Scala analysis: CD10_14_Egypt
Obi et Khen Bi / Omonogis / Golgotha - 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: 44.729 cents 44.729438 2: 116.101 cents 116.101440 3: 266.398 cents 266.397883 4: 399.906 cents 399.906377 5: 628.940 cents 628.940030 6: 813.416 cents 813.416264 7: 1006.155 cents 1006.154916 8: 1112.053 cents 1112.052955 9: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 87.9470 cents 87.9470 1: 44.7294 cents 44.7294 2: 71.3720 cents 71.3720 3: 150.2964 cents 150.2964 4: 133.5085 cents 133.5085 5: 229.0337 cents 229.0337 6: 184.4762 cents 184.4762 7: 192.7387 cents 192.7387 8: 105.8980 cents 105.8980 9: 87.9470 cents 87.9470
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 44.72944 cents 1: 1 71.37200 cents 1: 1 87.94705 cents 1: 1 105.89804 cents 1: 1 133.50849 cents 1: 1 150.29644 cents 1: 1 184.47623 cents 1: 1 192.73865 cents 1: 1 229.03365 cents 2: 1 116.10144 cents 2: 1 132.67648 cents 2: 1 193.84508 cents 2: 1 221.66844 cents 2: 1 283.80494 cents 2: 1 298.63669 cents 2: 1 362.54215 cents 2: 1 377.21489 cents 2: 1 413.50989 cents 3: 1 204.04849 cents 3: 1 238.57452 cents 3: 1 266.39788 cents 3: 1 355.17694 cents 3: 1 386.58374 cents 3: 1 483.11292 cents 3: 1 512.83859 cents 3: 1 547.01838 cents 3: 1 606.24854 cents 4: 1 309.94652 cents 4: 1 354.34493 cents 4: 1 399.90638 cents 4: 1 431.31317 cents 4: 1 571.05997 cents 4: 1 584.21059 cents 4: 1 697.31482 cents 4: 1 712.14658 cents 4: 1 739.75703 cents 5: 1 460.24297 cents 5: 1 487.85342 cents 5: 1 502.68518 cents 5: 1 615.78941 cents 5: 1 628.94003 cents 5: 1 768.68683 cents 5: 1 800.09362 cents 5: 1 845.65507 cents 5: 1 890.05348 cents 6: 1 593.75146 cents 6: 1 652.98162 cents 6: 1 687.16141 cents 6: 1 716.88708 cents 6: 1 813.41626 cents 6: 1 844.82306 cents 6: 1 933.60212 cents 6: 1 961.42548 cents 6: 1 995.95151 cents 7: 1 786.49011 cents 7: 1 822.78511 cents 7: 1 837.45785 cents 7: 1 901.36331 cents 7: 1 916.19506 cents 7: 1 978.33156 cents 7: 1 1006.15492 cents 7: 1 1067.32352 cents 7: 1 1083.89856 cents 8: 1 970.96635 cents 8: 1 1007.26135 cents 8: 1 1015.52377 cents 8: 1 1049.70356 cents 8: 1 1066.49151 cents 8: 1 1094.10196 cents 8: 1 1112.05295 cents 8: 1 1128.62800 cents 8: 1 1155.27056 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 : 44.7 116.1 266.4 399.9 628.9 813.4 1006.2 1112.1 1200.0 44.7 : 71.4 221.7 355.2 584.2 768.7 961.4 1067.3 1155.3 1200.0 116.1 : 