Scala analysis: CD01_17_rast_Egypt
Gazelle du désert / Il se leva et fit circuler les coupes - Darwîsh Muhammad al-Harîrî (rast, Egypt)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 208.586 cents 208.585775 2: 350.667 cents 350.667055 3: 497.160 cents 497.159885 4: 701.536 cents 701.535774 5: 819.179 cents 819.178837 6: 892.143 cents 892.142554 7: 1001.313 cents 1001.312595 8: 1035.506 cents 1035.506143 9: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 164.4939 cents 164.4939 1: 208.5858 cents 208.5858 2: 142.0813 cents 142.0813 3: 146.4928 cents 146.4928 4: 204.3759 cents 204.3759 5: 117.6431 cents 117.6431 6: 72.9637 cents 72.9637 7: 109.1700 cents 109.1700 8: 34.1935 cents 34.1935 9: 164.4939 cents 164.4939
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 34.19355 cents 1: 1 72.96372 cents 1: 1 109.17004 cents 1: 1 117.64306 cents 1: 1 142.08128 cents 1: 1 146.49283 cents 1: 1 164.49386 cents 1: 1 204.37589 cents 1: 1 208.58578 cents 2: 1 143.36359 cents 2: 1 182.13376 cents 2: 1 190.60678 cents 2: 1 198.68740 cents 2: 1 288.57411 cents 2: 1 322.01895 cents 2: 1 350.66705 cents 2: 1 350.86872 cents 2: 1 373.07963 cents 3: 1 216.32731 cents 3: 1 299.77682 cents 3: 1 307.85745 cents 3: 1 394.98267 cents 3: 1 407.27318 cents 3: 1 468.51178 cents 3: 1 492.95000 cents 3: 1 497.15989 cents 3: 1 515.16091 cents 4: 1 333.97037 cents 4: 1 380.82116 cents 4: 1 504.15271 cents 4: 1 516.44322 cents 4: 1 541.47550 cents 4: 1 549.35446 cents 4: 1 610.59306 cents 4: 1 661.65374 cents 4: 1 701.53577 cents 5: 1 498.46423 cents 5: 1 538.34626 cents 5: 1 589.40694 cents 5: 1 650.64554 cents 5: 1 658.52450 cents 5: 1 683.55678 cents 5: 1 695.84729 cents 5: 1 819.17884 cents 5: 1 866.02963 cents 6: 1 684.83909 cents 6: 1 702.84012 cents 6: 1 707.05000 cents 6: 1 731.48822 cents 6: 1 792.72682 cents 6: 1 805.01733 cents 6: 1 892.14255 cents 6: 1 900.22318 cents 6: 1 983.67269 cents 7: 1 826.92037 cents 7: 1 849.13128 cents 7: 1 849.33294 cents 7: 1 877.98105 cents 7: 1 911.42589 cents 7: 1 1001.31260 cents 7: 1 1009.39322 cents 7: 1 1017.86624 cents 7: 1 1056.63641 cents 8: 1 991.41422 cents 8: 1 995.62411 cents 8: 1 1035.50614 cents 8: 1 1053.50717 cents 8: 1 1057.91872 cents 8: 1 1082.35694 cents 8: 1 1090.82996 cents 8: 1 1127.03628 cents 8: 1 1165.80645 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 : 208.6 350.7 497.2 701.5 819.2 892.1 1001.3 1035.5 1200.0 208.6 : 142.1 288.6 492.9 610.6 683.6 792.7 826.9 991.4 1200.0 350.7 : 146.5 350.9 468.5 541.5 650.6 684.8 849.3 1057.9 1200.0 497.2 : 204.4 322.0 395.0 504.2 538.3 702.8 911.4 1053.5 1200.0 701.5 : 117.6 190.6 299.8 334.0 498.5 707.1 849.1 995.6 1200.0 819.2 : 73.0 182.1 216.3 380.8 589.4 731.5 878.0 1082.4 1200.0 892.1 : 109.2 143.4 307.9 516.4 658.5 805.0 1009.4 1127.0 1200.0 1001.3: 34.2 198.7 407.3 549.4 695.8 900.2 1017.9 1090.8 1200.0 1035.5: 164.5 373.1 515.2 661.7 866.0 983.7 1056.6 1165.