Scala analysis: CD15_17_Morocco
Dieu lui révéla tous les secrets - L'ensemble de 'Umar Fâ'id Al-Ju'aydî (unknown maqam, Morocco)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 208.962 cents 208.962166 2: 505.403 cents 505.402657 3: 716.918 cents 716.918422 4: 901.309 cents 901.308826 5: 996.378 cents 996.377966 6: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 203.6220 cents 203.6220 1: 208.9622 cents 208.9622 2: 296.4405 cents 296.4405 3: 211.5158 cents 211.5158 4: 184.3904 cents 184.3904 5: 95.0691 cents 95.0691 6: 203.6220 cents 203.6220
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 95.06914 cents 1: 1 184.39040 cents 1: 1 203.62203 cents 1: 1 208.96217 cents 1: 1 211.51576 cents 1: 1 296.44049 cents 2: 1 279.45954 cents 2: 1 298.69117 cents 2: 1 395.90617 cents 2: 1 412.58420 cents 2: 1 505.40266 cents 2: 1 507.95626 cents 3: 1 483.08158 cents 3: 1 490.97531 cents 3: 1 507.65334 cents 3: 1 692.34666 cents 3: 1 709.02469 cents 3: 1 716.91842 cents 4: 1 692.04374 cents 4: 1 694.59734 cents 4: 1 787.41580 cents 4: 1 804.09383 cents 4: 1 901.30883 cents 4: 1 920.54046 cents 5: 1 903.55951 cents 5: 1 988.48424 cents 5: 1 991.03783 cents 5: 1 996.37797 cents 5: 1 1015.60960 cents 5: 1 1104.93086 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 6.00000 = 6
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 0.0 : 209.0 505.4 716.9 901.3 996.4 1200.0 209.0 : 296.4 508.0 692.3 787.4 991.0 1200.0 505.4 : 211.5 395.9 491.0 694.6 903.6 1200.0 716.9 : 184.4 279.5 483.1 692.0 988.5 1200.0 901.3 : 95.1 298.7 507.7 804.1 1015.6 1200.0 996.4 : 203.6 412.6 709.0 920.5 1104.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 95.0691 .. 296.4405 cents 201.37135 cents 95.06914 cents 2: 279.4595 .. 507.9563 cents 228.49671 cents -16.98095 cents 3: 483.0816 .. 716.9184 cents 233.83684 cents -24.87468 cents 4: 692.0437 .. 920.5405 cents 228.49671 cents -24.87468 cents 5: 903.5595 .. 1104.9309 cents 201.37135 cents -16.98095 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 95.06914 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 296.44049 cents Average / Smallest step : 2.103732 Largest / Average step : 1.482202 Largest / Smallest step : 3.118157 Median interval of one step : 206.29210 cents, amount: 0 Least squares average step : 210.52360 cents, oct.: 1263.14162 cents Scale is not proper Step pattern alph. order: ABCDEF Step pattern size order : DFEBAC Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 0.30292 cents Scale diversity : 1.443082 Lumma stability : 0.158449 Lumma impropriety factor : 0.069759 Rothenberg efficiency : 0.333333 redundancy: 0.666667 Efficiency x scale size : 2.000000 Number of different interval sizes : 30 = 6.00000 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 6.00000 = 6 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 0.30292 cents Number of recognisable fifths : 5, average 700.9862 cents Number of appreciable fifths : 4, average 697.0031 cents Formal octave complements present : 1 = 16.6667% Limited inverse transpositions with margin 225.9431 cents: 3 -- Rational properties --
