Scala analysis: CD05_04_bayati_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:        149.350 cents     149.350450
  2:        303.441 cents     303.440689
  3:        505.510 cents     505.509906
  4:        619.631 cents     619.630614
  5:        876.575 cents     876.575448
  6:        994.799 cents     994.798875
  7:       1200.000 cents    1200.000000
SHOW/INTERVAL
  0:        205.2011 cents    205.2011
  1:        149.3505 cents    149.3505
  2:        154.0902 cents    154.0902
  3:        202.0692 cents    202.0692
  4:        114.1207 cents    114.1207
  5:        256.9448 cents    256.9448
  6:        118.2234 cents    118.2234
  7:        205.2011 cents    205.2011
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   1 114.12071 cents
  1:   1 118.22343 cents
  1:   1 149.35045 cents
  1:   1 154.09024 cents
  1:   1 202.06922 cents
  1:   1 205.20113 cents
  1:   1 256.94483 cents
  2:   1 303.44069 cents
  2:   1 316.18992 cents
  2:   1 323.42455 cents
  2:   1 354.55158 cents
  2:   1 356.15946 cents
  2:   1 371.06554 cents
  2:   1 375.16826 cents
  3:   1 470.28016 cents
  3:   1 472.77500 cents
  3:   1 489.28897 cents
  3:   1 505.50991 cents
  3:   1 508.64181 cents
  3:   1 573.13476 cents
  3:   1 580.36939 cents
  4:   1 619.63061 cents
  4:   1 626.86524 cents
  4:   1 691.35819 cents
  4:   1 694.49009 cents
  4:   1 710.71103 cents
  4:   1 727.22500 cents
  4:   1 729.71984 cents
  5:   1 824.83174 cents
  5:   1 828.93446 cents
  5:   1 843.84054 cents
  5:   1 845.44842 cents
  5:   1 876.57545 cents
  5:   1 883.81008 cents
  5:   1 896.55931 cents
  6:   1 943.05517 cents
  6:   1 994.79887 cents
  6:   1 997.93078 cents
  6:   1 1045.90976 cents
  6:   1 1050.64955 cents
  6:   1 1081.77657 cents
  6:   1 1085.87929 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   : 149.4 303.4 505.5 619.6 876.6 994.8  1200.0
 149.4 : 154.1 356.2 470.3 727.2 845.4 1050.6 1200.0
 303.4 : 202.1 316.2 573.1 691.4 896.6 1045.9 1200.0
 505.5 : 114.1 371.1 489.3 694.5 843.8 997.9  1200.0
 619.6 : 256.9 375.2 580.4 729.7 883.8 1085.9 1200.0
 876.6 : 118.2 323.4 472.8 626.9 828.9 943.1  1200.0
 994.8 : 205.2 354.6 508.6 710.7 824.8 1081.8 1200.0
 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  114.1207  .. 256.9448 cents      142.82413 cents                    114.12071 cents
  2:  303.4407  .. 375.1683 cents      71.72757 cents                     46.49586 cents
  3:  470.2802  .. 580.3694 cents      110.08922 cents                    95.11190 cents
  4:  619.6306  .. 729.7198 cents      110.08922 cents                    39.26123 cents
  5:  824.8317  .. 896.5593 cents      71.72757 cents                     95.11190 cents
  6:  943.0552  .. 1085.8793 cents     142.82413 cents                    46.49586 cents
SHOW DATA
Number of notes                     : 7
-- Interval properties --
Smallest interval                   : 114.12071 cents, class 1
Average step (divided formal octave): 171.4286 cents
Largest one step interval           : 256.94483 cents
Average / Smallest step             : 1.502169
Largest / Average step              : 1.498845
Largest / Smallest step             : 2.251518
Median interval of one step         : 154.09024 cents, amount: 1
Least squares average step          : 167.87825 cents, oct.:  1175.14772 cents
Scale is strictly proper
Step pattern alph. order: ABCDEFG
Step pattern size order : CDEAGBF
Scale is sum-free (all different intervals)
Scale is a Constant Structure, by a margin of 39.26123 cents
Scale diversity                     : 1.522807
Rothenberg stability                : 1.000000 = 1
Lumma stability                     : 0.458932
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        : 1.60788 cents
Number of recognisable fifths       : 3, average 698.8531 cents
Best fifths form a closed circle
Best major thirds form a closed circle
Formal octave complements present   : 1 = 14.2857%
Limited inverse transpositions with margin 110.0892 cents:
 2
-- Rational properties --
FIT/MODE
  7:  1 1 1 1 1 1 1  SP B ME I SD: 33.8133 c. M:-66.0837 c.  Lebeng
  8:  1 1 1 1 2 1 1   P M ME S SD: 31.7914 c. M: 55.5099 c. 
