Scala analysis: CD12_12_Iraq
Taqsîm, qânûn - Ensemble de Muhammad Al-Qubbbânjî (banjgah, Iraq)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 148.447 cents 148.446670 2: 357.660 cents 357.659718 3: 446.134 cents 446.133767 4: 543.270 cents 543.270482 5: 742.145 cents 742.144696 6: 841.910 cents 841.909543 7: 1052.022 cents 1052.022142 8: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 147.9779 cents 147.9779 1: 148.4467 cents 148.4467 2: 209.2130 cents 209.2130 3: 88.4740 cents 88.4740 4: 97.1367 cents 97.1367 5: 198.8742 cents 198.8742 6: 99.7648 cents 99.7648 7: 210.1126 cents 210.1126 8: 147.9779 cents 147.9779
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 88.47405 cents 1: 1 97.13671 cents 1: 1 99.76485 cents 1: 1 147.97786 cents 1: 1 148.44667 cents 1: 1 198.87421 cents 1: 1 209.21305 cents 1: 1 210.11260 cents 2: 1 185.61076 cents 2: 1 296.01093 cents 2: 1 296.42453 cents 2: 1 297.68710 cents 2: 1 298.63906 cents 2: 1 309.87745 cents 2: 1 357.65972 cents 2: 1 358.09046 cents 3: 1 384.48498 cents 3: 1 394.82381 cents 3: 1 395.77578 cents 3: 1 446.13377 cents 3: 1 457.85530 cents 3: 1 505.63758 cents 3: 1 506.53713 cents 3: 1 508.75166 cents 4: 1 484.24982 cents 4: 1 543.27048 cents 4: 1 593.69803 cents 4: 1 594.11162 cents 4: 1 605.88838 cents 4: 1 606.30197 cents 4: 1 656.72952 cents 4: 1 715.75018 cents 5: 1 691.24834 cents 5: 1 693.46287 cents 5: 1 694.36242 cents 5: 1 742.14470 cents 5: 1 753.86623 cents 5: 1 804.22422 cents 5: 1 805.17619 cents 5: 1 815.51502 cents 6: 1 841.90954 cents 6: 1 842.34028 cents 6: 1 890.12255 cents 6: 1 901.36094 cents 6: 1 902.31290 cents 6: 1 903.57547 cents 6: 1 903.98907 cents 6: 1 1014.38924 cents 7: 1 989.88740 cents 7: 1 990.78695 cents 7: 1 1001.12579 cents 7: 1 1051.55333 cents 7: 1 1052.02214 cents 7: 1 1100.23515 cents 7: 1 1102.86329 cents 7: 1 1111.52595 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 : 148.4 357.7 446.1 543.3 742.1 841.9 1052.0 1200.0 148.4 : 209.2 297.7 394.8 593.7 693.5 903.6 1051.6 1200.0 357.7 : 88.5 185.6 384.5 484.2 694.4 842.3 990.8 1200.0 446.1 : 97.1 296.0 395.8 605.9 753.9 902.3 1111.5 1200.0 543.3 : 198.9 298.6 508.8 656.7 805.2 1014.4 1102.9 1200.0 742.1 : 99.8 309.9 457.9 606.3 815.5 904.0 1001.1 1200.0 841.9 : 210.1 358.1 506.5 715.8 804.2 901.4 1100.2 1200.0 1052.0: 148.0 296.4 505.6 594.1 691.2 890.1 989.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 88.4740 .. 210.1126 cents 121.63855 cents 88.47405 cents 2: 185.6108 .. 358.0905 cents 172.47969 cents -24.50183 cents 3: 384.4850 .. 508.7517 cents 124.26668 cents 26.39452 cents 4: 484.2498 .. 