Scala analysis: CD05_14_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: 204.722 cents 204.721595 2: 345.597 cents 345.596627 3: 497.295 cents 497.295247 4: 700.613 cents 700.613479 5: 881.486 cents 881.485656 6: 1092.736 cents 1092.736452 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 107.2635 cents 107.2635 1: 204.7216 cents 204.7216 2: 140.8750 cents 140.8750 3: 151.6986 cents 151.6986 4: 203.3182 cents 203.3182 5: 180.8722 cents 180.8722 6: 211.2508 cents 211.2508 7: 107.2635 cents 107.2635
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 107.26355 cents 1: 1 140.87503 cents 1: 1 151.69862 cents 1: 1 180.87218 cents 1: 1 203.31823 cents 1: 1 204.72160 cents 1: 1 211.25080 cents 2: 1 292.57365 cents 2: 1 311.98514 cents 2: 1 318.51434 cents 2: 1 345.59663 cents 2: 1 355.01685 cents 2: 1 384.19041 cents 2: 1 392.12297 cents 3: 1 452.86018 cents 3: 1 495.89188 cents 3: 1 497.29525 cents 3: 1 499.38652 cents 3: 1 523.23594 cents 3: 1 535.88903 cents 3: 1 595.44121 cents 4: 1 604.55879 cents 4: 1 664.11097 cents 4: 1 676.76406 cents 4: 1 700.61348 cents 4: 1 702.70475 cents 4: 1 704.10812 cents 4: 1 747.13982 cents 5: 1 807.87703 cents 5: 1 815.80959 cents 5: 1 844.98315 cents 5: 1 854.40337 cents 5: 1 881.48566 cents 5: 1 888.01486 cents 5: 1 907.42635 cents 6: 1 988.74920 cents 6: 1 995.27840 cents 6: 1 996.68177 cents 6: 1 1019.12782 cents 6: 1 1048.30138 cents 6: 1 1059.12497 cents 6: 1 1092.73645 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 : 204.7 345.6 497.3 700.6 881.5 1092.7 1200.0 204.7 : 140.9 292.6 495.9 676.8 888.0 995.3 1200.0 345.6 : 151.7 355.0 535.9 747.1 854.4 1059.1 1200.0 497.3 : 203.3 384.2 595.4 702.7 907.4 1048.3 1200.0 700.6 : 180.9 392.1 499.4 704.1 845.0 996.7 1200.0 881.5 : 211.3 318.5 523.2 664.1 815.8 1019.1 1200.0 1092.7: 107.3 312.0 452.9 604.6 807.9 988.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 107.2635 .. 211.2508 cents 103.98725 cents 107.26355 cents 2: 292.5737 .. 392.1230 cents 99.54932 cents 81.32286 cents 3: 452.8602 .. 595.4412 cents 142.58103 cents 60.73720 cents 4: 604.5588 .. 747.1398 cents 142.58103 cents 9.11759 cents 5: 807.8770 .. 907.4263 cents 99.54932 cents 60.73720 cents 6: 988.7492 .. 