Scala analysis: CD10_05_Egypt
Megalo - 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: 31.226 cents 31.225865 2: 233.081 cents 233.081008 3: 336.179 cents 336.179228 4: 435.768 cents 435.767605 5: 558.925 cents 558.925310 6: 753.675 cents 753.675387 7: 938.094 cents 938.094439 8: 1116.513 cents 1116.512691 9: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 83.4873 cents 83.4873 1: 31.2259 cents 31.2259 2: 201.8551 cents 201.8551 3: 103.0982 cents 103.0982 4: 99.5884 cents 99.5884 5: 123.1577 cents 123.1577 6: 194.7501 cents 194.7501 7: 184.4191 cents 184.4191 8: 178.4183 cents 178.4183 9: 83.4873 cents 83.4873
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 31.22586 cents 1: 1 83.48731 cents 1: 1 99.58838 cents 1: 1 103.09822 cents 1: 1 123.15771 cents 1: 1 178.41825 cents 1: 1 184.41905 cents 1: 1 194.75008 cents 1: 1 201.85514 cents 2: 1 114.71317 cents 2: 1 202.68660 cents 2: 1 222.74608 cents 2: 1 233.08101 cents 2: 1 261.90556 cents 2: 1 304.95336 cents 2: 1 317.90778 cents 2: 1 362.83730 cents 2: 1 379.16913 cents 3: 1 293.13143 cents 3: 1 316.56832 cents 3: 1 325.84430 cents 3: 1 336.17923 cents 3: 1 404.54174 cents 3: 1 417.49616 cents 3: 1 446.32461 cents 3: 1 502.32683 cents 3: 1 557.58738 cents 4: 1 419.66654 cents 4: 1 435.76761 cents 4: 1 477.55048 cents 4: 1 494.98657 cents 4: 1 520.59438 cents 4: 1 527.69945 cents 4: 1 601.91521 cents 4: 1 641.07469 cents 4: 1 680.74509 cents 5: 1 519.25491 cents 5: 1 558.92531 cents 5: 1 598.08479 cents 5: 1 672.30055 cents 5: 1 679.40562 cents 5: 1 705.01343 cents 5: 1 722.44952 cents 5: 1 764.23239 cents 5: 1 780.33346 cents 6: 1 642.41262 cents 6: 1 697.67317 cents 6: 1 753.67539 cents 6: 1 782.50384 cents 6: 1 795.45826 cents 6: 1 863.82077 cents 6: 1 874.15570 cents 6: 1 883.43168 cents 6: 1 906.86857 cents 7: 1 820.83087 cents 7: 1 837.16270 cents 7: 1 882.09222 cents 7: 1 895.04664 cents 7: 1 938.09444 cents 7: 1 966.91899 cents 7: 1 977.25392 cents 7: 1 997.31340 cents 7: 1 1085.28683 cents 8: 1 998.14486 cents 8: 1 1005.24992 cents 8: 1 1015.58095 cents 8: 1 1021.58175 cents 8: 1 1076.84229 cents 8: 1 1096.90178 cents 8: 1 1100.41162 cents 8: 1 1116.51269 cents 8: 1 1168.77414 cents Highest number of different intervals for one interval class: 9 Average number of different intervals per interval class: 9.00000 = 9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 0.0 : 31.2 233.1 336.2 435.8 558.9 