Scala analysis: CD11_21_Iraq
Suite - Ensemble de Muhammad Al-Qubbbânjî (mansuri, Iraq)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 146.854 cents 146.853746 2: 350.321 cents 350.320855 3: 555.035 cents 555.034666 4: 666.535 cents 666.535088 5: 751.720 cents 751.720251 6: 845.533 cents 845.533302 7: 1048.015 cents 1048.014655 8: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 151.9853 cents 151.9853 1: 146.8537 cents 146.8537 2: 203.4671 cents 203.4671 3: 204.7138 cents 204.7138 4: 111.5004 cents 111.5004 5: 85.1852 cents 85.1852 6: 93.8131 cents 93.8131 7: 202.4814 cents 202.4814 8: 151.9853 cents 151.9853
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 85.18516 cents 1: 1 93.81305 cents 1: 1 111.50042 cents 1: 1 146.85375 cents 1: 1 151.98535 cents 1: 1 202.48135 cents 1: 1 203.46711 cents 1: 1 204.71381 cents 2: 1 178.99821 cents 2: 1 196.68558 cents 2: 1 296.29440 cents 2: 1 298.83909 cents 2: 1 316.21423 cents 2: 1 350.32085 cents 2: 1 354.46670 cents 2: 1 408.18092 cents 3: 1 290.49864 cents 3: 1 381.47957 cents 3: 1 401.39940 cents 3: 1 448.27975 cents 3: 1 501.32044 cents 3: 1 502.30620 cents 3: 1 519.68134 cents 3: 1 555.03467 cents 4: 1 492.97999 cents 4: 1 495.21245 cents 4: 1 533.46491 cents 4: 1 595.13350 cents 4: 1 604.86650 cents 4: 1 666.53509 cents 4: 1 704.78755 cents 4: 1 707.02001 cents 5: 1 644.96533 cents 5: 1 680.31866 cents 5: 1 697.69380 cents 5: 1 698.67956 cents 5: 1 751.72025 cents 5: 1 798.60060 cents 5: 1 818.52043 cents 5: 1 909.50136 cents 6: 1 791.81908 cents 6: 1 845.53330 cents 6: 1 849.67915 cents 6: 1 883.78577 cents 6: 1 901.16091 cents 6: 1 903.70560 cents 6: 1 1003.31442 cents 6: 1 1021.00179 cents 7: 1 995.28619 cents 7: 1 996.53289 cents 7: 1 997.51865 cents 7: 1 1048.01465 cents 7: 1 1053.14625 cents 7: 1 1088.49958 cents 7: 1 1106.18695 cents 7: 1 1114.81484 cents Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 8.00000 = 8
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 146.9 350.3 555.0 666.5 751.7 845.5 1048.0 1200.0 146.9 : 203.5 408.2 519.7 604.9 698.7 901.2 1053.1 1200.0 350.3 : 204.7 316.2 401.4 495.2 697.7 849.7 996.5 1200.0 555.0 : 111.5 196.7 290.5 493.0 645.0 791.8 995.3 1200.0 666.5 : 85.2 179.0 381.5 533.5 680.3 883.8 1088.5 1200.0 751.7 : 93.8 296.3 448.3 595.1 798.6 1003.3 1114.8 1200.0 845.5 : 202.5 354.5 501.3 704.8 909.5 1021.0 1106.2 1200.0 1048.0: 152.0 298.8 502.3 707.0 818.5 903.7 997.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 85.1852 .. 204.7138 cents 119.52865 cents 85.18516 cents 2: 178.9982 .. 408.1809 cents 229.18271 cents -25.71560 cents 3: 290.4986 .. 555.0347 cents 264.53603 cents -117.68228 cents 4: 492.9800 .. 707.0200 cents 214.04002 cents -62.05468 cents 5: 644.9653 .. 909.5014 cents 264.53603 cents -62.05468 cents 6: 791.8191 .. 