7 610.7 742.7 844.5 1065.4 1200.0 171.6 : 103.9 188.1 439.1 571.1 672.9 893.8 1028.4 1200.0 275.4 : 84.2 335.2 467.3 569.1 790.0 924.6 1096.1 1200.0 359.7 : 251.0 383.0 484.8 705.7 840.3 1011.9 1115.8 1200.0 610.7 : 132.0 233.8 454.7 589.3 760.9 864.8 949.0 1200.0 742.7 : 101.8 322.7 457.3 628.9 732.7 817.0 1068.0 1200.0 844.5 : 220.9 355.5 527.1 630.9 715.2 966.2 1098.2 1200.0 1065.4: 134.6 306.2 410.0 494.3 745.3 877.3 979.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 84.2301 .. 251.0078 cents 166.77769 cents 84.23012 cents 2: 188.0836 .. 383.0264 cents 194.94283 cents -62.92422 cents 3: 359.6513 .. 527.0847 cents 167.43339 cents -23.37509 cents 4: 494.2749 .. 705.7251 cents 211.45029 cents -32.80988 cents 5: 672.9153 .. 840.3487 cents 167.43340 cents -32.80988 cents 6: 816.9736 .. 1011.9164 cents 194.94283 cents -23.37509 cents 7: 948.9922 .. 1115.7699 cents 166.77769 cents -62.92422 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 84.23012 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 251.00781 cents Average / Smallest step : 1.780836 Largest / Average step : 1.673385 Largest / Smallest step : 2.980024 Median interval of one step : 133.32106 cents, amount: 0 Least squares average step : 147.46041 cents, oct.: 1179.68325 cents Scale is not proper Step pattern alph. order: ABCDEFGH Step pattern size order : FCAHDBGE Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 4.13435 cents Scale diversity : 1.721976 Lumma stability : 0.140384 Lumma impropriety factor : 0.198515 Rothenberg efficiency : 0.250000 redundancy: 0.750000 Efficiency x scale size : 2.000000 Number of different interval sizes : 56 = 8.00000 / class Number of one step interval sizes : 8 Highest interval variety : 8 Mean interval variety : 8.00000 = 8 Median interval variety : 8 Lowest interval variety : 8 Smallest interval difference : 2.04822 cents Number of recognisable fifths : 2, average 710.4467 cents Number of appreciable fifths : 1, average 705.7251 cents Formal octave complements present : 1 = 12.5000% -- Rational properties --
FIT/MODE
8: 1 1 0 2 1 1 1 1 N T3 SD: 31.8461 c. M: 59.6513 c. 10: 1 1 1 2 1 1 2 1 P D3 S SD: 24.4332 c. M: 51.5677 c. 13: 2 1 1 3 1 1 3 1 N SD: 20.9780 c. M:-42.3158 c. 14: 2 1 1 3 2 1 2 2 N SD: 19.5936 c. M: 36.8051 c. 16: 2 2 1 3 2 1 3 2 P T3 SD: 16.1560 c. M:-24.5788 c. 20: 3 2 1 4 2 2 4 2 N SD: 13.8617 c. M:-24.5788 c. 21: 3 2 1 5 2 2 4 2 N SD: 12.6629 c. M:-20.3378 c. 24: 3 2 2 5 3 2 4 3 N SD: 14.3120 c. M: 25.4212 c. 26: 4 2 2 5 3 2 5 3 N SD: 8.6491 c. M: 13.7138 c. 27: 4 2 2 6 3 2 5 3 N SD: 7.3586 c. M:-12.8778 c. 34: 5 3 2 7 4 3 6 4 N SD: 5.9431 c. M: 10.6591 c. 43: 6 4 3 9 5 3 8 5 N SD: 5.5333 c. M:-10.8106 c. 44: 6 4 3 9 5 4 8 5 N SD: 5.6313 c. M: 10.6591 c. 47: 7 4 3 10 5 4 9 5 N SD: 4.2907 c. M:-7.1557 c. 57: 8 5 4 12 6 5 11 6 N SD: 3.9489 c. M:-8.3077 c. 61: 9 5 4 13 7 5 11 7 N SD: 3.4770 c. M: 5.5530 c. 70: 10 6 5 15 7 6 13 8 N SD: 