Scala analysis: CD06_03_rast_Egypt
Voici le soleil et la lune - Muhammad al-Bahr (rast, Egypt)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 200.883 cents 200.882831 2: 362.976 cents 362.975833 3: 504.776 cents 504.775590 4: 700.681 cents 700.681215 5: 914.831 cents 914.831228 6: 1072.320 cents 1072.320034 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 127.6800 cents 127.6800 1: 200.8828 cents 200.8828 2: 162.0930 cents 162.0930 3: 141.7998 cents 141.7998 4: 195.9056 cents 195.9056 5: 214.1500 cents 214.1500 6: 157.4888 cents 157.4888 7: 127.6800 cents 127.6800
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 127.67997 cents 1: 1 141.79976 cents 1: 1 157.48881 cents 1: 1 162.09300 cents 1: 1 195.90562 cents 1: 1 200.88283 cents 1: 1 214.15001 cents 2: 1 285.16877 cents 2: 1 303.89276 cents 2: 1 328.56280 cents 2: 1 337.70538 cents 2: 1 362.97583 cents 2: 1 371.63882 cents 2: 1 410.05564 cents 3: 1 486.05160 cents 3: 1 490.65580 cents 3: 1 499.31878 cents 3: 1 499.79838 cents 3: 1 504.77559 cents 3: 1 551.85540 cents 3: 1 567.54444 cents 4: 1 632.45556 cents 4: 1 648.14461 cents 4: 1 695.22441 cents 4: 1 700.20162 cents 4: 1 700.68122 cents 4: 1 709.34420 cents 4: 1 713.94840 cents 5: 1 789.94436 cents 5: 1 828.36118 cents 5: 1 837.02417 cents 5: 1 862.29462 cents 5: 1 871.43720 cents 5: 1 896.10724 cents 5: 1 914.83123 cents 6: 1 985.84999 cents 6: 1 999.11717 cents 6: 1 1004.09438 cents 6: 1 1037.90700 cents 6: 1 1042.51119 cents 6: 1 1058.20024 cents 6: 1 1072.32003 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 7.00000 = 7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 200.9 363.0 504.8 700.7 914.8 1072.3 1200.0 200.9 : 162.1 303.9 499.8 713.9 871.4 999.1 1200.0 363.0 : 141.8 337.7 551.9 709.3 837.0 1037.9 1200.0 504.8 : 195.9 410.1 567.5 695.2 896.1 1058.2 1200.0 700.7 : 214.2 371.6 499.3 700.2 862.3 1004.1 1200.0 914.8 : 157.5 285.2 486.1 648.1 789.9 985.8 1200.0 1072.3: 127.7 328.6 490.7 632.5 828.4 1042.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 127.6800 .. 214.1500 cents 86.47005 cents 127.67997 cents 2: 285.1688 .. 410.0556 cents 124.88687 cents 71.01876 cents 3: 486.0516 .. 567.5444 cents 81.49284 cents 75.99597 cents 4: 632.4556 .. 713.9484 cents 81.49284 cents 64.91111 cents 5: 789.9444 .. 914.8312 cents 124.88687 cents 75.99597 cents 6: 985.8500 .. 1072.3200 cents 86.47005 cents 71.01876 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 127.67997 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 214.15001 cents Average / Smallest step : 1.342643 Largest / Average step : 1.249208 Largest / Smallest step : 1.677241 Median interval of one step : 162.09300 cents, amount: 1 Least squares average step : 176.08545 cents, oct.: 1232.59812 cents Scale is strictly proper Step pattern alph. order: ABCDEFG Step pattern size order : FDBEGCA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 64.91111 cents Scale diversity : 1.527440 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.511917 Rothenberg efficiency : 0.285714 redundancy: 0.714286 Efficiency x scale size : 2.000000 Number of different interval sizes : 42 = 7.00000 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 7.00000 = 7 Median interval variety : 7 Lowest interval variety : 7 Smallest interval difference : 