Scala analysis: CD05_12_rast_Egypt
Mon seigneur, je suis ton esclave - ‘Abduh al-Ḥāmūlī (rast, Egypt)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 214.376 cents 214.376235 2: 348.661 cents 348.660596 3: 487.512 cents 487.512008 4: 706.189 cents 706.188580 5: 822.017 cents 822.016510 6: 1099.029 cents 1099.028516 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 100.9715 cents 100.9715 1: 214.3762 cents 214.3762 2: 134.2844 cents 134.2844 3: 138.8514 cents 138.8514 4: 218.6766 cents 218.6766 5: 115.8279 cents 115.8279 6: 277.0120 cents 277.0120 7: 100.9715 cents 100.9715
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 100.97148 cents 1: 1 115.82793 cents 1: 1 134.28436 cents 1: 1 138.85141 cents 1: 1 214.37623 cents 1: 1 218.67657 cents 1: 1 277.01201 cents 2: 1 273.13577 cents 2: 1 315.34772 cents 2: 1 334.50450 cents 2: 1 348.66060 cents 2: 1 357.52798 cents 2: 1 377.98349 cents 2: 1 392.83994 cents 3: 1 449.63208 cents 3: 1 473.35591 cents 3: 1 487.51201 cents 3: 1 491.81234 cents 3: 1 493.81142 cents 3: 1 592.35973 cents 3: 1 611.51651 cents 4: 1 588.48349 cents 4: 1 607.64027 cents 4: 1 706.18858 cents 4: 1 708.18766 cents 4: 1 712.48799 cents 4: 1 726.64409 cents 4: 1 750.36792 cents 5: 1 807.16006 cents 5: 1 822.01651 cents 5: 1 842.47202 cents 5: 1 851.33940 cents 5: 1 865.49550 cents 5: 1 884.65228 cents 5: 1 926.86423 cents 6: 1 922.98799 cents 6: 1 981.32343 cents 6: 1 985.62377 cents 6: 1 1061.14859 cents 6: 1 1065.71564 cents 6: 1 1084.17207 cents 6: 1 1099.02852 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 7.00000 = 7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 214.4 348.7 487.5 706.2 822.0 1099.0 1200.0 214.4 : 134.3 273.1 491.8 607.6 884.7 985.6 1200.0 348.7 : 138.9 357.5 473.4 750.4 851.3 1065.7 1200.0 487.5 : 218.7 334.5 611.5 712.5 926.9 1061.1 1200.0 706.2 : 115.8 392.8 493.8 708.2 842.5 981.3 1200.0 822.0 : 277.0 378.0 592.4 726.6 865.5 1084.2 1200.0 1099.0: 101.0 315.3 449.6 588.5 807.2 923.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 100.9715 .. 277.0120 cents 176.04052 cents 100.97148 cents 2: 273.1358 .. 392.8399 cents 119.70416 cents -3.87623 cents 3: 449.6321 .. 611.5165 cents 161.88443 cents 56.79214 cents 4: 588.4835 .. 750.3679 cents 161.88443 cents -23.03302 cents 5: 807.1601 .. 926.8642 cents 119.70416 cents 56.79214 cents 6: 922.9880 .. 1099.0285 cents 176.04052 cents -3.87623 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 100.97148 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 277.01201 cents Average / Smallest step : 1.697792 Largest / Average step : 1.615903 Largest / Smallest step : 2.743468 Median interval of one step : 138.85141 cents, amount: 1 Least squares average step : 173.59458 cents, oct.: 1215.16207 cents Scale is not proper Step pattern alph. order: ABCDEFG Step pattern size order : ECDFBGA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 3.87623 cents Scale diversity : 1.548994 Lumma stability : 0.262939 Lumma impropriety factor : 0.025655 Rothenberg efficiency : 0.285714 redundancy: 0.714286 Efficiency x scale size : 2.000000 Number of different interval sizes : 42 = 7.00000 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 