Scala analysis: CD12_11_Iraq
Taqsîm, 'ûd - Ensemble de Muhammad Al-Qubbbânjî (lami, Iraq)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 290.421 cents 290.421452 2: 495.688 cents 495.688337 3: 681.758 cents 681.757564 4: 785.141 cents 785.140927 5: 992.372 cents 992.372400 6: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 207.6276 cents 207.6276 1: 290.4215 cents 290.4215 2: 205.2669 cents 205.2669 3: 186.0692 cents 186.0692 4: 103.3834 cents 103.3834 5: 207.2315 cents 207.2315 6: 207.6276 cents 207.6276
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 103.38336 cents 1: 1 186.06923 cents 1: 1 205.26689 cents 1: 1 207.23147 cents 1: 1 207.62760 cents 1: 1 290.42145 cents 2: 1 289.45259 cents 2: 1 310.61484 cents 2: 1 391.33611 cents 2: 1 414.85907 cents 2: 1 495.68834 cents 2: 1 498.04905 cents 3: 1 494.71948 cents 3: 1 496.68406 cents 3: 1 518.24244 cents 3: 1 681.75756 cents 3: 1 703.31594 cents 3: 1 705.28053 cents 4: 1 701.95095 cents 4: 1 704.31166 cents 4: 1 785.14093 cents 4: 1 808.66389 cents 4: 1 889.38516 cents 4: 1 910.54741 cents 5: 1 909.57855 cents 5: 1 992.37240 cents 5: 1 992.76853 cents 5: 1 994.73311 cents 5: 1 1013.93077 cents 5: 1 1096.61664 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 6.00000 = 6
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 0.0 : 290.4 495.7 681.8 785.1 992.4 1200.0 290.4 : 205.3 391.3 494.7 702.0 909.6 1200.0 495.7 : 186.1 289.5 496.7 704.3 994.7 1200.0 681.8 : 103.4 310.6 518.2 808.7 1013.9 1200.0 785.1 : 207.2 414.9 705.3 910.5 1096.6 1200.0 992.4 : 207.6 498.0 703.3 889.4 992.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 103.3834 .. 290.4215 cents 187.03809 cents 103.38336 cents 2: 289.4526 .. 498.0491 cents 208.59646 cents -0.96886 cents 3: 494.7195 .. 705.2805 cents 210.56105 cents -3.32958 cents 4: 701.9509 .. 910.5474 cents 208.59646 cents -3.32958 cents 5: 909.5785 .. 1096.6166 cents 187.03809 cents -0.96886 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 103.38336 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 290.42145 cents Average / Smallest step : 1.934547 Largest / Average step : 1.452107 Largest / Smallest step : 2.809170 Median interval of one step : 206.24918 cents, amount: 0 Least squares average step : 204.71974 cents, oct.: 1228.31845 cents Scale is not proper Step pattern alph. order: ABCDEF Step pattern size order : FCBADE Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 0.96886 cents Scale diversity : 1.464269 Lumma stability : 0.172306 Lumma impropriety factor : 0.007164 Rothenberg efficiency : 0.333333 redundancy: 0.666667 