1092.7365 cents 103.98725 cents 81.32286 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 107.26355 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 211.25080 cents Average / Smallest step : 1.598200 Largest / Average step : 1.232296 Largest / Smallest step : 1.969456 Median interval of one step : 180.87218 cents, amount: 1 Least squares average step : 175.38644 cents, oct.: 1227.70507 cents Scale is strictly proper Step pattern alph. order: ABCDEFG Step pattern size order : FBCEDGA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 9.11759 cents Scale diversity : 1.587577 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.423137 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 : 1.40336 cents Number of recognisable fifths : 3, average 702.4754 cents Best fifths form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 14.2857% -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 30.0863 c. M: 64.1650 c. Lebeng 10: 2 1 1 2 1 2 1 P M ME S SD: 23.9352 c. M: 41.4857 c. Sethares Neutral, Beatles-7, Dichotic-7 12: 2 1 2 2 2 2 1 P D3 S SD: 18.9155 c. M: 45.5966 c. Melodic Minor ascending, Jazz Minor, Minor-Major, Mela Gaurimanohari, Raga Kedar Bahar, Patdip (Patadeep), Velavali, Deshi(2), Mischung 1, Hawaiian 14: 2 2 2 2 2 3 1 P T3 SD: 19.5796 c. M: 33.2930 c. 17: 3 2 2 3 2 3 2 SP M ME S SD: 18.8099 c. M: 34.4268 c. Beatles-7, Dichotic-7 18: 3 2 2 3 3 3 2 P D3 SD: 21.2550 c. M: 33.9468 c. 19: 3 2 3 3 3 3 2 SP D3 S SD: 15.0684 c. M: 29.8072 c. Nineteen-tone Melodic Minor 20: 3 3 2 4 3 3 2 P T3 SD: 16.8971 c. M: 24.7216 c. 21: 4 2 3 3 3 4 2 SP T3 SD: 15.7156 c. M: 24.3428 c. 22: 4 2 3 4 3 4 2 P SD: 10.0686 c. M: 18.3239 c. Twenty-two tone Melodic Minor 24: 4 3 3 4 4 4 2 P SD: 7.9724 c. M:-18.5143 c. Maqam Mahur 29: 5 3 4 5 4 5 3 SP SD: 9.7605 c. M: 16.8744 c. Twenty-nine tone Melodic Minor 31: 5 4 4 5 5 5 3 SP SD: 6.9614 c. M: 11.1732 c. 34: 6 4 4 6 5 6 3 P SD: 4.5366 c. M:-7.3445 c. 41: 7 5 5 7 6 7 4 SP SD: 4.5211 c. M: 9.8096 c. 46: 8 5 6 8 7 8 4 P SD: 4.0122 c. M: 6.4662 c. 53: 9 6 7 9 8 9 5 SP SD: 3.3071 c. M: 5.9740 c. 65: 11 8 8 11 10 11 6 SP SD: 3.0650 c. M:-5.1726 c. 77: 13 9 10 13 12 13 7 SP SD: 3.0331 c. M:-6.8260 c. 80: 14 9 10 14 12 14 7 P SD: 3.1668 c. M:-5.2784 c. 82: 14 10 10 14 12 15 7 P SD: 3.1653 c. M:-5.6229 c. 86: 15 10 11 14 13 15 8 SP SD: 3.5919 c. M:-5.0303 c. 87: 15 10 11 15 13 15 8 SP SD: 1.8908 c. M: 3.0813 c. 101: 17 12 13 17 15 18 9 SP SD: 1.5576 c. M: 2.7414 c. 135: 23 16 17 23 20 24 12 SP SD: 0.9715 c. M:-1.6087 c. 159: 27 19 20 27 24 28 14 SP SD: 1.2297 c. M:-1.6032 c. 181: 31 21 23 31 27 32 16 SP SD: 1.0329 c. M:-2.1490 c. 188: 32 22 24 32 28 33 17 SP SD: 0.8976 c. M:-1.5142 c. 212: 36 25 27 36 32 37 19 SP SD: 0.9039 c. M:-1.5332 c. 246: 42 29 31 42 37 43 22 SP SD: 0.9306 c. M:-1.8255 c. 271: 46 32 34 46 41 48 24 SP SD: 0.8436 