Scala analysis: CD10_07_Egypt
Agyos Esheros / Tralmustos Avi - Mîkhâ'îl Jirjis al-Batânûnî (unknown maqam, Egypt)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 174.835 cents 174.834849 2: 393.775 cents 393.775153 3: 498.502 cents 498.502426 4: 547.896 cents 547.896365 5: 665.589 cents 665.588673 6: 942.793 cents 942.793335 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 257.2067 cents 257.2067 1: 174.8348 cents 174.8348 2: 218.9403 cents 218.9403 3: 104.7273 cents 104.7273 4: 49.3939 cents 49.3939 5: 117.6923 cents 117.6923 6: 277.2047 cents 277.2047 7: 257.2067 cents 257.2067
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 49.39394 cents 1: 1 104.72727 cents 1: 1 117.69231 cents 1: 1 174.83485 cents 1: 1 218.94030 cents 1: 1 257.20667 cents 1: 1 277.20466 cents 2: 1 154.12121 cents 2: 1 167.08625 cents 2: 1 323.66758 cents 2: 1 393.77515 cents 2: 1 394.89697 cents 2: 1 432.04151 cents 2: 1 534.41133 cents 3: 1 271.81352 cents 3: 1 373.06152 cents 3: 1 444.29091 cents 3: 1 498.50243 cents 3: 1 650.98182 cents 3: 1 652.10363 cents 3: 1 709.24618 cents 4: 1 490.75382 cents 4: 1 547.89637 cents 4: 1 549.01818 cents 4: 1 701.49757 cents 4: 1 755.70909 cents 4: 1 826.93848 cents 4: 1 928.18648 cents 5: 1 665.58867 cents 5: 1 767.95849 cents 5: 1 805.10303 cents 5: 1 806.22485 cents 5: 1 876.33242 cents 5: 1 1032.91375 cents 5: 1 1045.87879 cents 6: 1 922.79534 cents 6: 1 942.79333 cents 6: 1 981.05970 cents 6: 1 1025.16515 cents 6: 1 1082.30769 cents 6: 1 1095.27273 cents 6: 1 1150.60606 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 : 174.8 393.8 498.5 547.9 665.6 942.8 1200.0 174.8 : 218.9 323.7 373.1 490.8 768.0 1025.2 1200.0 393.8 : 104.7 154.1 271.8 549.0 806.2 981.1 1200.0 498.5 : 49.4 167.1 444.3 701.5 876.3 1095.3 1200.0 547.9 : 117.7 394.9 652.1 826.9 1045.9 1150.6 1200.0 665.6 : 277.2 534.4 709.2 928.2 1032.9 1082.3 1200.0 942.8 : 257.2 432.0 651.0 755.7 805.1 922.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 49.3939 .. 277.2047 cents 227.81072 cents 49.39394 cents 2: 154.1212 .. 534.4113 cents 380.29011 cents -123.08345 cents 3: 271.8135 .. 709.2462 cents 437.43266 cents -262.59781 cents 4: 490.7538 .. 928.1865 cents 437.43266 cents -218.49235 cents 5: 665.5887 .. 1045.8788 cents 380.29011 cents -262.59781 cents 6: 922.7953 .. 1150.6061 cents 227.81072 cents -123.08345 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 49.39394 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 277.20466 cents Average / Smallest step : 3.470640 Largest / Average step : 1.617027 Largest / Smallest step : 5.612119 Median interval of one step : 174.83485 cents, amount: 1 Least squares average step : 157.38701 cents, oct.: 1101.70906 cents Scale is not proper Step pattern alph. order: ABCDEFG Step pattern size order : DEBACGF Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 5.39114 cents Scale diversity : 1.700348 Lumma stability : 0.082323 Lumma impropriety factor : 0.743131 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 : 1.12182 cents Number of recognisable fifths : 2, average 705.3719 cents Formal octave complements present : 1 = 14.2857% -- Rational properties --
