Scala analysis: CD10_06_Egypt
Ehone - Mîkhâ'îl Jirjis al-Batânûnî (unknown maqam, Egypt)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 118.724 cents 118.723890 2: 238.906 cents 238.905985 3: 439.857 cents 439.857077 4: 641.853 cents 641.852501 5: 727.399 cents 727.398888 6: 820.341 cents 820.340861 7: 878.430 cents 878.430150 8: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 321.5698 cents 321.5698 1: 118.7239 cents 118.7239 2: 120.1821 cents 120.1821 3: 200.9511 cents 200.9511 4: 201.9954 cents 201.9954 5: 85.5464 cents 85.5464 6: 92.9420 cents 92.9420 7: 58.0893 cents 58.0893 8: 321.5698 cents 321.5698
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 58.08929 cents 1: 1 85.54639 cents 1: 1 92.94197 cents 1: 1 118.72389 cents 1: 1 120.18209 cents 1: 1 200.95109 cents 1: 1 201.99542 cents 1: 1 321.56985 cents 2: 1 151.03126 cents 2: 1 178.48836 cents 2: 1 238.90598 cents 2: 1 287.54181 cents 2: 1 321.13319 cents 2: 1 379.65914 cents 2: 1 402.94652 cents 2: 1 440.29374 cents 3: 1 236.57765 cents 3: 1 380.48378 cents 3: 1 439.85708 cents 3: 1 472.60111 cents 3: 1 488.49290 cents 3: 1 498.38303 cents 3: 1 523.12861 cents 3: 1 560.47583 cents 4: 1 438.57307 cents 4: 1 558.14750 cents 4: 1 581.43488 cents 4: 1 591.32500 cents 4: 1 608.67500 cents 4: 1 618.56512 cents 4: 1 641.85250 cents 4: 1 761.42693 cents 5: 1 639.52417 cents 5: 1 676.87139 cents 5: 1 701.61697 cents 5: 1 711.50710 cents 5: 1 727.39889 cents 5: 1 760.14292 cents 5: 1 819.51622 cents 5: 1 963.42235 cents 6: 1 759.70626 cents 6: 1 797.05348 cents 6: 1 820.34086 cents 6: 1 878.86681 cents 6: 1 912.45819 cents 6: 1 961.09402 cents 6: 1 1021.51164 cents 6: 1 1048.96874 cents 7: 1 878.43015 cents 7: 1 998.00458 cents 7: 1 999.04891 cents 7: 1 1079.81791 cents 7: 1 1081.27611 cents 7: 1 1107.05803 cents 7: 1 1114.45361 cents 7: 1 1141.91071 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 : 118.7 238.9 439.9 641.9 727.4 820.3 878.4 1200.0 118.7 : 120.2 321.1 523.1 608.7 701.6 759.7 1081.3 1200.0 238.9 : 201.0 402.9 488.5 581.4 639.5 961.1 1079.8 1200.0 439.9 : 202.0 287.5 380.5 438.6 760.1 878.9 999.0 1200.0 641.9 : 85.5 178.5 236.6 558.1 676.9 797.1 998.0 1200.0 727.4 : 92.9 151.0 472.6 591.3 711.5 912.5 1114.5 1200.0 820.3 : 58.1 379.7 498.4 618.6 819.5 1021.5 1107.1 1200.0 878.4 : 321.6 440.3 560.5 761.4 963.4 1049.0 1141.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 58.0893 .. 321.5698 cents 263.48056 cents 58.08929 cents 2: 151.0313 .. 440.2937 cents 289.26248 cents -170.53859 cents 3: 236.5776 .. 560.4758 cents 323.89819 cents -203.71609 cents 4: 438.5731 .. 761.4269 cents 322.85385 cents -121.90276 cents 5: 639.5242 .. 963.4224 cents 323.89819 cents -121.90276 cents 6: 759.7063 .. 1048.9687 cents 289.26248 cents -203.71609 cents 7: 878.4301 .. 1141.9107 cents 263.48056 cents -170.53859 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 58.08929 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 321.56985 cents Average / Smallest step : 2.582232 Largest / Average step : 2.143799 Largest / Smallest step : 5.535786 Median interval of one step : 119.45299 cents, amount: 0 Least squares average step : 141.13514 cents, oct.: 1129.08109 cents Scale is not proper Step pattern alph. order: ABCDEFGH Step pattern size order : DEFGBCAH Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 0.43666 cents Scale diversity : 1.703687 Lumma stability : 0.096815 Lumma impropriety factor : 0.682408 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 : 0.43666 cents Number of recognisable fifths : 2, average 706.5620 cents Formal octave complements present : 1 = 12.5000% -- Rational properties --