753.7 938.1 1116.5 1200.0 31.2 : 201.9 305.0 404.5 527.7 722.4 906.9 1085.3 1168.8 1200.0 233.1 : 103.1 202.7 325.8 520.6 705.0 883.4 966.9 998.1 1200.0 336.2 : 99.6 222.7 417.5 601.9 780.3 863.8 895.0 1096.9 1200.0 435.8 : 123.2 317.9 502.3 680.7 764.2 795.5 997.3 1100.4 1200.0 558.9 : 194.8 379.2 557.6 641.1 672.3 874.2 977.3 1076.8 1200.0 753.7 : 184.4 362.8 446.3 477.6 679.4 782.5 882.1 1005.2 1200.0 938.1 : 178.4 261.9 293.1 495.0 598.1 697.7 820.8 1015.6 1200.0 1116.5: 83.5 114.7 316.6 419.7 519.3 642.4 837.2 1021.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 31.2259 .. 201.8551 cents 170.62928 cents 31.22586 cents 2: 114.7132 .. 379.1691 cents 264.45595 cents -87.14197 cents 3: 293.1314 .. 557.5874 cents 264.45595 cents -86.03770 cents 4: 419.6665 .. 680.7451 cents 261.07855 cents -137.92084 cents 5: 519.2549 .. 780.3335 cents 261.07855 cents -161.49017 cents 6: 642.4126 .. 906.8686 cents 264.45596 cents -137.92084 cents 7: 820.8309 .. 1085.2868 cents 264.45595 cents -86.03770 cents 8: 998.1449 .. 1168.7741 cents 170.62928 cents -87.14197 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 31.22586 cents, class 1 Average step (divided formal octave): 133.3333 cents Largest one step interval : 201.85514 cents Average / Smallest step : 4.269964 Largest / Average step : 1.513914 Largest / Smallest step : 6.464357 Median interval of one step : 123.15771 cents, amount: 1 Least squares average step : 129.34890 cents, oct.: 1164.14013 cents Scale is not proper Step pattern alph. order: ABCDEFGHI Step pattern size order : AIDCEHGFB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 0.83145 cents Scale diversity : 1.719445 Lumma stability : 0.052043 Lumma impropriety factor : 0.589189 Rothenberg efficiency : 0.222222 redundancy: 0.777778 Efficiency x scale size : 2.000000 Number of different interval sizes : 72 = 9.00000 / class Number of one step interval sizes : 9 Highest interval variety : 9 Mean interval variety : 9.00000 = 9 Median interval variety : 9 Lowest interval variety : 9 Smallest interval difference : 0.83145 cents Number of recognisable fifths : 2, average 701.3433 cents Formal octave complements present : 1 = 11.1111% -- Rational properties --
FIT/MODE