FIT/MODE
7: 1 1 1 0 1 1 2 N T3 SD: 40.9252 c. M: 85.6505 c. 9: 1 2 1 0 1 2 2 N SD: 21.6368 c. M: 41.5015 c. 13: 2 2 1 1 1 3 3 N SD: 20.2353 c. M: 36.9640 c. 14: 2 3 1 0 2 3 3 N SD: 20.7234 c. M:-34.7963 c. 15: 2 3 1 1 1 4 3 N SD: 15.5770 c. M: 25.5887 c. 19: 3 3 2 1 2 4 4 N SD: 15.9090 c. M:-29.1482 c. 20: 3 4 1 1 2 5 4 N SD: 14.3747 c. M:-26.2248 c. 21: 3 4 2 1 2 5 4 N SD: 17.2306 c. M:-28.6352 c. 22: 3 4 2 1 2 5 5 N SD: 9.9631 c. M: 15.5206 c. 27: 4 5 2 1 3 6 6 N SD: 7.9513 c. M: 14.5630 c. 33: 5 6 3 1 3 8 7 N SD: 6.9141 c. M: 11.0432 c. 42: 6 8 3 2 4 10 9 N SD: 6.6614 c. M: 12.7881 c. 43: 6 8 4 2 4 10 9 N SD: 5.8267 c. M:-10.2432 c. 48: 7 9 4 2 5 11 10 N SD: 5.1541 c. M:-9.4113 c. 55: 8 10 5 2 6 12 12 N SD: 4.7133 c. M:-10.7750 c. 57: 8 11 5 2 6 13 12 N SD: 5.5077 c. M:-8.0955 c. 60: 9 11 5 2 6 14 13 N SD: 4.9144 c. M: 7.8964 c. 61: 9 11 5 3 6 14 13 N SD: 3.1903 c. M: 6.6991 c. 70: 10 13 6 3 7 16 15 N SD: 1.8153 c. M: 3.4063 c. 94: 14 17 8 4 9 22 20 N SD: 1.9688 c. M:-3.8886 c. 103: 15 19 9 4 10 24 22 N SD: 1.4527 c. M:-2.4684 c. 125: 18 23 11 5 12 29 27 N SD: 1.6598 c. M: 3.1887 c. 144: 21 26 13 6 14 33 31 N SD: 1.3925 c. M: 2.1085 c. 149: 22 27 13 6 15 34 32 N SD: 1.4864 c. M:-2.8677 c. 159: 23 29 14 7 15 37 34 N SD: 1.4725 c. M:-3.0470 c. 164: 24 30 14 7 16 38 35 N SD: 0.8769 c. M:-1.3468 c. 186: 27 34 16 8 18 43 40 N SD: 0.8926 c. M: 1.7282 c. 234: 34 43 20 10 23 54 50 N SD: 0.8484 c. M:-1.0966 c. 247: 36 45 22 10 24 57 53 N SD: 0.8417 c. M:-1.9024 c. 265: 39 48 23 11 26 61 57 N SD: 0.7694 c. M:-1.7689 c. 267: 39 49 23 11 26 62 57 N SD: 0.8228 c. M:-1.7305 c. 274: 40 50 24 11 27 63 59 N SD: 0.5956 c. M: 1.1875 c. 289: 42 53 25 12 28 67 62 N SD: 0.5765 c. M: 1.2288 c. 308: 45 56 27 13 30 71 66 N SD: 0.6422 c. M:-1.4543 c. 335: 49 61 29 14 33 77 72 N SD: 0.5172 c. M: 0.7038 c. 344: 50 63 30 14 34 79 74 N SD: 0.5141 c. M: 0.9329 c. 359: 52 66 31 15 35 83 77 N SD: 0.5281 c. M: 1.0187 c. 411: 60 75 36 17 40 95 88 N SD: 0.5293 c. M:-1.0087 c. 433: 63 79 38 18 42 100 93 N SD: 0.4507 c. M:-0.8334 c. 438: 64 80 38 18 43 101 94 N SD: 0.3716 c. M:-0.7454 c. 467: 68 85 41 19 46 108 100 N SD: 0.3376 c. M: 0.6274 c. 537: 78 98 47 22 53 124 115 N SD: 0.3535 c. M: 0.5332 c. 561: 82 102 49 23 55 130 120 N SD: 0.3494 c. M:-0.5662 c. 570: 83 104 50 23 56 132 122 N SD: 0.3237 c. M: 0.5279 c. 624: 91 114 54 26 61 144 134 N SD: 0.3220 c. M: 0.4856 c. 631: 92 115 55 26 62 146 135 N SD: 0.2235 c. M:-0.4713 c. 640: 93 117 56 26 63 148 137 N SD: 0.2782 c. M: 0.4598 c. 653: 95 119 57 27 64 151 140 N SD: 0.3323 c. M: 0.5133 c. 694: 101 127 60 29 68 160 149 N SD: 0.3323 c. M: 0.5197 c. 701: 102 128 61 29 69 162 150 N SD: 0.2617 c. M:-0.4306 c. 734: 107 134 64 30 72 170 157 N SD: 0.2522 c. M:-0.5309 c. 756: 