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 34.1935 .. 208.5858 cents 174.39223 cents 34.19355 cents 2: 143.3636 .. 373.0796 cents 229.71604 cents -65.22219 cents 3: 216.3273 .. 515.1609 cents 298.83361 cents -156.75233 cents 4: 333.9704 .. 701.5358 cents 367.56540 cents -181.19054 cents 5: 498.4642 .. 866.0296 cents 367.56540 cents -203.07155 cents 6: 684.8391 .. 983.6727 cents 298.83361 cents -181.19054 cents 7: 826.9204 .. 1056.6364 cents 229.71604 cents -156.75233 cents 8: 991.4142 .. 1165.8065 cents 174.39223 cents -65.22219 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 34.19355 cents, class 1 Average step (divided formal octave): 133.3333 cents Largest one step interval : 208.58578 cents Average / Smallest step : 3.899371 Largest / Average step : 1.564393 Largest / Smallest step : 6.100150 Median interval of one step : 142.08128 cents, amount: 1 Least squares average step : 142.98081 cents, oct.: 1286.82725 cents Scale is not proper Step pattern alph. order: ABCDEFGHI Step pattern size order : IEFHDBCAG Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 1.28231 cents Scale diversity : 1.645128 Lumma stability : 0.056989 Lumma impropriety factor : 0.748158 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 : 0.20166 cents Number of recognisable fifths : 4, average 701.8183 cents Formal octave complements present : 1 = 11.1111% -- Rational properties --
FIT/MODE
9: 1 1 1 2 1 0 1 0 2 N SD: 72.4902 c. M: 102.1728 c. 10: 2 1 1 2 1 0 1 1 1 N SD: 30.8187 c. M: 52.1426 c. 12: 2 1 2 2 1 1 1 0 2 N SD: 21.9678 c. M: 50.6671 c. 13: 2 2 1 3 1 1 1 0 2 N SD: 24.1425 c. M:-36.9258 c. 16: 3 2 2 2 2 1 1 1 2 N SD: 19.2607 c. M:-27.8401 c. 17: 3 2 2 3 2 1 1 1 2 N S SD: 15.5846 c. M:-27.8800 c. 22: 4 2 3 4 2 1 2 1 3 N SD: 12.8852 c. M: 23.3943 c. 24: 4 3 3 4 2 2 2 1 3 N SD: 8.9811 c. M: 19.1788 c. 31: 5 4 4 5 3 2 3 1 4 N SD: 7.0955 c. M: 15.0374 c. 34: 6 4 4 6 3 2 3 1 5 N SD: 7.5180 c. M: 13.0773 c. 38: 7 4 5 6 4 2 4 1 5 N SD: 7.2500 c. M:-12.4669 c. 41: 7 5 5 7 4 2 4 1 6 N SD: 6.4607 c. M: 14.0938 c. 44: 8 5 5 8 4 3 4 1 6 N SD: 6.0300 c. M:-9.5960 c. 48: 8 6 6 8 5 3 4 1 7 N SD: 5.6991 c. M: 10.5061 c. 50: 9 6 6 8 5 3 5 1 7 N SD: 5.8098 c. M:-9.3329 c. 51: 9 6 6 9 5 3 5 1 7 N SD: 4.4164 c. M:-10.4521 c. 57: 10 7 7 9 6 3 6 1 8 N SD: 6.0977 c. M:-9.2137 c. 58: 10 7 7 10 6 3 5 2 8 N SD: 4.1272 c. M:-8.4074 c. 63: 11 7 8 11 6 4 6 1 9 N SD: 4.7269 c. M:-8.2112 c. 65: 11 8 8 11 6 4 6 2 9 N SD: 3.9037 c. M: 6.8711 c. 73: 13 8 9 13 7 4 7 2 10 N SD: 3.7980 c. M: 5.4616 c. 75: 13 9 9 13 7 5 7 2 10 N SD: 3.3240 c. M:-6.6874 c. 79: 14 9 10 13 8 5 7 2 11 N SD: 2.7656 c. M:-4.1059 c. 82: 14 10 10 14 8 5 7 3 11 N SD: 2.7108 c. M: 6.1906 c. 97: 17 11 12 17 9 6 9 3 13 N SD: 2.6447 c. M: 4.2753 c. 104: 18 12 13 18 10 6 10 3 14 N SD: 2.4994 c. M: 4.5132 c. 109: 19 13 13 19 10 7 10 3 15 N SD: 2.0125 c. M: 4.4999 c. 114: 20 13 14 20 11 7 10 3 16 N SD: 2.6204 c. M: 