Scala analysis: CD16_18_Morocco

Parcours le Monde, tu en saisiras les secrets - L'ensemble de 'Umar Fâ'id Al-Ju'aydî (ushshaq, Morocco)

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

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:        213.147 cents     213.146692
  2:        504.808 cents     504.808386
  3:        705.733 cents     705.733203
  4:        908.648 cents     908.647596
  5:        994.399 cents     994.398922
  6:       1200.000 cents    1200.000000
SHOW/INTERVAL
  0:        205.6011 cents    205.6011
  1:        213.1467 cents    213.1467
  2:        291.6617 cents    291.6617
  3:        200.9248 cents    200.9248
  4:        202.9144 cents    202.9144
  5:         85.7513 cents     85.7513
  6:        205.6011 cents    205.6011
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   1 85.75133 cents
  1:   1 200.92482 cents
  1:   1 202.91439 cents
  1:   1 205.60108 cents
  1:   1 213.14669 cents
  1:   1 291.66169 cents
  2:   1 288.66572 cents
  2:   1 291.35240 cents
  2:   1 403.83921 cents
  2:   1 418.74777 cents
  2:   1 492.58651 cents
  2:   1 504.80839 cents
  3:   1 489.59054 cents
  3:   1 494.26680 cents
  3:   1 504.49910 cents
  3:   1 695.50090 cents
  3:   1 705.73320 cents
  3:   1 710.40946 cents
  4:   1 695.19161 cents
  4:   1 707.41349 cents
  4:   1 781.25223 cents
  4:   1 796.16079 cents
  4:   1 908.64760 cents
  4:   1 911.33428 cents
  5:   1 908.33831 cents
  5:   1 986.85331 cents
  5:   1 994.39892 cents
  5:   1 997.08561 cents
  5:   1 999.07518 cents
  5:   1 1114.24867 cents
Highest number of different intervals for one interval class: 6
Average number of different intervals per interval class: 6.00000 = 6
SHOW/LINE/CENTS INTERVALS
         1     2     3     4     5      6     
 0.0   : 213.1 504.8 705.7 908.6 994.4  1200.0
 213.1 : 291.7 492.6 695.5 781.3 986.9  1200.0
 504.8 : 200.9 403.8 489.6 695.2 908.3  1200.0
 705.7 : 202.9 288.7 494.3 707.4 999.1  1200.0
 908.6 : 85.8  291.4 504.5 796.2 997.1  1200.0
 994.4 : 205.6 418.7 710.4 911.3 1114.2 1200.0
 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  85.7513   .. 291.6617 cents      205.91037 cents                    85.75133 cents
  2:  288.6657  .. 504.8084 cents      216.14267 cents                   -2.99597 cents
  3:  489.5905  .. 710.4095 cents      220.81893 cents                   -15.21785 cents
  4:  695.1916  .. 911.3343 cents      216.14267 cents                   -15.21785 cents
  5:  908.3383  .. 1114.2487 cents     205.91037 cents                   -2.99597 cents
SHOW DATA
Number of notes                     : 6
-- Interval properties --
Smallest interval                   : 85.75133 cents, class 1
Average step (divided formal octave): 200.0000 cents
Largest one step interval           : 291.66169 cents
Average / Smallest step             : 2.332325
Largest / Average step              : 1.458308
Largest / Smallest step             : 3.401250
Median interval of one step         : 204.25774 cents, amount: 0
Least squares average step          : 210.40163 cents, oct.:  1262.40976 cents
Scale is not proper
Step pattern alph. order: ABCDEF
Step pattern size order : EFBCAD
Scale is sum-free (all different intervals)
Scale is a Constant Structure, by a margin of 0.30929 cents
Scale diversity                     : 1.364418
Lumma stability                     : 0.142919
Lumma impropriety factor            : 0.030356
Rothenberg efficiency               : 0.333333   redundancy: 0.666667
Efficiency x scale size             : 2.000000
Number of different interval sizes  : 30 = 6.00000 / class
Number of one step interval sizes   : 6
Highest interval variety            : 6
Mean interval variety               : 6.00000 = 6
Median interval variety             : 6
Lowest interval variety             : 6
Smallest interval difference        : 0.30929 cents
Number of recognisable fifths       : 5, average 702.8497 cents
Formal octave complements present   : 1 = 16.6667%
Limited inverse transpositions with margin 216.1427 cents:
 3
-- Rational properties --
FIT/MODE
  6:  1 1 1 1 1 1  SP B ME I SD: 75.4683 c. M: 108.6476 c.  Whole-tone, Messiaen mode 1, Raga Gopriya, Anhemitonic Hexatonic
  7:  1 2 1 1 1 1   P M ME   SD: 31.7581 c. M: 51.5047 c. 