FIT/MODE
6: 1 1 1 1 1 1 SP B ME I SD: 76.5251 c. M: 116.9184 c. Whole-tone, Messiaen mode 1, Raga Gopriya, Anhemitonic Hexatonic 7: 1 2 1 1 1 1 P M ME SD: 30.1342 c. M: 44.1660 c. 11: 2 3 2 1 1 2 N SD: 28.5792 c. M:-46.7179 c. 12: 2 3 2 2 1 2 P G D3 SD: 8.2722 c. M: 16.9184 c. Mixolydian Hexatonic, P'yongjo: Korea, Yosen: Japan, Raga Darbar, Narayani, Suposhini, Andolika, Gorakh Kalyan, Rakta Hauns 17: 3 4 3 3 1 3 P G D3 SD: 9.9183 c. M:-16.3382 c. 23: 4 6 4 3 2 4 N SD: 10.6566 c. M:-16.3365 c. 28: 5 7 5 4 2 5 N SD: 7.7295 c. M:-11.6530 c. 29: 5 7 5 5 2 5 P G D3 SD: 7.7074 c. M: 13.4701 c. 35: 6 9 6 5 3 6 N SD: 5.7872 c. M: 9.8803 c. 40: 7 10 7 6 3 7 N SD: 3.5143 c. M: 6.3780 c. 52: 9 13 9 8 4 9 N SD: 2.1404 c. M: 4.0703 c. 64: 11 16 11 10 5 11 N SD: 2.4568 c. M: 4.4184 c. 102: 18 25 18 16 8 17 N SD: 2.6662 c. M:-4.5735 c. 105: 18 26 19 16 8 18 N SD: 2.3558 c. M: 3.2479 c. 114: 20 28 20 18 9 19 N SD: 2.3272 c. M:-3.9543 c. 116: 20 29 20 18 9 20 N SD: 2.1871 c. M: 3.2745 c. 117: 20 29 21 18 9 20 N SD: 2.1472 c. M: 3.8340 c. 124: 22 30 22 19 10 21 N SD: 1.9478 c. M:-3.9411 c. 125: 22 31 22 19 10 21 N SD: 2.2849 c. M:-3.3973 c. 129: 22 32 23 20 10 22 N SD: 2.2566 c. M: 4.3110 c. 131: 23 32 23 20 11 22 N SD: 2.1857 c. M: 3.5989 c. 136: 24 33 24 21 11 23 N SD: 1.8702 c. M:-2.8025 c. 137: 24 34 24 21 11 23 N SD: 1.6175 c. M:-2.6265 c. 149: 26 37 26 23 12 25 N SD: 1.2794 c. M:-2.2798 c. 166: 29 41 29 26 13 28 N SD: 1.2387 c. M:-2.3056 c. 188: 33 46 33 29 15 32 N SD: 1.3127 c. M: 2.0248 c. 189: 33 47 33 29 15 32 N SD: 1.1036 c. M:-2.5339 c. 194: 34 48 34 30 15 33 N SD: 1.2185 c. M:-1.8138 c. 201: 35 50 35 31 16 34 N SD: 0.9068 c. M:-2.0600 c. 206: 36 51 36 32 16 35 N SD: 0.9408 c. M:-1.6038 c. 218: 38 54 38 34 17 37 N SD: 0.9053 c. M:-1.4435 c. 254: 44 63 45 39 20 43 N SD: 0.8113 c. M:-1.1918 c. 266: 46 66 47 41 21 45 N SD: 0.7657 c. M: 1.4434 c. 276: 48 68 49 42 22 47 N SD: 0.7796 c. M: 1.3088 c. 288: 50 71 51 44 23 49 N SD: 0.8161 c. M: 1.3088 c. 306: 53 76 54 47 24 52 N SD: 0.6491 c. M: 1.1190 c. 318: 55 79 56 49 25 54 N SD: 0.6363 c. M: 1.4150 c. 346: 60 86 61 53 27 59 N SD: 0.8017 c. M: 1.0022 c. 352: 61 87 62 54 28 60 N SD: 0.9429 c. M: 1.3088 c. 353: 61 88 62 54 28 60 N SD: 0.8414 c. M: 1.5967 c. 358: 62 89 63 55 28 61 N SD: 0.6911 c. M: 1.1409 c. 361: 63 89 64 55 29 61 N SD: 0.6276 c. M:-1.0871 c. 373: 65 92 66 57 30 63 N SD: 0.5028 c. M:-0.9411 c. 