Scala analysis: CD05_15_Egypt
Suite - ‘Abduh al-Ḥāmūlī (bayati, Egypt)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 202.647 cents 202.647269 2: 343.532 cents 343.531990 3: 496.674 cents 496.673768 4: 697.967 cents 697.966711 5: 887.435 cents 887.435407 6: 1054.359 cents 1054.358861 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 145.6411 cents 145.6411 1: 202.6473 cents 202.6473 2: 140.8847 cents 140.8847 3: 153.1418 cents 153.1418 4: 201.2929 cents 201.2929 5: 189.4687 cents 189.4687 6: 166.9235 cents 166.9235 7: 145.6411 cents 145.6411
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 140.88472 cents 1: 1 145.64114 cents 1: 1 153.14178 cents 1: 1 166.92345 cents 1: 1 189.46870 cents 1: 1 201.29294 cents 1: 1 202.64727 cents 2: 1 294.02650 cents 2: 1 312.56459 cents 2: 1 343.53199 cents 2: 1 348.28841 cents 2: 1 354.43472 cents 2: 1 356.39215 cents 2: 1 390.76164 cents 3: 1 489.17313 cents 3: 1 495.31944 cents 3: 1 496.67377 cents 3: 1 502.03329 cents 3: 1 515.21186 cents 3: 1 543.90342 cents 3: 1 557.68509 cents 4: 1 642.31491 cents 4: 1 656.09658 cents 4: 1 684.78814 cents 4: 1 697.96671 cents 4: 1 703.32623 cents 4: 1 704.68056 cents 4: 1 710.82687 cents 5: 1 809.23836 cents 5: 1 843.60785 cents 5: 1 845.56528 cents 5: 1 851.71159 cents 5: 1 856.46801 cents 5: 1 887.43541 cents 5: 1 905.97350 cents 6: 1 997.35273 cents 6: 1 998.70706 cents 6: 1 1010.53130 cents 6: 1 1033.07655 cents 6: 1 1046.85822 cents 6: 1 1054.35886 cents 6: 1 1059.11528 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 : 202.6 343.5 496.7 698.0 887.4 1054.4 1200.0 202.6 : 140.9 294.0 495.3 684.8 851.7 997.4 1200.0 343.5 : 153.1 354.4 543.9 710.8 856.5 1059.1 1200.0 496.7 : 201.3 390.8 557.7 703.3 906.0 1046.9 1200.0 698.0 : 189.5 356.4 502.0 704.7 845.6 998.7 1200.0 887.4 : 166.9 312.6 515.2 656.1 809.2 1010.5 1200.0 1054.4: 145.6 348.3 489.2 642.3 843.6 1033.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 140.8847 .. 202.6473 cents 61.76255 cents 140.88472 cents 2: 294.0265 .. 390.7616 cents 96.73514 cents 91.37923 cents 3: 489.1731 .. 557.6851 cents 68.51196 cents 98.41149 cents 4: 642.3149 .. 710.8269 cents 68.51196 cents 84.62981 cents 5: 809.2384 .. 905.9735 cents 96.73514 cents 98.41149 cents 6: 997.3527 .. 1059.1153 cents 61.76255 cents 91.37923 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 140.88472 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 202.64727 cents Average / Smallest step : 1.216800 Largest / Average step : 1.182109 Largest / Smallest step : 1.438391 Median interval of one step : 166.92345 cents, amount: 1 Least squares average step : 173.82093 cents, oct.: 1216.74648 cents Scale is strictly proper Step pattern alph. order: ABCDEFG Step pattern size order : GACFEDB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 84.62981 cents Scale diversity : 1.411453 