FIT/MODE
8: 1 1 1 1 1 0 1 2 N T3 SD: 39.5112 c. M: 70.3409 c. 9: 1 1 1 2 0 1 1 2 N D3 SD: 35.8903 c. M: 60.7322 c. 10: 1 1 2 1 1 1 0 3 N SD: 25.7002 c. M: 41.8525 c. 11: 1 1 2 2 1 1 0 3 N SD: 24.4582 c. M:-52.3864 c. 12: 1 1 2 2 1 1 1 3 N T3 SD: 29.2280 c. M: 41.8525 c. 13: 1 2 2 2 1 1 1 3 N SD: 24.6378 c. M:-44.6468 c. 15: 1 2 2 3 1 1 1 4 N SD: 21.1060 c. M: 39.8571 c. 16: 2 1 3 3 1 1 1 4 N SD: 20.5274 c. M:-33.1475 c. 18: 2 2 3 3 1 1 1 5 N SD: 19.0589 c. M:-27.7607 c. 19: 2 2 3 3 2 1 1 5 N SD: 12.8479 c. M:-30.4958 c. 20: 2 2 3 4 1 2 1 5 N SD: 14.2870 c. M:-21.5699 c. 21: 2 2 4 3 2 1 1 6 N SD: 14.6097 c. M: 21.2873 c. 22: 2 2 4 4 1 2 1 6 N SD: 11.5540 c. M: 20.7242 c. 25: 2 3 4 4 2 2 1 7 N SD: 12.1441 c. M: 22.7239 c. 26: 3 2 5 4 2 2 1 7 N SD: 12.1335 c. M:-21.6814 c. 27: 3 2 5 4 2 2 2 7 N SD: 14.5198 c. M: 20.3409 c. 28: 3 2 5 5 2 2 1 8 N SD: 12.8583 c. M: 24.6203 c. 30: 3 3 5 5 2 3 1 8 N SD: 7.4997 c. M:-19.6591 c. 31: 3 3 5 6 2 2 2 8 N SD: 9.8317 c. M:-16.2120 c. 32: 3 3 6 5 2 3 1 9 N SD: 10.3162 c. M: 15.9301 c. 35: 3 4 6 6 2 3 2 9 N SD: 8.7249 c. M: 15.8667 c. 37: 4 3 7 6 2 3 2 10 N SD: 10.0075 c. M:-14.1970 c. 38: 4 4 6 6 3 3 2 10 N SD: 6.9975 c. M:-13.7256 c. 41: 4 4 7 7 3 3 2 11 N SD: 2.4917 c. M: 4.7596 c. 79: 8 8 13 13 6 6 4 21 N SD: 2.4991 c. M:-4.1320 c. 101: 10 10 17 17 7 8 5 27 N SD: 1.1004 c. M: 2.6464 c. 120: 12 12 20 20 9 9 6 32 N SD: 1.3975 c. M:-2.6011 c. 142: 14 14 24 24 10 11 7 38 N SD: 0.9170 c. M: 2.2863 c. 180: 18 18 30 30 13 14 9 48 N SD: 1.0836 c. M: 1.8525 c. 221: 22 22 37 37 16 17 11 59 N SD: 0.6613 c. M:-1.2079 c. 262: 26 26 44 44 19 20 13 70 N SD: 0.6101 c. M:-0.9592 c. 325: 32 33 54 55 23 25 16 87 N SD: 0.5757 c. M:-1.0940 c. 363: 36 36 61 61 26 28 18 97 N SD: 0.5346 c. M:-0.9087 c. 366: 36 37 61 62 26 28 18 98 N SD: 0.5316 c. M:-0.7704 c. 376: 37 38 63 63 27 29 18 101 N SD: 0.4676 c. M: 0.7706 c. 417: 41 42 70 70 30 32 20 112 N SD: 0.4689 c. M: 0.7383 c. 426: 42 43 71 72 30 33 21 114 N SD: 0.4720 c. M: 0.6383 c. 452: 45 45 76 76 32 35 22 121 N SD: 0.4720 c. M:-0.8509 c. 467: 46 47 78 79 33 36 23 125 N SD: 0.4143 c. M: 0.6406 c. 477: 47 48 80 80 34 37 23 128 N SD: 0.3325 c. M: 0.4849 c. 518: 51 52 87 87 37 40 25 139 N SD: 0.3151 c. M: 0.5772 c. 597: 59 60 100 100 43 46 29 160 N SD: 0.3070 c. M: 0.6465 c. 619: 61 62 104 104 44 48 30 166 N SD: 0.3221 c. M: 0.4686 c. 638: 63 64 107 107 46 49 31 171 N SD: 0.2918 c. M:-0.5008 c. 698: 69 70 117 117 50 54 34 187 N SD: 0.2619 c. M: 0.5918 c. 739: 73 74 124 124 53 57 36 198 N SD: 0.2291 c. M: 0.4452 c. 780: 77 78 131 131 56 60 38 209 N SD: 0.2713 c. M: 0.4444 c. 810: 80 81 136 136 58 63 39 217 N SD: 0.2545 c. M:-0.3999 c. 873: 86 88 146 147 62 68 42 234 N SD: 0.2463 c. M: 0.5108 c. 914: 90 92 153 154 65 71 44 245 N SD: 0.2257 c. M: 0.5620 c. 970: 96 97 163 163 69 75 47 260 N SD: 0.2234 c. M:-0.5553 c. 980: 