Scala analysis: CD05_15_Egypt

Suite - ‘Abduh al-Ḥāmūlī (bayati, Egypt)

Generated by Scala: https://www.huygens-fokker.org/scala/

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:        202.647 cents     202.647269
  2:        343.532 cents     343.531990
  3:        496.674 cents     496.673768
  4:        697.967 cents     697.966711
  5:        887.435 cents     887.435407
  6:       1054.359 cents    1054.358861
  7:       1200.000 cents    1200.000000
SHOW/INTERVAL
  0:        145.6411 cents    145.6411
  1:        202.6473 cents    202.6473
  2:        140.8847 cents    140.8847
  3:        153.1418 cents    153.1418
  4:        201.2929 cents    201.2929
  5:        189.4687 cents    189.4687
  6:        166.9235 cents    166.9235
  7:        145.6411 cents    145.6411
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   1 140.88472 cents
  1:   1 145.64114 cents
  1:   1 153.14178 cents
  1:   1 166.92345 cents
  1:   1 189.46870 cents
  1:   1 201.29294 cents
  1:   1 202.64727 cents
  2:   1 294.02650 cents
  2:   1 312.56459 cents
  2:   1 343.53199 cents
  2:   1 348.28841 cents
  2:   1 354.43472 cents
  2:   1 356.39215 cents
  2:   1 390.76164 cents
  3:   1 489.17313 cents
  3:   1 495.31944 cents
  3:   1 496.67377 cents
  3:   1 502.03329 cents
  3:   1 515.21186 cents
  3:   1 543.90342 cents
  3:   1 557.68509 cents
  4:   1 642.31491 cents
  4:   1 656.09658 cents
  4:   1 684.78814 cents
  4:   1 697.96671 cents
  4:   1 703.32623 cents
  4:   1 704.68056 cents
  4:   1 710.82687 cents
  5:   1 809.23836 cents
  5:   1 843.60785 cents
  5:   1 845.56528 cents
  5:   1 851.71159 cents
  5:   1 856.46801 cents
  5:   1 887.43541 cents
  5:   1 905.97350 cents
  6:   1 997.35273 cents
  6:   1 998.70706 cents
  6:   1 1010.53130 cents
  6:   1 1033.07655 cents
  6:   1 1046.85822 cents
  6:   1 1054.35886 cents
  6:   1 1059.11528 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   : 202.6 343.5 496.7 698.0 887.4 1054.4 1200.0
 202.6 : 140.9 294.0 495.3 684.8 851.7 997.4  1200.0
 343.5 : 153.1 354.4 543.9 710.8 856.5 1059.1 1200.0
 496.7 : 201.3 390.8 557.7 703.3 906.0 1046.9 1200.0
 698.0 : 189.5 356.4 502.0 704.7 845.6 998.7  1200.0
 887.4 : 166.9 312.6 515.2 656.1 809.2 1010.5 1200.0
 1054.4: 145.6 348.3 489.2 642.3 843.6 1033.1 1200.0
 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  140.8847  .. 202.6473 cents      61.76255 cents                     140.88472 cents
  2:  294.0265  .. 390.7616 cents      96.73514 cents                     91.37923 cents
  3:  489.1731  .. 557.6851 cents      68.51196 cents                     98.41149 cents
  4:  642.3149  .. 710.8269 cents      68.51196 cents                     84.62981 cents
  5:  809.2384  .. 905.9735 cents      96.73514 cents                     98.41149 cents
  6:  997.3527  .. 1059.1153 cents     61.76255 cents                     91.37923 cents
SHOW DATA
Number of notes                     : 7
-- Interval properties --
Smallest interval                   : 140.88472 cents, class 1
Average step (divided formal octave): 171.4286 cents
Largest one step interval           : 202.64727 cents
Average / Smallest step             : 1.216800
Largest / Average step              : 1.182109
Largest / Smallest step             : 1.438391
Median interval of one step         : 166.92345 cents, amount: 1
Least squares average step          : 173.82093 cents, oct.:  1216.74648 cents
Scale is strictly proper
Step pattern alph. order: ABCDEFG
Step pattern size order : GACFEDB
Scale is sum-free (all different intervals)
Scale is a Constant Structure, by a margin of 84.62981 cents
Scale diversity                     : 1.411453
Rothenberg stability                : 1.000000 = 1
Lumma stability                     : 0.621651
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        : 1.35433 cents
Number of recognisable fifths       : 4, average 704.2001 cents
Best fifths form a closed circle
Best major thirds form a closed circle
Best minor thirds form a closed circle
Formal octave complements present   : 1 = 14.2857%
Limited inverse transpositions with margin 78.1970 cents:
 1
-- Rational properties --
FIT/MODE
  7:  1 1 1 1 1 1 1  SP B ME I SD: 20.7640 c. M: 31.2187 c.  Lebeng
 16:  3 2 2 2 3 2 2  SP M ME S SD: 20.6902 c. M:-31.4680 c.  Antiphrygian
 17:  3 2 2 3 3 2 2  SP   D3 S SD: 12.9479 c. M:-30.2117 c.  Pseudo Rast
 19:  3 2 3 3 3 3 2  SP   D3 S SD: 14.1989 c. M: 27.7425 c.  Nineteen-tone Melodic Minor
 22:  4 2 3 4 3 3 3  SP   D3   SD: 13.1085 c. M: 17.9952 c.  Dorian Porcupine
 24:  4 3 3 4 4 3 3  SP   D3 S SD: 5.8665 c. M:-12.5646 c.  Arabic Diatonic, Maqam Rast, Quasi-equal Heptatonic, Neutral Diatonic Phrygian
 31:  5 4 4 5 5 4 4  SP   D3 S SD: 5.8997 c. M: 9.1976 c.  Neutral Diatonic Phrygian, Rast
 41:  7 5 5 7 6 6 5  SP        SD: 4.9780 c. M: 9.3866 c. 