Efficiency x scale size : 2.000000 Number of different interval sizes : 30 = 6.00000 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 6.00000 = 6 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 0.39613 cents Number of recognisable fifths : 4, average 703.7148 cents Formal octave complements present : 1 = 16.6667% Limited inverse transpositions with margin 206.2357 cents: 1 -- Rational properties --
FIT/MODE
6: 1 1 1 1 1 1 SP B ME I SD: 63.6338 c. M: 95.6883 c. Whole-tone, Messiaen mode 1, Raga Gopriya, Anhemitonic Hexatonic 7: 2 1 1 1 1 1 P M ME SD: 40.0118 c. M:-72.0019 c. 9: 2 2 1 1 1 2 N SD: 31.3995 c. M: 59.0391 c. 12: 3 2 2 1 2 2 P G D3 SD: 10.9704 c. M:-18.2424 c. Phrygian Hexatonic, Raga Desya Todi, Gopikavasantam (Gopika Basant), Jayantasri 28: 7 5 4 2 5 5 N SD: 10.6898 c. M:-18.5974 c. 29: 7 5 4 3 5 5 P SD: 8.0689 c. M: 19.6886 c. 30: 7 5 5 3 5 5 SP D3 SD: 10.3020 c. M: 15.6883 c. 32: 8 5 5 3 5 6 N SD: 9.2360 c. M: 17.3724 c. 33: 8 6 5 3 5 6 N SD: 9.9649 c. M:-14.8591 c. 34: 8 6 5 3 6 6 P SD: 6.8873 c. M: 11.1693 c. 41: 10 7 6 4 7 7 P SD: 4.3961 c. M: 8.5868 c. 46: 11 8 7 4 8 8 P SD: 2.3017 c. M: 3.4967 c. 58: 14 10 9 5 10 10 P SD: 0.8171 c. M:-1.0660 c. 162: 39 28 25 14 28 28 P SD: 0.6886 c. M: 1.5326 c. 220: 53 38 34 19 38 38 P SD: 0.6396 c. M: 1.3305 c. 278: 67 48 43 24 48 48 P SD: 0.6399 c. M: 1.2128 c. 289: 70 49 45 25 50 50 N SD: 0.7392 c. M: 1.5707 c. 301: 73 51 47 26 52 52 N SD: 0.6213 c. M: 1.3362 c. 342: 83 58 53 30 59 59 N SD: 0.7876 c. M: 1.0558 c. 347: 84 59 54 30 60 60 N SD: 0.5217 c. M: 1.1638 c. 359: 87 61 56 31 62 62 N SD: 0.4862 c. M: 0.9808 c. 371: 90 63 58 32 64 64 N SD: 0.6756 c. M:-0.8429 c. 375: 91 64 58 32 65 65 N SD: 0.6012 c. M: 1.1409 c. 380: 92 65 59 33 65 66 N SD: 0.5989 c. M:-1.1749 c. 387: 94 66 60 33 67 67 N SD: 0.5623 c. M:-1.0514 c. 393: 95 67 61 34 68 68 N SD: 0.5857 c. M: 1.0318 c. 405: 98 69 63 35 70 70 N SD: 0.3856 c. M: 0.8735 c. 417: 101 71 65 36 72 72 N SD: 0.4185 c. M: 0.7243 c. 451: 109 77 70 39 78 78 N SD: 0.4475 c. M: 0.7881 c. 463: 112 79 72 40 80 80 N SD: 0.3093 c. M: 0.6559 c. 475: 115 81 74 41 82 82 N SD: 0.3935 c. M:-0.5433 c. 491: 119 84 76 42 85 85 N SD: 0.3597 c. M: 0.6195 c. 509: 123 87 79 44 88 88 N SD: 0.3568 c. M: 0.5999 c. 521: 126 89 81 45 90 90 N SD: 0.2789 c. M: 0.4868 c. 549: 133 94 85 47 95 95 N SD: 0.3054 c. M:-0.4865 c. 567: 137 97 88 49 98 98 N SD: 0.3040 c. M: 0.4744 c. 579: 140 99 90 50 100 100 N SD: 0.2796 c. M:-0.3737 c. 607: 147 104 94 52 105 105 N SD: 0.2831 c. M:-0.5225 c. 625: 151 107 97 54 108 108 N SD: 0.2814 c. M: 0.5015 c. 653: 158 112 101 