150.3 283.8 512.8 697.3 890.1 996.0 1083.9 1128.6 1200.0 266.4 : 133.5 362.5 547.0 739.8 845.7 933.6 978.3 1049.7 1200.0 399.9 : 229.0 413.5 606.2 712.1 800.1 844.8 916.2 1066.5 1200.0 628.9 : 184.5 377.2 483.1 571.1 615.8 687.2 837.5 971.0 1200.0 813.4 : 192.7 298.6 386.6 431.3 502.7 653.0 786.5 1015.5 1200.0 1006.2: 105.9 193.8 238.6 309.9 460.2 593.8 822.8 1007.3 1200.0 1112.1: 87.9 132.7 204.0 354.3 487.9 716.9 901.4 1094.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 44.7294 .. 229.0337 cents 184.30421 cents 44.72944 cents 2: 116.1014 .. 413.5099 cents 297.40845 cents -112.93221 cents 3: 204.0485 .. 606.2485 cents 402.20005 cents -209.46140 cents 4: 309.9465 .. 739.7570 cents 429.81051 cents -296.30201 cents 5: 460.2430 .. 890.0535 cents 429.81051 cents -279.51407 cents 6: 593.7515 .. 995.9515 cents 402.20005 cents -296.30201 cents 7: 786.4901 .. 1083.8986 cents 297.40845 cents -209.46140 cents 8: 970.9663 .. 1155.2706 cents 184.30421 cents -112.93221 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 44.72944 cents, class 1 Average step (divided formal octave): 133.3333 cents Largest one step interval : 229.03365 cents Average / Smallest step : 2.980886 Largest / Average step : 1.717752 Largest / Smallest step : 5.120423 Median interval of one step : 133.50849 cents, amount: 1 Least squares average step : 131.37003 cents, oct.: 1182.33023 cents Scale is not proper Step pattern alph. order: ABCDEFGHI Step pattern size order : ABFEIGHDC Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 0.83201 cents Scale diversity : 1.793452 Lumma stability : 0.074549 Lumma impropriety factor : 0.806498 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 : 0.83201 cents Number of recognisable fifths : 4, average 703.3775 cents Number of appreciable fifths : 2, average 704.7307 cents Formal octave complements present : 1 = 11.1111% -- Rational properties --
FIT/MODE
9: 0 1 1 1 2 1 2 0 1 N SD: 32.6983 c. M:-60.5118 c. 10: 0 1 1 1 2 2 1 1 1 N S SD: 31.6354 c. M: 46.1549 c. 12: 0 1 2 1 2 2 2 1 1 N SD: 22.5826 c. M: 44.7294 c. 13: 0 1 2 1 3 2 2 1 1 N SD: 21.9096 c. M: 44.7294 c. 15: 1 0 2 2 3 2 3 1 1 N SD: 22.9859 c. M: 36.1014 c. 18: 1 1 2 2 3 3 3 2 1 N SD: 15.9392 c. M: 28.9400 c. 19: 1 1 2 2 4 3 3 2 1 N SD: 14.0302 c. M:-24.7892 c. 23: 1 1 3 3 4 4 3 2 2 N SD: 12.8411 c. M:-21.3663 c. 24: 1 1 3 3 4 4 4 2 2 N SD: 13.9707 c. M: 28.9400 c. 25: 1 1 3 3 5 4 4 2 2 N SD: 