Scala analysis: CD16_13_Morocco

Nous nous sommes trouvés dans un jardin - 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:        218.643 cents     218.643024
  2:        404.627 cents     404.626664
  3:        508.990 cents     508.990258
  4:        711.845 cents     711.844767
  5:        908.653 cents     908.653055
  6:       1012.508 cents    1012.507568
  7:       1200.000 cents    1200.000000
SHOW/INTERVAL
  0:        187.4924 cents    187.4924
  1:        218.6430 cents    218.6430
  2:        185.9836 cents    185.9836
  3:        104.3636 cents    104.3636
  4:        202.8545 cents    202.8545
  5:        196.8083 cents    196.8083
  6:        103.8545 cents    103.8545
  7:        187.4924 cents    187.4924
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   1 103.85451 cents
  1:   1 104.36359 cents
  1:   1 185.98364 cents
  1:   1 187.49243 cents
  1:   1 196.80829 cents
  1:   1 202.85451 cents
  1:   1 218.64302 cents
  2:   1 290.34723 cents
  2:   1 291.34695 cents
  2:   1 300.66280 cents
  2:   1 307.21810 cents
  2:   1 399.66280 cents
  2:   1 404.62666 cents
  2:   1 406.13546 cents
  3:   1 488.15523 cents
  3:   1 493.20174 cents
  3:   1 503.51731 cents
  3:   1 504.02639 cents
  3:   1 508.99026 cents
  3:   1 509.98997 cents
  3:   1 592.11910 cents
  4:   1 607.88090 cents
  4:   1 690.01003 cents
  4:   1 691.00974 cents
  4:   1 695.97361 cents
  4:   1 696.48269 cents
  4:   1 706.79826 cents
  4:   1 711.84477 cents
  5:   1 793.86454 cents
  5:   1 795.37334 cents
  5:   1 800.33720 cents
  5:   1 892.78190 cents
  5:   1 899.33720 cents
  5:   1 908.65306 cents
  5:   1 909.65277 cents
  6:   1 981.35698 cents
  6:   1 997.14549 cents
  6:   1 1003.19171 cents
  6:   1 1012.50757 cents
  6:   1 1014.01636 cents
  6:   1 1095.63641 cents
  6:   1 1096.14549 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   : 218.6 404.6 509.0 711.8 908.7 1012.5 1200.0
 218.6 : 186.0 290.3 493.2 690.0 793.9 981.4  1200.0
 404.6 : 104.4 307.2 504.0 607.9 795.4 1014.0 1200.0
 509.0 : 202.9 399.7 503.5 691.0 909.7 1095.6 1200.0
 711.8 : 196.8 300.7 488.2 706.8 892.8 997.1  1200.0
 908.7 : 103.9 291.3 510.0 696.0 800.3 1003.2 1200.0
 1012.5: 187.5 406.1 592.1 696.5 899.3 1096.1 1200.0
 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  103.8545  .. 218.6430 cents      114.78851 cents                    103.85451 cents
  2:  290.3472  .. 406.1355 cents      115.78822 cents                    71.70421 cents
  3:  488.1552  .. 592.1191 cents      103.96386 cents                    82.01978 cents
  4:  607.8809  .. 711.8448 cents      103.96386 cents                    15.76181 cents
  5:  793.8645  .. 909.6528 cents      115.78822 cents                    82.01978 cents
  6:  981.3570  .. 1096.1455 cents     114.78851 cents                    71.70421 cents
SHOW DATA
Number of notes                     : 7
-- Interval properties --
Smallest interval                   : 103.85451 cents, class 1
Average step (divided formal octave): 171.4286 cents
Largest one step interval           : 218.64302 cents
Average / Smallest step             : 1.650661
Largest / Average step              : 1.275418
Largest / Smallest step             : 2.105282
Median interval of one step         : 187.49243 cents, amount: 1
Least squares average step          : 174.43255 cents, oct.:  1221.02784 cents
Scale is strictly proper
Step pattern alph. order: ABCDEFG
Step pattern size order : GCBFEAD
Scale is sum-free (all different intervals)
Scale is a Constant Structure, by a margin of 15.76181 cents
Scale diversity                     : 1.420028
Rothenberg stability                : 1.000000 = 1
Lumma stability                     : 0.442432
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        : 0.50908 cents
Number of recognisable fifths       : 6, average 698.6865 cents
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 114.7885 cents:
 1
-- Rational properties --
FIT/MODE
  7:  1 1 1 1 1 1 1  SP B ME I SD: 37.1616 c. M: 61.7695 c.  Lebeng
  9:  2 1 1 1 2 1 1   P M ME S SD: 34.8541 c. M:-54.1591 c. 