 10:  1 1 2 1 2 1 2   P M ME S SD: 34.7871 c. M: 63.4407 c. 
 11:  1 2 2 1 2 1 2   P M ME S SD: 27.2206 c. M: 40.2595 c.  Orgone-7
 12:  1 2 2 1 3 1 2   P   D3   SD: 22.1643 c. M: 49.3505 c.  Locrian natural 6, Maqam Tarznauyn
 14:  2 2 2 1 3 2 2   P   T3   SD: 23.9693 c. M:-39.4165 c. 
 15:  2 2 2 2 3 1 3  SP   D3 S SD: 19.5521 c. M: 34.7989 c. 
 16:  2 2 3 1 4 1 3   P      S SD: 15.6670 c. M:-23.4246 c. 
 17:  2 2 3 2 3 2 3  SP M ME S SD: 16.0399 c. M: 29.5166 c.  Safi al-Din's maqam Higazi
 19:  2 3 3 2 4 2 3  SP   D3   SD: 12.7142 c. M: 23.0347 c. 
 23:  3 3 4 2 5 2 4  SP      S SD: 9.0134 c. M:-16.2292 c. 
 29:  4 3 5 3 6 3 5  SP        SD: 9.2084 c. M:-16.1668 c. 
 31:  4 4 5 3 7 3 5  SP      S SD: 7.5506 c. M:-13.7471 c. 
 33:  4 4 6 3 7 3 6  SP      S SD: 7.2747 c. M: 12.9807 c. 
 40:  5 5 7 4 8 4 7  SP      S SD: 5.4276 c. M:-10.3694 c. 
 41:  5 5 7 4 9 4 7  SP      S SD: 5.5447 c. M: 10.7578 c. 
 47:  6 6 8 4 10 5 8  SP        SD: 4.9254 c. M: 8.4903 c. 
 48:  6 6 8 5 10 5 8  SP      S SD: 3.7982 c. M: 5.5099 c. 
 64:  8 8 11 6 14 6 11  SP      S SD: 2.2846 c. M:-4.6746 c. 
 99:  12 13 17 9 21 10 17  SP        SD: 2.5584 c. M: 3.8959 c. 
 104: 13 13 18 10 22 10 18  SP      S SD: 2.2433 c. M:-3.4463 c. 
 111: 14 14 19 10 24 11 19  SP        SD: 1.8442 c. M: 3.4144 c. 
 118: 15 15 20 11 25 12 20  SP        SD: 2.0515 c. M:-3.1919 c. 
 122: 15 16 20 12 26 12 21  SP        SD: 1.8376 c. M: 3.8706 c. 
 130: 16 17 22 12 28 13 22  SP        SD: 1.4586 c. M:-2.1824 c. 
 145: 18 19 24 14 31 14 25  SP        SD: 1.3472 c. M:-2.7662 c. 
 159: 20 20 27 15 34 16 27  SP        SD: 1.1220 c. M:-1.5929 c. 
 182: 23 23 31 17 39 18 31  SP        SD: 1.2453 c. M:-2.2979 c. 
 186: 23 24 31 18 40 18 32  SP        SD: 1.1047 c. M: 2.2841 c. 
 209: 26 27 35 20 45 20 36  SP        SD: 0.9898 c. M:-1.8935 c. 
 233: 29 30 39 22 50 23 40  SP        SD: 0.8542 c. M: 1.6049 c. 
 240: 30 31 40 23 51 24 41  SP        SD: 0.9081 c. M: 1.5754 c. 
 256: 32 33 43 24 55 25 44  SP        SD: 0.7928 c. M:-1.2468 c. 
 281: 35 36 47 27 60 28 48  SP        SD: 0.7665 c. M: 1.5953 c. 
 297: 37 38 50 28 64 29 51  SP        SD: 0.6840 c. M: 1.4488 c. 
 304: 38 39 51 29 65 30 52  SP        SD: 0.3427 c. M:-0.6495 c. 
 498: 62 64 84 47 107 49 85  SP        SD: 0.3488 c. M:-0.5330 c. 
 515: 64 66 87 49 110 51 88  SP        SD: 0.2948 c. M: 0.5281 c. 
 620: 77 80 104 59 133 61 106  SP        SD: 0.2739 c. M:-0.4303 c. 
