Scala analysis: CD16_02_Morocco

Tûshiya - 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:        210.855 cents     210.854799
  2:        400.897 cents     400.896898
  3:        504.071 cents     504.070734
  4:        703.217 cents     703.216644
  5:        892.702 cents     892.701608
  6:       1015.824 cents    1015.823877
  7:       1200.000 cents    1200.000000
SHOW/INTERVAL
  0:        184.1761 cents    184.1761
  1:        210.8548 cents    210.8548
  2:        190.0421 cents    190.0421
  3:        103.1738 cents    103.1738
  4:        199.1459 cents    199.1459
  5:        189.4850 cents    189.4850
  6:        123.1223 cents    123.1223
  7:        184.1761 cents    184.1761
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   1 103.17384 cents
  1:   1 123.12227 cents
  1:   1 184.17612 cents
  1:   1 189.48496 cents
  1:   1 190.04210 cents
  1:   1 199.14591 cents
  1:   1 210.85480 cents
  2:   1 293.21594 cents
  2:   1 302.31975 cents
  2:   1 307.29839 cents
  2:   1 312.60723 cents
  2:   1 388.63087 cents
  2:   1 395.03092 cents
  2:   1 400.89690 cents
  3:   1 491.80471 cents
  3:   1 492.36185 cents
  3:   1 496.78336 cents
  3:   1 504.07073 cents
  3:   1 511.75314 cents
  3:   1 518.15319 cents
  3:   1 585.07302 cents
  4:   1 614.92698 cents
  4:   1 681.84681 cents
  4:   1 688.24686 cents
  4:   1 695.92927 cents
  4:   1 703.21664 cents
  4:   1 707.63815 cents
  4:   1 708.19529 cents
  5:   1 799.10310 cents
  5:   1 804.96908 cents
  5:   1 811.36913 cents
  5:   1 887.39277 cents
  5:   1 892.70161 cents
  5:   1 897.68025 cents
  5:   1 906.78406 cents
  6:   1 989.14520 cents
  6:   1 1000.85409 cents
  6:   1 1009.95790 cents
  6:   1 1010.51504 cents
  6:   1 1015.82388 cents
  6:   1 1076.87773 cents
  6:   1 1096.82616 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   : 210.9 400.9 504.1 703.2 892.7 1015.8 1200.0
 210.9 : 190.0 293.2 492.4 681.8 805.0 989.1  1200.0
 400.9 : 103.2 302.3 491.8 614.9 799.1 1010.0 1200.0
 504.1 : 199.1 388.6 511.8 695.9 906.8 1096.8 1200.0
 703.2 : 189.5 312.6 496.8 707.6 897.7 1000.9 1200.0
 892.7 : 123.1 307.3 518.2 708.2 811.4 1010.5 1200.0
 1015.8: 184.2 395.0 585.1 688.2 887.4 1076.9 1200.0
 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  103.1738  .. 210.8548 cents      107.68096 cents                    103.17384 cents
  2:  293.2159  .. 400.8969 cents      107.68096 cents                    82.36114 cents
  3:  491.8047  .. 585.0730 cents      93.26831 cents                     90.90781 cents
  4:  614.9270  .. 708.1953 cents      93.26831 cents                     29.85396 cents
  5:  799.1031  .. 906.7841 cents      107.68096 cents                    90.90781 cents
  6:  989.1452  .. 1096.8262 cents     107.68096 cents                    82.36114 cents
SHOW DATA
Number of notes                     : 7
-- Interval properties --
Smallest interval                   : 103.17384 cents, class 1
Average step (divided formal octave): 171.4286 cents
Largest one step interval           : 210.85480 cents
Average / Smallest step             : 1.661551
Largest / Average step              : 1.229986
Largest / Smallest step             : 2.043685
Median interval of one step         : 189.48496 cents, amount: 1
Least squares average step          : 173.54413 cents, oct.:  1214.80893 cents
Scale is strictly proper
Step pattern alph. order: ABCDEFG
Step pattern size order : GEAFDBC
Scale is sum-free (all different intervals)
Scale is a Constant Structure, by a margin of 29.85396 cents
Scale diversity                     : 1.470740
Rothenberg stability                : 1.000000 = 1
Lumma stability                     : 0.485616
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        : 0.55714 cents
Number of recognisable fifths       : 5, average 700.6452 cents
Number of appreciable fifths        : 4, average 703.7448 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 107.6810 cents:
 1
-- Rational properties --
FIT/MODE
  7:  1 1 1 1 1 1 1  SP B ME I SD: 31.0774 c. M: 58.0398 c.  Lebeng
  9:  2 1 1 1 2 1 1   P M ME S SD: 36.9244 c. M:-55.8119 c. 
