Scala analysis: CD08_13_Egypt
Improvisation de conclusion, Nay - Mustafa Fahreddin Dede (unknown maqam, Egypt)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 74.625 cents 74.625079 2: 150.594 cents 150.593608 3: 283.042 cents 283.042181 4: 485.707 cents 485.706946 5: 613.125 cents 613.125252 6: 737.929 cents 737.928839 7: 892.596 cents 892.595927 8: 981.990 cents 981.990176 9: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 218.0098 cents 218.0098 1: 74.6251 cents 74.6251 2: 75.9685 cents 75.9685 3: 132.4486 cents 132.4486 4: 202.6648 cents 202.6648 5: 127.4183 cents 127.4183 6: 124.8036 cents 124.8036 7: 154.6671 cents 154.6671 8: 89.3942 cents 89.3942 9: 218.0098 cents 218.0098
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 74.62508 cents 1: 1 75.96853 cents 1: 1 89.39425 cents 1: 1 124.80359 cents 1: 1 127.41831 cents 1: 1 132.44857 cents 1: 1 154.66709 cents 1: 1 202.66477 cents 1: 1 218.00982 cents 2: 1 150.59361 cents 2: 1 208.41710 cents 2: 1 244.06134 cents 2: 1 252.22189 cents 2: 1 279.47067 cents 2: 1 292.63490 cents 2: 1 307.40407 cents 2: 1 330.08307 cents 2: 1 335.11334 cents 3: 1 283.04218 cents 3: 1 368.60343 cents 3: 1 368.86492 cents 3: 1 382.02915 cents 3: 1 406.88898 cents 3: 1 411.08187 cents 3: 1 454.88666 cents 3: 1 462.07116 cents 3: 1 462.53164 cents 4: 1 457.99768 cents 4: 1 485.70695 cents 4: 1 496.28323 cents 4: 1 501.05200 cents 4: 1 536.69624 cents 4: 1 538.50017 cents 4: 1 586.87475 cents 4: 1 587.33523 cents 4: 1 609.55375 cents 5: 1 590.44625 cents 5: 1 612.66477 cents 5: 1 613.12525 cents 5: 1 661.49983 cents 5: 1 663.30376 cents 5: 1 698.94800 cents 5: 1 703.71677 cents 5: 1 714.29305 cents 5: 1 742.00232 cents 6: 1 737.46836 cents 6: 1 737.92884 cents 6: 1 745.11334 cents 6: 1 788.91813 cents 6: 1 793.11102 cents 6: 1 817.97085 cents 6: 1 831.13508 cents 6: 1 831.39657 cents 6: 1 916.95782 cents 7: 1 864.88666 cents 7: 1 869.91693 cents 7: 1 892.59593 cents 7: 1 907.36510 cents 7: 1 920.52933 cents 7: 1 947.77811 cents 7: 1 955.93866 cents 7: 1 991.58290 cents 7: 1 1049.40639 cents 8: 1 981.99018 cents 8: 1 997.33523 cents 8: 1 1045.33291 cents 8: 1 1067.55143 cents 8: 1 1072.58169 cents 8: 1 1075.19641 cents 8: 1 1110.60575 cents 8: 1 1124.03147 cents 8: 1 1125.37492 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 : 74.6 150.6 283.0 485.7 613.1 737.9 892.6 982.0 1200.0 74.6 : 76.0 208.4 411.1 538.5 663.3 818.0 907.4 1125.4 1200.0 150.6 : 132.4 335.1 