715.7502 cents 231.50035 cents -24.50184 cents 5: 691.2483 .. 815.5150 cents 124.26668 cents -24.50184 cents 6: 841.9095 .. 1014.3892 cents 172.47969 cents 26.39452 cents 7: 989.8874 .. 1111.5260 cents 121.63855 cents -24.50184 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 88.47405 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 210.11260 cents Average / Smallest step : 1.695412 Largest / Average step : 1.400751 Largest / Smallest step : 2.374850 Median interval of one step : 148.21226 cents, amount: 0 Least squares average step : 147.55679 cents, oct.: 1180.45432 cents Scale is not proper Step pattern alph. order: ABCDEFGH Step pattern size order : EGABFCHD Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 13.26345 cents Scale diversity : 1.526217 Lumma stability : 0.191448 Lumma impropriety factor : 0.081673 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 : 0.41360 cents Number of recognisable fifths : 4, average 698.7060 cents Number of appreciable fifths : 3, average 693.0245 cents Formal octave complements present : 1 = 12.5000% -- Rational properties --
FIT/MODE
8: 1 1 1 1 1 1 1 1 SP B ME I SD: 35.3563 c. M:-58.0905 c. 9: 1 2 0 1 2 0 2 1 N SD: 34.5801 c. M:-57.8553 c. 10: 1 2 1 1 1 1 2 1 P D3 I SD: 28.4092 c. M:-56.7295 c. 11: 1 2 1 1 2 1 2 1 P M ME SD: 26.2114 c. M: 39.3558 c. 13: 2 2 1 1 2 1 2 2 N SD: 20.2213 c. M: 36.6375 c. 14: 2 2 1 1 3 1 2 2 N T3 SD: 21.0219 c. M:-29.2839 c. 16: 2 3 1 1 3 1 3 2 N SD: 11.2004 c. M: 18.2705 c. 24: 3 4 2 2 4 2 4 3 P SD: 5.6188 c. M:-8.0905 c. 40: 5 7 3 3 7 3 7 5 N SD: 3.5877 c. M:-7.8553 c. 57: 7 10 4 5 9 5 10 7 N SD: 2.8010 c. M: 5.3026 c. 73: 9 13 5 6 12 6 13 9 N SD: 2.2509 c. M:-3.9841 c. 81: 10 14 6 7 13 7 14 10 N SD: 2.2245 c. M:-4.8777 c. 91: 11 16 7 7 15 8 16 11 N SD: 2.5532 c. M: 3.6832 c. 97: 12 17 7 8 16 8 17 12 N SD: 0.6737 c. M:-1.1032 c. 285: 35 50 21 23 47 24 50 35 N SD: 0.5985 c. M: 1.0921 c. 309: 38 54 23 25 51 26 54 38 N SD: 0.5335 c. M: 0.8739 c. 325: 40 57 24 26 54 27 57 40 N SD: 0.4407 c. M: 0.7544 c. 349: 43 61 26 28 58 29 61 43 N SD: 0.4554 c. M:-0.8576 c. 382: 47 67 28 31 63 32 67 47 N SD: 0.4494 c. M: 0.8027 c. 406: 50 71 30 33 67 34 71 50 N SD: 0.3736 c. M: 0.6634 c. 422: 52 74 31 34 70 35 74 52 N SD: 0.3373 c. M:-0.6341 c. 446: 55 78 33 36 74 37 78 55 N SD: 0.3207 c. M:-0.5030 c. 543: 67 95 40 44 90 45 95 67 N SD: 0.2865 c. M:-0.3967 c. 778: 96 136 57 63 129 65 136 96 N SD: 0.2645 c. M: 0.3754 c. 802: 99 140 59 65 133 67 140 99 N SD: 0.2343 c. M:-0.4845 c. 842: 104 147 62 68 140 70 147 104 N SD: 0.2424 c. M:-0.3731 c. 899: 111 157 66 73 149 75 157 111 N SD: 0.2068 c. M:-0.3596 c. 939: 116 164 69 76 156 78 164 