 12:  2 2 1 2 2 1 2   P M ME S SD: 10.8325 c. M: 18.6430 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
 32:  6 5 3 5 5 3 5   P   T3 S SD: 7.8742 c. M:-16.0097 c. 
 33:  6 5 3 6 5 3 5  SP   T3   SD: 6.4591 c. M:-15.4280 c. 
 38:  7 6 3 7 6 3 6   P   T3   SD: 6.7482 c. M:-14.4710 c. 
 39:  7 6 4 6 7 3 6  SP        SD: 8.1418 c. M:-14.4239 c. 
 42:  8 6 4 7 7 3 7   P        SD: 6.9913 c. M: 12.5076 c. 
 44:  8 7 4 7 7 4 7   P   T3 S SD: 5.3286 c. M:-9.1916 c. 
 45:  8 7 4 8 7 4 7  SP   T3   SD: 4.2449 c. M:-8.1552 c. 
 54:  10 8 5 9 9 5 8  SP      S SD: 4.4669 c. M:-9.7147 c. 
 57:  10 9 5 10 9 5 9  SP   T3   SD: 4.3450 c. M: 8.1167 c. 
 59:  11 9 5 10 10 5 9  SP      S SD: 3.6659 c. M:-6.6012 c. 
 62:  11 10 5 11 10 5 10   P   T3   SD: 4.2356 c. M: 6.0560 c. 
 66:  12 10 6 11 11 6 10  SP      S SD: 2.9665 c. M:-5.6743 c. 
 71:  13 11 6 12 12 6 11  SP      S SD: 2.0206 c. M:-4.0230 c. 
 83:  15 13 7 14 14 7 13  SP      S SD: 2.0224 c. M: 3.4110 c. 
 103: 19 16 9 17 17 9 16  SP      S SD: 2.1701 c. M:-3.6311 c. 
 104: 19 16 9 18 17 9 16  SP        SD: 2.1305 c. M:-3.5398 c. 
 115: 21 18 10 19 19 10 18  SP      S SD: 1.5590 c. M:-2.3299 c. 
 116: 21 18 10 20 19 10 18  SP        SD: 1.5141 c. M: 2.0937 c. 
 128: 23 20 11 22 21 11 20  SP        SD: 1.6828 c. M: 3.0180 c. 
 136: 25 21 12 23 22 12 21  SP        SD: 1.9312 c. M:-2.8611 c. 
 148: 27 23 13 25 24 13 23  SP        SD: 1.0751 c. M:-1.8206 c. 
 160: 29 25 14 27 26 14 25  SP        SD: 0.7768 c. M: 1.1531 c. 
 219: 40 34 19 37 36 19 34  SP        SD: 0.7465 c. M:-1.1911 c. 
 231: 42 36 20 39 38 20 36  SP        SD: 0.3764 c. M:-0.5681 c. 
 531: 97 82 46 90 87 46 83  SP        SD: 0.3014 c. M:-0.5660 c. 
 543: 99 84 47 92 89 47 85  SP        SD: 0.3534 c. M: 0.7030 c. 
 646: 118 100 56 109 106 56 101  SP        SD: 0.3083 c. M:-0.5520 c. 
 679: 124 105 59 115 111 59 106  SP        SD: 0.2661 c. M:-0.5028 c. 