c. M: 1.3543 c. 282: 48 33 36 48 42 50 25 SP SD: 0.8332 c. M:-1.5142 c. 289: 49 34 37 49 43 51 26 SP SD: 0.9749 c. M: 1.2614 c. 294: 50 35 37 50 44 52 26 SP SD: 0.9268 c. M:-1.4273 c. 300: 51 35 38 51 45 53 27 SP SD: 1.0606 c. M: 1.5966 c. 301: 51 36 38 51 45 53 27 SP SD: 0.9275 c. M: 1.3993 c. 302: 52 35 38 51 46 53 27 SP SD: 0.9274 c. M:-1.9009 c. 305: 52 36 38 52 46 54 27 SP SD: 0.7583 c. M: 1.5575 c. 312: 53 37 39 53 47 55 28 SP SD: 0.7024 c. M: 1.1414 c. 324: 55 38 41 55 49 57 29 SP SD: 0.7328 c. M: 1.1522 c. 336: 57 40 42 57 51 59 30 SP SD: 0.7160 c. M: 1.1502 c. 347: 59 41 44 59 52 61 31 SP SD: 0.6653 c. M:-1.4038 c. 358: 61 42 45 61 54 63 32 SP SD: 0.4849 c. M: 1.2059 c. 389: 66 46 49 66 59 68 35 SP SD: 0.6440 c. M: 1.1226 c. 392: 67 46 49 67 59 69 35 SP SD: 0.5789 c. M: 1.3769 c. 399: 68 47 50 68 60 70 36 SP SD: 0.5784 c. M: 1.0546 c. 403: 69 47 51 68 61 71 36 SP SD: 0.4368 c. M: 0.8616 c. 406: 69 48 51 69 61 72 36 SP SD: 0.5915 c. M:-0.8596 c. 423: 72 50 53 72 64 74 38 SP SD: 0.5465 c. M: 0.8413 c. 427: 73 50 54 72 65 75 38 SP SD: 0.5413 c. M:-0.9499 c. 434: 74 51 55 73 66 76 39 SP SD: 0.5274 c. M: 1.0743 c. 437: 75 51 55 74 66 77 39 SP SD: 0.5234 c. M:-1.2281 c. 444: 76 52 56 75 67 78 40 SP SD: 0.5131 c. M: 0.8446 c. 451: 77 53 57 76 68 80 40 SP SD: 0.5581 c. M: 0.8352 c. 456: 78 53 58 77 69 80 41 SP SD: 0.5101 c. M: 0.8598 c. 459: 78 54 58 78 69 81 41 SP SD: 0.4482 c. M: 0.8000 c. 468: 80 55 59 79 71 82 42 SP SD: 0.4433 c. M: 0.6135 c. 493: 84 58 62 84 74 87 44 SP SD: 0.3648 c. M: 0.7435 c. 504: 86 59 64 85 76 89 45 SP SD: 0.3606 c. M: 0.6135 c. 517: 88 61 65 88 78 91 46 SP SD: 0.4248 c. M: 0.5834 c. 524: 89 62 66 89 79 92 47 SP SD: 0.4104 c. M: 0.9048 c. 528: 90 62 67 89 80 93 47 SP SD: 0.3631 c. M: 0.6135 c. 538: 92 63 68 91 81 95 48 SP SD: 0.2820 c. M:-0.4829 c. 562: 96 66 71 95 85 99 50 SP SD: 0.3074 c. M:-0.5020 c. 569: 97 67 72 96 86 100 51 SP SD: 0.2818 c. M: 0.4377 c. 591: 101 69 75 100 89 104 53 SP SD: 0.2764 c. M: 0.4190 c. 615: 105 72 78 104 93 108 55 SP SD: 0.2341 c. M:-0.4656 c. 750: 128 88 95 127 113 132 67 SP SD: 0.1468 c. M:-0.3048 c. 927: 158 109 117 157 140 163 83 SP SD: 0.1698 c. M: 0.2899 c. 1021: 174 120 129 173 154 180 91 SP SD: 0.1600 c. M:-0.3096 c. 1062: 181 125 134 180 160 187 95 SP SD: 0.1245 c. M: 0.2018 c. 1108: 189 130 140 188 167 195 99 SP SD: 0.1004 c. M: 0.1833 c. 1511: 258 177 191 256 228 266 135 SP SD: 0.1166 c. M:-0.1758 c. 1518: 259 178 192 257 229 267 136 SP SD: 0.1398 c. M: 0.2463 c. 1542: 263 181 195 261 233 271 138 SP SD: 