 12:  2 2 1 2 2 1 2   P M ME S SD: 8.0108 c. M: 15.8239 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
 27:  5 4 2 5 4 3 4  SP        SD: 8.2662 c. M: 15.1818 c. 
 31:  5 5 3 5 5 3 5  SP M DE S SD: 9.4542 c. M: 17.3064 c.  Intense Diatonic Hypophrygian, M.Mixolydian
 33:  6 5 3 5 6 3 5  SP   T3   SD: 8.4965 c. M:-16.3893 c. 
 34:  6 5 3 6 5 4 5  SP        SD: 7.8721 c. M: 12.6616 c. 
 38:  7 6 3 6 6 4 6   P        SD: 7.2724 c. M:-10.1978 c. 
 39:  7 6 3 7 6 4 6  SP        SD: 5.0719 c. M: 11.7630 c. 
 46:  8 7 4 8 7 5 7  SP        SD: 5.4023 c. M: 9.5926 c. 
 50:  9 8 4 8 8 5 8   P        SD: 5.5075 c. M: 7.8239 c. 
 51:  9 8 4 9 8 5 8  SP        SD: 4.2474 c. M: 9.9531 c. 
 57:  10 9 5 9 9 6 9  SP        SD: 4.9915 c. M: 8.4911 c. 
 58:  10 9 5 10 9 6 9  SP        SD: 4.5732 c. M: 7.7934 c. 
 63:  11 10 5 11 10 6 10  SP        SD: 4.2946 c. M: 8.8326 c. 
 65:  11 11 5 11 10 7 10  SP        SD: 4.8620 c. M: 7.7779 c. 
 66:  12 10 6 11 10 7 10  SP        SD: 4.1913 c. M:-7.3270 c. 
 67:  12 10 6 11 11 7 10  SP        SD: 4.2465 c. M: 6.8670 c. 
 70:  12 11 6 12 11 7 11  SP        SD: 4.4593 c. M: 6.9279 c. 
 72:  13 11 6 12 12 7 11  SP        SD: 4.0616 c. M:-7.2984 c. 
 73:  13 11 7 12 11 8 11  SP        SD: 4.2920 c. M: 6.3764 c. 
 74:  13 12 6 12 12 8 11  SP        SD: 3.6156 c. M: 5.9193 c. 
 78:  14 12 7 13 12 8 12  SP        SD: 2.7984 c. M:-4.5298 c. 
 90:  16 14 8 15 14 9 14  SP        SD: 2.1445 c. M:-3.4500 c. 
 102: 18 16 9 17 16 10 16  SP        SD: 2.0875 c. M: 4.0592 c. 
 126: 22 20 11 21 20 13 19  SP        SD: 1.7836 c. M:-3.2237 c. 
 138: 24 22 12 23 22 14 21  SP        SD: 1.6029 c. M:-2.9506 c. 
 152: 27 24 13 25 24 16 23  SP        SD: 1.5665 c. M:-2.5972 c. 
 155: 27 25 13 26 24 16 24  SP        SD: 1.5527 c. M: 2.3790 c. 
 164: 29 26 14 27 26 17 25  SP        SD: 0.9994 c. M:-1.5421 c. 