3.5452 c. M:-6.4837 c. 71: 10 6 5 15 8 6 13 8 N SD: 2.7463 c. M: 4.9987 c. 90: 13 8 6 19 10 7 17 10 N SD: 2.9374 c. M:-4.5788 c. 91: 13 8 6 19 10 8 17 10 N SD: 2.6801 c. M: 4.2162 c. 97: 14 8 7 20 11 8 18 11 N SD: 2.4210 c. M: 4.4736 c. 100: 14 9 7 21 11 8 19 11 N SD: 2.3375 c. M: 4.4830 c. 114: 16 10 8 24 12 10 21 13 N SD: 2.7535 c. M: 5.8357 c. 116: 17 10 8 24 13 10 21 13 N SD: 2.7050 c. M:-4.2943 c. 118: 17 10 8 25 13 10 22 13 N SD: 1.6820 c. M: 3.7191 c. 126: 18 11 9 26 14 11 23 14 N SD: 1.5211 c. M:-3.1360 c. 131: 19 11 9 28 14 11 24 15 N SD: 2.0308 c. M:-3.0813 c. 134: 19 12 9 28 15 11 25 15 N SD: 1.5611 c. M: 2.6920 c. 153: 22 13 11 32 17 13 28 17 N SD: 1.5189 c. M:-2.5758 c. 161: 23 14 11 34 18 13 30 18 N SD: 1.4291 c. M:-2.6639 c. 179: 26 15 13 37 20 15 33 20 N SD: 1.4223 c. M:-2.7339 c. 187: 27 16 13 39 21 16 34 21 N SD: 1.3161 c. M:-2.5758 c. 188: 27 16 13 40 20 16 35 21 N SD: 1.5787 c. M: 2.2522 c. 189: 27 16 14 39 21 16 35 21 N SD: 1.3167 c. M: 2.4053 c. 196: 28 17 14 41 21 17 36 22 N SD: 1.0404 c. M: 1.8614 c. 230: 33 20 16 48 25 20 42 26 N SD: 0.9095 c. M: 1.8082 c. 247: 35 22 17 52 27 21 45 28 N SD: 1.1155 c. M: 1.5273 c. 250: 36 21 18 52 28 21 46 28 N SD: 0.9986 c. M: 1.8212 c. 257: 37 22 18 54 28 22 47 29 N SD: 0.6697 c. M:-1.1949 c. 287: 41 25 20 60 32 24 53 32 N SD: 0.6638 c. M:-1.5731 c. 301: 43 26 21 63 33 26 55 34 N SD: 0.7068 c. M: 1.1495 c. 313: 45 27 22 65 35 26 58 35 N SD: 0.8244 c. M:-1.0922 c. 314: 45 27 22 66 34 27 58 35 N SD: 0.6563 c. M: 1.2765 c. 330: 47 29 23 69 36 28 61 37 N SD: 0.6091 c. M:-0.9424 c. 344: 49 30 24 72 38 29 63 39 N SD: 0.5941 c. M: 1.4230 c. 357: 51 31 25 75 39 30 66 40 N SD: 0.4954 c. M:-1.1056 c. 391: 56 34 27 82 43 33 72 44 N SD: 0.4287 c. M:-0.7936 c. 401: 57 35 28 84 44 34 74 45 N SD: 0.4967 c. M: 0.9942 c. 428: 61 37 30 90 47 36 79 48 N SD: 0.5046 c. M: 0.7728 c. 448: 64 39 31 94 49 38 83 50 N SD: 0.5358 c. M: 0.7330 c. 454: 65 39 32 95 50 38 84 51 N SD: 0.5163 c. M: 1.3112 c. 462: 66 40 32 97 51 39 85 52 N SD: 0.4872 c. M: 1.2098 c. 470: 67 41 33 98 52 40 86 53 N SD: 0.4531 c. M: 0.6956 c. 483: 69 42 34 101 53 41 89 54 N SD: 0.3667 c. M:-0.5971 c. 517: 74 45 36 108 57 44 95 58 N SD: 0.3307 c. M:-0.7877 c. 554: 79 48 39 116 61 47 102 62 N SD: 0.2770 c. M: 0.4486 c. 580: 83 50 41 121 64 49 107 65 N SD: 0.2377 c. M:-0.3487 c. 658: 94 57 46 138 72 56 121 74 N SD: 0.2623 c. M: 0.4285 c. 784: 112 68 55 164 86 67 144 88 N SD: 0.1996 c. M:-0.4149 c. 827: 118 72 58 173 91 70 152 93 N SD: 0.2378 c. M: 0.3465 c. 837: 120 72 59 175 92 71 154 94 N SD: 0.2009 c. M:-0.4753 c. 874: 125 76 61 183 96 74 161 98 N SD: 0.2356 c. M:-0.5513 c. 881: 126 76 62 184 97 75 162 99 N SD: 0.2363 c. M: 0.4435 c. 884: 126 77 62 185 97 75 163 99 N SD: 0.2345 c. M: 0.5270 c. 908: 130 78 64 190 100 77 167 102 N SD: 0.2274 c. M: 0.5313 c. 918: 131 80 64 192 101 78 169 103 N SD: 0.2160 c. M:-0.3958 c. 945: 135 82 66 198 104 80 174 106 N SD: 