12.7539 c. M: 26.3979 c. 26: 1 2 3 3 5 4 4 2 2 N SD: 13.1403 c. M:-22.3601 c. 27: 1 2 3 3 5 4 5 2 2 N SD: 9.3171 c. M:-17.2319 c. 30: 1 2 4 3 6 4 5 3 2 N SD: 8.3397 c. M:-13.6021 c. 31: 1 2 4 3 6 5 5 3 2 N SD: 6.8659 c. M: 12.8096 c. 44: 2 2 6 5 8 7 7 4 3 N SD: 6.1607 c. M:-9.8160 c. 49: 2 3 6 5 10 7 8 4 4 N SD: 6.0121 c. M: 10.0121 c. 50: 2 3 6 6 9 8 8 4 4 N SD: 4.6724 c. M:-8.0936 c. 54: 2 3 7 6 10 9 8 5 4 N SD: 4.5523 c. M:-8.8060 c. 55: 2 3 7 6 11 8 9 5 4 N SD: 4.4937 c. M: 7.1791 c. 63: 2 4 8 7 12 10 10 5 5 N SD: 3.9965 c. M: 7.2911 c. 72: 3 4 9 8 14 11 11 7 5 N SD: 3.6089 c. M: 6.1549 c. 80: 3 5 10 9 15 12 13 7 6 N SD: 2.8389 c. M:-5.0936 c. 81: 3 5 10 9 15 13 13 7 6 N SD: 2.4843 c. M: 6.7178 c. 86: 3 5 11 10 16 13 14 8 6 N SD: 3.1713 c. M:-4.7448 c. 93: 3 6 12 10 18 14 15 8 7 N SD: 2.8700 c. M: 6.0198 c. 99: 4 6 12 11 19 15 16 9 7 N SD: 2.4369 c. M:-5.1107 c. 105: 4 6 13 12 20 16 17 9 8 N SD: 1.9211 c. M: 3.5407 c. 112: 4 7 14 12 22 17 18 10 8 N SD: 2.0491 c. M: 3.4778 c. 134: 5 8 17 15 25 21 21 12 10 N SD: 1.9404 c. M: 3.1698 c. 135: 5 8 17 15 26 21 21 12 10 N SD: 1.7641 c. M:-4.3615 c. 136: 5 8 17 15 26 21 22 12 10 N SD: 1.5733 c. M: 2.8476 c. 153: 6 9 19 17 29 24 24 14 11 N SD: 1.6004 c. M:-2.3294 c. 162: 6 10 20 18 31 25 26 14 12 N SD: 1.1001 c. M:-2.4171 c. 168: 6 10 21 19 32 26 27 15 12 N SD: 1.4191 c. M:-2.2328 c. 189: 7 11 24 21 36 29 30 17 14 N SD: 1.2418 c. M: 2.9803 c. 193: 7 12 24 21 37 30 31 17 14 N SD: 1.2719 c. M:-2.0333 c. 204: 8 12 25 23 39 31 33 18 15 N SD: 1.2380 c. M:-2.3294 c. 206: 8 12 26 23 39 32 33 18 15 N SD: 1.4023 c. M:-2.1177 c. 208: 8 12 26 23 40 32 33 19 15 N SD: 1.2579 c. M: 2.3088 c. 215: 8 13 27 24 41 33 34 19 16 N SD: 1.3610 c. M:-1.9541 c. 216: 8 13 27 24 41 33 35 19 16 N SD: 0.9657 c. M: 2.3052 c. 217: 8 13 27 24 42 33 35 19 16 N SD: 0.8840 c. M: 1.7497 c. 235: 9 14 29 26 45 36 38 21 17 N SD: 1.1043 c. M: 1.6085 c. 246: 9 15 31 27 47 38 39 22 18 N SD: 0.9700 c. M:-1.8948 c. 248: 9 15 31 28 47 38 40 22 18 N SD: 0.7791 c. M:-1.7065 c. 261: 10 15 33 29 50 40 42 23 19 N SD: 0.7390 c. M:-1.2476 c. 298: 11 18 37 33 57 46 48 26 22 N SD: 0.6572 c. M: 1.2487 c. 328: 12 20 41 36 63 50 53 29 24 N SD: 0.7434 c. M: 1.2211 c. 330: 12 20 41 37 63 51 53 29 24 N SD: 0.7575 c. M:-1.1292 c. 341: 13 20 43 38 65 52 55 30 25 N SD: 0.7486 c. M:-1.2666 c. 342: 13 20 43 38 65 53 55 30 25 N SD: 0.5673 c. M:-0.8846 c. 351: 13 21 44 39 67 54 56 31 26 