0.47960 cents Number of recognisable fifths : 5, average 703.8800 cents Best fifths form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 14.2857% -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 31.2334 c. M: 57.6884 c. Lebeng 10: 2 1 1 2 2 1 1 P D3 S SD: 25.7051 c. M:-45.1688 c. Pseudo Rast 12: 2 2 1 2 2 2 1 P M ME S SD: 18.4429 c. M:-37.0242 c. G.Lydian, M.Ionian, M.Hypolydian, Major, Bilaval That, Mela Shankarabharanam, Raga Atana, Ghana Heptatonic, Peruvian Major, Matzore, Rast ascending: Greece, 4th plagal Byzantine, Ararai: Ethiopia, Makam Cargah, Ajam Ashiran, Dastgah-e Mahur, Dastgah-e Rast Panjgah, Xin: China, DS2, Heptatonia prima 16: 3 2 2 2 3 2 2 SP M ME S SD: 18.9470 c. M: 25.6812 c. Antiphrygian 17: 3 2 2 3 3 2 2 SP D3 S SD: 8.8627 c. M: 13.4965 c. Pseudo Rast 29: 5 4 3 5 5 4 3 SP SD: 5.7719 c. M:-9.4380 c. 36: 6 5 4 6 6 5 4 SP SD: 6.4320 c. M: 14.8312 c. Fourth plagal Byzantine Liturgical mode 43: 7 6 5 7 8 5 5 SP SD: 5.6498 c. M: 11.8549 c. 46: 8 6 5 8 8 6 5 SP SD: 4.9790 c. M: 9.1234 c. Arabic Diatonic 50: 8 7 6 8 9 7 5 SP SD: 5.0324 c. M: 8.8828 c. 53: 9 7 6 9 9 7 6 SP SD: 5.4188 c. M: 9.1709 c. 55: 9 8 6 9 10 7 6 SP SD: 3.9844 c. M:-7.9333 c. 60: 10 8 7 10 11 8 6 SP SD: 4.1162 c. M:-7.6800 c. 64: 11 8 8 10 12 8 7 SP SD: 4.6654 c. M: 6.9312 c. 66: 11 9 8 11 11 9 7 SP SD: 4.2034 c. M:-8.4097 c. 67: 11 9 8 11 12 9 7 SP SD: 2.9390 c. M: 4.7669 c. 76: 13 10 9 12 14 10 8 SP SD: 2.8679 c. M: 5.9444 c. 84: 14 11 10 14 15 11 9 SP SD: 2.9073 c. M: 5.8330 c. 96: 16 13 11 16 17 13 10 SP SD: 2.2957 c. M: 4.7756 c. 97: 16 13 12 16 17 13 10 SP SD: 3.1291 c. M:-4.4734 c. 100: 17 13 12 16 18 13 11 SP SD: 3.1114 c. M: 4.6812 c. 102: 17 14 12 17 18 13 11 SP SD: 2.4778 c. M:-5.2011 c. 106: 18 14 13 17 19 14 11 SP SD: 2.5794 c. M:-4.6584 c. 109: 18 15 13 18 19 14 12 SP SD: 2.5699 c. M: 4.4301 c. 112: 19 15 13 18 20 15 12 SP SD: 2.5697 c. M: 4.2526 c. 113: 19 15 14 18 20 15 12 SP SD: 2.1236 c. M:-4.9589 c. 115: 19 16 13 19 21 15 12 SP SD: 2.6019 c. M: 3.9060 c. 119: 20 16 14 19 22 15 13 SP SD: 2.5181 c. M: 4.8829 c. 121: 20 17 14 20 21 16 13 SP SD: 2.4660 c. M:-3.9663 c. 122: 20 17 14 20 22 16 13 SP SD: 2.1876 c. M: 4.1615 c. 130: 22 17 16 21 23 17 14 SP SD: 1.9379 c. M: 2.9758 c. 135: 23 18 16 22 24 18 14 SP SD: 2.1309 c. M:-3.5616 c. 138: 23 19 16 23 24 18 15 SP SD: 2.0776 c. M:-3.6666 c. 139: 23 19 16 23 25 18 15 SP SD: 1.9759 c. M: 4.0562 c. 142: 24 19 17 23 25 19 15 SP SD: 1.4668 c. M:-2.2667 c. 159: 27 21 19 26 28 21 17 SP SD: 1.4204 c. M:-2.8908 c. 161: 27 22 19 26 29 21 17 SP SD: 1.4188 c. M:-2.2416 c. 168: 28 23 20 27 30 22 18 SP SD: 1.1745 c. M:-2.3673 c. 178: 30 24 21 29 32 23 19 SP SD: 1.0803 c. M:-2.0227 c. 185: 31 25 22 30 33 24 20 SP SD: 0.9069 c. M: 2.0498 c. 199: 33 27 24 32 36 26 21 SP SD: 1.3927 c. M: 1.8879 c. 202: 34 27 24 33 36 27 21 SP SD: 1.2107 c. M:-2.9275 c. 205: 34 28 24 34 36 27 22 SP SD: 1.3292 c. M: 1.8584 c. 207: 35 28 24 34 37 27 22 SP SD: 1.2601 c. M:-2.2416 c. 209: 35 28 25 34 37 28 22 SP SD: 1.0264 c. M: 1.9126 c. 214: 36 29 25 35 38 28 23 SP SD: 0.8990 c. M:-1.5101 c. 228: 38 31 27 37 41 30 24 SP SD: 0.7832 c. M:-1.3642 c. 245: 41 33 29 40 44 32 26 SP SD: 0.4973 c. M:-1.0871 c. 252: 42 34 30 41 45 33 27 SP SD: 0.7054 c. M: 1.0711 c. 264: 44 36 31 43 47 35 28 SP SD: 0.6893 c. M: 1.1949 c. 