1021.0018 cents 229.18271 cents -117.68228 cents 7: 995.2862 .. 1114.8148 cents 119.52865 cents -25.71560 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 85.18516 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 204.71381 cents Average / Smallest step : 1.760870 Largest / Average step : 1.364759 Largest / Smallest step : 2.403163 Median interval of one step : 149.41955 cents, amount: 0 Least squares average step : 151.69923 cents, oct.: 1213.59386 cents Scale is not proper Step pattern alph. order: ABCDEFGH Step pattern size order : DGHCABFE Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 5.79577 cents Scale diversity : 1.591360 Lumma stability : 0.141975 Lumma impropriety factor : 0.342421 Rothenberg efficiency : 0.250000 redundancy: 0.750000 Efficiency x scale size : 2.000000 Number of different interval sizes : 56 = 8.00000 / class Number of one step interval sizes : 8 Highest interval variety : 8 Mean interval variety : 8.00000 = 8 Median interval variety : 8 Lowest interval variety : 8 Smallest interval difference : 0.98576 cents Number of recognisable fifths : 4, average 702.0452 cents Formal octave complements present : 1 = 12.5000% -- Rational properties --
FIT/MODE
8: 1 1 2 0 1 1 1 1 N T3 SD: 38.6724 c. M: 66.5351 c. 9: 1 2 1 1 1 0 2 1 N SD: 31.3726 c. M:-49.6791 c. 10: 1 2 2 1 0 1 2 1 N SD: 31.1349 c. M:-53.4649 c. 11: 1 2 2 1 1 1 2 1 N D3 SD: 24.7846 c. M:-42.8944 c. 13: 2 2 2 1 1 1 2 2 N SD: 21.3858 c. M:-37.7616 c. 14: 2 2 2 2 1 1 2 2 P D3 S SD: 21.1813 c. M: 40.7490 c. 16: 2 3 2 2 1 1 3 2 N SD: 15.8950 c. M: 30.0347 c. 17: 2 3 3 1 2 1 3 2 N SD: 15.1673 c. M: 31.2410 c. 18: 2 3 3 2 1 2 3 2 N SD: 16.1049 c. M: 21.7013 c. 20: 2 4 3 2 1 2 3 3 N SD: 19.0564 c. M: 31.7203 c. 21: 3 3 4 2 1 2 3 3 N SD: 15.3607 c. M:-24.5748 c. 23: 3 4 4 2 1 2 4 3 N SD: 13.2216 c. M: 21.2855 c. 24: 3 4 4 2 2 2 4 3 N SD: 6.4770 c. M: 16.5351 c. 30: 4 5 5 3 2 2 5 4 N SD: 8.9154 c. M:-13.4649 c. 31: 4 5 5 3 2 3 5 4 N SD: 8.8003 c. M: 16.2364 c. 32: 4 5 6 3 2 3 5 4 N SD: 8.6344 c. M:-16.9667 c. 33: 4 6 5 3 3 2 6 4 N SD: 9.2434 c. M:-13.3155 c. 34: 4 6 6 3 2 3 6 4 N SD: 6.8865 c. M:-10.8089 c. 41: 5 7 7 4 3 3 7 5 N SD: 4.6676 c. M:-9.2554 c. 48: 6 8 8 5 3 4 8 6 N SD: 4.0905 c. M:-8.4649 c. 54: 7 9 9 5 4 4 9 7 N SD: 4.0628 c. M:-8.7018 c. 57: 7 10 9 6 4 4 10 7 N SD: 5.4624 c. M: 7.6662 c. 58: 7 10 10 5 4 5 10 7 N SD: 4.2595 c. M:-7.1578 c. 65: 8 11 11 6 5 5 11 8 N SD: 2.8542 c. M:-5.2028 c. 72: 9 12 12 7 5 6 12 9 N SD: 2.7888 c. M: 5.0347 c. 88: 11 15 15 8 6 7 15 11 N SD: 2.5937 c. M:-4.2246 c. 99: 12 17 17 9 7 8 16 13 N SD: 2.4966 c. M: 5.5904 c. 104: 13 17 18 10 7 8 18 13 N SD: 2.5799 c. M: 4.1670 c. 112: 14 19 19 10 8 9 19 14 N SD: 2.1700 c. M:-3.2506 c. 117: 14 20 20 11 8 9 20 15 N SD: 2.4354 c. M: 4.5077 c. 121: 