462.5 587.3 742.0 831.4 1049.4 1124.0 1200.0 283.0 : 202.7 330.1 454.9 609.6 698.9 917.0 991.6 1067.6 1200.0 485.7 : 127.4 252.2 406.9 496.3 714.3 788.9 864.9 997.3 1200.0 613.1 : 124.8 279.5 368.9 586.9 661.5 737.5 869.9 1072.6 1200.0 737.9 : 154.7 244.1 462.1 536.7 612.7 745.1 947.8 1075.2 1200.0 892.6 : 89.4 307.4 382.0 458.0 590.4 793.1 920.5 1045.3 1200.0 982.0 : 218.0 292.6 368.6 501.1 703.7 831.1 955.9 1110.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 74.6251 .. 218.0098 cents 143.38474 cents 74.62508 cents 2: 150.5936 .. 335.1133 cents 184.51973 cents -67.41622 cents 3: 283.0422 .. 462.5316 cents 179.48946 cents -52.07116 cents 4: 457.9977 .. 609.5537 cents 151.55606 cents -4.53396 cents 5: 590.4463 .. 742.0023 cents 151.55606 cents -19.10749 cents 6: 737.4684 .. 916.9578 cents 179.48946 cents -4.53396 cents 7: 864.8867 .. 1049.4064 cents 184.51973 cents -52.07116 cents 8: 981.9902 .. 1125.3749 cents 143.38475 cents -67.41622 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 74.62508 cents, class 1 Average step (divided formal octave): 133.3333 cents Largest one step interval : 218.00982 cents Average / Smallest step : 1.786709 Largest / Average step : 1.635074 Largest / Smallest step : 2.921402 Median interval of one step : 127.41831 cents, amount: 1 Least squares average step : 124.78968 cents, oct.: 1123.10712 cents Scale is not proper Step pattern alph. order: ABCDEFGHI Step pattern size order : ABFHEDGCI Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 3.11102 cents Scale diversity : 1.619340 Lumma stability : 0.124375 Lumma impropriety factor : 0.222625 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 : 0.26149 cents Number of recognisable fifths : 3, average 705.6526 cents Number of appreciable fifths : 2, average 701.3324 cents Formal octave complements present : 1 = 11.1111% -- Rational properties --
FIT/MODE
9: 0 1 1 1 1 1 1 1 2 N T3 SD: 63.1288 c. M: 92.5959 c. 10: 0 1 1 2 1 1 1 1 2 N D3 SD: 36.7177 c. M: 74.6251 c. 12: 1 1 1 2 1 1 2 1 2 P D3 SD: 24.8703 c. M:-49.4064 c. 13: 1 1 1 2 2 1 2 1 2 N D3 SD: 24.0997 c. M:-34.0218 c. 15: 1 1 2 2 2 1 2 1 3 N D3 SD: 18.8613 c. M:-36.9578 c. 16: 1 1 2 2 2 2 2 1 3 N T3 SD: 14.8500 c. M: 35.7069 c. 17: 1 1 2 3 2 1 3 1 3 N SD: 16.1974 c. M: 32.0465 c. 18: 1 1 2 3 2 2 2 2 3 N SD: 15.5707 c. M: 25.9293 c. 22: 1 2 2 4 2 2 3 2 4 N SD: 15.2951 c. M: 28.8379 c. 23: 1 2 2 4 3 2 3 2 4 N SD: 13.4747 c. M: 22.4512 c. 24: 2 1 3 4 2 3 3 2 