97 98 164 165 70 76 47 263 N SD: 0.2143 c. M: 0.4710 c. 993: 98 100 166 167 71 77 48 266 N SD: 0.1980 c. M:-0.3689 c. 1034: 102 104 173 174 74 80 50 277 N SD: 0.1798 c. M: 0.3486 c. 1094: 108 110 183 184 78 85 53 293 N SD: 0.1656 c. M: 0.2595 c. 1135: 112 114 190 191 81 88 55 304 N SD: 0.1333 c. M: 0.3098 c. 1432: 142 143 240 241 102 111 69 384 N SD: 0.1322 c. M:-0.2705 c. 1473: 146 147 247 248 105 114 71 395 N SD: 0.1435 c. M: 0.2224 c. 1486: 147 149 249 250 106 115 72 398 N SD: 0.1490 c. M:-0.2506 c. 1526: 151 153 255 257 109 118 74 409 N SD: 0.1405 c. M: 0.2765 c. 1567: 155 157 262 264 112 121 76 420 N SD: 0.1348 c. M: 0.2910 c. 1587: 157 159 266 267 113 123 77 425 N SD: 0.1180 c. M:-0.2185 c. 1628: 161 163 273 274 116 126 79 436 N SD: 0.1263 c. M:-0.1939 c. 1729: 171 173 290 291 123 134 84 463 N SD: 0.1257 c. M:-0.2280 c. 1757: 174 176 294 296 125 136 85 471 N SD: 0.0970 c. M:-0.1509 c. 1798: 178 180 301 303 128 139 87 482 N SD: 0.0967 c. M:-0.1942 c. 1899: 188 190 318 320 135 147 92 509 N SD: 0.0887 c. M:-0.1696 c. 2019: 200 202 338 340 144 156 98 541 N SD: 0.0808 c. M:-0.1468 c. 2049: 203 205 343 345 146 159 99 549 N SD: 0.0845 c. M:-0.1634 c. 2090: 207 209 350 352 149 162 101 560 N SD: 0.0791 c. M:-0.1376 c. 2171: 215 217 364 365 155 168 105 582 N SD: 0.0996 c. M: 0.1252 c. 2191: 217 219 367 369 156 170 106 587 N SD: 0.0820 c. M:-0.1260 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: 12.7219 cents 3 x x 4 x x x 5:6 S SD: 19.4964 cents 4 x x 5 x 6 x 7:8 S SD: 27.0251 cents 5 x 6 x 7 x 8 x 10 S SD: 24.3077 cents 6 x 7:8 x 9 x 10:12 S SD: 13.9290 cents 7 x 8:9:10 x 11:12:14 S SD: 11.9032 cents 8 x 9:10 x 12:13 x 16 SD: 14.3478 cents 9 x 10:12:13:14 x 15:18 S SD: 14.9522 cents 10:11 x 13:14:15:16:17:20 SD: 12.9188 cents 11:12:13:14:16:17 x 18:22 SD: 10.5474 cents 12:13:14:15:17:18:19:20:24 SD: 10.3449 cents 13:14:15:17:19:20:21:22:26 SD: 6.2324 cents 15:16:17:19:22:23:24:25:30 SD: 5.8194 cents 23:25:26:30:33:35:37:38:46 SD: 5.7947 cents 25:27:29:32:36:38:40:42:50 SD: 4.4078 cents 27:29:31:35:39:41:43:45:54 SD: 2.5298 cents 41:44:47:53:59:62:66:68:82 SD: 2.2687 cents 42:45:48:54:61:64:67:70:84 SD: 2.0887 cents 53:57:61:68:77:81:85:88:106 SD: 1.8577 cents 55:59:63:71:80:84:88:91:110 SD: 1.7511 cents 56:60:64:72:81:85:90:93:112 SD: 1.3521 cents 69:74:79:89:100:105:111:115:138 SD: 1.0508 cents 86:92:99:111:125:131:138:143:172 SD: 1.0411 cents 94:101:108:121:136:143:151:156:188 SD: 0.8860 cents 100:107:115:129:145:152:161:166:200 SD: 0.7830 cents 115:123:132:148:167:175:185:191:230 SD: 0.7777 cents 127:136:146:164:184:193:204:211:254 SD: 0.5907 cents 142:152:163:183:206:216:228:236:284 SD: 0.3822 cents 183:196:210:236:265:279:294:304:366 SD: 0.3748 cents 236:253:271:304:342:359:379:392:472 SD: 0.3308 cents 256:274:294:330:371:390:411:425:512 SD: 0.2851 cents 283:303:325:365:410:431:455:470:566 SD: 0.2775 cents 297:318:341:383:430:452:477:493:594 SD: 0.2234 cents 310:332:356:400:449:472:498:515:620 SD: 0.2189 cents 325:348:373:419:471:495:522:540:650 SD: 0.1710 cents 366:392:420:472:530:557:588:608:732 SD: 0.1687 cents 419:449:481:540:607:638:673:696:838 SD: 0.1644 cents 439:470:504:566:636:668:705:729:878 SD: 0.1263 cents 508:544:583:655:736:773:816:844:1016 SD: 0.1218 cents