15 20 21 11 9 9 21 15 N SD: 2.2167 c. M:-3.2250 c. 126: 15 22 21 12 9 10 21 16 N SD: 2.0069 c. M: 3.9966 c. 140: 17 24 24 13 10 11 23 18 N SD: 2.0069 c. M:-3.0381 c. 141: 17 24 24 13 10 11 24 18 N SD: 2.1048 c. M: 2.9801 c. 142: 17 24 25 13 10 11 24 18 N SD: 2.0565 c. M: 3.8420 c. 147: 18 25 25 14 10 12 24 19 N SD: 1.9596 c. M:-3.4463 c. 153: 19 26 26 14 11 12 26 19 N SD: 1.8551 c. M:-2.9657 c. 155: 19 26 27 14 11 12 26 20 N SD: 1.6389 c. M: 2.8534 c. 158: 19 27 27 15 11 12 27 20 N SD: 1.4728 c. M: 2.5499 c. 182: 22 31 31 17 13 14 31 23 N SD: 1.0231 c. M: 1.7988 c. 203: 25 34 35 19 14 16 34 26 N SD: 1.1006 c. M: 1.7092 c. 212: 26 36 36 20 15 16 36 27 N SD: 1.0625 c. M: 2.1371 c. 220: 27 37 38 20 16 17 37 28 N SD: 0.8798 c. M:-1.3290 c. 236: 29 40 40 22 17 18 40 30 N SD: 0.7582 c. M: 1.4655 c. 268: 33 45 46 25 19 21 45 34 N SD: 0.6391 c. M: 1.0671 c. 335: 41 57 57 31 24 26 57 42 N SD: 0.6413 c. M:-1.5376 c. 342: 42 58 58 32 24 27 58 43 N SD: 0.6080 c. M:-1.1082 c. 353: 43 60 60 33 25 28 59 45 N SD: 0.6563 c. M: 0.9892 c. 356: 44 60 61 33 25 28 60 45 N SD: 0.7628 c. M:-1.4609 c. 369: 45 63 63 34 26 29 62 47 N SD: 0.6332 c. M:-1.0629 c. 385: 47 65 66 36 27 30 65 49 N SD: 0.6628 c. M: 1.2299 c. 393: 48 67 67 36 28 31 66 50 N SD: 0.6020 c. M: 0.8862 c. 409: 50 69 70 38 29 32 69 52 N SD: 0.6084 c. M: 1.1766 c. 417: 51 71 71 39 29 33 70 53 N SD: 0.5977 c. M:-1.0908 c. 426: 52 72 73 40 30 33 72 54 N SD: 0.5845 c. M:-1.0705 c. 434: 53 74 74 40 31 34 73 55 N SD: 0.4716 c. M:-0.8312 c. 441: 54 75 75 41 31 35 74 56 N SD: 0.4597 c. M:-0.7252 c. 450: 55 76 77 42 32 35 76 57 N SD: 0.4002 c. M: 0.9875 c. 497: 61 84 85 46 35 39 84 63 N SD: 0.3929 c. M: 0.8148 c. 538: 66 91 92 50 38 42 91 68 N SD: 0.2620 c. M:-0.3794 c. 562: 69 95 96 52 40 44 95 71 N SD: 0.2606 c. M:-0.4772 c. 819: 100 139 140 76 58 64 138 104 N SD: 0.2231 c. M: 0.3956 c. 843: 103 143 144 78 60 66 142 107 N SD: 0.2033 c. M: 0.3429 c. 884: 108 150 151 82 63 69 149 112 N SD: 0.1695 c. M:-0.3159 c. 891: 109 151 152 83 63 70 150 113 N SD: 0.1645 c. M:-0.2579 c. 1113: 136 189 190 103 79 87 188 141 N SD: 0.1864 c. M: 0.2503 c. 1120: 137 190 191 104 80 87 189 142 N SD: 0.1778 c. M:-0.4226 c. 1127: 138 191 192 105 80 88 190 143 N SD: 0.1491 c. M: 0.2875 c. 1161: 142 197 198 108 82 91 196 147 N SD: 0.1243 c. M: 0.2991 c. 1226: 150 208 209 114 87 96 207 155 N SD: 0.1160 c. M:-0.2725 c. 1381: 169 234 236 128 98 108 233 175 N SD: 0.1046 c. M:-0.2152 c. 1446: 177 245 247 134 103 113 244 183 N SD: 0.1150 c. M:-0.1521 c. 1635: 200 277 279 152 116 128 276 207 N SD: 0.1271 c. M: 0.2291 c. 1658: 203 281 283 154 118 129 280 210 N SD: 0.1229 c. M:-0.2701 c. 1665: 204 282 284 155 118 130 281 211 N SD: 0.1001 c. M:-0.1733 c. 1764: 216 299 301 164 125 138 298 223 N SD: 0.1188 c. M:-0.2847 c. 1775: 217 