 176: 31 28 15 29 28 18 27  SP        SD: 0.7077 c. M:-1.3758 c. 
 188: 33 30 16 31 30 19 29  SP        SD: 0.8004 c. M:-1.2308 c. 
 222: 39 35 19 37 35 23 34  SP        SD: 0.7321 c. M: 1.3680 c. 
 234: 41 37 20 39 37 24 36  SP        SD: 0.7752 c. M: 1.5066 c. 
 266: 47 42 23 44 42 27 41  SP        SD: 0.7898 c. M:-1.1924 c. 
 273: 48 43 24 45 43 28 42  SP        SD: 0.6766 c. M:-1.4238 c. 
 300: 53 47 26 50 47 31 46  SP        SD: 0.6822 c. M:-1.1452 c. 
 312: 55 49 27 52 49 32 48  SP        SD: 0.5434 c. M: 0.8969 c. 
 360: 63 57 31 60 57 37 55  SP        SD: 0.6763 c. M: 0.8969 c. 
 371: 65 59 32 61 59 38 57  SP        SD: 0.5946 c. M: 1.3299 c. 
 386: 68 61 33 64 61 40 59  SP        SD: 0.4929 c. M:-0.7564 c. 
 398: 70 63 34 66 63 41 61  SP        SD: 0.3735 c. M: 0.7041 c. 
 410: 72 65 35 68 65 42 63  SP        SD: 0.3969 c. M: 0.7776 c. 
 476: 84 75 41 79 75 49 73  SP        SD: 0.3702 c. M:-0.9099 c. 
 488: 86 77 42 81 77 50 75  SP        SD: 0.2576 c. M:-0.6206 c. 
 536: 94 85 46 89 85 55 82  SP        SD: 0.3871 c. M:-0.5940 c. 
 574: 101 91 49 95 91 59 88  SP        SD: 0.3849 c. M: 0.7776 c. 
 614: 108 97 53 102 97 63 94  SP        SD: 0.3148 c. M:-0.4628 c. 
 626: 110 99 54 104 99 64 96  SP        SD: 0.2756 c. M:-0.5891 c. 
 659: 116 104 57 109 104 68 101  SP        SD: 0.3177 c. M: 0.4406 c. 
 664: 117 105 57 110 105 68 102  SP        SD: 0.2773 c. M:-0.5910 c. 
 671: 118 106 58 111 106 69 103  SP        SD: 0.2461 c. M: 0.3850 c. 
 683: 120 108 59 113 108 70 105  SP        SD: 0.2501 c. M: 0.4348 c. 
 769: 135 122 66 128 121 79 118  SP        SD: 0.2333 c. M:-0.5545 c. 
 790: 139 125 68 131 125 81 121  SP        SD: 0.2704 c. M:-0.4629 c. 
 802: 141 127 69 133 127 82 123  SP        SD: 0.2364 c. M:-0.5652 c. 
 848: 149 134 73 141 134 87 130  SP        SD: 0.2305 c. M: 0.4252 c. 
 886: 156 140 76 147 140 91 136  SP        SD: 0.2216 c. M:-0.4319 c. 
 898: 158 142 77 149 142 92 138  SP        SD: 0.2140 c. M: 0.3213 c. 
 945: 166 150 81 157 149 97 145  SP        SD: 0.1790 c. M:-0.3729 c. 
 985: 173 156 85 163 156 101 151  SP        SD: 0.2105 c. M:-0.2947 c. 
 1012: 178 160 87 168 160 104 155  SP        SD: 0.1900 c. M:-0.3817 c. 
 1024: 180 162 88 170 162 105 157  SP        SD: 0.1530 c. M:-0.2671 c. 
 1128: 198 179 97 187 178 116 173  SP        SD: 0.1460 c. M: 0.2165 c. 
 1167: 205 185 100 194 184 120 179  SP        SD: 0.1309 c. M: 0.2147 c. 