9: 0 1 1 1 1 1 2 1 1 N T3 SD: 55.5465 c. M: 99.7477 c. 10: 0 2 1 1 1 1 2 1 1 N D3 SD: 30.1497 c. M:-44.2324 c. 11: 0 2 1 1 1 2 2 1 1 N SD: 21.4080 c. M:-43.7237 c. 14: 0 3 1 1 2 2 2 2 1 N SD: 20.2220 c. M:-41.0747 c. 15: 0 3 1 1 2 2 3 2 1 N SD: 21.5799 c. M: 35.7676 c. 17: 0 3 2 1 2 3 2 3 1 N SD: 18.2504 c. M: 31.2259 c. 19: 1 3 1 2 2 3 3 3 1 N SD: 16.5498 c. M:-31.9320 c. 22: 0 4 2 2 2 4 3 3 2 N SD: 16.0902 c. M: 31.2259 c. 24: 1 4 2 2 2 4 4 3 2 N SD: 13.0804 c. M:-18.7741 c. 25: 1 4 2 2 3 4 4 3 2 N SD: 12.8090 c. M:-21.9056 c. 27: 1 4 3 2 3 4 4 4 2 N SD: 11.3244 c. M:-19.3763 c. 28: 1 4 3 2 3 5 4 4 2 N SD: 10.1704 c. M: 18.7953 c. 30: 1 5 2 3 3 5 4 5 2 N SD: 9.3409 c. M: 18.0944 c. 32: 1 5 3 3 3 5 5 5 2 N SD: 6.7301 c. M:-14.2324 c. 37: 1 6 3 3 4 6 6 5 3 N SD: 8.7722 c. M: 14.1460 c. 38: 1 6 4 3 4 6 6 5 3 N SD: 8.3713 c. M: 12.0284 c. 40: 1 7 3 4 4 6 6 6 3 N SD: 7.7043 c. M:-14.2324 c. 41: 1 7 3 4 4 7 6 6 3 N SD: 5.7756 c. M: 14.2280 c. 43: 1 7 4 4 4 7 7 6 3 N SD: 6.1534 c. M:-10.7440 c. 45: 1 8 4 3 5 7 7 7 3 N SD: 6.2055 c. M:-10.4874 c. 46: 1 8 4 4 4 8 7 7 3 N SD: 5.3453 c. M: 11.0992 c. 56: 1 10 5 4 6 9 9 8 4 N SD: 5.2029 c. M: 9.7973 c. 58: 1 10 5 5 6 9 9 9 4 N SD: 5.7549 c. M: 10.5362 c. 60: 2 10 5 5 6 10 9 9 4 N SD: 4.8799 c. M:-8.7741 c. 61: 2 10 5 5 6 10 10 9 4 N SD: 5.2829 c. M:-8.1184 c. 64: 2 10 6 5 7 10 10 10 4 N SD: 5.0055 c. M:-8.4873 c. 67: 2 11 6 5 7 11 10 10 5 N SD: 4.3624 c. M: 6.7512 c. 68: 2 11 6 6 7 11 10 10 5 N SD: 4.0873 c. M:-5.7806 c. 69: 2 11 6 6 7 11 11 10 5 N SD: 4.0639 c. M: 6.9941 c. 72: 2 12 6 6 7 12 11 11 5 N SD: 3.8642 c. M: 8.9253 c. 75: 2 13 6 6 8 12 12 11 5 N SD: 3.5543 c. M:-6.9190 c. 78: 2 13 7 6 8 13 12 12 5 N SD: 3.4123 c. M:-6.5642 c. 82: 2 14 7 7 8 14 12 12 6 N SD: 3.2989 c. M:-7.3002 c. 83: 2 14 7 7 9 13 13 12 6 N SD: 2.7297 c. M:-4.9301 c. 86: 2 15 7 7 9 14 13 13 6 N SD: 2.3817 c. M:-4.1283 c. 107: 3 18 9 9 11 17 17 16 7 N SD: 2.6555 c. M:-4.9826 c. 110: 3 18 10 9 11 18 17 16 8 N SD: 2.2196 c. M: 3.9901 c. 113: 3 19 10 9 12 18 17 17 8 N SD: 2.2224 c. M:-3.9065 c. 114: 3 19 10 9 12 19 17 17 8 N SD: 2.1427 c. M:-4.2193 c. 118: 3 20 10 10 12 19 18 18 8 N SD: 1.3366 c. M: 2.5012 c. 182: 5 30 16 15 19 29 28 27 13 N SD: 1.6145 c. M: 2.3118 c. 185: 5 31 16 15 19 30 29 27 13 N SD: 1.2329 c. M:-2.4461 c. 189: 5 32 16 16 19 31 29 28 13 N SD: 1.3406 c. M:-2.3276 c. 196: 5 33 17 16 20 32 30 29 14 N SD: 1.1730 c. M: 2.2270 c. 206: 5 35 18 17 21 33 32 31 14 N SD: 1.3875 c. M: 2.2191 c. 215: 6 36 18 18 22 35 33 32 15 N SD: 1.0352 c. M:-2.2625 c. 217: 6 36 19 18 22 35 34 32 15 N SD: 1.2484 c. M:-1.9977 c. 221: 6 37 19 18 23 36 34 33 15 N SD: 1.1143 