0.1345 c. M:-0.2264 c. 1552: 265 182 196 263 234 273 139 SP SD: 0.1219 c. M: 0.2107 c. 1576: 269 185 199 267 238 277 141 SP SD: 0.1218 c. M:-0.2402 c. 1600: 273 188 202 271 241 282 143 SP SD: 0.1165 c. M: 0.2357 c. 1612: 275 189 204 273 243 284 144 SP SD: 0.0950 c. M: 0.1872 c. 1646: 281 193 208 279 248 290 147 SP SD: 0.0785 c. M:-0.1387 c. 1677: 286 197 212 284 253 295 150 SP SD: 0.0593 c. M:-0.0886 c. 1812: 309 213 229 307 273 319 162 SP SD: 0.0584 c. M:-0.0987 c. 2215: 378 260 280 375 334 390 198 SP SD: 0.0577 c. M: 0.1169 c. 2396: 409 281 303 406 361 422 214 SP SD: 0.0613 c. M:-0.1198 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: 0.6708 cents 3 x x 4 x 5 x 6 S SD: 0.9898 cents 4 x 5 x 6:7 x 8 S SD: 24.0936 cents 5 x 6:7 x 8:9:10 S SD: 27.1308 cents 6:7 x 8:9:10:11:12 S SD: 12.6430 cents 7:8 x 9:11:12:13:14 SD: 19.9886 cents 8:9:10:11:12:13:15:16 SD: 11.3176 cents 9:10:11:12:13:15:17:18 SD: 9.7674 cents 14:16:17:19:21:23:26:28 SD: 7.4295 cents 15:17:18:20:22:25:28:30 SD: 7.2965 cents 18:20:22:24:27:30:34:36 SD: 3.4435 cents 24:27:29:32:36:40:45:48 SD: 2.6890 cents 32:36:39:43:48:53:60:64 SD: 2.4665 cents 40:45:49:53:60:67:75:80 SD: 2.4324 cents 42:47:51:56:63:70:79:84 SD: 2.0264 cents 48:54:59:64:72:80:90:96 SD: 1.8420 cents 54:61:66:72:81:90:102:108 SD: 1.5818 cents 63:71:77:84:94:105:118:126 SD: 1.5539 cents 72:81:88:96:108:120:135:144 SD: 0.8393 cents 118:133:144:157:177:196:222:236 SD: 0.7562 cents 126:142:154:168:189:210:237:252 SD: 0.6381 cents 136:153:166:181:204:226:256:272 SD: 0.6215 cents 144:162:176:192:216:240:271:288 SD: 0.6110 cents 150:169:183:200:225:250:282:300 SD: 0.5624 cents 168:189:205:224:252:280:316:336 SD: 0.5213 cents 184:207:225:245:276:306:346:368 SD: 0.5197 cents 190:214:232:253:285:316:357:380 SD: 0.3757 cents 199:224:243:265:298:331:374:398 SD: 0.3223 cents 208:234:254:277:312:346:391:416 SD: 0.3042 cents 271:305:331:361:406:451:509:542 SD: 0.2890 cents 285:321:348:380:427:474:536:570 SD: 0.2765 cents 303:341:370:404:454:504:570:606 SD: 0.2397 cents 325:366:397:433:487:541:611:650 SD: 0.2363 cents 327:368:399:436:490:544:615:654 SD: 0.2356 cents 343:386:419:457:514:571:645:686 SD: 0.2164 cents 349:393:426:465:523:581:656:698 SD: 0.2052 cents 357:402:436:476:535:594:671:714 SD: 0.1806 cents 367:413:448:489:550:611:690:734 SD: 0.1728 cents 375:422:458:500:562:624:705:750 SD: 0.1447 cents 493:555:602:657:739:820:927:986 SD: 0.1299 cents 517:582:631:689:775:860:972:1034 SD: 0.1292 cents 565:636:690:753:847:940:1062:1130 SD: 0.0895 cents