0.1464 c. M: 0.2863 c. 1071: 153 93 75 224 118 91 197 120 N SD: 0.1720 c. M:-0.3349 c. 1097: 157 95 77 229 121 93 202 123 N SD: 0.1686 c. M: 0.2672 c. 1124: 161 97 79 235 124 95 207 126 N SD: 0.1863 c. M:-0.3827 c. 1134: 162 98 80 237 125 96 209 127 N SD: 0.1640 c. M: 0.2889 c. 1141: 163 99 80 239 125 97 210 128 N SD: 0.1638 c. M:-0.3838 c. 1167: 167 101 82 244 128 99 215 131 N SD: 0.1851 c. M: 0.2671 c. 1168: 167 101 82 244 129 99 215 131 N SD: 0.1492 c. M: 0.3852 c. 1238: 177 107 87 259 136 105 228 139 N SD: 0.1206 c. M: 0.2181 c. 1364: 195 118 96 285 150 116 251 153 N SD: 0.0978 c. M:-0.1727 c. 1525: 218 132 107 319 168 129 281 171 N SD: 0.0812 c. M: 0.1551 c. 1721: 246 149 121 360 189 146 317 193 N SD: 0.0875 c. M:-0.1485 c. 1755: 251 152 123 367 193 149 323 197 N SD: 0.0753 c. M:-0.1343 c. 2309: 330 200 162 483 254 196 425 259 N SD: 0.0300 c. M: 0.0649 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x 4 S SD: 20.3614 cents 3 x x x 4 x 5 x 6 S SD: 39.8219 cents 4 x x 5 x 6 x 7:8 S SD: 27.0315 cents 5 x 6 x 7 x 8:9:10 S SD: 15.0217 cents 6 x 7 x x 9:10:11:12 SD: 11.9632 cents 7 x 8:9:10:11 x 13:14 SD: 16.0898 cents 8:9 x 10:11:12:13:15:16 SD: 12.3522 cents 9:10 x 11:13:14:15:17:18 SD: 9.3656 cents 10:11:12 x 14:15:16:19:20 SD: 12.0877 cents 11:12:13:14:16:17:18:20:22 S SD: 10.1012 cents 12:13:14:15:17:18:20:22:24 SD: 9.2163 cents 13:14:15:16:19:20:21:24:26 SD: 8.8497 cents 15:17:18 x 21:23:24:28:30 SD: 10.7206 cents 16:18:19:20:23:25:26:30:32 SD: 7.8977 cents 17:19:20:21:24:26:28:31:34 SD: 5.2542 cents 19:21:22:23:27:29:31:35:38 SD: 4.8284 cents 21:23:25:26:30:32:34:39:42 SD: 4.6306 cents 22:24:26:27:31:34:36:41:44 SD: 4.4724 cents 28:31:33:34:40:43:46:52:56 SD: 3.8869 cents 29:32:34:36:41:45:47:54:58 SD: 3.6589 cents 30:33:35:37:43:46:49:56:60 SD: 2.9262 cents 35:39:41:43:50:54:57:65:70 SD: 2.5411 cents 40:44:47:49:57:61:65:74:80 SD: 2.1469 cents 47:52:55:58:67:72:77:87:94 SD: 1.6488 cents 64:71:75:79:91:98:104:118:128 SD: 1.6382 cents 65:72:76:80:92:100:106:120:130 SD: 1.6201 cents 68:75:80:84:97:104:111:126:136 SD: 1.6136 cents 69:76:81:85:98:106:112:128:138 SD: 1.1844 cents 86:95:101:106:122:132:140:159:172 SD: 0.8492 cents 99:109:116:122:141:152:161:183:198 SD: 0.8147 cents 116:128:136:143:165:178:189:215:232 SD: 0.5471 cents 134:148:157:165:191:206:218:248:268 SD: 0.5304 cents 151:167:177:186:215:232:246:279:302 SD: 0.5287 cents 173:191:203:213:246:266:282:320:346 SD: 0.4062 cents 213:235:250:262:303:327:347:394:426 SD: 0.3519 cents 220:243:258:271:313:338:358:407:440 SD: 0.2876 cents 267:295:313:329:380:410:435:494:534 SD: 0.2815 cents 307:339:360:378:437:471:500:568:614 SD: 0.2387 cents 308:340:361:379:438:473:502:570:616 SD: 0.2325 cents 347:383:407:427:494:533:565:642:694 SD: 0.1895 cents 355:392:416:437:505:545:578:657:710 SD: 0.1692 cents 442:488:518:544:629:679:720:818:884 SD: 0.1304 cents 528:583:619:650:751:811:860:977:1056 SD: 0.1055 cents