c. M:-2.0393 c. 225: 6 38 19 19 23 36 35 33 16 N SD: 1.2154 c. M: 1.8460 c. 226: 6 38 19 19 23 37 35 33 16 N SD: 1.0964 c. M:-1.7286 c. 228: 6 38 20 19 23 37 35 34 16 N SD: 0.9556 c. M: 1.5021 c. 242: 6 41 21 20 25 39 37 36 17 N SD: 0.8820 c. M: 1.4738 c. 258: 7 43 22 22 26 42 40 38 18 N SD: 0.9768 c. M:-1.4417 c. 261: 7 44 22 22 27 42 40 39 18 N SD: 0.9925 c. M:-1.9942 c. 271: 7 46 23 22 28 44 42 40 19 N SD: 0.9839 c. M: 1.8193 c. 272: 7 46 23 23 28 44 42 40 19 N SD: 0.9173 c. M:-1.6114 c. 275: 7 46 24 23 28 45 42 41 19 N SD: 0.8252 c. M: 1.8083 c. 303: 8 51 26 25 31 49 47 45 21 N SD: 0.5619 c. M: 1.2001 c. 371: 10 62 32 31 38 60 57 55 26 N SD: 0.5698 c. M:-1.1191 c. 385: 10 65 33 32 39 63 59 57 27 N SD: 0.5636 c. M: 1.0032 c. 417: 11 70 36 34 43 68 64 62 29 N SD: 0.5247 c. M: 1.2352 c. 432: 11 73 37 36 44 70 67 64 30 N SD: 0.5214 c. M: 0.8976 c. 449: 12 75 39 37 46 73 69 67 31 N SD: 0.4598 c. M:-0.8454 c. 457: 12 77 39 38 47 74 70 68 32 N SD: 0.3907 c. M: 0.6765 c. 490: 13 82 42 41 50 80 75 73 34 N SD: 0.4445 c. M: 0.6690 c. 500: 13 84 43 42 51 81 77 74 35 N SD: 0.4236 c. M:-1.0324 c. 532: 14 89 46 44 55 86 82 79 37 N SD: 0.3731 c. M: 0.7502 c. 535: 14 90 46 44 55 87 82 80 37 N SD: 0.3701 c. M: 0.6274 c. 546: 14 92 47 45 56 89 84 81 38 N SD: 0.3688 c. M: 0.6836 c. 578: 15 97 50 48 59 94 89 86 40 N SD: 0.3132 c. M: 0.5551 c. 586: 15 99 50 49 60 95 90 87 41 N SD: 0.3280 c. M: 0.5091 c. 618: 16 104 53 51 64 100 95 92 43 N SD: 0.3301 c. M: 0.8161 c. 650: 17 109 56 54 67 105 100 97 45 N SD: 0.3195 c. M: 0.4656 c. 664: 17 112 57 55 68 108 102 99 46 N SD: 0.2787 c. M: 0.5030 c. 721: 19 121 62 60 74 117 111 107 50 N SD: 0.3073 c. M:-0.6018 c. 732: 19 123 63 61 75 119 112 109 51 N SD: 0.2466 c. M:-0.4230 c. 807: 21 136 69 67 83 131 124 120 56 N SD: 0.1922 c. M:-0.3762 c. 917: 24 154 79 76 94 149 141 136 64 N SD: 0.1508 c. M: 0.2641 c. 1035: 27 174 89 86 106 168 159 154 72 N SD: 0.0856 c. M:-0.1744 c. 1653: 43 278 142 137 170 268 254 246 115 N SD: 0.1020 c. M: 0.1959 c. 1724: 45 290 148 143 177 280 265 256 120 N SD: 0.0949 c. M:-0.1886 c. 1842: 48 310 158 153 189 299 283 274 128 N SD: 0.0694 c. M:-0.1437 c. 1952: 51 328 168 162 200 317 300 290 136 N SD: 0.0874 c. M:-0.1266 c. 2038: 53 343 175 169 209 331 313 303 142 N SD: 0.0820 c. M: 0.1422 c. 2153: 56 362 185 179 221 349 331 320 150 N SD: 0.0885 c. M: 0.1222 c. 2374: 62 399 204 197 244 385 365 353 165 N SD: 0.0737 c. M:-0.1311 c.
