Scala analysis: CD07_09_Egypt

Introduction instrumentale - Taha Abû Mandûr (unknown maqam, Egypt)

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

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:        187.606 cents     187.606180
  2:        381.895 cents     381.894737
  3:        504.027 cents     504.026551
  4:        702.824 cents     702.824252
  5:        856.765 cents     856.765325
  6:        968.590 cents     968.590389
  7:       1200.000 cents    1200.000000
SHOW/INTERVAL
  0:        231.4096 cents    231.4096
  1:        187.6062 cents    187.6062
  2:        194.2886 cents    194.2886
  3:        122.1318 cents    122.1318
  4:        198.7977 cents    198.7977
  5:        153.9411 cents    153.9411
  6:        111.8251 cents    111.8251
  7:        231.4096 cents    231.4096
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   1 111.82506 cents
  1:   1 122.13181 cents
  1:   1 153.94107 cents
  1:   1 187.60618 cents
  1:   1 194.28856 cents
  1:   1 198.79770 cents
  1:   1 231.40961 cents
  2:   1 265.76614 cents
  2:   1 316.42037 cents
  2:   1 320.92952 cents
  2:   1 343.23468 cents
  2:   1 352.73877 cents
  2:   1 381.89474 cents
  2:   1 419.01579 cents
  3:   1 464.56384 cents
  3:   1 474.87059 cents
  3:   1 497.17575 cents
  3:   1 504.02655 cents
  3:   1 515.21807 cents
  3:   1 530.84085 cents
  3:   1 613.30435 cents
  4:   1 586.69565 cents
  4:   1 669.15915 cents
  4:   1 684.78193 cents
  4:   1 695.97345 cents
  4:   1 702.82425 cents
  4:   1 725.12941 cents
  4:   1 735.43616 cents
  5:   1 780.98421 cents
  5:   1 818.10526 cents
  5:   1 847.26123 cents
  5:   1 856.76532 cents
  5:   1 879.07048 cents
  5:   1 883.57963 cents
  5:   1 934.23386 cents
  6:   1 968.59039 cents
  6:   1 1001.20230 cents
  6:   1 1005.71144 cents
  6:   1 1012.39382 cents
  6:   1 1046.05893 cents
  6:   1 1077.86819 cents
  6:   1 1088.17494 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   : 187.6 381.9 504.0 702.8 856.8 968.6  1200.0
 187.6 : 194.3 316.4 515.2 669.2 781.0 1012.4 1200.0
 381.9 : 122.1 320.9 474.9 586.7 818.1 1005.7 1200.0
 504.0 : 198.8 352.7 464.6 696.0 883.6 1077.9 1200.0
 702.8 : 153.9 265.8 497.2 684.8 879.1 1001.2 1200.0
 856.8 : 111.8 343.2 530.8 725.1 847.3 1046.1 1200.0
 968.6 : 231.4 419.0 613.3 735.4 934.2 1088.2 1200.0
 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  111.8251  .. 231.4096 cents      119.58455 cents                    111.82506 cents
  2:  265.7661  .. 419.0158 cents      153.24965 cents                    34.35653 cents
  3:  464.5638  .. 613.3043 cents      148.74051 cents                    45.54805 cents
  4:  586.6957  .. 735.4362 cents      148.74051 cents                   -26.60870 cents
  5:  780.9842  .. 934.2339 cents      153.24965 cents                    45.54805 cents
  6:  968.5904  .. 1088.1749 cents     119.58455 cents                    34.35653 cents
SHOW DATA
Number of notes                     : 7
-- Interval properties --
Smallest interval                   : 111.82506 cents, class 1
Average step (divided formal octave): 171.4286 cents
Largest one step interval           : 231.40961 cents
Average / Smallest step             : 1.533007
Largest / Average step              : 1.349889
Largest / Smallest step             : 2.069389
Median interval of one step         : 187.60618 cents, amount: 1
Least squares average step          : 169.78672 cents, oct.:  1188.50706 cents
Scale is not proper
Step pattern alph. order: ABCDEFG
Step pattern size order : DEBFCAG
Scale is sum-free (all different intervals)
Scale is a Constant Structure, by a margin of 26.60870 cents
Scale diversity                     : 1.649988
Lumma stability                     : 0.319549
Lumma impropriety factor            : 0.022174
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        : 4.50914 cents
Number of recognisable fifths       : 2, average 699.3989 cents
Best fifths form a closed circle
Formal octave complements present   : 1 = 14.2857%
-- Rational properties --
FIT/MODE
  7:  1 1 1 1 1 1 1  SP B ME I SD: 28.7390 c. M:-59.9810 c.  Lebeng
  9:  1 2 1 1 1 1 2   N   D3 S SD: 37.6164 c. M: 56.7653 c. 