7.00000 = 7 Median interval variety : 7 Lowest interval variety : 7 Smallest interval difference : 1.99908 cents Number of recognisable fifths : 3, average 708.9547 cents Formal octave complements present : 1 = 14.2857% Limited inverse transpositions with margin 176.0405 cents: 4 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 36.2772 c. M: 70.4571 c. Lebeng 10: 2 1 1 2 1 2 1 P M ME S SD: 15.6654 c. M:-25.6238 c. Sethares Neutral, Beatles-7, Dichotic-7 17: 3 2 2 3 2 4 1 N SD: 15.2087 c. M:-30.3832 c. 22: 4 2 3 4 2 5 2 P SD: 9.0437 c. M: 21.3879 c. Twenty-two tone Harmonic Minor 27: 5 3 3 5 3 6 2 N SD: 10.5845 c. M:-22.4279 c. 29: 5 3 4 5 3 7 2 N SD: 10.8139 c. M:-18.2129 c. 32: 6 3 4 6 3 7 3 P SD: 7.7373 c. M: 11.5285 c. 34: 6 4 4 6 3 8 3 P S SD: 5.3196 c. M: 10.2518 c. 39: 7 4 5 7 4 9 3 N SD: 6.3468 c. M: 10.1991 c. 44: 8 5 5 8 4 10 4 P S SD: 4.6246 c. M: 8.1194 c. 51: 9 6 6 9 5 12 4 N SD: 4.1081 c. M:-6.8538 c. 61: 11 7 7 11 6 14 5 N SD: 3.3944 c. M:-5.4378 c. 73: 13 8 9 13 7 17 6 N SD: 2.6758 c. M:-5.6387 c. 82: 15 9 9 15 8 19 7 N SD: 3.3044 c. M:-5.1360 c. 83: 15 9 10 15 8 19 7 N SD: 2.2317 c. M:-4.0543 c. 99: 18 11 11 18 10 23 8 N SD: 2.9440 c. M:-4.0018 c. 106: 19 12 12 19 11 24 9 N SD: 2.5336 c. M:-4.3986 c. 107: 19 12 12 20 10 25 9 N SD: 2.4380 c. M: 5.2690 c. 110: 20 12 13 20 10 26 9 N SD: 2.8565 c. M: 3.8347 c. 111: 20 12 13 20 11 26 9 N SD: 2.3180 c. M:-3.6742 c. 114: 20 13 13 21 11 26 10 N SD: 2.6076 c. M: 4.2917 c. 117: 21 13 14 21 11 27 10 N SD: 2.1070 c. M:-4.7957 c. 121: 22 13 14 22 12 28 10 N SD: 2.0021 c. M:-3.8056 c. 128: 23 14 15 23 13 29 11 N SD: 1.9883 c. M: 3.0636 c. 131: 23 15 15 24 13 30 11 N SD: 1.8734 c. M: 3.6892 c. 140: 25 16 16 25 14 32 12 N SD: 1.8575 c. M: 3.3314 c. 141: 25 16 16 26 14 32 12 N SD: 1.7804 c. M:-3.5154 c. 145: 26 16 17 26 14 34 12 N SD: 1.6888 c. M: 2.7403 c. 155: 28 17 18 28 15 36 13 N SD: 1.2342 c. M:-2.3980 c. 158: 28 18 18 29 15 37 13 N SD: 1.3963 c. M:-2.2373 c. 165: 29 19 19 30 16 38 14 N SD: 1.3917 c. M: 3.4671 c. 168: 30 19 19 31 16 39 14 N SD: 1.0166 c. M: 1.7977 c. 190: 34 21 22 35 18 44 16 N SD: 0.8911 c. M: 1.2922 c. 241: 43 27 28 44 23 56 20 N SD: 0.6715 c. M:-1.3864 c. 251: 45 28 29 46 24 58 21 N SD: 0.6592 c. M:-1.3811 c. 285: 51 32 33 52 27 66 24 N SD: 0.7507 c. M:-1.1798 c. 286: 51 32 33 52 28 66 24 N SD: 0.6364 c. M: 1.2935 c. 296: 53 33 34 54 29 68 25 N SD: 0.6506 c. M: 1.0255 c. 320: 57 36 37 58 31 74 27 N SD: 0.5950 c. M: 1.1886 c. 330: 59 37 38 60 32 76 28 N SD: 0.4730 c. M: 0.8467 c. 369: 66 41 43 67 36 85 31 N SD: 0.4574 c. M:-0.7477 c. 403: 72 45 47 73 39 93 34 N SD: 0.3952 c. M:-0.8255 c. 413: 74 46 48 75 40 95 35 N SD: 0.4476 c. M: 0.7234 c. 416: 74 47 48 76 40 96 35 N SD: 0.4282 c. M: 0.9147 c. 438: 78 49 51 80 42 101 37 N SD: 0.4783 c. M: 0.7154 c. 476: 85 53 55 87 46 110 40 N SD: 0.4846 c. M: 0.9574 c. 488: 87 55 56 89 47 113 41 N SD: 0.4753 c. M: 0.7050 c. 498: 89 56 57 91 48 115 42 N SD: 0.4351 c. M: 0.7650 c. 510: 91 57 59 93 49 118 43 N SD: 0.4300 c. M: 0.8400 c. 520: 93 58 60 95 50 120 44 N SD: 0.3770 c. M: 0.5889 c. 527: 94 59 61 96 51 122 44 N SD: 0.3669 c. M:-0.7817 c. 537: 96 60 62 98 52 124 45 N SD: 