FIT/HARMONIC
1 x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x 4 S SD: 25.8602 cents 3 x x x x 4 x 5 x 6 S SD: 27.0677 cents 4 x x x 5 x 6:7 x 8 S SD: 19.4697 cents 5 x x 6 x 7:8:9 x 10 S SD: 20.8806 cents 6 x 7 x x 8:9:10:11:12 S SD: 20.3578 cents 7 x 8 x 9:10:11:12:13:14 S SD: 11.3360 cents 8 x 9 x 10:11:12:14:15:16 S SD: 12.5939 cents 9 x 10:11 x 12:14:15:17:18 SD: 14.0362 cents 10 x 11:12:13:14:15:17:19:20 SD: 11.8813 cents 11 x x 13:14:15:17:19:21:22 SD: 7.9498 cents 12 x 14 x 15:17:19:21:23:24 SD: 13.0343 cents 13:14:15:16:17:18:20:22:25:26 SD: 12.2083 cents 14:15:16:17:18:19:22:24:27:28 SD: 11.0984 cents 15:16:17:18:19:21:23:26:29:30 SD: 10.7920 cents 18:19:21:22:23:25:28:31:34:36 SD: 8.4323 cents 20:21:23:24:26:28:31:34:38:40 SD: 7.5882 cents 21:22:24:26:27:29:32:36:40:42 SD: 7.1890 cents 22:23:25:27:28:30:34:38:42:44 SD: 6.5337 cents 24:25:27:29:31:33:37:41:46:48 SD: 5.9075 cents 27:28:31:33:35:37:42:46:51:54 SD: 5.1462 cents 28:29:32:34:36:39:43:48:53:56 SD: 4.1249 cents 29:30:33:35:37:40:45:50:55:58 SD: 4.0072 cents 32:33:37:39:41:44:49:55:61:64 SD: 3.8798 cents 33:34:38:40:42:46:51:57:63:66 SD: 3.8794 cents 34:35:39:41:44:47:53:58:65:68 SD: 3.6370 cents 35:36:40:43:45:48:54:60:67:70 SD: 3.4400 cents 36:37:41:44:46:50:56:62:69:72 SD: 3.3505 cents 39:40:45:47:50:54:60:67:74:78 SD: 2.9830 cents 41:42:47:50:53:57:63:70:78:82 SD: 2.8044 cents 42:43:48:51:54:58:65:72:80:84 SD: 1.2466 cents 92:94:105:112:118:127:142:158:175:184 SD: 1.2030 cents 95:97:109:115:122:131:147:163:181:190 SD: 1.1540 cents 97:99:111:118:125:134:150:167:185:194 SD: 0.7549 cents 118:120:135:143:152:163:182:203:225:236 SD: 0.6833 cents 126:128:144:153:162:174:195:217:240:252 SD: 0.6635 cents 150:153:172:182:193:207:232:258:286:300 SD: 0.6209 cents 154:157:176:187:198:213:238:265:293:308 SD: 0.5741 cents 158:161:181:192:203:218:244:272:301:316 SD: 0.5226 cents 160:163:183:194:206:221:247:275:305:320 SD: 0.4317 cents 168:171:192:204:216:232:260:289:320:336 SD: 0.3878 cents 220:224:252:267:283:304:340:378:419:440 SD: 0.3231 cents 270:275:309:328:347:373:417:464:515:540 SD: 0.2970 cents 284:289:325:345:365:392:439:488:541:568 SD: 0.2725 cents 321:327:367:390:413:443:496:552:612:642 SD: 0.2619 cents 328:334:375:398:422:453:507:564:625:656 SD: 0.2155 cents 381:388:436:463:490:526:589:655:726:762 SD: 0.1792 cents 438:446:501:532:563:605:677:753:835:876 SD: 0.1569 cents 444:452:508:539:571:613:686:763:846:888 SD: 0.1433 cents 499:508:571:606:642:689:771:858:951:998 SD: 0.0982 cents 541:551:619:657:696:747:836:930:1031:1082 SD: 0.0875 cents