Scala analysis: CD09_11_Egypt
Ô mère ! ô Sultân ! - Umm Ibrâhîm Al-Mahdiyya (unknown maqam, Egypt)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 137.934 cents 137.933551 2: 321.310 cents 321.310428 3: 425.260 cents 425.260292 4: 632.233 cents 632.232650 5: 812.144 cents 812.143761 6: 949.783 cents 949.782650 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 250.2174 cents 250.2174 1: 137.9336 cents 137.9336 2: 183.3769 cents 183.3769 3: 103.9499 cents 103.9499 4: 206.9724 cents 206.9724 5: 179.9111 cents 179.9111 6: 137.6389 cents 137.6389 7: 250.2174 cents 250.2174
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 103.94986 cents 1: 1 137.63889 cents 1: 1 137.93355 cents 1: 1 179.91111 cents 1: 1 183.37688 cents 1: 1 206.97236 cents 1: 1 250.21735 cents 2: 1 287.32674 cents 2: 1 310.92222 cents 2: 1 317.55000 cents 2: 1 321.31043 cents 2: 1 386.88347 cents 2: 1 387.85624 cents 2: 1 388.15090 cents 3: 1 425.26029 cents 3: 1 490.83333 cents 3: 1 494.29910 cents 3: 1 524.52236 cents 3: 1 525.78979 cents 3: 1 567.76735 cents 3: 1 571.52778 cents 4: 1 628.47222 cents 4: 1 632.23265 cents 4: 1 674.21021 cents 4: 1 675.47764 cents 4: 1 705.70090 cents 4: 1 709.16667 cents 4: 1 774.73971 cents 5: 1 811.84910 cents 5: 1 812.14376 cents 5: 1 813.11653 cents 5: 1 878.68957 cents 5: 1 882.45000 cents 5: 1 889.07778 cents 5: 1 912.67326 cents 6: 1 949.78265 cents 6: 1 993.02764 cents 6: 1 1016.62312 cents 6: 1 1020.08889 cents 6: 1 1062.06645 cents 6: 1 1062.36111 cents 6: 1 1096.05014 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 : 137.9 321.3 425.3 632.2 812.1 949.8 1200.0 137.9 : 183.4 287.3 494.3 674.2 811.8 1062.1 1200.0 321.3 : 103.9 310.9 490.8 628.5 878.7 1016.6 1200.0 425.3 : 207.0 386.9 524.5 774.7 912.7 1096.1 1200.0 632.2 : 179.9 317.5 567.8 705.7 889.1 993.0 1200.0 812.1 : 137.6 387.9 525.8 709.2 813.1 1020.1 1200.0 949.8 : 250.2 388.2 571.5 675.5 882.5 1062.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 103.9499 .. 250.2174 cents 146.26749 cents 103.94986 cents 2: 287.3267 .. 388.1509 cents 100.82416 cents 37.10939 cents 3: 425.2603 .. 571.5278 cents 146.26749 cents 37.10939 cents 4: 628.4722 .. 774.7397 cents 146.26749 cents 56.94444 cents 5: 811.8491 .. 912.6733 cents 100.82416 cents 37.10939 cents 6: 949.7826 .. 1096.0501 cents 146.26749 cents 37.10939 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 103.94986 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 250.21735 cents Average / Smallest step : 1.649147 Largest / Average step : 1.459601 Largest / Smallest step : 2.407096 Median interval of one step : 179.91111 cents, amount: 1 Least squares average step : 162.46200 cents, oct.: 1137.23403 cents Scale is strictly proper Step pattern alph. order: ABCDEFG Step pattern size order : CEAFDBG Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 37.10939 cents Scale diversity : 1.593076 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.344401 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 : 0.29466 cents Number of recognisable fifths : 2, average 707.4338 cents Best fifths form a closed circle Formal octave complements present : 1 = 14.2857% -- Rational properties --