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.621651 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 : 1.35433 cents Number of recognisable fifths : 4, average 704.2001 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 78.1970 cents: 1 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 20.7640 c. M: 31.2187 c. Lebeng 16: 3 2 2 2 3 2 2 SP M ME S SD: 20.6902 c. M:-31.4680 c. Antiphrygian 17: 3 2 2 3 3 2 2 SP D3 S SD: 12.9479 c. M:-30.2117 c. Pseudo Rast 19: 3 2 3 3 3 3 2 SP D3 S SD: 14.1989 c. M: 27.7425 c. Nineteen-tone Melodic Minor 22: 4 2 3 4 3 3 3 SP D3 SD: 13.1085 c. M: 17.9952 c. Dorian Porcupine 24: 4 3 3 4 4 3 3 SP D3 S SD: 5.8665 c. M:-12.5646 c. Arabic Diatonic, Maqam Rast, Quasi-equal Heptatonic, Neutral Diatonic Phrygian 31: 5 4 4 5 5 4 4 SP D3 S SD: 5.8997 c. M: 9.1976 c. Neutral Diatonic Phrygian, Rast 41: 7 5 5 7 6 6 5 SP SD: 4.9780 c. M: 9.3866 c. 43: 7 5 6 7 7 6 5 SP S SD: 5.7146 c. M: 8.6483 c. 46: 8 5 6 8 7 6 6 SP SD: 5.5592 c. M: 10.8806 c. 49: 8 6 6 8 8 7 6 SP SD: 6.3078 c. M: 12.2524 c. 50: 8 6 7 8 8 7 6 SP S SD: 5.7402 c. M: 10.6473 c. 53: 9 6 7 9 8 8 6 SP SD: 4.6195 c. M:-9.7921 c. 55: 9 7 7 9 9 7 7 SP D3 S SD: 5.3139 c. M:-7.1100 c. 58: 10 7 7 10 9 8 7 SP SD: 4.1545 c. M:-8.1921 c. 65: 11 8 8 11 10 9 8 SP SD: 3.2594 c. M:-7.2372 c. 66: 11 8 8 11 11 9 8 SP SD: 3.8886 c. M: 7.0576 c. 72: 12 9 9 12 11 10 9 SP SD: 3.7771 c. M:-6.4680 c. 77: 13 9 10 13 12 11 9 SP SD: 2.5467 c. M:-5.3814 c. 84: 14 10 11 14 13 12 10 SP SD: 2.1835 c. M:-3.3262 c. 101: 17 12 13 17 16 14 12 SP SD: 2.3557 c. M:-3.6537 c. 107: 18 13 13 18 17 15 13 SP SD: 2.3029 c. M:-4.1316 c. 108: 18 13 14 18 17 15 13 SP SD: 1.9487 c. M:-3.3262 c. 126: 21 15 16 21 20 18 15 SP SD: 1.9886 c. M:-2.7840 c. 130: 22 15 17 22 20 18 16 SP SD: 1.9258 c. M:-3.5718 c. 142: 24 17 18 24 22 20 17 SP SD: 2.0059 c. M:-3.4417 c. 143: 24 17 18 24 23 20 17 SP SD: 1.6752 c. M:-2.9838 c. 149: 25 18 19 25 23 21 18 SP SD: 1.9483 c. M:-2.7767 c. 150: 25 18 19 25 24 21 18 SP SD: 1.4423 c. M: 2.6473 c. 165: 28 19 21 28 26 23 20 SP SD: 1.1054 c. M: 2.1283 c. 172: 29 20 22 29 27 24 21 SP SD: 1.0299 c. M: 1.6715 c. 189: 32 22 24 32 30 26 23 SP SD: 0.8667 c. M:-1.4535 c. 196: 33 23 25 33 31 27 24 SP SD: 0.6740 c. M: 1.2976 c. 230: 39 27 29 39 36 32 28 SP SD: 0.7729 c. M:-1.1637 c. 273: 46 32 35 46 43 38 33 SP SD: 0.5480 c. M:-0.9344 c. 380: 64 45 48 64 60 53 46 SP SD: 0.4912 c. M: 0.8843 c. 430: 73 50 55 72 68 60 52 SP SD: 0.4773 c. M:-1.0737 c. 437: 74 51 56 73 69 61 53 SP SD: 0.3755 c. M:-0.5564 c. 454: 77 53 58 76 72 63 55 SP SD: 0.4446 c. M:-0.8770 c. 461: 78 54 59 77 73 64 56 SP SD: 0.2913 c. M:-0.5063 c. 626: 106 73 80 105 99 87 76 SP SD: 0.2804 c. M:-0.5476 c. 633: 107 74 81 106 100 88 77 SP SD: 0.2613 c. M: 0.4040 c. 657: 111 77 84 110 104 91 80 SP SD: 0.2375 c. M: 0.4776 c. 710: 120 83 91 119 112 99 86 SP SD: 0.2293 