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