4 N SD: 14.2722 c. M:-25.3749 c. 26: 1 2 3 4 3 3 3 2 5 N SD: 15.4932 c. M: 28.4712 c. 27: 2 1 3 5 3 3 3 2 5 N SD: 11.5691 c. M:-17.6267 c. 29: 2 2 3 5 3 3 4 2 5 N SD: 10.5069 c. M:-17.7489 c. 31: 2 2 3 6 3 3 4 2 6 N SD: 9.0154 c. M:-17.5189 c. 32: 2 2 4 5 3 4 4 2 6 N SD: 8.9003 c. M:-16.9578 c. 34: 2 2 4 6 3 4 4 3 6 N SD: 7.4754 c. M: 13.1253 c. 39: 2 3 4 7 4 4 5 3 7 N SD: 5.5299 c. M: 13.0866 c. 46: 3 3 5 8 5 4 6 4 8 N SD: 7.4931 c. M:-12.9617 c. 47: 3 3 5 8 5 5 6 3 9 N SD: 4.2414 c. M: 11.7774 c. 50: 3 3 6 8 6 5 6 4 9 N SD: 5.6549 c. M:-10.8747 c. 51: 3 3 6 9 5 5 7 4 9 N SD: 5.6950 c. M: 9.4171 c. 54: 3 4 6 9 6 5 7 4 10 N SD: 5.4531 c. M:-9.0970 c. 55: 3 4 6 9 6 6 7 4 10 N SD: 4.0200 c. M: 9.1705 c. 59: 4 3 7 10 6 6 8 4 11 N SD: 4.7292 c. M: 8.2207 c. 62: 4 4 7 10 7 6 8 5 11 N SD: 4.1930 c. M:-7.2804 c. 65: 4 4 7 11 7 7 8 5 12 N SD: 4.0612 c. M: 6.4421 c. 67: 4 4 8 11 7 7 9 5 12 N SD: 3.7669 c. M: 7.3100 c. 77: 5 5 8 13 8 8 10 6 14 N SD: 3.7736 c. M: 5.4613 c. 78: 5 5 8 14 8 8 10 6 14 N SD: 3.4839 c. M:-6.6007 c. 81: 5 5 9 14 8 9 10 6 15 N SD: 3.1786 c. M: 5.7178 c. 82: 5 5 9 14 9 8 11 6 15 N SD: 3.2678 c. M: 6.2215 c. 86: 5 6 9 15 9 9 11 6 16 N SD: 3.0881 c. M: 5.2460 c. 94: 6 6 10 16 10 10 12 7 17 N SD: 1.6390 c. M:-2.5979 c. 143: 9 9 16 24 15 15 18 11 26 N SD: 1.3871 c. M: 3.0854 c. 161: 10 10 18 27 17 17 21 12 29 N SD: 1.2664 c. M: 1.9451 c. 192: 12 12 21 33 20 20 25 14 35 N SD: 1.0206 c. M:-1.7931 c. 208: 13 13 23 35 22 22 27 15 38 N SD: 0.9872 c. M:-1.6348 c. 225: 14 14 25 38 24 23 29 17 41 N SD: 1.0428 c. M: 1.9293 c. 237: 15 15 26 40 25 25 30 18 43 N SD: 0.9422 c. M: 1.4567 c. 242: 15 15 27 41 26 25 31 18 44 N SD: 0.9171 c. M: 1.8333 c. 254: 16 16 28 43 27 26 33 19 46 N SD: 0.7301 c. M:-1.0480 c. 304: 19 19 34 51 32 32 39 23 55 N SD: 0.7187 c. M: 1.2831 c. 309: 19 20 34 52 33 32 40 23 56 N SD: 0.5378 c. M:-0.8627 c. 319: 20 20 35 54 34 33 41 24 58 N SD: 0.5730 c. M: 1.0599 c. 368: 23 23 41 62 39 38 48 27 67 N SD: 0.5673 c. M: 0.9723 c. 374: 23 24 41 63 40 39 48 28 68 N SD: 0.5942 c. M: 1.2150 c. 390: 24 25 43 66 41 41 50 29 71 N SD: 0.4805 c. M: 0.8176 c. 462: 29 29 51 78 49 48 60 34 84 N SD: 0.4010 c. M:-0.9106 c. 480: 30 30 53 81 51 50 62 36 87 N SD: 0.4866 c. M: 0.7069 c. 484: 30 31 53 82 51 51 62 36 88 N SD: 0.4821 c. M:-0.9141 c. 496: 31 31 55 84 52 52 64 37 90 N SD: 0.4697 c. M: 1.0285 c. 501: 31 32 55 85 53 52 65 37 91 N SD: 0.3921 c. M:-0.8172 c. 527: 33 33 58 89 56 55 68 39 96 N SD: 0.4782 