3.9272 c. 116: 20 14 14 20 11 7 11 3 16 N SD: 1.6175 c. M: 2.4874 c. 133: 23 16 16 23 13 8 12 4 18 N SD: 1.3942 c. M:-2.2236 c. 183: 32 22 22 31 18 11 17 5 25 N SD: 1.4654 c. M:-3.4313 c. 188: 33 22 23 32 18 12 17 5 26 N SD: 1.2851 c. M: 2.1576 c. 195: 34 23 24 33 19 12 18 5 27 N SD: 0.9736 c. M:-1.7643 c. 212: 37 25 26 36 21 13 19 6 29 N SD: 1.0320 c. M:-2.1971 c. 243: 42 29 30 41 24 15 22 7 33 N SD: 1.1009 c. M:-1.6846 c. 246: 43 29 30 42 24 15 22 7 34 N SD: 0.8581 c. M: 1.3598 c. 253: 44 30 31 43 25 15 23 7 35 N SD: 0.7962 c. M: 1.5140 c. 277: 48 33 34 47 27 17 25 8 38 N SD: 0.4966 c. M:-1.0351 c. 328: 57 39 40 56 32 20 30 9 45 N SD: 0.5750 c. M:-1.1264 c. 393: 68 47 48 67 38 24 36 11 54 N SD: 0.5994 c. M: 0.9522 c. 410: 71 49 50 70 40 25 37 12 56 N SD: 0.5536 c. M:-0.9033 c. 459: 80 54 56 78 45 28 42 13 63 N SD: 0.5396 c. M: 0.8822 c. 472: 82 56 58 80 46 29 43 13 65 N SD: 0.5212 c. M:-1.1452 c. 476: 83 56 58 81 47 29 43 14 65 N SD: 0.4685 c. M: 0.6954 c. 483: 84 57 59 82 48 29 44 14 66 N SD: 0.4538 c. M: 0.9147 c. 495: 86 59 60 84 49 30 45 14 68 N SD: 0.4488 c. M: 0.9297 c. 568: 99 67 69 97 56 34 52 16 78 N SD: 0.4143 c. M: 0.6810 c. 592: 103 70 72 101 58 36 54 17 81 N SD: 0.2555 c. M: 0.5383 c. 640: 111 76 78 109 63 39 58 18 88 N SD: 0.2987 c. M: 0.5061 c. 671: 117 79 82 114 66 41 61 19 92 N SD: 0.2984 c. M:-0.6542 c. 737: 128 87 90 126 72 45 67 21 101 N SD: 0.2978 c. M: 0.5992 c. 753: 131 89 92 128 74 46 68 22 103 N SD: 0.2646 c. M: 0.5158 c. 760: 132 90 93 129 75 46 69 22 104 N SD: 0.2495 c. M: 0.4831 c. 787: 137 93 96 134 77 48 72 22 108 N SD: 0.2436 c. M:-0.4663 c. 804: 140 95 98 137 79 49 73 23 110 N SD: 0.2364 c. M:-0.3948 c. 845: 147 100 103 144 83 51 77 24 116 N SD: 0.1751 c. M: 0.3082 c. 869: 151 103 106 148 85 53 79 25 119 N SD: 0.1372 c. M: 0.3066 c. 1081: 188 128 132 184 106 66 98 31 148 N SD: 0.1599 c. M:-0.3644 c. 1088: 189 129 133 185 107 66 99 31 149 N SD: 0.1695 c. M:-0.3065 c. 1122: 195 133 137 191 110 68 102 32 154 N SD: 0.1444 c. M: 0.2431 c. 1197: 208 142 146 204 117 73 109 34 164 N SD: 0.1380 c. M:-0.2186 c. 1509: 262 179 184 257 148 92 137 43 207 N SD: 0.1271 c. M: 0.2359 c. 1547: 269 183 189 263 152 94 141 44 212 N SD: 0.1210 c. M: 0.3076 c. 1673: 291 198 204 285 164 102 152 48 229 N SD: 0.1139 c. M:-0.2380 c. 1680: 292 199 205 286 165 102 153 48 230 N SD: 0.0957 c. M:-0.2081 c. 1714: 298 203 209 292 168 104 156 49 235 N SD: 0.0936 c. M: 0.1939 c. 1765: 307 209 215 301 173 107 161 50 242 N SD: 0.1215 c. M: 0.1627 c. 1789: 311 212 218 305 175 109 163 51 245 N SD: 0.1147 c. M: 0.1738 c. 1793: 312 212 219 305 176 109 163 51 246 N SD: 0.1118 c. M:-0.2263 c. 1824: 317 216 223 310 179 111 166 52 250 N SD: 0.1079 c. M: 0.2200 c. 1859: 323 220 227 317 182 113 169 53 255 N SD: 0.1030 c. M: 0.1560 c. 1926: 335 228 235 328 189 117 175 55 264 N SD: 0.0822 c. M:-0.1370 c. 2042: 355 242 249 348 200 124 186 58 280 N SD: 0.0798 c. M:-0.1655 c.