FIT/MODE
7: 0 1 1 1 1 1 2 N T3 SD: 111.3287 c. M: 149.8819 c. 8: 1 1 1 1 1 1 2 P M ME S SD: 35.0324 c. M: 62.1438 c. 9: 1 1 1 2 1 1 2 P M ME S SD: 27.3834 c. M: 54.6438 c. 11: 1 2 1 2 1 2 2 P M ME S SD: 26.3705 c. M: 48.5074 c. 12: 1 2 1 2 2 1 3 P D3 SD: 29.7511 c. M: 49.7826 c. Ultralocrian, Superlocrian Diminished, Mixolydian sharp 1 13: 2 2 1 2 2 1 3 N T3 SD: 31.7255 c. M:-47.9203 c. 14: 2 2 1 2 2 2 3 P T3 SD: 24.9049 c. M: 40.7152 c. 15: 2 2 1 3 2 2 3 P T3 SD: 14.3374 c. M: 25.2603 c. 19: 2 3 2 3 3 2 4 SP D3 SD: 8.7410 c. M:-16.8450 c. 25: 3 4 2 4 4 3 5 SP SD: 8.3242 c. M:-14.6896 c. 33: 4 5 3 5 5 4 7 SP SD: 9.0950 c. M: 14.0508 c. 34: 4 5 3 6 5 4 7 SP SD: 2.5753 c. M: 3.6634 c. 87: 10 13 8 15 13 10 18 SP SD: 2.1883 c. M: 4.0690 c. 93: 11 14 8 16 14 11 19 SP SD: 2.5091 c. M:-5.0561 c. 96: 11 15 8 17 14 11 20 SP SD: 2.4433 c. M:-5.2673 c. 105: 12 16 9 18 16 12 22 SP SD: 1.8323 c. M: 3.6612 c. 124: 14 19 11 21 19 14 26 SP SD: 1.8083 c. M: 3.2004 c. 139: 16 21 12 24 21 16 29 SP SD: 1.3678 c. M: 2.2387 c. 158: 18 24 14 27 24 18 33 SP SD: 1.2404 c. M: 2.3231 c. 167: 19 26 14 29 25 19 35 SP SD: 1.1674 c. M:-2.0429 c. 192: 22 29 17 33 29 22 40 SP SD: 1.0658 c. M: 2.5604 c. 198: 23 30 17 34 30 23 41 SP SD: 1.1895 c. M: 1.9296 c. 201: 23 31 17 35 30 23 42 SP SD: 0.7685 c. M: 1.3797 c. 220: 25 34 19 38 33 25 46 SP SD: 0.7391 c. M: 1.5699 c. 235: 27 36 20 41 35 27 49 SP SD: 0.6735 c. M: 1.4305 c. 254: 29 39 22 44 38 29 53 SP SD: 0.5076 c. M: 0.9257 c. 313: 36 48 27 54 47 36 65 SP SD: 0.5604 c. M:-1.0161 c. 321: 37 49 28 55 48 37 67 SP SD: 0.5529 c. M: 0.9288 c. 355: 41 54 31 61 53 41 74 SP SD: 0.4905 c. M: 0.8762 c. 359: 41 55 31 62 54 41 75 SP SD: 0.5333 c. M: 0.8862 c. 384: 44 59 33 66 58 44 80 SP SD: 0.4949 c. M: 0.9827 c. 393: 45 60 34 68 59 45 82 SP SD: 0.4667 c. M: 0.8328 c. 418: 48 64 36 72 63 48 87 SP SD: 0.3654 c. M: 0.6537 c. 452: 52 69 39 78 68 52 94 SP SD: 0.3560 c. M:-0.6598 c. 471: 54 72 41 81 71 54 98 SP SD: 0.3868 c. M:-0.5951 c. 522: 60 80 45 90 78 60 109 SP SD: 0.3448 c. M: 0.6495 c. 556: 64 85 48 96 83 64 116 SP SD: 0.2828 c. M: 0.6330 c. 567: 65 87 49 98 85 65 118 SP SD: 0.4082 c. M:-0.5716 c. 575: 66 88 50 99 86 66 120 SP SD: 0.2493 c. M:-0.4788 c. 609: 70 93 53 105 91 70 127 SP SD: 0.2155 c. M:-0.3555 c. 714: 82 109 62 123 107 82 149 SP SD: 0.2338 c. M: 0.3791 c. 773: 89 118 67 133 116 89 161 SP SD: 0.2293 c. M: 0.4086 c. 776: 89 119 67 134 116 89 162 SP SD: 0.2502 c. M:-0.3391 c. 807: 93 123 70 139 121 93 168 SP SD: 0.2492 c. M:-0.4032 c. 810: 93 124 70 140 121 93 169 SP SD: 0.2061 c. M:-0.3599 c. 922: 106 141 80 159 138 106 192 SP SD: 0.2205 c. M:-0.3362 c. 940: 108 144 81 