116 N SD: 0.2137 c. M:-0.3473 c. 996: 123 174 73 81 165 83 174 123 N SD: 0.2066 c. M: 0.3506 c. 1036: 128 181 76 84 172 86 181 128 N SD: 0.2102 c. M:-0.3263 c. 1140: 141 199 84 92 189 95 199 141 N SD: 0.2055 c. M: 0.4432 c. 1219: 151 212 90 99 202 101 214 150 N SD: 0.2123 c. M: 0.3176 c. 1224: 151 214 90 99 203 102 214 151 N SD: 0.1889 c. M: 0.4075 c. 1308: 162 228 96 106 217 109 229 161 N SD: 0.1951 c. M:-0.2923 c. 1316: 163 229 97 107 218 109 231 162 N SD: 0.2009 c. M: 0.2682 c. 1321: 163 231 97 107 219 110 231 163 N SD: 0.1803 c. M: 0.3770 c. 1383: 171 241 102 112 229 115 242 171 N SD: 0.2153 c. M: 0.3952 c. 1385: 171 242 102 112 230 115 242 171 N SD: 0.2133 c. M:-0.3824 c. 1396: 173 243 103 113 231 116 245 172 N SD: 0.1994 c. M: 0.3623 c. 1405: 174 245 103 114 233 117 246 173 N SD: 0.1822 c. M: 0.2975 c. 1410: 174 246 104 114 234 117 247 174 N SD: 0.2083 c. M: 0.3616 c. 1412: 175 246 104 114 234 118 247 174 N SD: 0.1901 c. M:-0.3001 c. 1418: 175 248 104 115 235 118 248 175 N SD: 0.1846 c. M: 0.3508 c. 1420: 176 247 105 115 235 118 249 175 N SD: 0.1666 c. M:-0.2857 c. 1425: 176 249 105 115 236 119 249 176 N SD: 0.1974 c. M: 0.2500 c. 1429: 177 249 105 116 237 119 250 176 N SD: 0.1914 c. M:-0.3578 c. 1436: 178 250 106 116 238 119 252 177 N SD: 0.1890 c. M: 0.4054 c. 1442: 178 252 106 117 239 120 252 178 N SD: 0.1845 c. M: 0.3191 c. 1444: 179 251 107 117 239 120 253 178 N SD: 0.1842 c. M: 0.3190 c. 1447: 179 252 107 117 240 120 254 178 N SD: 0.1681 c. M:-0.3621 c. 1460: 181 254 108 118 242 121 256 180 N SD: 0.1661 c. M:-0.3205 c. 1507: 186 263 111 122 250 125 264 186 N SD: 0.1911 c. M: 0.3378 c. 1509: 187 263 111 122 250 126 264 186 N SD: 0.1664 c. M:-0.2611 c. 1517: 188 264 112 123 251 126 266 187 N SD: 0.1588 c. M:-0.2679 c. 1544: 191 269 114 125 256 128 271 190 N SD: 0.1434 c. M:-0.3095 c. 1606: 199 280 118 130 266 134 281 198 N SD: 0.1558 c. M:-0.2481 c. 1630: 202 284 120 132 270 136 285 201 N SD: 0.1509 c. M:-0.2990 c. 1641: 203 286 121 133 272 136 288 202 N SD: 0.1328 c. M:-0.2630 c. 1648: 204 287 122 133 273 137 289 203 N SD: 0.1412 c. M:-0.2255 c. 1719: 213 299 127 139 285 143 301 212 N SD: 0.1402 c. M:-0.2444 c. 1732: 214 302 128 140 287 144 303 214 N SD: 0.1475 c. M: 0.2900 c. 1738: 215 303 128 141 288 144 305 214 N SD: 0.1343 c. M: 0.2525 c. 1745: 216 304 129 141 289 145 306 215 N SD: 0.1191 c. M: 0.1903 c. 1816: 225 316 134 147 301 151 318 224 N SD: 0.1188 c. M:-0.2317 c. 1829: 226 319 135 148 303 152 320 226 N SD: 0.1395 c. M: 0.2999 c. 1840: 228 320 136 149 305 153 322 227 N SD: 0.1340 c. M: 0.2684 c. 1842: 228 321 136 149 305 153 323 227 N SD: 0.1096 c. M: 0.2157 