 1179: 207 187 101 196 186 121 181  SP        SD: 0.1333 c. M: 0.2539 c. 
 1343: 236 213 115 223 212 138 206  SP        SD: 0.1311 c. M:-0.2945 c. 
 1355: 238 215 116 225 214 139 208  SP        SD: 0.1283 c. M:-0.2839 c. 
 1362: 239 216 117 226 215 140 209  SP        SD: 0.1446 c. M: 0.2821 c. 
 1428: 251 226 123 237 225 147 219  SP        SD: 0.1396 c. M: 0.2646 c. 
 1433: 252 227 123 238 226 147 220  SP        SD: 0.1333 c. M:-0.2196 c. 
 1440: 253 228 124 239 227 148 221  SP        SD: 0.0986 c. M: 0.2016 c. 
 1452: 255 230 125 241 229 149 223  SP        SD: 0.0951 c. M: 0.1396 c. 
 1616: 284 256 139 268 255 166 248  SP        SD: 0.0805 c. M:-0.1372 c. 
 1628: 286 258 140 270 257 167 250  SP        SD: 0.0719 c. M:-0.1062 c. 
 1850: 325 293 159 307 292 190 284  SP        SD: 0.0776 c. M: 0.1611 c. 
 2152: 378 341 185 357 340 221 330  SP        SD: 0.0742 c. M:-0.1613 c. 
 2164: 380 343 186 359 342 222 332  SP        SD: 0.0732 c. M: 0.1339 c. 
 2242: 394 355 193 372 354 230 344  SP        SD: 0.0666 c. M:-0.1220 c. 
 2254: 396 357 194 374 356 231 346  SP        SD: 0.0639 c. M:-0.1112 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: 0.6308 cents
 3 x x 4 x 5 x 6  S SD: 3.4305 cents
 4 x 5 x 6 x 7:8  S SD: 12.3062 cents
 5 x 6:7 x 8:9:10  S SD: 28.0486 cents
 6:7 x 8:9:10:11:12  S SD: 11.0179 cents
 7:8:9 x 11:12:13:14    SD: 18.7253 cents
 8:9:10:11:12:13:14:16  S SD: 12.3104 cents
 10:11 x 13:15:17:18:20    SD: 12.0941 cents
 12:14:15:16:18:20:22:24  S SD: 9.6710 cents
 14:16:18:19:21:23:25:28    SD: 8.3782 cents
 15:17:19:20:23:25:27:30    SD: 5.6536 cents
 22:25:28:29:33:37:40:44    SD: 5.4852 cents
 23:26:29:31:35:39:41:46    SD: 5.3663 cents
 24:27:30:32:36:40:43:48    SD: 2.8842 cents
 30:34:38:40:45:50:54:60    SD: 2.0915 cents
 46:52:58:62:69:77:83:92    SD: 2.0246 cents
 53:60:67:71:80:89:95:106    SD: 1.9586 cents
 54:61:68:72:81:90:97:108    SD: 1.5254 cents
 62:70:78:83:93:104:111:124    SD: 1.2769 cents
 68:77:86:91:102:114:122:136    SD: 1.2039 cents
 80:90:101:107:120:134:144:160    SD: 1.1105 cents
 92:104:116:123:138:154:165:184    SD: 0.7357 cents
 124:140:156:166:186:208:223:248    SD: 0.6818 cents
 130:147:164:174:195:218:234:260    SD: 0.5663 cents
 154:174:194:206:231:258:277:308    SD: 0.2867 cents
 307:347:387:411:461:514:552:614    SD: 0.2484 cents
 323:365:407:432:485:541:581:646    SD: 0.2126 cents
 387:437:488:518:581:648:696:774    SD: 0.1589 cents
 471:532:594:630:707:789:847:942    SD: 0.1511 cents
 479:541:604:641:719:802:861:958    SD: 0.1400 cents
 495:559:624:662:743:829:890:990    SD: 0.1266 cents
 541:611:682:724:812:906:973:1082    SD: 0.0833 cents