 691: 126 107 60 117 113 60 108  SP        SD: 0.1891 c. M: 0.4041 c. 
 762: 139 118 66 129 125 66 119  SP        SD: 0.1656 c. M: 0.3288 c. 
 910: 166 141 79 154 149 79 142  SP        SD: 0.1827 c. M:-0.2581 c. 
 922: 168 143 80 156 151 80 144  SP        SD: 0.1074 c. M: 0.1932 c. 
 1273: 232 197 111 215 209 110 199  SP        SD: 0.1132 c. M: 0.2276 c. 
 1421: 259 220 124 240 233 123 222  SP        SD: 0.1041 c. M:-0.2286 c. 
 1426: 260 221 124 241 234 123 223  SP        SD: 0.1339 c. M:-0.1828 c. 
 1433: 261 222 125 242 235 124 224  SP        SD: 0.1001 c. M: 0.1605 c. 
 1504: 274 233 131 254 247 130 235  SP        SD: 0.0847 c. M: 0.1426 c. 
 1652: 301 256 144 279 271 143 258  SP        SD: 0.0898 c. M:-0.2107 c. 
 1664: 303 258 145 281 273 144 260  SP        SD: 0.0816 c. M:-0.1444 c. 
 1964: 358 304 171 332 322 170 307  SP        SD: 0.0836 c. M: 0.1460 c. 
 2035: 371 315 177 344 334 176 318  SP        SD: 0.0842 c. M:-0.1285 c. 
 2183: 398 338 190 369 358 189 341  SP        SD: 0.0595 c. M:-0.1385 c. 
 2195: 400 340 191 371 360 190 343  SP        SD: 0.0396 c. M: 0.0709 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: 4.9449 cents
 3 x x 4 x 5 x 6  S SD: 8.8820 cents
 4 x 5 x 6 x 7:8  S SD: 12.0966 cents
 5 x 6:7 x 8:9:10  S SD: 29.9122 cents
 6:7 x 8:9:10:11:12  S SD: 11.1705 cents
 7:8:9 x 11:12:13:14    SD: 16.8150 cents
 8:9:10:11:12 x 14:16  S SD: 10.9924 cents
 10:11:13 x 15:17:18:20    SD: 12.4270 cents
 12:14:15:16:18:20:22:24  S SD: 9.9257 cents
 14:16:18:19:21:24:25:28    SD: 6.7693 cents
 15:17:19:20:23:25:27:30    SD: 5.6317 cents
 20:23:25:27:30:34:36:40    SD: 4.9777 cents
 23:26:29:31:35:39:41:46    SD: 3.2138 cents
 29:33:37:39:44:49:52:58    SD: 2.9807 cents
 30:34:38:40:45:51:54:60    SD: 2.7421 cents
 35:40:44:47:53:59:63:70    SD: 2.5557 cents
 38:43:48:51:57:64:68:76    SD: 1.9336 cents
 45:51:57:60:68:76:81:90    SD: 1.9221 cents
 53:60:67:71:80:90:95:106    SD: 1.3926 cents
 65:74:82:87:98:110:117:130    SD: 1.3563 cents
 67:76:85:90:101:113:120:134    SD: 1.3248 cents
 73:83:92:98:110:123:131:146    SD: 1.1470 cents
 87:99:110:117:131:147:156:174    SD: 1.0736 cents
 88:100:111:118:133:149:158:176    SD: 0.8474 cents
 103:117:130:138:155:174:185:206    SD: 0.8352 cents
 106:120:134:142:160:179:190:212    SD: 0.8139 cents
 126:143:159:169:190:213:226:252    SD: 0.3495 cents
 216:245:273:290:326:365:388:432    SD: 0.3229 cents
 258:293:326:346:389:436:463:516    SD: 0.3046 cents
 281:319:355:377:424:475:504:562    SD: 0.2145 cents
 342:388:432:459:516:578:614:684    SD: 0.1141 cents
 468:531:591:628:706:791:840:936    SD: 0.0969 cents