Scala analysis: CD13_10_Iraq
Taqsîm mesuré, santûr - Ensemble de Muhammad Al-Qubbbânjî (tahir, hadidi, Iraq)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 181.746 cents 181.746203 2: 374.064 cents 374.064444 3: 594.979 cents 594.978785 4: 746.378 cents 746.377759 5: 871.363 cents 871.362622 6: 976.167 cents 976.167076 7: 1080.357 cents 1080.357362 8: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 119.6426 cents 119.6426 1: 181.7462 cents 181.7462 2: 192.3182 cents 192.3182 3: 220.9143 cents 220.9143 4: 151.3990 cents 151.3990 5: 124.9849 cents 124.9849 6: 104.8045 cents 104.8045 7: 104.1903 cents 104.1903 8: 119.6426 cents 119.6426
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 104.19029 cents 1: 1 104.80445 cents 1: 1 119.64264 cents 1: 1 124.98486 cents 1: 1 151.39897 cents 1: 1 181.74620 cents 1: 1 192.31824 cents 1: 1 220.91434 cents 2: 1 208.99474 cents 2: 1 223.83292 cents 2: 1 229.78932 cents 2: 1 276.38384 cents 2: 1 301.38884 cents 2: 1 372.31332 cents 2: 1 374.06444 cents 2: 1 413.23258 cents 3: 1 328.63738 cents 3: 1 333.97960 cents 3: 1 381.18829 cents 3: 1 405.57913 cents 3: 1 493.70708 cents 3: 1 497.29818 cents 3: 1 564.63156 cents 3: 1 594.97879 cents 4: 1 453.62224 cents 4: 1 485.37858 cents 4: 1 510.38358 cents 4: 1 597.89737 cents 4: 1 602.10263 cents 4: 1 689.61642 cents 4: 1 714.62142 cents 4: 1 746.37776 cents 5: 1 605.02121 cents 5: 1 635.36844 cents 5: 1 702.70182 cents 5: 1 706.29292 cents 5: 1 794.42087 cents 5: 1 818.81171 cents 5: 1 866.02040 cents 5: 1 871.36262 cents 6: 1 786.76742 cents 6: 1 825.93556 cents 6: 1 827.68668 cents 6: 1 898.61116 cents 6: 1 923.61616 cents 6: 1 970.21068 cents 6: 1 976.16708 cents 6: 1 991.00526 cents 7: 1 979.08566 cents 7: 1 1007.68176 cents 7: 1 1018.25380 cents 7: 1 1048.60103 cents 7: 1 1075.01514 cents 7: 1 1080.35736 cents 7: 1 1095.19555 cents 7: 1 1095.80971 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 : 181.7 374.1 595.0 746.4 871.4 976.2 1080.4 1200.0 181.7 : 192.3 413.2 564.6 689.6 794.4 898.6 1018.3 1200.0 374.1 : 220.9 372.3 497.3 602.1 706.3 825.9 1007.7 1200.0 595.0 : 151.4 276.4 381.2 485.4 605.0 786.8 979.1 1200.0 746.4 : 125.0 229.8 334.0 453.6 635.4 827.7 1048.6 1200.0 871.4 : 104.8 209.0 328.6 510.4 702.7 923.6 1075.0 1200.0 976.2 : 104.2 223.8 405.6 597.9 818.8 970.2 1095.2 1200.0 1080.4: 119.6 301.4 493.7 714.6 866.0 991.0 1095.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 104.1903 .. 220.9143 cents 116.72405 cents 104.19029 cents 2: 208.9947 .. 413.2326 cents 204.23784 cents -11.91960 cents 3: 328.6374 .. 594.9788 cents 266.34141 cents -84.59520 cents 4: 453.6222 .. 746.3778 cents 292.75552 cents -141.35654 cents 5: 605.0212 .. 871.3626 cents 266.34141 cents -141.35654 cents 6: 786.7674 .. 991.0053 cents 204.23784 cents -84.59520 cents 7: 979.0857 .. 1095.8097 cents 116.72406 cents -11.91960 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 104.19029 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 220.91434 cents Average / Smallest step : 1.439674 Largest / Average step : 1.472762 Largest / Smallest step : 2.120297 Median interval of one step : 138.19192 cents, amount: 0 Least squares average step : 162.14039 cents, oct.: 1297.12312 cents Scale is not proper Step pattern alph. order: ABCDEFGH Step pattern size order : FGHEDBAC Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 2.91858 cents Scale diversity : 1.600519 Lumma stability : 0.173650 Lumma impropriety factor : 0.396452 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 : 0.61417 cents Number of recognisable fifths : 4, average 703.3081 cents Number of appreciable fifths : 3, average 699.5371 cents Formal octave complements present : 1 = 12.5000% -- Rational properties --