 43:  7 5 6 7 7 6 5  SP      S SD: 5.7146 c. M: 8.6483 c. 
 46:  8 5 6 8 7 6 6  SP        SD: 5.5592 c. M: 10.8806 c. 
 49:  8 6 6 8 8 7 6  SP        SD: 6.3078 c. M: 12.2524 c. 
 50:  8 6 7 8 8 7 6  SP      S SD: 5.7402 c. M: 10.6473 c. 
 53:  9 6 7 9 8 8 6  SP        SD: 4.6195 c. M:-9.7921 c. 
 55:  9 7 7 9 9 7 7  SP   D3 S SD: 5.3139 c. M:-7.1100 c. 
 58:  10 7 7 10 9 8 7  SP        SD: 4.1545 c. M:-8.1921 c. 
 65:  11 8 8 11 10 9 8  SP        SD: 3.2594 c. M:-7.2372 c. 
 66:  11 8 8 11 11 9 8  SP        SD: 3.8886 c. M: 7.0576 c. 
 72:  12 9 9 12 11 10 9  SP        SD: 3.7771 c. M:-6.4680 c. 
 77:  13 9 10 13 12 11 9  SP        SD: 2.5467 c. M:-5.3814 c. 
 84:  14 10 11 14 13 12 10  SP        SD: 2.1835 c. M:-3.3262 c. 
 101: 17 12 13 17 16 14 12  SP        SD: 2.3557 c. M:-3.6537 c. 
 107: 18 13 13 18 17 15 13  SP        SD: 2.3029 c. M:-4.1316 c. 
 108: 18 13 14 18 17 15 13  SP        SD: 1.9487 c. M:-3.3262 c. 
 126: 21 15 16 21 20 18 15  SP        SD: 1.9886 c. M:-2.7840 c. 
 130: 22 15 17 22 20 18 16  SP        SD: 1.9258 c. M:-3.5718 c. 
 142: 24 17 18 24 22 20 17  SP        SD: 2.0059 c. M:-3.4417 c. 
 143: 24 17 18 24 23 20 17  SP        SD: 1.6752 c. M:-2.9838 c. 
 149: 25 18 19 25 23 21 18  SP        SD: 1.9483 c. M:-2.7767 c. 
 150: 25 18 19 25 24 21 18  SP        SD: 1.4423 c. M: 2.6473 c. 
 165: 28 19 21 28 26 23 20  SP        SD: 1.1054 c. M: 2.1283 c. 
 172: 29 20 22 29 27 24 21  SP        SD: 1.0299 c. M: 1.6715 c. 
 189: 32 22 24 32 30 26 23  SP        SD: 0.8667 c. M:-1.4535 c. 
 196: 33 23 25 33 31 27 24  SP        SD: 0.6740 c. M: 1.2976 c. 
 230: 39 27 29 39 36 32 28  SP        SD: 0.7729 c. M:-1.1637 c. 
 273: 46 32 35 46 43 38 33  SP        SD: 0.5480 c. M:-0.9344 c. 
 380: 64 45 48 64 60 53 46  SP        SD: 0.4912 c. M: 0.8843 c. 
 430: 73 50 55 72 68 60 52  SP        SD: 0.4773 c. M:-1.0737 c. 
 437: 74 51 56 73 69 61 53  SP        SD: 0.3755 c. M:-0.5564 c. 
 454: 77 53 58 76 72 63 55  SP        SD: 0.4446 c. M:-0.8770 c. 
 461: 78 54 59 77 73 64 56  SP        SD: 0.2913 c. M:-0.5063 c. 
 626: 106 73 80 105 99 87 76  SP        SD: 0.2804 c. M:-0.5476 c. 
 633: 107 74 81 106 100 88 77  SP        SD: 0.2613 c. M: 0.4040 c. 