110 138 66 31 74 175 162 N SD: 0.2442 c. M: 0.5093 c. 775: 113 141 68 32 76 179 166 N SD: 0.2363 c. M: 0.4848 c. 802: 117 146 70 33 79 185 172 N SD: 0.2185 c. M: 0.2654 c. 826: 120 151 72 34 81 191 177 N SD: 0.2339 c. M: 0.5007 c. 878: 128 160 77 36 86 203 188 N SD: 0.1924 c. M:-0.3586 c. 905: 132 165 79 37 89 209 194 N SD: 0.1306 c. M: 0.2721 c. 948: 138 173 83 39 93 219 203 N SD: 0.1867 c. M:-0.2446 c. 975: 142 178 85 40 96 225 209 N SD: 0.1307 c. M:-0.2575 c. 1064: 155 194 93 44 104 246 228 N SD: 0.1271 c. M:-0.2239 c. 1091: 159 199 95 45 107 252 234 N SD: 0.1376 c. M: 0.2439 c. 1237: 180 226 108 51 121 286 265 N SD: 0.1417 c. M: 0.2188 c. 1264: 184 231 110 52 124 292 271 N SD: 0.1192 c. M:-0.2122 c. 1338: 195 244 117 55 131 309 287 N SD: 0.1115 c. M: 0.1924 c. 1408: 205 257 123 58 138 325 302 N SD: 0.0982 c. M: 0.1797 c. 1502: 219 274 131 62 147 347 322 N SD: 0.0975 c. M:-0.1729 c. 1572: 229 287 137 65 154 363 337 N SD: 0.0920 c. M:-0.1952 c. 1825: 266 333 159 75 179 422 391 N SD: 0.1128 c. M: 0.1703 c. 1853: 270 338 162 76 182 428 397 N SD: 0.0901 c. M:-0.1484 c. 1875: 273 342 164 77 184 433 402 N SD: 0.0893 c. M: 0.1752 c. 1895: 276 346 165 78 186 438 406 N SD: 0.0977 c. M: 0.1391 c. 1969: 287 359 172 81 193 455 422 N SD: 0.0500 c. M:-0.0763 c. 2039: 297 372 178 84 200 471 437 N SD: 0.0317 c. M: 0.0527 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x 4 S SD: 18.1832 cents 3 x x 4 x x 5:6 S SD: 19.4788 cents 4 x 5 x x 6:7:8 S SD: 11.3354 cents 5 x 6 x 7 x 9:10 SD: 28.3930 cents 6:7 x 8 x 9:10:12 S SD: 22.9852 cents 7:8:9 x x 10:12:14 S SD: 17.0735 cents 8:9:10 x 11:12:14:16 S SD: 8.9953 cents 9:10:11:12 x 13:16:18 SD: 12.7881 cents 10:11 x 13:14:15:17:20 SD: 11.9747 cents 11:12:14 x 15:16:19:22 SD: 6.5954 cents 12:13:15:16 x 18:21:24 SD: 9.6768 cents 14:15:18 x 19:21:24:28 SD: 13.4986 cents 15:17:19:20:21:22:26:30 SD: 8.1883 cents 17:19:21 x 23:25:29:34 SD: 7.5164 cents 18:20:23:24:25:26:31:36 SD: 6.8046 cents 19:21:24:25:26:28:33:38 SD: 4.2570 cents 20:22:25:27 x 29:34:40 SD: 6.8254 cents 21:23:26:28:29:31:36:42 SD: 4.8773 cents 27:30:34:36:37:40:47:54 SD: 3.4884 cents 30:33:38:40:41:44:52:60 SD: 3.1384 cents 36:40:45:48:49:53:62:72 SD: 2.6044 cents 47:52:59:63:64:69:81:94 SD: 2.2894 cents 48:53:60:64:66:71:83:96 SD: 2.2775 cents 51:56:64:68:70:75:88:102 SD: 1.8879 cents 54:60:68:72:74:79:93:108 SD: 1.7036 cents 66:73:83:88:91:97:114:132 SD: 1.3472 cents 75:83:94:100:103:110:129:150 SD: 0.8102 cents 94:104:118:125:129:138:162:188 SD: 0.7384 cents 102:113:128:136:140:150:176:204 SD: 0.5314 cents 177:196:222:236:243:260:305:354 SD: 0.3708 cents 188:208:236:251:258:276:324:376 SD: 0.3007 cents 207:229:260:276:284:304:357:414 SD: 0.1905 cents 282:312:354:376:387:414:486:564 SD: 0.1592 cents 384:425:482:512:527:564:662:768 SD: 0.1385 cents 489:541:614:652:671:718:843:978 SD: 0.1202 cents 572:633:718:763:785:840:986:1144 SD: 0.1131 cents 591:654:742:788:811:868:1019:1182 SD: 0.1130 cents