c. M: 0.6975 c. 534: 33 34 59 90 57 55 69 40 97 N SD: 0.3935 c. M: 0.8502 c. 605: 38 38 67 102 64 63 78 45 110 N SD: 0.3470 c. M:-0.7468 c. 612: 38 39 67 104 65 63 79 46 111 N SD: 0.4829 c. M: 0.6892 c. 613: 38 39 68 103 65 64 79 46 111 N SD: 0.4036 c. M:-0.8077 c. 615: 38 39 68 104 65 64 79 46 112 N SD: 0.4453 c. M: 0.8886 c. 616: 38 39 68 104 66 64 79 46 112 N SD: 0.4763 c. M: 0.6420 c. 623: 39 39 69 105 66 65 80 47 113 N SD: 0.4249 c. M: 0.7821 c. 628: 39 40 69 106 67 65 81 47 114 N SD: 0.2579 c. M:-0.3618 c. 644: 40 41 71 109 68 67 83 48 117 N SD: 0.2502 c. M:-0.6285 c. 742: 46 47 82 125 79 77 96 55 135 N SD: 0.2866 c. M: 0.5317 c. 805: 50 51 89 136 85 84 104 60 146 N SD: 0.2494 c. M: 0.4544 c. 820: 51 52 90 139 87 85 106 61 149 N SD: 0.2474 c. M: 0.6032 c. 836: 52 53 92 141 89 87 108 62 152 N SD: 0.2401 c. M: 0.5395 c. 852: 53 54 94 144 90 89 110 63 155 N SD: 0.2338 c. M: 0.4492 c. 902: 56 57 100 152 96 94 116 67 164 N SD: 0.2260 c. M:-0.4304 c. 914: 57 58 101 154 97 95 118 68 166 N SD: 0.2459 c. M:-0.5464 c. 932: 58 59 103 157 99 97 120 70 169 N SD: 0.2369 c. M:-0.4133 c. 963: 60 61 106 163 102 100 124 72 175 N SD: 0.2022 c. M: 0.3841 c. 979: 61 62 108 165 104 102 126 73 178 N SD: 0.1890 c. M: 0.3137 c. 1018: 63 65 112 172 108 106 131 76 185 N SD: 0.1920 c. M: 0.3618 c. 1077: 67 68 119 182 114 112 139 80 196 N SD: 0.2100 c. M: 0.3746 c. 1090: 68 69 120 184 116 113 141 81 198 N SD: 0.1917 c. M: 0.3142 c. 1124: 70 71 124 190 119 117 145 84 204 N SD: 0.1587 c. M: 0.3139 c. 1156: 72 73 128 195 123 120 149 86 210 N SD: 0.1902 c. M:-0.3696 c. 1171: 73 74 129 198 124 122 151 87 213 N SD: 0.1699 c. M: 0.3157 c. 1221: 76 77 135 206 130 127 157 91 222 N SD: 0.1548 c. M: 0.2251 c. 1366: 85 86 151 231 145 142 176 102 248 N SD: 0.1522 c. M: 0.3740 c. 1386: 86 88 153 234 147 144 179 103 252 N SD: 0.1325 c. M: 0.2665 c. 1480: 92 94 163 250 157 154 191 110 269 N SD: 0.1087 c. M:-0.2172 c. 1530: 95 97 169 258 163 159 197 114 278 N SD: 0.1192 c. M: 0.2167 c. 1625: 101 103 179 275 172 169 210 121 295 N SD: 0.1637 c. M: 0.2114 c. 1628: 101 103 180 275 173 169 210 121 296 N SD: 0.1262 c. M: 0.2251 c. 1675: 104 106 185 283 178 174 216 125 304 N SD: 0.1092 c. M:-0.2188 c. 1722: 107 109 190 291 183 179 222 128 313 N SD: 0.0797 c. M: 0.1154 c. 2026: 126 128 224 342 215 211 261 151 368 N SD: 0.0711 c. M: 0.1494 c. 2280: 142 144 252 385 242 237 294 170 414 N SD: 0.0774 c. M:-0.1157 c. 2327: 145 147 257 393 247 242 300 173 423 