378: 66 93 67 58 30 64 N SD: 0.4650 c. M: 0.6408 c. 390: 68 96 69 60 31 66 N SD: 0.4167 c. M: 0.7873 c. 413: 72 102 73 63 33 70 N SD: 0.4185 c. M:-0.7571 c. 418: 73 103 74 64 33 71 N SD: 0.4208 c. M:-0.7849 c. 425: 74 105 75 65 34 72 N SD: 0.2995 c. M: 0.6029 c. 430: 75 106 76 66 34 73 N SD: 0.2235 c. M:-0.3402 c. 442: 77 109 78 68 35 75 N SD: 0.1924 c. M: 0.4253 c. 494: 86 122 87 76 39 84 N SD: 0.2292 c. M: 0.4265 c. 631: 110 156 111 97 50 107 N SD: 0.2232 c. M:-0.4611 c. 643: 112 159 113 99 51 109 N SD: 0.2052 c. M:-0.3516 c. 855: 149 211 151 131 68 145 N SD: 0.1822 c. M:-0.2746 c. 867: 151 214 153 133 69 147 N SD: 0.1566 c. M: 0.2708 c. 919: 160 227 162 141 73 156 N SD: 0.1437 c. M: 0.3295 c. 1061: 185 262 187 163 84 180 N SD: 0.1488 c. M:-0.2744 c. 1068: 186 264 188 164 85 181 N SD: 0.1574 c. M:-0.2512 c. 1073: 187 265 189 165 85 182 N SD: 0.0961 c. M:-0.1711 c. 1498: 261 370 264 230 119 254 N SD: 0.0951 c. M:-0.1507 c. 1515: 264 374 267 233 120 257 N SD: 0.0832 c. M:-0.1467 c. 1567: 273 387 276 241 124 266 N SD: 0.0773 c. M: 0.1348 c. 1873: 326 463 330 288 148 318 N SD: 0.0914 c. M:-0.1327 c. 1928: 336 476 340 296 153 327 N SD: 0.0911 c. M:-0.1665 c. 1940: 338 479 342 298 154 329 N SD: 0.0739 c. M:-0.1169 c. 1980: 345 489 349 304 157 336 N SD: 0.0724 c. M:-0.1287 c. 1992: 347 492 351 306 158 338 N SD: 0.0567 c. M: 0.1040 c. 2246: 391 555 396 345 178 381 N SD: 0.0525 c. M:-0.0896 c. 2298: 400 568 405 353 182 390 N SD: 0.0541 c. M: 0.0849 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x 4 S SD: 7.4817 cents 3 x 4 x 5 x 6 S SD: 6.1594 cents 4 x 5:6 x 7:8 S SD: 30.7868 cents 5:6:7 x 8:9:10 S SD: 31.9088 cents 6:7:8:9:10:11:12 H SD: 13.6689 cents 7:8:9:11:12 x 14 SD: 20.7369 cents 8:9:11:12:13:14:16 SD: 13.7549 cents 9:10:12:14:15:16:18 S SD: 9.6474 cents 14:16:19:21:24:25:28 SD: 8.0400 cents 15:17:20:23:25:27:30 SD: 6.2011 cents 18:20:24:27:30:32:36 S SD: 5.9413 cents 21:24:28:32:35:37:42 SD: 5.8600 cents 22:25:29:33:37:39:44 SD: 5.6321 cents 23:26:31:35:39:41:46 SD: 3.4344 cents 32:36:43:48:54:57:64 SD: 2.9680 cents 39:44:52:59:66:69:78 SD: 2.4642 cents 41:46:55:62:69:73:82 SD: 1.7601 cents 47:53:63:71:79:84:94 SD: 1.6334 cents 53:60:71:80:89:94:106 SD: 1.5437 cents 62:70:83:94:104:110:124 SD: 1.3146 cents 76:86:102:115:128:135:152 SD: 1.1271 cents 85:96:114:129:143:151:170 SD: 1.0762 cents 86:97:115:130:145:153:172 SD: 0.7199 cents 117:132:157:177:197:208:234 SD: 0.6322 cents 139:157:186:210:234:247:278 SD: 0.5905 cents 148:167:198:224:249:263:296 SD: 0.3377 cents 195:220:261:295:328:347:390 SD: 0.3143 cents 265:299:355:401:446:471:530 SD: 0.1792 cents 351:396:470:531:591:624:702 SD: 0.1359 cents 460:519:616:696:774:818:920 SD: 0.0881 cents 546:616:731:826:919:971:1092 SD: 0.0794 cents