N SD: 0.4948 c. M: 1.0267 c. 423: 16 25 53 47 81 65 68 37 31 N SD: 0.5526 c. M:-0.9373 c. 435: 16 26 55 48 83 67 70 38 32 N SD: 0.5405 c. M:-1.1883 c. 463: 17 28 58 51 89 71 74 41 34 N SD: 0.5644 c. M:-0.8656 c. 465: 17 28 58 52 89 71 75 41 34 N SD: 0.4753 c. M: 0.8585 c. 477: 18 28 60 53 91 73 77 42 35 N SD: 0.3743 c. M: 0.8376 c. 487: 18 29 61 54 93 75 78 43 36 N SD: 0.5286 c. M: 0.8161 c. 506: 19 30 63 57 96 78 81 45 37 N SD: 0.4917 c. M:-0.8841 c. 519: 19 31 65 58 99 80 83 46 38 N SD: 0.4084 c. M: 0.7988 c. 528: 20 31 66 59 101 81 85 46 39 N SD: 0.4877 c. M:-0.7251 c. 531: 20 31 67 59 101 82 85 47 39 N SD: 0.4481 c. M: 0.8472 c. 540: 20 32 68 60 103 83 87 47 40 N SD: 0.4241 c. M: 0.9418 c. 546: 20 33 68 61 104 84 88 48 40 N SD: 0.3873 c. M: 0.7734 c. 559: 21 33 70 62 107 86 90 49 41 N SD: 0.3395 c. M:-0.6429 c. 571: 21 34 72 63 109 88 92 50 42 N SD: 0.4628 c. M: 0.6069 c. 586: 22 35 73 65 112 90 94 52 43 N SD: 0.4267 c. M: 0.6942 c. 589: 22 35 74 65 113 90 95 52 43 N SD: 0.3981 c. M:-0.6016 c. 599: 22 36 75 67 114 92 96 53 44 N SD: 0.3808 c. M:-0.7614 c. 612: 23 36 77 68 117 94 98 54 45 N SD: 0.3100 c. M:-0.4717 c. 618: 23 37 77 69 118 95 99 55 45 N SD: 0.3013 c. M:-0.5684 c. 639: 24 38 80 71 122 98 103 56 47 N SD: 0.2754 c. M:-0.4179 c. 693: 26 41 87 77 132 107 111 61 51 N SD: 0.2670 c. M:-0.4365 c. 807: 30 48 101 90 154 124 130 71 59 N SD: 0.2177 c. M:-0.5365 c. 891: 33 53 112 99 170 137 143 79 65 N SD: 0.2146 c. M:-0.4050 c. 910: 34 54 114 101 174 140 146 80 67 N SD: 0.1965 c. M: 0.4046 c. 918: 34 55 115 102 175 141 148 81 67 N SD: 0.2686 c. M:-0.3810 c. 940: 35 56 118 104 180 144 151 83 69 N SD: 0.2522 c. M:-0.4217 c. 941: 35 56 118 105 179 145 151 83 69 N SD: 0.2096 c. M:-0.5187 c. 996: 37 59 125 111 190 153 160 88 73 N SD: 0.1783 c. M: 0.4388 c. 1053: 39 63 132 117 201 162 169 93 77 N SD: 0.1869 c. M: 0.2850 c. 1095: 41 65 137 122 209 168 176 97 80 N SD: 0.1619 c. M:-0.2758 c. 1158: 43 69 145 129 221 178 186 102 85 N SD: 0.0920 c. M: 0.1699 c. 1801: 67 107 226 200 344 277 289 159 132 N SD: 0.0988 c. M: 0.1658 c. 1900: 71 113 238 211 363 292 305 168 139 N SD: 0.1044 c. M:-0.1576 c. 2005: 75 119 251 223 383 308 322 177 147 N SD: 0.0793 c. M:-0.1583 c. 2017: 75 120 253 224 385 310 324 178 148 N SD: 0.1029 c. M:-0.1366 c. 2086: 78 124 261 232 398 321 335 184 153 N SD: 0.0936 c. M: 0.1768 c. 2253: 84 134 282 251 430 346 362 199 165 N SD: 0.0661 c. M: 0.1007 c.