c. 1866: 231 325 138 151 309 155 327 230 N SD: 0.1039 c. M:-0.1685 c. 1963: 243 342 145 159 325 163 344 242 N SD: 0.1008 c. M:-0.1834 c. 2044: 253 356 151 165 339 170 358 252 N SD: 0.1000 c. M: 0.2176 c. 2052: 254 358 151 166 340 171 359 253 N SD: 0.1163 c. M:-0.2350 c. 2060: 255 359 152 167 341 171 361 254 N SD: 0.1078 c. M:-0.2247 c. 2068: 256 360 153 167 343 172 362 255 N SD: 0.1050 c. M: 0.2129 c. 2101: 260 366 155 170 348 175 368 259 N SD: 0.0988 c. M: 0.2123 c. 2125: 263 370 157 172 352 177 372 262 N SD: 0.0908 c. M: 0.2009 c. 2141: 265 373 158 173 355 178 375 264 N SD: 0.0748 c. M: 0.1598 c. 2165: 268 377 160 175 359 180 379 267 N SD: 0.0752 c. M: 0.1539 c. 2222: 275 387 164 180 368 185 389 274 N SD: 0.0723 c. M: 0.1440 c. 2238: 277 390 165 181 371 186 392 276 N SD: 0.0601 c. M: 0.1069 c. 2262: 280 394 167 183 375 188 396 279 N SD: 0.0530 c. M: 0.1000 c. 2359: 292 411 174 191 391 196 413 291 N SD: 0.0442 c. M:-0.0908 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: 20.0948 cents 3 x x x 4 x 5 x 6 S SD: 20.6755 cents 4 x 5 x x 6 x 7:8 S SD: 24.1840 cents 5 x 6 x 7 x 8:9:10 S SD: 14.5426 cents 6 x 7 x 8:9:10:11:12 S SD: 19.5165 cents 7:8 x 9:10:11 x 13:14 SD: 20.0619 cents 8:9:10 x 11:12:13:15:16 SD: 11.8605 cents 9:10:11 x 12:14:15:17:18 SD: 12.7993 cents 10:11:12:13:14:15:16:18:20 S SD: 10.6373 cents 11:12 x 14:15:17:18:20:22 SD: 5.3457 cents 12:13:15 x 16:18:20:22:24 SD: 11.4179 cents 13:14:16:17:18:20:21:24:26 S SD: 4.6536 cents 21:23:26:27:29:32:34:39:42 SD: 4.3396 cents 24:26:30:31:33:37:39:44:48 SD: 4.0583 cents 30:33:37:39:41:46:49:55:60 SD: 2.6292 cents 35:38:43:45:48:54:57:64:70 SD: 2.1793 cents 43:47:53:56:59:66:70:79:86 SD: 1.7571 cents 54:59:66:70:74:83:88:99:108 SD: 1.6165 cents 65:71:80:84:89:100:106:119:130 SD: 1.1846 cents 78:85:96:101:107:120:127:143:156 SD: 0.8426 cents 109:119:134:141:149:167:177:200:218 SD: 0.7669 cents 112:122:138:145:153:172:182:206:224 SD: 0.7541 cents 122:133:150:158:167:187:198:224:244 SD: 0.6089 cents 136:148:167:176:186:209:221:250:272 SD: 0.5489 cents 157:171:193:203:215:241:255:288:314 SD: 0.4111 cents 166:181:204:215:227:255:270:305:332 SD: 0.3878 cents 187:204:230:242:256:287:304:343:374 SD: 0.3857 cents 200:218:246:259:274:307:325:367:400 SD: 0.3804 cents 201:219:247:260:275:309:327:369:402 SD: 0.3403 cents 258:281:317:334:353:396:420:474:516 SD: 0.3231 cents 269:293:331:348:368:413:437:494:538 SD: 0.3193 cents 279:304:343:361:382:428:454:512:558 SD: 0.2572 cents 323:352:397:418:442:496:525:593:646 SD: 0.1646 cents 415:452:510:537:568:637:675:762:830 SD: 0.1339 cents 592:645:728:766:810:909:963:1087:1184 SD: 0.0972 cents