0.2499 c. M:-0.4128 c. 571: 102 64 66 104 55 132 48 N SD: 0.1446 c. M: 0.3002 c. 940: 168 105 109 171 91 217 79 N SD: 0.1378 c. M: 0.2311 c. 1108: 198 124 128 202 107 256 93 N SD: 0.1174 c. M:-0.2495 c. 1115: 199 125 129 203 108 257 94 N SD: 0.1537 c. M:-0.2256 c. 1130: 202 126 131 206 109 261 95 N SD: 0.1485 c. M: 0.3420 c. 1191: 213 133 138 217 115 275 100 N SD: 0.1505 c. M:-0.2333 c. 1283: 229 144 148 234 124 296 108 N SD: 0.1434 c. M: 0.2166 c. 1305: 233 146 151 238 126 301 110 N SD: 0.1184 c. M: 0.1779 c. 1356: 242 152 157 247 131 313 114 N SD: 0.1042 c. M: 0.2169 c. 1460: 261 163 169 266 141 337 123 N SD: 0.1272 c. M: 0.1674 c. 1511: 270 169 175 275 146 349 127 N SD: 0.0905 c. M: 0.1661 c. 1521: 272 170 176 277 147 351 128 N SD: 0.0975 c. M:-0.2194 c. 1546: 276 173 179 282 149 357 130 N SD: 0.1032 c. M:-0.1504 c. 1679: 300 188 194 306 162 388 141 N SD: 0.1023 c. M:-0.1972 c. 1686: 301 189 195 307 163 389 142 N SD: 0.0930 c. M: 0.1414 c. 1762: 315 197 204 321 170 407 148 N SD: 0.1015 c. M:-0.1769 c. 1876: 335 210 217 342 181 433 158 N SD: 0.0663 c. M: 0.0946 c. 1937: 346 217 224 353 187 447 163 N SD: 0.0637 c. M:-0.1262 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 2.1168 cents 3 x x 4 x 5 x 6 S SD: 21.0752 cents 4 x 5 x 6 x x 8 S SD: 12.6301 cents 5 x 6:7 x 8:9:10 S SD: 25.9352 cents 6:7 x 8:9:10:11:12 S SD: 16.0189 cents 7:8 x 9 x 11:13:14 SD: 14.6148 cents 8:9:10:11:12:13:15:16 SD: 11.1345 cents 9:10:11:12 x 14:17:18 SD: 11.0545 cents 10:11:12:13:15:16:19:20 SD: 9.9715 cents 13:15:16:17:20:21:25:26 SD: 9.5752 cents 14:16:17:19:21:23:26:28 SD: 9.3682 cents 15:17:18:20:23:24:28:30 SD: 7.5061 cents 16:18:20:21:24:26:30:32 SD: 6.8267 cents 18:20:22:24:27:29:34:36 SD: 4.8866 cents 22:25:27:29:33:35:42:44 SD: 4.3680 cents 28:32:34:37:42:45:53:56 SD: 3.2399 cents 31:35:38:41:47:50:58:62 SD: 3.1620 cents 36:41:44:48:54:58:68:72 SD: 2.3210 cents 44:50:54:58:66:71:83:88 SD: 2.1515 cents 46:52:56:61:69:74:87:92 SD: 1.4873 cents 62:70:76:82:93:100:117:124 SD: 1.3859 cents 68:77:83:90:102:109:128:136 SD: 1.2678 cents 76:86:93:101:114:122:143:152 SD: 1.2045 cents 77:87:94:102:116:124:145:154 SD: 1.0094 cents 89:101:109:118:134:143:168:178 SD: 0.8308 cents 99:112:121:131:149:159:187:198 SD: 0.6206 cents 107:121:131:142:161:172:202:214 SD: 0.5249 cents 135:153:165:179:203:217:255:270 SD: 0.4923 cents 166:188:203:220:250:267:313:332 SD: 0.4583 cents 175:198:214:232:263:281:330:350 SD: 0.3834 cents 197:223:241:261:296:317:372:394 SD: 0.3700 cents 206:233:252:273:310:331:389:412 SD: 0.3658 cents 212:240:259:281:319:341:400:424 SD: 0.3604 cents 242:274:296:321:364:389:457:484 SD: 0.3431 cents 264:299:323:350:397:424:498:528 SD: 0.3306 cents 274:310:335:363:412:441:517:548 SD: 0.3155 cents 282:319:345:374:424:453:532:564 SD: 0.3151 cents 296:335:362:392:445:476:558:592 SD: 0.2794 cents 310:351:379:411:466:498:585:620 SD: 0.2785 cents 319:361:390:423:480:513:602:638 SD: 0.2655 cents 326:369:399:432:490:524:615:652 SD: 0.2038 cents 372:421:455:493:559:598:702:744 SD: 0.1745 cents 403:456:493:534:606:648:760:806 SD: 0.1444 cents 502:568:614:665:755:807:947:1004 SD: 0.1421 cents 538:609:658:713:809:865:1015:1076 SD: 0.0395 cents