 10:  2 2 2 2 0 2   P M DE   SD: 29.8899 c. M:-51.3524 c. 
 12:  2 3 2 2 1 2   P G D3   SD: 7.4719 c. M: 13.1467 c.  Mixolydian Hexatonic, P'yongjo: Korea, Yosen: Japan, Raga Darbar, Narayani, Suposhini, Andolika, Gorakh Kalyan, Rakta Hauns
 17:  3 4 3 3 1 3   P G D3   SD: 6.2611 c. M: 10.6907 c. 
 29:  5 7 5 5 2 5   P G D3   SD: 4.4162 c. M: 8.2567 c. 
 41:  7 10 7 7 3 7   P G D3   SD: 4.7265 c. M: 8.2686 c. 
 54:  10 13 9 9 4 9   N        SD: 5.6044 c. M:-9.0755 c. 
 57:  10 14 9 10 4 10   N        SD: 5.2234 c. M: 10.9964 c. 
 61:  11 15 10 10 5 10   N        SD: 5.0633 c. M:-8.8798 c. 
 62:  11 15 10 11 4 11   N        SD: 4.7821 c. M: 8.9590 c. 
 66:  12 16 11 11 5 11   N        SD: 3.7977 c. M:-5.6011 c. 
 71:  13 17 12 12 5 12   N        SD: 3.8553 c. M:-6.5716 c. 
 78:  14 19 13 13 6 13   N        SD: 2.8708 c. M:-5.6011 c. 
 83:  15 20 14 14 6 14   N        SD: 2.5041 c. M:-3.7208 c. 
 95:  17 23 16 16 7 16   N        SD: 1.7470 c. M:-3.4958 c. 
 100: 18 24 17 17 7 17   N        SD: 2.1500 c. M:-3.3524 c. 
 107: 19 26 18 18 8 18   N        SD: 1.5631 c. M:-3.7319 c. 
 111: 20 27 18 19 8 19   N        SD: 2.2295 c. M:-3.2997 c. 
 112: 20 27 19 19 8 19   N        SD: 1.4835 c. M:-2.0667 c. 
 124: 22 30 21 21 9 21   N        SD: 1.2769 c. M:-2.3753 c. 
 157: 28 38 26 27 11 27   N        SD: 1.2096 c. M: 2.5485 c. 
 169: 30 41 28 29 12 29   N        SD: 1.1769 c. M: 2.7746 c. 
 180: 32 44 30 30 13 31   N        SD: 1.2529 c. M: 1.9809 c. 
 185: 33 45 31 31 13 32   N        SD: 1.1510 c. M: 1.9665 c. 
 197: 35 48 33 33 14 34   N        SD: 0.8839 c. M: 1.5055 c. 
 209: 37 51 35 35 15 36   N        SD: 0.8476 c. M: 1.4706 c. 
 214: 38 52 36 36 15 37   N        SD: 0.8416 c. M: 1.8756 c. 
 226: 40 55 38 38 16 39   N        SD: 0.7731 c. M: 1.4786 c. 
 235: 42 57 39 40 17 40   N        SD: 0.9373 c. M:-1.3458 c. 
 238: 42 58 40 40 17 41   N        SD: 0.8883 c. M: 1.3820 c. 
 247: 44 60 41 42 18 42   N        SD: 0.8812 c. M:-1.5525 c. 
 252: 45 61 42 43 18 43   N        SD: 0.7869 c. M:-1.1390 c. 
 264: 47 64 44 45 19 45   N        SD: 0.7107 c. M: 1.1877 c. 
 281: 50 68 47 48 20 48   N        SD: 0.7607 c. M: 1.1069 c. 
 292: 52 71 49 49 21 50   N        SD: 0.6054 c. M:-1.1161 c. 
 304: 54 74 51 51 22 52   N        SD: 0.5169 c. M:-0.8457 c. 
 309: 55 75 52 52 22 53   N        SD: 0.4811 c. M:-1.0629 c. 
 321: 57 78 54 54 23 55   N        SD: 0.3494 c. M:-0.8089 c. 
 333: 59 81 56 56 24 57   N        SD: 0.4154 c. M:-0.5731 c. 
 444: 79 108 74 75 32 76   N        SD: 0.3932 c. M:-0.5970 c. 
 449: 80 109 75 76 32 77   N        SD: 0.3166 c. M:-0.6618 c. 
 461: 82 112 77 78 33 79   N        SD: 0.2070 c. M: 0.3102 c. 
 478: 85 116 80 81 34 82   N        SD: 0.2132 c. M: 0.2939 c. 
 490: 87 119 82 83 35 84   N        SD: 0.2272 c. M: 0.4271 c. 
 585: 104 142 98 99 42 100   N        SD: 0.2270 c. M:-0.4729 c. 