FIT/MODE
8: 1 1 2 1 1 0 1 1 N T3 SD: 41.9446 c. M: 76.1671 c. 9: 1 2 1 2 1 0 1 1 N SD: 44.0944 c. M:-61.9707 c. 10: 1 2 2 1 1 1 1 1 N D3 S SD: 27.3325 c. M: 61.7462 c. 11: 2 1 2 2 1 1 1 1 N SD: 28.3122 c. M: 49.5242 c. 12: 2 2 2 2 1 1 1 1 N S SD: 26.6467 c. M:-53.6222 c. 16: 2 3 3 2 2 1 1 2 N S SD: 18.6751 c. M: 31.7462 c. 17: 3 2 3 3 1 2 1 2 N SD: 23.3703 c. M: 30.2729 c. 18: 3 3 3 2 2 2 1 2 N SD: 15.7270 c. M:-25.9356 c. 19: 3 3 3 3 2 1 2 2 N SD: 15.6544 c. M: 28.7987 c. 20: 3 3 4 2 2 2 2 2 N SD: 16.4582 c. M: 31.3626 c. 21: 3 3 4 3 2 2 2 2 N SD: 15.4139 c. M: 31.2073 c. 22: 3 4 4 3 2 2 2 2 N S SD: 10.3459 c. M: 18.1098 c. 26: 4 4 5 3 3 2 2 3 N SD: 8.3116 c. M: 18.8189 c. 28: 4 5 5 3 3 3 2 3 N SD: 10.9403 c. M: 17.8063 c. 32: 5 5 6 4 3 3 3 3 N SD: 5.0403 c. M: 8.8626 c. 48: 7 8 9 6 5 4 4 5 N SD: 4.0002 c. M: 6.7462 c. 58: 9 9 11 7 6 5 5 6 N SD: 3.3593 c. M:-5.0212 c. 80: 12 13 15 10 8 7 7 8 N SD: 2.3876 c. M:-5.0212 c. 87: 13 14 16 11 9 8 7 9 N SD: 2.5103 c. M: 4.4953 c. 103: 16 16 19 13 11 9 9 10 N SD: 2.4066 c. M:-4.6616 c. 111: 17 18 20 14 12 9 10 11 N SD: 2.5599 c. M:-4.3139 c. 113: 17 18 21 14 12 10 10 11 N SD: 1.7793 c. M: 3.0149 c. 119: 18 19 22 15 12 11 10 12 N SD: 1.7284 c. M: 4.1357 c. 150: 23 24 27 19 16 13 13 15 N SD: 1.7290 c. M: 2.9788 c. 151: 23 24 28 19 16 13 13 15 N SD: 1.2603 c. M:-2.8096 c. 154: 23 25 28 20 16 13 14 15 N SD: 1.9660 c. M: 2.7710 c. 157: 24 25 29 20 16 14 13 16 N SD: 1.7100 c. M:-2.6668 c. 161: 24 26 30 20 17 14 14 16 N SD: 1.3024 c. M: 2.8642 c. 167: 25 27 31 21 17 15 14 17 N SD: 1.5247 c. M: 2.5131 c. 171: 26 27 32 21 18 15 15 17 N SD: 1.4030 c. M: 2.5181 c. 172: 26 28 31 22 18 15 15 17 N SD: 1.2792 c. M:-2.6797 c. 183: 28 29 34 23 19 16 16 18 N SD: 1.2195 c. M:-1.8604 c. 193: 29 31 36 24 20 17 17 19 N SD: 1.1113 c. M:-1.9124 c. 198: 30 32 36 25 21 17 17 20 N SD: 1.0781 c. M:-1.6931 c. 212: 32 34 39 27 22 18 19 21 N SD: 1.0620 c. M: 2.5822 c. 230: 35 37 42 29 24 20 20 23 N SD: 0.6878 c. M:-1.5877 c. 262: 40 42 48 33 27 23 23 26 N SD: 0.9073 c. M:-1.5081 c. 264: 40 42 49 33 28 23 23 26 N SD: 1.0056 c. M:-1.4608 c. 270: 41 43 50 34 28 24 23 27 N SD: 0.7038 c. M:-1.6107 c. 289: 44 46 53 37 30 25 25 29 N SD: 0.7641 c. M: 1.2072 c. 299: 45 48 55 38 31 26 26 30 N SD: 0.7598 c. M: 1.1442 c. 311: 47 50 57 39 33 27 27 31 N SD: 0.7128 c. M: 1.6832 c. 331: 50 53 61 42 34 29 29 33 N SD: 0.6643 c. M: 1.2720 c. 343: 52 55 63 43 36 30 30 34 N SD: 0.5134 c. M: 1.1883 c. 381: 58 61 70 48 40 33 33 38 N SD: 0.5826 c. M:-1.0783 c. 391: 59 63 72 49 41 34 34 39 N SD: 0.3906 c. M: 0.6720 c. 482: 73 77 89 61 50 42 42 48 N SD: 0.3003 c. M: 0.6205 c. 642: 97 103 118 81 67 56 56 64 N SD: 0.3968 c. M: 0.5863 c. 653: 99 105 120 82 68 57 57 65 N SD: 0.3925 c. M:-0.8207 c. 654: 99 105 120 83 68 57 57 65 N SD: 0.2859 c. M: 0.4834 c. 680: 103 109 125 86 71 59 59 