N SD: 0.0757 c. M:-0.1493 c. 2374: 148 150 262 401 252 247 306 177 431 N SD: 0.0895 c. M:-0.1854 c. 2382: 148 151 263 402 253 248 307 177 433 N SD: 0.0776 c. M: 0.1262 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: 17.9869 cents 3 x x x 4 x x 5 x 6 S SD: 4.9450 cents 4 x x x 5 x 6 x 7:8 S SD: 26.6299 cents 5 x x 6 x 7:8 x 9:10 S SD: 18.9809 cents 6 x x 7:8 x 9:10:11:12 S SD: 13.2443 cents 7 x x 8:9:10:11:12 x 14 S SD: 15.7240 cents 8 x 9 x x 11:12:13:14:16 SD: 17.3536 cents 9 x 10:11:12:13:14:15:16:18 S SD: 10.3485 cents 10 x 11:12:13:14:15:17:18:20 SD: 10.0309 cents 11 x 12:13:15:16:17:18:19:22 SD: 10.5005 cents 12 x 13:14:16:17:18:20:21:24 S SD: 5.8577 cents 13 x 14:15:17:19:20:22:23:26 SD: 8.4277 cents 14 x 15:16:19:20:21:23:25:28 SD: 11.4534 cents 15:16 x 18:20:21:23:25:26:30 SD: 8.3713 cents 16:17 x 19:21:23:25:27:28:32 SD: 6.9989 cents 18:19:20:21:24:26:28:30:32:36 S SD: 6.4143 cents 19:20:21:22:25:27:29:32:34:38 SD: 5.5388 cents 21:22:23:25:28:30:32:35:37:42 SD: 3.0493 cents 40:42:44:47:53:57:61:67:71:80 SD: 2.4985 cents 43:45:47:51:57:61:66:72:76:86 SD: 1.8481 cents 62:65:68:73:82:88:95:104:109:124 SD: 1.6648 cents 64:67:70:75:85:91:98:107:113:128 SD: 1.4588 cents 68:71:74:80:90:97:104:114:120:136 SD: 0.6573 cents 111:116:121:131:147:158:170:186:196:222 SD: 0.6005 cents 141:147:154:166:187:201:216:236:249:282 SD: 0.5914 cents 157:164:171:185:208:224:240:263:277:314 SD: 0.5783 cents 163:170:178:192:216:232:250:273:287:326 SD: 0.5761 cents 164:171:179:193:217:234:251:275:289:328 SD: 0.5096 cents 179:187:195:211:237:255:274:300:316:358 SD: 0.4521 cents 186:194:203:219:246:265:285:311:328:372 SD: 0.4225 cents 207:216:226:244:274:295:317:347:365:414 SD: 0.3324 cents 231:241:252:272:306:329:354:387:407:462 SD: 0.3005 cents 254:265:277:299:336:362:389:425:448:508 SD: 0.2798 cents 275:287:300:324:364:392:421:461:485:550 SD: 0.2573 cents 299:312:326:352:396:426:458:501:527:598 SD: 0.2319 cents 320:334:349:377:424:456:490:536:564:640 SD: 0.2255 cents 339:354:370:399:449:483:519:568:598:678 SD: 0.2248 cents 365:381:398:430:483:520:559:611:644:730 SD: 0.2027 cents 384:401:419:452:508:547:588:643:677:768 SD: 0.1935 cents 405:423:442:477:536:577:620:678:714:810 SD: 0.1735 cents 461:481:503:543:610:657:706:772:813:922 SD: 0.1688 cents 473:494:516:557:626:674:724:792:834:946 SD: 0.1394 cents 562:587:613:662:744:801:861:941:991:1124 SD: 0.1287 cents 574:599:626:676:760:818:879:961:1012:1148 SD: 0.1240 cents