 770: 137 187 129 130 55 132   N        SD: 0.1924 c. M:-0.3598 c. 
 782: 139 190 131 132 56 134   N        SD: 0.1238 c. M: 0.2077 c. 
 799: 142 194 134 135 57 137   N        SD: 0.1243 c. M: 0.1776 c. 
 811: 144 197 136 137 58 139   N        SD: 0.1257 c. M: 0.2461 c. 
 1243: 221 302 208 210 89 213   N        SD: 0.1256 c. M:-0.2081 c. 
 1255: 223 305 210 212 90 215   N        SD: 0.1255 c. M: 0.2811 c. 
 1260: 224 306 211 213 90 216   N        SD: 0.0966 c. M:-0.1866 c. 
 1272: 226 309 213 215 91 218   N        SD: 0.0871 c. M: 0.1570 c. 
 1581: 281 384 265 267 113 271   N        SD: 0.1042 c. M:-0.1491 c. 
 1593: 283 387 267 269 114 273   N        SD: 0.0954 c. M: 0.1730 c. 
 1750: 311 425 293 296 125 300   N        SD: 0.1030 c. M: 0.1332 c. 
 1780: 316 433 298 301 127 305   N        SD: 0.0974 c. M:-0.1354 c. 
 1845: 328 448 309 312 132 316   N        SD: 0.0926 c. M:-0.1866 c. 
 1857: 330 451 311 314 133 318   N        SD: 0.0918 c. M: 0.1234 c. 
 2054: 365 499 344 347 147 352   N        SD: 0.0856 c. M: 0.1763 c. 
 2071: 368 503 347 350 148 355   N        SD: 0.0839 c. M: 0.1247 c. 
 2083: 370 506 349 352 149 357   N        SD: 0.0914 c. M: 0.1516 c. 
 2166: 385 526 363 366 155 371   N        SD: 0.0882 c. M:-0.1497 c. 
 2178: 387 529 365 368 156 373   N        SD: 0.0858 c. M: 0.1252 c. 
 2241: 398 545 375 379 160 384   N        SD: 0.0653 c. M:-0.1448 c. 
 2253: 400 548 377 381 161 386   N        SD: 0.0628 c. M:-0.1184 c. 
 2270: 403 552 380 384 162 389   N        SD: 0.0576 c. M: 0.1070 c. 
 2365: 420 575 396 400 169 405   N        SD: 0.0706 c. M:-0.1050 c. 
FIT/HARMONIC
 1 x x x x x 2  S SD: 0.0000 cents
 2 x x 3 x x 4  S SD: 1.8891 cents
 3 x 4 x 5 x 6  S SD: 8.4043 cents
 4 x 5:6 x 7:8  S SD: 30.3204 cents
 5:6:7 x 8:9:10  S SD: 32.3102 cents
 6:7:8:9:10:11:12  H SD: 13.4962 cents
 7:8:9:11:12 x 14    SD: 21.6127 cents
 8:9:11:12 x 14:16    SD: 10.8013 cents
 12:14:16:18:20:21:24  S SD: 10.7887 cents
 14:16:19:21:24:25:28    SD: 6.6608 cents
 22:25:29:33:37:39:44    SD: 4.9175 cents
 23:26:31:35:39:41:46    SD: 4.2881 cents
 30:34:40:45:51:53:60    SD: 2.6687 cents
 32:36:43:48:54:57:64    SD: 2.2239 cents
 44:50:59:66:74:78:88    SD: 2.2046 cents
 45:51:60:68:76:80:90    SD: 1.9997 cents
 53:60:71:80:90:94:106    SD: 1.8671 cents
 54:61:72:81:91:96:108    SD: 1.6160 cents
 62:70:83:93:105:110:124    SD: 1.0336 cents
 68:77:91:102:115:121:136    SD: 0.9182 cents
 106:120:142:159:179:188:212    SD: 0.8664 cents
 107:121:143:161:181:190:214    SD: 0.5812 cents
 139:157:186:209:235:247:278    SD: 0.4377 cents
 175:198:234:263:296:311:350    SD: 0.4298 cents
 183:207:245:275:309:325:366    SD: 0.3136 cents
 236:267:316:355:399:419:472    SD: 0.2575 cents
 268:303:359:403:453:476:536    SD: 0.2568 cents
 290:328:388:436:490:515:580    SD: 0.1704 cents
 419:474:561:630:708:744:838    SD: 0.1536 cents
 443:501:593:666:749:787:886    SD: 0.1242 cents
 481:544:644:723:813:854:962    SD: 0.1211 cents
 558:631:747:839:943:991:1116    SD: 0.0948 cents
 594:672:795:893:1004:1055:1188    SD: 0.0858 cents