56 113 113 N SD: 0.2728 c. M:-0.4832 c. 711: 172 122 110 61 123 123 N SD: 0.2584 c. M:-0.5142 c. 792: 192 135 123 68 137 137 N SD: 0.2531 c. M:-0.4876 c. 838: 203 143 130 72 145 145 N SD: 0.2287 c. M: 0.4154 c. 850: 206 145 132 73 147 147 N SD: 0.2050 c. M:-0.4021 c. 877: 212 150 136 76 151 152 N SD: 0.3060 c. M: 0.3634 c. 879: 213 150 136 76 152 152 N SD: 0.2789 c. M: 0.5289 c. 884: 214 151 137 76 153 153 N SD: 0.2669 c. M: 0.5255 c. 889: 215 152 138 77 153 154 N SD: 0.2630 c. M:-0.4609 c. 891: 216 152 138 77 154 154 N SD: 0.2479 c. M:-0.4876 c. 896: 217 153 139 77 155 155 N SD: 0.1693 c. M: 0.3195 c. 908: 220 155 141 78 157 157 N SD: 0.1742 c. M:-0.3274 c. 954: 231 163 148 82 165 165 N SD: 0.1231 c. M: 0.2353 c. 1012: 245 173 157 87 175 175 N SD: 0.0942 c. M: 0.1607 c. 1070: 259 183 166 92 185 185 N SD: 0.0879 c. M:-0.1510 c. 1174: 284 201 182 101 203 203 N SD: 0.0960 c. M: 0.1324 c. 1380: 334 236 214 119 238 239 N SD: 0.0886 c. M: 0.1985 c. 1438: 348 246 223 124 248 249 N SD: 0.0820 c. M: 0.1610 c. 2186: 529 374 339 188 378 378 N SD: 0.0807 c. M: 0.1455 c. 2218: 537 379 344 191 383 384 N SD: 0.0963 c. M: 0.1271 c. 2227: 539 381 345 192 385 385 N SD: 0.0913 c. M:-0.1736 c. 2230: 540 381 346 192 385 386 N SD: 0.0841 c. M:-0.1615 c. 2244: 543 384 348 193 388 388 N SD: 0.0816 c. M:-0.1410 c. 2276: 551 389 353 196 393 394 N SD: 0.0743 c. M: 0.1053 c. 2288: 554 391 355 197 395 396 N SD: 0.0712 c. M:-0.1380 c. 2334: 565 399 362 201 403 404 N SD: 0.0544 c. M: 0.0845 c. 2392: 579 409 371 206 413 414 N SD: 0.0376 c. M: 0.0647 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x 4 S SD: 10.0987 cents 3 x 4 x 5 x 6 S SD: 33.0819 cents 4:5 x 6 x 7:8 S SD: 25.1964 cents 5:6:7 x 8:9:10 S SD: 19.6219 cents 6:7:8:9 x 11:12 SD: 12.9862 cents 9:11:12:13:14:16:18 SD: 12.5979 cents 10:12:13:15:16:18:20 SD: 10.8207 cents 12:14:16:18:19:21:24 SD: 6.7311 cents 17:20:23:25:27:30:34 SD: 6.1795 cents 21:25:28:31:33:37:42 SD: 3.0680 cents 33:39:44:49:52:59:66 SD: 2.3648 cents 39:46:52:58:61:69:78 SD: 2.3105 cents 45:53:60:67:71:80:90 SD: 1.9916 cents 49:58:65:73:77:87:98 SD: 1.8560 cents 54:64:72:80:85:96:108 SD: 0.9853 cents 66:78:88:98:104:117:132 SD: 0.7420 cents 120:142:160:178:189:213:240 SD: 0.5259 cents 160:189:213:237:252:284:320 SD: 0.5126 cents 181:214:241:268:285:321:362 SD: 0.4172 cents 220:260:293:326:346:390:440 SD: 0.3873 cents 230:272:306:341:362:408:460 SD: 0.2359 cents 284:336:378:421:447:504:568 SD: 0.1999 cents 296:350:394:439:466:525:592 SD: 0.1792 cents 350:414:466:519:551:621:700 SD: 0.1228 cents 570:674:759:845:897:1011:1140 SD: 0.0771 cents