162 141 108 196 SP SD: 0.2185 c. M:-0.3917 c. 949: 109 145 82 164 142 109 198 SP SD: 0.2143 c. M: 0.3920 c. 959: 110 147 83 165 144 110 200 SP SD: 0.2079 c. M: 0.3244 c. 968: 111 148 84 167 145 111 202 SP SD: 0.1819 c. M: 0.3302 c. 974: 112 149 84 168 146 112 203 SP SD: 0.1761 c. M:-0.2501 c. 993: 114 152 86 171 149 114 207 SP SD: 0.1272 c. M: 0.2085 c. 1027: 118 157 89 177 154 118 214 SP SD: 0.0844 c. M:-0.1687 c. 1625: 187 248 141 280 244 186 339 SP SD: 0.1158 c. M:-0.1639 c. 1636: 188 250 142 282 245 188 341 SP SD: 0.0988 c. M:-0.1676 c. 1741: 200 266 151 300 261 200 363 SP SD: 0.1148 c. M: 0.1966 c. 1803: 207 276 156 311 270 207 376 SP SD: 0.1078 c. M: 0.1637 c. 1826: 210 279 158 315 274 209 381 SP SD: 0.0895 c. M: 0.1660 c. 1860: 214 284 161 321 279 213 388 SP SD: 0.0863 c. M:-0.1310 c. 1995: 229 305 173 344 299 229 416 SP SD: 0.0949 c. M: 0.1892 c. 2029: 233 310 176 350 304 233 423 SP SD: 0.0940 c. M: 0.1670 c. 2088: 240 319 181 360 313 240 435 SP SD: 0.0911 c. M:-0.2174 c. 2181: 251 333 189 376 327 250 455 SP SD: 0.0849 c. M:-0.1682 c. 2255: 259 345 195 389 338 259 470 SP SD: 0.0826 c. M:-0.1086 c. 2289: 263 350 198 395 343 263 477 SP SD: 0.0809 c. M:-0.1518 c. 2308: 265 353 200 398 346 265 481 SP SD: 0.0777 c. M: 0.1519 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: 34.8612 cents 3 x x 4 x x 5:6 S SD: 32.6223 cents 4 x x 5:6 x 7:8 S SD: 20.5254 cents 5 x 6 x 7:8:9:10 S SD: 16.8586 cents 6 x 7:8:9 x 10:12 S SD: 26.3839 cents 7 x 8:9:10:11:12:14 S SD: 16.3257 cents 8:9 x 10:12:13:14:16 S SD: 18.1806 cents 9:10:11:12:13:14:16:18 S SD: 15.8760 cents 10:11:12:13:14:16:17:20 SD: 10.1494 cents 11:12:13:14:16:18:19:22 SD: 8.0451 cents 14:15:17:18:20:22:24:28 SD: 6.4397 cents 15:16:18:19:22:24:26:30 SD: 6.2815 cents 21:23:25:27:30:34:36:42 SD: 6.1246 cents 22:24:26:28:32:35:38:44 SD: 5.7226 cents 23:25:28:29:33:37:40:46 SD: 5.0006 cents 25:27:30:32:36:40:43:50 SD: 1.9197 cents 50:54:60:64:72:80:87:100 SD: 1.7211 cents 59:64:71:75:85:94:102:118 SD: 1.7140 cents 64:69:77:82:92:102:111:128 SD: 1.6325 cents 68:74:82:87:98:109:118:136 SD: 1.5857 cents 72:78:87:92:104:115:125:144 SD: 1.3551 cents 75:81:90:96:108:120:130:150 SD: 1.1786 cents 82:89:99:105:118:131:142:164 SD: 1.0379 cents 93:101:112:119:134:149:161:186 SD: 0.9258 cents 97:105:117:124:140:155:168:194 SD: 0.6664 cents 122:132:147:156:176:195:211:244 SD: 0.4783 cents 182:197:219:233:262:291:315:364 SD: 0.4438 cents 215:233:259:275:310:344:372:430 SD: 0.3987 cents 216:234:260:276:311:345:374:432 SD: 0.3269 cents 241:261:290:308:347:385:417:482 SD: 0.2895 cents 279:302:336:357:402:446:483:558 SD: 0.2619 cents 313:339:377:400:451:500:542:626 SD: 0.2550 cents 324:351:390:414:467:518:561:648 SD: 0.2129 cents 338:366:407:432:487:540:585:676 SD: 0.1668 cents 431:467:519:551:621:689:746:862 SD: 0.1445 cents 456:494:549:583:657:729:789:912 SD: 0.1264 cents 506:548:609:647:729:809:876:1012 SD: 0.1114 cents