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