 660: 82 85 111 63 141 65 113  SP        SD: 0.2250 c. M:-0.3694 c. 
 724: 90 93 122 69 155 71 124  SP        SD: 0.1958 c. M: 0.3237 c. 
 802: 100 103 135 76 172 79 137  SP        SD: 0.2232 c. M:-0.3000 c. 
 819: 102 105 138 78 175 81 140  SP        SD: 0.1719 c. M: 0.3850 c. 
 883: 110 113 149 84 189 87 151  SP        SD: 0.1576 c. M: 0.3829 c. 
 964: 120 124 162 92 206 95 165  SP        SD: 0.1968 c. M:-0.2938 c. 
 988: 123 127 166 94 212 97 169  SP        SD: 0.1955 c. M:-0.3476 c. 
 1013: 126 130 171 96 217 100 173  SP        SD: 0.1769 c. M:-0.3144 c. 
 1028: 128 132 173 98 220 101 176  SP        SD: 0.1334 c. M: 0.2463 c. 
 1135: 141 146 191 108 243 112 194  SP        SD: 0.1296 c. M: 0.2756 c. 
 1158: 144 149 195 110 248 114 198  SP        SD: 0.1210 c. M:-0.1896 c. 
 1317: 164 169 222 125 282 130 225  SP        SD: 0.1071 c. M:-0.1897 c. 
 1439: 179 185 242 137 308 142 246  SP        SD: 0.0962 c. M: 0.1590 c. 
 1462: 182 188 246 139 313 144 250  SP        SD: 0.1073 c. M:-0.2529 c. 
 1503: 187 193 253 143 322 148 257  SP        SD: 0.0647 c. M: 0.1207 c. 
 1807: 225 232 304 172 387 178 309  SP        SD: 0.0641 c. M: 0.1419 c. 
 1977: 246 254 333 188 423 195 338  SP        SD: 0.0704 c. M:-0.1047 c. 
 2041: 254 262 344 194 437 201 349  SP        SD: 0.0615 c. M:-0.1246 c. 
 2274: 283 292 383 216 487 224 389  SP        SD: 0.0554 c. M: 0.1055 c. 
 2322: 289 298 391 221 497 229 397  SP        SD: 0.0571 c. M: 0.0897 c. 
 2345: 292 301 395 223 502 231 401  SP        SD: 0.0488 c. M:-0.0764 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: 41.1622 cents
 3 x x 4 x 5 x 6  S SD: 3.5948 cents
 4 x 5 x 6 x 7:8  S SD: 29.9164 cents
 5 x 6 x 7:8:9:10  S SD: 15.4937 cents
 6 x 7:8:9:10:11:12  S SD: 17.6448 cents
 7 x 8:9:10:12 x 14  S SD: 23.1389 cents
 8:9:10:11 x 13:14:16    SD: 19.6618 cents
 9:10:11:12:13:15:16:18    SD: 8.3692 cents
 12:13:14:16:17:20:21:24    SD: 7.1728 cents
 20:22:24:27:29:33:36:40    SD: 5.9962 cents
 21:23:25:28:30:35:37:42    SD: 2.8299 cents
 32:35:38:43:46:53:57:64    SD: 2.0736 cents
 47:51:56:63:67:78:83:94    SD: 2.0479 cents
 53:58:63:71:76:88:94:106    SD: 1.3694 cents
 67:73:80:90:96:111:119:134    SD: 1.0935 cents
 68:74:81:91:97:113:121:136    SD: 0.9882 cents
 79:86:94:106:113:131:140:158    SD: 0.9291 cents
 88:96:105:118:126:146:156:176    SD: 0.7696 cents
 100:109:119:134:143:166:178:200    SD: 0.6298 cents
 121:132:144:162:173:201:215:242    SD: 0.4808 cents
 156:170:186:209:223:259:277:312    SD: 0.3223 cents
 188:205:224:252:269:312:334:376    SD: 0.2785 cents
 256:279:305:343:366:425:455:512    SD: 0.2693 cents
 277:302:330:371:396:460:492:554    SD: 0.2663 cents
 334:364:398:447:478:554:593:668    SD: 0.2620 cents
 344:375:410:461:492:571:611:688    SD: 0.2276 cents
 402:438:479:538:575:667:714:804    SD: 0.1967 cents
 434:473:517:581:621:720:771:868    SD: 0.1488 cents
 511:557:609:684:731:848:908:1022    SD: 0.1390 cents
 569:620:678:762:814:944:1011:1138    SD: 0.1268 cents
 590:643:703:790:844:979:1048:1180    SD: 0.0780 cents