 10:  2 1 1 2 1 1 2   P   D3 I SD: 25.2180 c. M:-52.3938 c. 
 12:  2 2 1 2 2 1 2   P M ME S SD: 21.9135 c. M:-43.2347 c.  G.Hypophrygian, G.Ionian (Iastian), M.Mixolydian, G.M.Hypoionian, Hypermixolydian, Mischung 3, Khamaj That, Mela Harikambhoji, Raga Balahamsa, Bhim, Devamanohari, Harini, Janjhuti, Kaamaai, Khambhavati, Surati, Gregorian nr.7, Enharmonic Byzantine Liturgical, Rast descending: Greece, Ching, Shang: China
 14:  2 2 2 2 2 1 3   P   T3   SD: 20.1636 c. M: 39.0376 c. 
 15:  2 3 1 3 2 1 3   N   T3   SD: 19.1827 c. M: 27.6062 c. 
 17:  3 2 2 3 2 2 3  SP   D3 I SD: 16.9437 c. M: 28.9536 c.  Safi al-Din's maqam Rast
 19:  3 3 2 3 3 1 4   N        SD: 13.5368 c. M:-27.4452 c. 
 21:  3 4 2 3 3 2 4   N   T3 S SD: 11.9266 c. M:-18.1053 c. 
 24:  4 4 2 4 3 2 5   N        SD: 11.3198 c. M: 18.5904 c. 
 25:  4 4 3 4 3 2 5   N        SD: 12.0689 c. M:-23.9734 c. 
 26:  4 4 3 4 4 2 5   P        SD: 10.0007 c. M:-20.1578 c. 
 28:  4 5 3 4 4 3 5   P   T3 S SD: 11.7575 c. M:-17.1239 c. 
 31:  5 5 3 5 4 3 6   N        SD: 4.2575 c. M: 6.0501 c. 
 53:  8 9 5 9 7 5 10   N        SD: 4.2227 c. M: 6.4741 c. 
 57:  9 9 6 9 8 5 11   N        SD: 4.1405 c. M: 8.0874 c. 
 60:  9 10 6 10 8 5 12   N        SD: 4.9265 c. M: 8.5904 c. 
 63:  10 10 6 11 8 6 12   N        SD: 3.7477 c. M: 8.7885 c. 
 67:  10 11 7 11 9 6 13   N        SD: 4.4936 c. M: 8.5017 c. 
 69:  11 11 7 11 9 7 13   N        SD: 4.0557 c. M: 7.1721 c. 
 72:  11 12 7 12 9 7 14   N        SD: 3.6642 c. M: 6.7653 c. 
 78:  12 13 8 13 10 7 15   N        SD: 3.3096 c. M:-4.8681 c. 
 84:  13 14 8 14 11 8 16   N        SD: 2.6874 c. M: 4.0266 c. 
 97:  15 16 10 16 12 9 19   N        SD: 2.5520 c. M: 3.6419 c. 
 98:  15 16 10 16 13 9 19   N        SD: 2.6745 c. M: 4.8651 c. 
 104: 16 17 11 17 13 10 20   N        SD: 2.1917 c. M:-3.6658 c. 
 109: 17 18 11 18 14 10 21   N        SD: 1.8761 c. M:-3.4264 c. 
 123: 19 20 13 20 16 11 24   N        SD: 2.0214 c. M:-3.2905 c. 
 126: 20 20 13 21 16 12 24   N        SD: 1.7574 c. M:-2.8700 c. 
 135: 21 22 14 22 17 13 26   N        SD: 1.6983 c. M: 3.4320 c. 
 140: 22 23 14 23 18 13 27   N        SD: 1.6263 c. M:-3.8195 c. 
 147: 23 24 15 24 19 14 28   N        SD: 1.5302 c. M:-2.8382 c. 
 154: 24 25 16 25 20 14 30   N        SD: 1.4376 c. M:-2.4670 c. 
 160: 25 26 16 27 20 15 31   N        SD: 1.2954 c. M:-2.1757 c. 
 167: 26 27 17 28 21 16 32   N        SD: 1.1727 c. M: 1.6755 c. 
 186: 29 30 19 31 24 17 36   N        SD: 0.8478 c. M:-1.2992 c. 
 217: 34 35 22 36 28 20 42   N        SD: 0.5414 c. M: 0.8485 c. 