274: 46 37 32 45 49 36 29 SP SD: 0.6073 c. M: 1.1260 c. 281: 47 38 33 46 50 37 30 SP SD: 0.5307 c. M: 0.9522 c. 387: 65 52 46 63 69 51 41 SP SD: 0.4180 c. M:-0.6676 c. 430: 72 58 51 70 77 56 46 SP SD: 0.3677 c. M: 0.6921 c. 442: 74 60 52 72 79 58 47 SP SD: 0.3361 c. M:-0.8251 c. 459: 77 62 54 75 82 60 49 SP SD: 0.2978 c. M: 0.4246 c. 509: 85 69 60 83 91 67 54 SP SD: 0.3154 c. M: 0.4899 c. 526: 88 71 62 86 94 69 56 SP SD: 0.2725 c. M: 0.5931 c. 668: 112 90 79 109 119 88 71 SP SD: 0.2224 c. M: 0.4600 c. 694: 116 94 82 113 124 91 74 SP SD: 0.2315 c. M: 0.3930 c. 711: 119 96 84 116 127 93 76 SP SD: 0.2536 c. M: 0.5901 c. 820: 137 111 97 134 146 108 87 SP SD: 0.2467 c. M: 0.3950 c. 837: 140 113 99 137 149 110 89 SP SD: 0.2017 c. M:-0.3941 c. 872: 146 118 103 142 156 114 93 SP SD: 0.2436 c. M:-0.3269 c. 884: 148 119 105 144 158 116 94 SP SD: 0.2370 c. M: 0.5324 c. 896: 150 121 106 146 160 118 95 SP SD: 0.2017 c. M:-0.4478 c. 913: 153 123 108 149 163 120 97 SP SD: 0.1470 c. M: 0.2157 c. 1098: 184 148 130 179 196 144 117 SP SD: 0.1426 c. M:-0.2101 c. 1250: 209 169 148 204 223 164 133 SP SD: 0.1302 c. M: 0.2428 c. 1279: 214 173 151 209 228 168 136 SP SD: 0.0971 c. M:-0.1788 c. 1355: 227 183 160 221 242 178 144 SP SD: 0.1126 c. M: 0.1646 c. 1524: 255 206 180 249 272 200 162 SP SD: 0.0883 c. M:-0.1294 c. 1709: 286 231 202 279 305 224 182 SP SD: 0.0755 c. M: 0.1141 c. 1990: 333 269 235 325 355 261 212 SP SD: 0.0752 c. M: 0.1592 c. 2096: 351 283 248 342 374 275 223 SP SD: 0.0841 c. M:-0.1862 c. 2125: 356 287 251 347 379 279 226 SP SD: 0.0946 c. M:-0.1525 c. 2163: 362 292 256 353 386 284 230 SP SD: 0.0725 c. M: 0.1464 c. 2192: 367 296 259 358 391 288 233 SP SD: 0.0571 c. M:-0.1252 c. 2209: 370 298 261 361 394 290 235 SP SD: 0.0792 c. M:-0.1131 c. 2218: 371 300 262 362 396 291 236 SP SD: 0.0694 c. M: 0.1615 c. 2235: 374 302 264 365 399 293 238 SP SD: 0.0637 c. M: 0.1053 c. 2377: 398 321 281 388 424 312 253 SP SD: 0.0431 c. M: 0.0647 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 0.6369 cents 3 x x 4 x 5 x 6 S SD: 10.4023 cents 4 x 5 x 6:7 x 8 S SD: 14.7091 cents 5 x 6:7 x 8:9:10 S SD: 29.3316 cents 6:7 x 8:9:10:11:12 S SD: 12.7551 cents 7:8 x 9:11:12:13:14 SD: 18.8581 cents 8:9:10:11:12:14:15:16 S SD: 10.9651 cents 13:15:16:17:19:22:24:26 SD: 10.9547 cents 14:16:17:19:21:24:26:28 SD: 7.2095 cents 16:18:20:21:24:27:30:32 S SD: 6.4616 cents 18:20:22:24:27:31:33:36 SD: 6.1432 cents 22:25:27:29:33:37:41:44 SD: 5.4241 cents 24:27:30:32:36:41:45:48 SD: 4.5306 cents 26:29:32:35:39:44:48:52 SD: 2.8055 cents 30:34:37:40:45:51:56:60 SD: 2.7814 cents 42:47:52:56:63:71:78:84 SD: 1.8409 cents 50:56:62:67:75:85:93:100 SD: 1.6589 cents 56:63:69:75:84:95:104:112 SD: 0.5465 cents 154:173:190:206:231:261:286:308 SD: 0.3571 cents 210:236:259:281:315:356:390:420 SD: 0.3145 cents 227:255:280:304:340:385:422:454 SD: 0.2882 cents 283:318:349:379:424:480:526:566 SD: 0.2485 cents 317:356:391:424:475:538:589:634 SD: 0.2426 cents 325:365:401:435:487:551:604:650 SD: 0.2076 cents 343:385:423:459:514:582:637:686 SD: 0.1942 cents 373:419:460:499:559:633:693:746 SD: 0.1923 cents 381:428:470:510:571:646:708:762 SD: 0.1607 cents 399:448:492:534:598:677:741:798 SD: 0.1350 cents 455:511:561:609:682:772:845:910 SD: 0.1252 cents 553:621:682:740:829:938:1027:1106 SD: 0.1179 cents