FIT/HARMONIC
1 x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x x 4 S SD: 36.5075 cents 3 x x x 4 x 5 x x 6 S SD: 40.3650 cents 4 x x x 5:6 x 7 x 8 S SD: 20.7807 cents 5 x x 6 x 7:8:9 x 10 S SD: 13.7280 cents 6 x x 7:8:9:10:11 x 12 S SD: 24.6432 cents 7 x x 8:9:10:11 x 13:14 SD: 12.0114 cents 8 x x 9:10:12:13:14:15:16 S SD: 15.7239 cents 9 x 10 x 11:13:14:16:17:18 SD: 14.1319 cents 10 x 11:12:13:14:16:18:19:20 S SD: 12.5331 cents 11 x 12:13:14:16:18:20:21:22 S SD: 8.6910 cents 12 x 13:14:15:17:19:21:23:24 SD: 7.1575 cents 13 x 14:15:16:19:21:23:25:26 SD: 7.8487 cents 14 x 15:16:18:20:22:25:27:28 SD: 8.1073 cents 15 x 16:18:19:22:24:27:29:30 SD: 8.5527 cents 16 x 17:19:20:23:26:29:30:32 SD: 6.9898 cents 17 x 18:20:21:24:27:30:32:34 S SD: 7.5694 cents 18 x 19:21:23:26:29:32:34:36 SD: 4.8991 cents 19 x 20:22:24:27:30:34:36:38 SD: 5.4422 cents 20 x 21:23:25:29:32:36:38:40 SD: 5.7548 cents 21 x 22:24:26:30:34:38:40:42 SD: 8.3036 cents 22:23:24:26:28:32:35:39:42:44 SD: 6.8700 cents 23:24:25:27:29:33:37:41:44:46 SD: 4.9961 cents 27:28:29:31:34:39:43:48:51:54 SD: 4.2658 cents 28:29:30:33:35:40:45:50:53:56 SD: 3.5714 cents 30:31:32:35:38:43:48:54:57:60 SD: 2.2649 cents 41:42:44:48:52:59:66:73:78:82 SD: 2.2157 cents 42:43:45:49:53:60:67:75:80:84 SD: 1.6024 cents 43:44:46:50:54:62:69:77:82:86 SD: 1.4438 cents 70:72:75:82:88:101:112:125:133:140 SD: 1.3038 cents 72:74:77:84:91:104:115:129:137:144 SD: 1.2125 cents 73:75:78:85:92:105:117:131:139:146 SD: 0.9427 cents 85:87:91:99:107:122:136:152:162:170 SD: 0.8833 cents 103:106:110:120:130:148:165:184:196:206 SD: 0.8394 cents 112:115:120:131:141:161:179:200:213:224 SD: 0.7621 cents 114:117:122:133:144:164:182:204:217:228 SD: 0.7253 cents 115:118:123:134:145:165:184:206:219:230 SD: 0.6982 cents 142:146:152:166:179:204:227:254:270:284 SD: 0.6657 cents 143:147:153:167:180:206:229:256:272:286 SD: 0.6536 cents 146:150:156:170:184:210:234:261:278:292 SD: 0.6499 cents 150:154:160:175:189:216:240:268:285:300 SD: 0.5920 cents 155:159:166:181:195:223:248:277:295:310 SD: 0.5388 cents 157:161:168:183:198:226:251:281:298:314 SD: 0.5043 cents 162:166:173:189:204:233:259:290:308:324 SD: 0.4675 cents 185:190:198:216:233:266:296:331:352:370 SD: 0.3775 cents 228:234:244:266:287:328:365:408:433:456 SD: 0.3605 cents 230:236:246:268:290:331:368:411:437:460 SD: 0.3278 cents 235:241:251:274:296:338:376:420:447:470 SD: 0.3152 cents 265:272:283:309:334:381:424:474:504:530 SD: 0.3055 cents 270:277:289:315:340:388:432:483:513:540 SD: 0.2842 cents 301:309:322:351:379:433:482:538:572:602 SD: 0.2744 cents 331:340:354:386:417:476:530:592:629:662 SD: 0.2725 cents 335:344:358:391:422:482:536:599:637:670 SD: 0.2567 cents 342:351:366:399:431:492:547:612:650:684 SD: 0.2385 cents 343:352:367:400:432:493:549:613:652:686 SD: 0.2165 cents 374:384:400:436:471:538:598:669:711:748 SD: 0.2114 cents 377:387:403:440:475:542:603:674:717:754 SD: 0.1981 cents 415:426:444:484:523:597:664:742:789:830 SD: 0.1509 cents 420:431:449:490:529:604:672:751:798:840 SD: 0.1359 cents 504:517:539:588:635:725:806:901:958:1008 SD: 0.1356 cents 505:518:540:589:636:726:808:903:960:1010 SD: 0.1246 cents 534:548:571:623:673:768:854:955:1015:1068 SD: 0.1128 cents 577:592:617:673:727:830:923:1032:1097:1154 SD: 0.0871 cents