 321: 50 52 33 53 41 30 62   N        SD: 0.5140 c. M: 0.6906 c. 
 333: 52 54 34 55 43 31 64   N        SD: 0.4931 c. M:-0.8923 c. 
 364: 57 59 37 60 47 34 70   N        SD: 0.4548 c. M:-0.6404 c. 
 493: 77 80 50 82 63 46 95   N        SD: 0.2798 c. M:-0.6240 c. 
 524: 82 85 53 87 67 49 101   N        SD: 0.2721 c. M:-0.5480 c. 
 538: 84 87 55 89 69 50 104   N        SD: 0.3224 c. M: 0.5606 c. 
 550: 86 89 56 91 71 51 106   N        SD: 0.2876 c. M:-0.6892 c. 
 647: 101 105 66 107 83 60 125   N        SD: 0.2744 c. M:-0.4557 c. 
 678: 106 110 69 112 87 63 131   N        SD: 0.2854 c. M: 0.4488 c. 
 685: 107 111 70 113 88 64 132   N        SD: 0.2495 c. M:-0.4990 c. 
 710: 111 115 72 118 91 66 137   N        SD: 0.1898 c. M: 0.3646 c. 
 857: 134 139 87 142 110 80 165   N        SD: 0.2131 c. M:-0.3711 c. 
 871: 136 141 89 144 112 81 168   N        SD: 0.1863 c. M: 0.2644 c. 
 902: 141 146 92 149 116 84 174   N        SD: 0.1670 c. M: 0.3852 c. 
 1031: 161 167 105 171 132 96 199   N        SD: 0.1501 c. M: 0.2153 c. 
 1062: 166 172 108 176 136 99 205   N        SD: 0.1370 c. M: 0.2681 c. 
 1178: 184 191 120 195 151 110 227   N        SD: 0.1333 c. M:-0.2179 c. 
 1286: 201 208 131 213 165 120 248   N        SD: 0.1409 c. M: 0.2462 c. 
 1364: 213 221 139 226 175 127 263   N        SD: 0.1118 c. M: 0.2162 c. 
 1395: 218 226 142 231 179 130 269   N        SD: 0.0423 c. M: 0.0793 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: 0.4346 cents
 3 x x 4 x 5 x 6  S SD: 9.4114 cents
 4 x 5 x 6 x 7:8  S SD: 1.1275 cents
 5 x 6:7 x 8:9:10  S SD: 24.3367 cents
 6:7 x 8:9:10:11:12  S SD: 19.4401 cents
 7:8:9 x x 11:12:14    SD: 21.4488 cents
 8:9:10:11:12:13:14:16  S SD: 7.5408 cents
 16:18:20:21:24:26:28:32  S SD: 5.8118 cents
 20:22:25:27:30:33:35:40    SD: 4.2285 cents
 24:27:30:32:36:39:42:48  S SD: 3.4570 cents
 33:37:41:44:50:54:58:66    SD: 3.2973 cents
 36:40:45:48:54:59:63:72    SD: 1.3205 cents
 44:49:55:59:66:72:77:88    SD: 1.0500 cents
 80:89:100:107:120:131:140:160    SD: 0.8892 cents
 106:118:132:142:159:174:185:212    SD: 0.8453 cents
 122:136:152:163:183:200:213:244    SD: 0.7025 cents
 130:145:162:174:195:213:227:260    SD: 0.6502 cents
 142:158:177:190:213:233:248:284    SD: 0.6311 cents
 166:185:207:222:249:272:290:332    SD: 0.5032 cents
 175:195:218:234:263:287:306:350    SD: 0.4709 cents
 183:204:228:245:275:300:320:366    SD: 0.4635 cents
 192:214:239:257:288:315:336:384    SD: 0.4390 cents
 219:244:273:293:329:359:383:438    SD: 0.3336 cents
 228:254:284:305:342:374:399:456    SD: 0.2893 cents
 272:303:339:364:408:446:476:544    SD: 0.2208 cents
 340:379:424:455:510:558:595:680    SD: 0.2044 cents
 376:419:469:503:564:617:658:752    SD: 0.1962 cents
 429:478:535:574:644:704:751:858    SD: 0.1880 cents
 453:505:565:606:680:743:793:906    SD: 0.1740 cents
 479:534:597:641:719:786:838:958    SD: 0.1724 cents
 515:574:642:689:773:845:901:1030    SD: 0.0999 cents
 551:614:687:737:827:904:964:1102    SD: 0.0991 cents
 559:623:697:748:839:917:978:1118    SD: 0.0523 cents