301 303 165 126 139 299 225 N SD: 0.1148 c. M:-0.2132 c. 1863: 228 316 318 173 132 146 314 236 N SD: 0.1145 c. M:-0.1994 c. 1887: 231 320 322 175 134 148 318 239 N SD: 0.1112 c. M:-0.2537 c. 1959: 240 332 334 182 139 153 331 248 N SD: 0.1103 c. M: 0.2041 c. 1970: 241 334 336 183 140 154 332 250 N SD: 0.1288 c. M: 0.2989 c. 1984: 243 336 339 184 141 155 335 251 N SD: 0.1179 c. M:-0.2073 c. 1991: 244 337 340 185 141 156 336 252 N SD: 0.1157 c. M:-0.2080 c. 2000: 245 339 341 186 142 156 338 253 N SD: 0.1070 c. M:-0.1853 c. 2004: 245 340 342 186 142 157 338 254 N SD: 0.1075 c. M: 0.2232 c. 2011: 246 341 343 187 143 157 339 255 N SD: 0.0910 c. M: 0.1778 c. 2045: 250 347 349 190 145 160 345 259 N SD: 0.0678 c. M: 0.1545 c. 2069: 253 351 353 192 147 162 349 262 N SD: 0.0723 c. M: 0.1262 c. 2099: 257 356 358 195 149 164 354 266 N SD: 0.0767 c. M:-0.1317 c. 2281: 279 387 389 212 162 178 385 289 N SD: 0.0591 c. M: 0.1146 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x x 4 S SD: 17.7100 cents 3 x x 4 x x 5 x 6 S SD: 22.9861 cents 4 x 5 x 6 x x 7:8 S SD: 23.4799 cents 5 x 6:7 x x 8:9:10 S SD: 12.4855 cents 6 x 7:8:9 x 10:11:12 S SD: 18.9850 cents 7:8:9 x 10:11 x 13:14 SD: 22.4897 cents 8:9:10:11:12 x 13:15:16 SD: 12.3427 cents 10:11:12:14:15 x 16:18:20 S SD: 10.5765 cents 11:12:13:15:16:17:18:20:22 SD: 8.4941 cents 13:14:16:18:19:20:21:24:26 S SD: 4.0263 cents 22:24:27:30:32:34:36:40:44 S SD: 3.7519 cents 24:26:29:33:35:37:39:44:48 SD: 3.5535 cents 32:35:39:44:47:49:52:59:64 SD: 2.7738 cents 35:38:43:48:51:54:57:64:70 SD: 2.3542 cents 44:48:54:61:65:68:72:81:88 SD: 2.3366 cents 45:49:55:62:66:69:73:82:90 SD: 2.1864 cents 48:52:59:66:71:74:78:88:96 SD: 2.1207 cents 53:58:65:73:78:82:86:97:106 SD: 1.6514 cents 59:64:72:81:87:91:96:108:118 SD: 1.5505 cents 66:72:81:91:97:102:108:121:132 SD: 1.1766 cents 79:86:97:109:116:122:129:145:158 SD: 0.9338 cents 90:98:110:124:132:139:147:165:180 SD: 0.7733 cents 103:112:126:142:151:159:168:189:206 SD: 0.7335 cents 111:121:136:153:163:171:181:203:222 SD: 0.7121 cents 124:135:152:171:182:191:202:227:248 SD: 0.6634 cents 125:136:153:172:184:193:204:229:250 SD: 0.5695 cents 138:150:169:190:203:213:225:253:276 SD: 0.4638 cents 156:170:191:215:229:241:254:286:312 SD: 0.4626 cents 191:208:234:263:281:295:311:350:382 SD: 0.4023 cents 215:234:263:296:316:332:350:394:430 SD: 0.3705 cents 249:271:305:343:366:384:406:456:498 SD: 0.2912 cents 272:296:333:375:400:420:443:498:544 SD: 0.2692 cents 281:306:344:387:413:434:458:515:562 SD: 0.2061 cents 362:394:443:499:532:559:590:663:724 SD: 0.1487 cents 500:544:612:689:735:772:815:916:1000 SD: 0.1398 cents 530:577:649:730:779:818:864:971:1060 SD: 0.1388 cents 543:591:665:748:798:838:885:995:1086 SD: 0.1347 cents 553:602:677:762:813:854:901:1013:1106 SD: 0.1260 cents