FIT/HARMONIC
1 x x x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x x x 4 S SD: 0.2096 cents 3 x x 4 x x 5 x x 6 S SD: 2.6113 cents 4 x 5 x 6 x x 7 x 8 S SD: 12.0578 cents 5 x 6:7 x 8 x 9 x 10 S SD: 18.7693 cents 6:7 x 8:9 x 10 x 11:12 S SD: 10.0702 cents 7:8 x 9 x 11:12 x 13:14 SD: 15.5453 cents 8:9:10:11:12:13 x 14:15:16 S SD: 11.5386 cents 9:10:11:12 x 14:15:16 x 18 S SD: 8.7239 cents 10:11:12:13:15:16:17:18 x 20 SD: 9.6568 cents 11:12:13:15:17:18 x x 20:22 SD: 16.0036 cents 12:14:15:16:18:19:20:21:22:24 S SD: 8.9820 cents 13:15:16:17:20:21:22:23:24:26 SD: 8.5825 cents 14:16:17:19:21:22:23:25 x 28 SD: 8.0397 cents 15:17:18:20:23:24:25:27 x 30 SD: 6.9922 cents 16:18:20:21:24:26:27 x 29:32 SD: 6.4563 cents 18:20:22:24:27:29:30:32:33:36 SD: 3.5470 cents 20:23:24:27:30:32:33:36 x 40 SD: 7.6768 cents 21:24:26:28:31:34:35:37:38:42 SD: 5.4572 cents 22:25:27:29:33:35:37:39:40:44 SD: 3.3986 cents 25:28:31:33:37:40:42:45 x 50 SD: 5.2306 cents 26:29:32:35:39:42:44:46:47:52 SD: 4.3450 cents 27:30:33:36:40:43:45:48:49:54 SD: 4.1962 cents 28:32:34:37:42:45:47:50:51:56 SD: 3.4685 cents 30:34:37:40:45:48:50:53:55:60 SD: 3.0667 cents 32:36:39:43:48:51:54:57:58:64 SD: 2.8815 cents 36:41:44:48:54:58:60:64:65:72 SD: 2.6623 cents 40:45:49:53:60:64:67:71:73:80 SD: 1.7613 cents 48:54:59:64:72:77:80:86:87:96 SD: 1.6869 cents 54:61:66:72:81:87:90:96:98:108 SD: 1.4112 cents 70:79:86:93:105:112:117:125:127:140 SD: 1.2369 cents 76:86:93:101:114:122:127:136:138:152 SD: 1.1655 cents 84:95:103:112:126:135:141:150:153:168 SD: 0.8941 cents 94:106:115:125:141:151:157:168:171:188 SD: 0.7980 cents 102:115:125:136:153:164:171:182:186:204 SD: 0.7054 cents 111:125:136:148:166:178:186:198:202:222 SD: 0.7008 cents 116:131:142:155:174:186:194:207:211:232 SD: 0.6451 cents 126:142:154:168:189:202:211:225:229:252 SD: 0.5697 cents 142:160:174:189:213:228:238:253:258:284 SD: 0.4872 cents 156:176:191:208:234:250:261:278:284:312 SD: 0.4131 cents 210:237:257:280:315:337:352:374:382:420 SD: 0.3808 cents 226:255:277:301:339:363:378:403:411:452 SD: 0.3188 cents 249:281:305:332:373:400:417:444:453:498 SD: 0.3116 cents 258:291:316:344:387:414:432:460:469:516 SD: 0.1646 cents 436:492:534:581:654:700:730:777:793:872 SD: 0.1544 cents 476:537:583:634:714:764:797:849:866:952 SD: 0.1490 cents 530:598:649:706:795:851:887:945:964:1060 SD: 0.1445 cents 547:617:670:729:820:878:916:975:995:1094 SD: 0.1303 cents 562:634:688:749:843:902:941:1002:1022:1124 SD: 0.0831 cents