68 N SD: 0.2389 c. M:-0.4021 c. 712: 108 114 131 90 74 62 62 71 N SD: 0.1786 c. M: 0.3244 c. 873: 132 140 161 110 91 76 76 87 N SD: 0.1712 c. M: 0.3029 c. 1055: 160 169 194 133 110 92 92 105 N SD: 0.1769 c. M:-0.2443 c. 1103: 167 177 203 139 115 96 96 110 N SD: 0.1343 c. M: 0.2831 c. 1293: 196 207 238 163 135 113 112 129 N SD: 0.1226 c. M: 0.2061 c. 1315: 199 211 242 166 137 115 114 131 N SD: 0.1262 c. M:-0.2588 c. 1373: 208 220 253 173 143 120 119 137 N SD: 0.0905 c. M:-0.2142 c. 1624: 246 260 299 205 169 142 141 162 N SD: 0.1110 c. M: 0.1804 c. 1716: 260 275 316 216 179 150 149 171 N SD: 0.1020 c. M: 0.2239 c. 1775: 269 284 327 224 185 155 154 177 N SD: 0.0913 c. M: 0.2053 c. 1823: 276 292 336 230 190 159 158 182 N SD: 0.1139 c. M: 0.1753 c. 1844: 279 296 339 233 192 161 160 184 N SD: 0.1091 c. M: 0.1849 c. 1854: 281 297 341 234 193 162 161 185 N SD: 0.1140 c. M: 0.1652 c. 1855: 281 297 342 234 193 162 161 185 N SD: 0.0978 c. M:-0.1695 c. 1876: 284 301 345 237 195 164 163 187 N SD: 0.0936 c. M: 0.1473 c. 2005: 304 321 369 253 209 175 174 200 N SD: 0.0812 c. M:-0.1989 c. 2015: 305 323 371 254 210 176 175 201 N SD: 0.0931 c. M: 0.1743 c. 2027: 307 325 373 256 211 177 176 202 N SD: 0.0703 c. M:-0.1442 c. 2085: 316 334 384 263 217 182 181 208 N SD: 0.0794 c. M:-0.1291 c. 2166: 328 347 399 273 226 189 188 216 N SD: 0.0692 c. M: 0.1174 c. 2198: 333 352 405 277 229 192 191 219 N SD: 0.0646 c. M:-0.1077 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x x 4 S SD: 22.2114 cents 3 x x 4 x 5 x x 6 S SD: 32.6004 cents 4 x 5 x 6 x 7 x 8 S SD: 11.6654 cents 5 x 6:7 x 8:9 x 10 S SD: 18.5598 cents 6:7 x 8:9:10 x 11:12 S SD: 23.4197 cents 7:8:9:10:11 x 12:13:14 S SD: 14.2174 cents 8:9:10:11:12:13:14:15:16 H SD: 9.3443 cents 9:10:11:13:14:15:16:17:18 SD: 7.6875 cents 15:17:19:21:23:25:26:28:30 SD: 7.2833 cents 17:19:21:24:26:28:30:32:34 SD: 3.1338 cents 29:32:36:41:45:48:51:54:58 SD: 2.4082 cents 37:41:46:52:57:61:65:69:74 SD: 1.2348 cents 46:51:57:65:71:76:81:86:92 SD: 1.1215 cents 54:60:67:76:83:89:95:101:108 SD: 1.0712 cents 83:92:103:117:128:137:146:155:166 SD: 0.8216 cents 100:111:124:141:154:165:176:187:200 SD: 0.8080 cents 107:119:133:151:165:177:188:200:214 SD: 0.7035 cents 119:132:148:168:183:197:209:222:238 SD: 0.6476 cents 136:151:169:192:209:225:239:254:272 SD: 0.5024 cents 165:183:205:233:254:273:290:308:330 SD: 0.4942 cents 171:190:212:241:263:283:301:319:342 SD: 0.4914 cents 173:192:215:244:266:286:304:323:346 SD: 0.4121 cents 208:231:258:293:320:344:366:388:416 SD: 0.4067 cents 215:239:267:303:331:356:378:401:430 SD: 0.3804 cents 217:241:269:306:334:359:381:405:434 SD: 0.3434 cents 254:282:315:358:391:420:446:474:508 SD: 0.3127 cents 261:290:324:368:402:432:459:487:522 SD: 0.2835 cents 278:309:345:392:428:460:489:519:556 SD: 0.2768 cents 298:331:370:420:459:493:524:556:596 SD: 0.2658 cents 315:350:391:444:485:521:554:588:630 SD: 0.2275 cents 353:392:438:498:543:584:620:659:706 SD: 0.2170 cents 390:433:484:550:600:645:685:728:780 SD: 0.1805 cents 434:482:539:612:668:718:763:810:868 SD: 0.1569 cents 514:571:638:725:791:850:903:959:1028 SD: 0.1489 cents 532:591:660:750:819:880:935:993:1064 SD: 0.1410 cents 561:623:696:791:863:928:986:1047:1122 SD: 0.1409 cents 568:631:705:801:874:940:998:1060:1136 SD: 0.1254 cents