c. M: 0.4334 c. 734: 124 86 94 123 116 102 89 SP SD: 0.2014 c. M:-0.3290 c. 817: 138 96 104 137 129 114 99 SP SD: 0.2072 c. M: 0.2923 c. 841: 142 99 107 141 133 117 102 SP SD: 0.1698 c. M:-0.3443 c. 964: 163 113 123 162 152 134 117 SP SD: 0.1776 c. M:-0.3735 c. 971: 164 114 124 163 153 135 118 SP SD: 0.1441 c. M:-0.2825 c. 1013: 171 119 129 170 160 141 123 SP SD: 0.1700 c. M: 0.3263 c. 1037: 175 122 132 174 164 144 126 SP SD: 0.1593 c. M: 0.2418 c. 1090: 184 128 139 183 172 152 132 SP SD: 0.1443 c. M:-0.3200 c. 1114: 188 131 142 187 176 155 135 SP SD: 0.1292 c. M:-0.2192 c. 1286: 217 151 164 216 203 179 156 SP SD: 0.1281 c. M: 0.2508 c. 1310: 221 154 167 220 207 182 159 SP SD: 0.1300 c. M: 0.2045 c. 1474: 249 173 188 247 233 205 179 SP SD: 0.1160 c. M: 0.2734 c. 1551: 262 182 198 260 245 216 188 SP SD: 0.0837 c. M:-0.1866 c. 1558: 263 183 199 261 246 217 189 SP SD: 0.0986 c. M: 0.1490 c. 1575: 266 185 201 264 249 219 191 SP SD: 0.0979 c. M:-0.1836 c. 1582: 267 186 202 265 250 220 192 SP SD: 0.0959 c. M:-0.1657 c. 1747: 295 205 223 293 276 243 212 SP SD: 0.0516 c. M: 0.0861 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: 1.9941 cents 3 x x 4 x 5 x 6 S SD: 1.1228 cents 4 x 5 x 6:7 x 8 S SD: 23.0090 cents 5 x 6:7 x 8:9:10 S SD: 24.4430 cents 6:7 x 8:9:10:11:12 S SD: 10.7715 cents 7:8 x 9:10:12:13:14 S SD: 19.3453 cents 8:9:10:11:12:13:15:16 SD: 12.9236 cents 9:10:11:12:13:15:17:18 SD: 11.4103 cents 10:11:12:13:15:17:18:20 SD: 11.3739 cents 12:13:15:16:18:20:22:24 SD: 11.0546 cents 13:15:16:17:19:22:24:26 SD: 10.6926 cents 14:16:17:19:21:23:26:28 SD: 7.8160 cents 15:17:18:20:22:25:28:30 SD: 7.6824 cents 18:20:22:24:27:30:33:36 S SD: 3.1202 cents 24:27:29:32:36:40:44:48 SD: 2.5028 cents 42:47:51:56:63:70:77:84 SD: 1.8613 cents 54:61:66:72:81:90:99:108 SD: 1.6741 cents 55:62:67:73:82:92:101:110 SD: 1.6042 cents 63:71:77:84:94:105:116:126 SD: 1.2628 cents 64:72:78:85:96:107:118:128 SD: 1.2485 cents 72:81:88:96:108:120:132:144 SD: 1.1852 cents 73:82:89:97:109:122:134:146 SD: 1.0027 cents 81:91:99:108:121:135:149:162 SD: 0.8831 cents 87:98:106:116:130:145:160:174 SD: 0.8216 cents 105:118:128:140:157:175:193:210 SD: 0.5462 cents 145:163:177:193:217:242:267:290 SD: 0.5087 cents 169:190:206:225:253:282:311:338 SD: 0.3417 cents 250:281:305:333:374:417:460:500 SD: 0.3398 cents 274:308:334:365:410:457:504:548 SD: 0.3023 cents 306:344:373:408:458:511:563:612 SD: 0.2842 cents 314:353:383:418:470:524:577:628 SD: 0.2820 cents 322:362:393:429:482:538:592:644 SD: 0.2752 cents 328:369:400:437:491:548:603:656 SD: 0.2539 cents 346:389:422:461:518:578:636:692 SD: 0.1789 cents 379:426:462:505:567:633:697:758 SD: 0.1711 cents 427:480:521:569:639:713:785:854 SD: 0.1476 cents 433:487:528:577:648:723:796:866 SD: 0.1367 cents 451:507:550:601:675:753:829:902 SD: 0.0913 cents 596:670:727:794:892:995:1096:1192 SD: 0.0809 cents