 657: 111 77 84 110 104 91 80  SP        SD: 0.2375 c. M: 0.4776 c. 
 710: 120 83 91 119 112 99 86  SP        SD: 0.2293 c. M: 0.4334 c. 
 734: 124 86 94 123 116 102 89  SP        SD: 0.2014 c. M:-0.3290 c. 
 817: 138 96 104 137 129 114 99  SP        SD: 0.2072 c. M: 0.2923 c. 
 841: 142 99 107 141 133 117 102  SP        SD: 0.1698 c. M:-0.3443 c. 
 964: 163 113 123 162 152 134 117  SP        SD: 0.1776 c. M:-0.3735 c. 
 971: 164 114 124 163 153 135 118  SP        SD: 0.1441 c. M:-0.2825 c. 
 1013: 171 119 129 170 160 141 123  SP        SD: 0.1700 c. M: 0.3263 c. 
 1037: 175 122 132 174 164 144 126  SP        SD: 0.1593 c. M: 0.2418 c. 
 1090: 184 128 139 183 172 152 132  SP        SD: 0.1443 c. M:-0.3200 c. 
 1114: 188 131 142 187 176 155 135  SP        SD: 0.1292 c. M:-0.2192 c. 
 1286: 217 151 164 216 203 179 156  SP        SD: 0.1281 c. M: 0.2508 c. 
 1310: 221 154 167 220 207 182 159  SP        SD: 0.1300 c. M: 0.2045 c. 
 1474: 249 173 188 247 233 205 179  SP        SD: 0.1160 c. M: 0.2734 c. 
 1551: 262 182 198 260 245 216 188  SP        SD: 0.0837 c. M:-0.1866 c. 
 1558: 263 183 199 261 246 217 189  SP        SD: 0.0986 c. M: 0.1490 c. 
 1575: 266 185 201 264 249 219 191  SP        SD: 0.0979 c. M:-0.1836 c. 
 1582: 267 186 202 265 250 220 192  SP        SD: 0.0959 c. M:-0.1657 c. 
 1747: 295 205 223 293 276 243 212  SP        SD: 0.0516 c. M: 0.0861 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: 1.9941 cents
 3 x x 4 x 5 x 6  S SD: 1.1228 cents
 4 x 5 x 6:7 x 8  S SD: 23.0090 cents
 5 x 6:7 x 8:9:10  S SD: 24.4430 cents
 6:7 x 8:9:10:11:12  S SD: 10.7715 cents
 7:8 x 9:10:12:13:14  S SD: 19.3453 cents
 8:9:10:11:12:13:15:16    SD: 12.9236 cents
 9:10:11:12:13:15:17:18    SD: 11.4103 cents
 10:11:12:13:15:17:18:20    SD: 11.3739 cents
 12:13:15:16:18:20:22:24    SD: 11.0546 cents
 13:15:16:17:19:22:24:26    SD: 10.6926 cents
 14:16:17:19:21:23:26:28    SD: 7.8160 cents
 15:17:18:20:22:25:28:30    SD: 7.6824 cents
 18:20:22:24:27:30:33:36  S SD: 3.1202 cents
 24:27:29:32:36:40:44:48    SD: 2.5028 cents
 42:47:51:56:63:70:77:84    SD: 1.8613 cents
 54:61:66:72:81:90:99:108    SD: 1.6741 cents
 55:62:67:73:82:92:101:110    SD: 1.6042 cents
 63:71:77:84:94:105:116:126    SD: 1.2628 cents
 64:72:78:85:96:107:118:128    SD: 1.2485 cents
 72:81:88:96:108:120:132:144    SD: 1.1852 cents
 73:82:89:97:109:122:134:146    SD: 1.0027 cents
 81:91:99:108:121:135:149:162    SD: 0.8831 cents
 87:98:106:116:130:145:160:174    SD: 0.8216 cents
 105:118:128:140:157:175:193:210    SD: 0.5462 cents
 145:163:177:193:217:242:267:290    SD: 0.5087 cents
 169:190:206:225:253:282:311:338    SD: 0.3417 cents
 250:281:305:333:374:417:460:500    SD: 0.3398 cents
 274:308:334:365:410:457:504:548    SD: 0.3023 cents
 306:344:373:408:458:511:563:612    SD: 0.2842 cents
 314:353:383:418:470:524:577:628    SD: 0.2820 cents
 322:362:393:429:482:538:592:644    SD: 0.2752 cents
 328:369:400:437:491:548:603:656    SD: 0.2539 cents
 346:389:422:461:518:578:636:692    SD: 0.1789 cents
 379:426:462:505:567:633:697:758    SD: 0.1711 cents
 427:480:521:569:639:713:785:854    SD: 0.1476 cents
 433:487:528:577:648:723:796:866    SD: 0.1367 cents
 451:507:550:601:675:753:829:902    SD: 0.0913 cents
 596:670:727:794:892:995:1096:1192    SD: 0.0809 cents