Scala analysis: CD16_05_Morocco
Un jour merveilleux - L'ensemble de 'Umar Fâ'id Al-Ju'aydî (ushshaq, Morocco)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 204.738 cents 204.738229 2: 498.055 cents 498.055417 3: 711.880 cents 711.880228 4: 886.980 cents 886.979798 5: 1005.347 cents 1005.346531 6: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 194.6535 cents 194.6535 1: 204.7382 cents 204.7382 2: 293.3172 cents 293.3172 3: 213.8248 cents 213.8248 4: 175.0996 cents 175.0996 5: 118.3667 cents 118.3667 6: 194.6535 cents 194.6535
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 118.36673 cents 1: 1 175.09957 cents 1: 1 194.65347 cents 1: 1 204.73823 cents 1: 1 213.82481 cents 1: 1 293.31719 cents 2: 1 293.46630 cents 2: 1 313.02020 cents 2: 1 388.92438 cents 2: 1 399.39170 cents 2: 1 498.05542 cents 2: 1 507.14200 cents 3: 1 488.11977 cents 3: 1 507.29111 cents 3: 1 517.75843 cents 3: 1 682.24157 cents 3: 1 692.70889 cents 3: 1 711.88023 cents 4: 1 692.85800 cents 4: 1 701.94458 cents 4: 1 800.60830 cents 4: 1 811.07562 cents 4: 1 886.97980 cents 4: 1 906.53370 cents 5: 1 906.68281 cents 5: 1 986.17519 cents 5: 1 995.26177 cents 5: 1 1005.34653 cents 5: 1 1024.90043 cents 5: 1 1081.63327 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 : 204.7 498.1 711.9 887.0 1005.3 1200.0 204.7 : 293.3 507.1 682.2 800.6 995.3 1200.0 498.1 : 213.8 388.9 507.3 701.9 906.7 1200.0 711.9 : 175.1 293.5 488.1 692.9 986.2 1200.0 887.0 : 118.4 313.0 517.8 811.1 1024.9 1200.0 1005.3: 194.7 399.4 692.7 906.5 1081.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 118.3667 .. 293.3172 cents 174.95046 cents 118.36673 cents 2: 293.4663 .. 507.1420 cents 213.67570 cents 0.14912 cents 3: 488.1198 .. 711.8802 cents 223.76046 cents -19.02223 cents 4: 692.8580 .. 906.5337 cents 213.67570 cents -19.02223 cents 5: 906.6828 .. 1081.6333 cents 174.95045 cents 0.14912 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 118.36673 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 293.31719 cents Average / Smallest step : 1.689664 Largest / Average step : 1.466586 Largest / Smallest step : 2.478037 Median interval of one step : 199.69585 cents, amount: 0 Least squares average step : 210.01254 cents, oct.: 1260.07527 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 0.14911 cents Scale diversity : 1.466083 Lumma stability : 0.197526 Lumma impropriety factor : 0.031704 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 : 0.14911 cents Number of recognisable fifths : 4, average 699.8479 cents Formal octave complements present : 1 = 16.6667% Limited inverse transpositions with margin 204.5891 cents: 3 -- Rational properties --
FIT/MODE
6: 1 1 1 1 1 1 SP B ME I SD: 70.4137 c. M: 111.8802 c. Whole-tone, Messiaen mode 1, Raga Gopriya, Anhemitonic Hexatonic 7: 1 2 1 1 1 1 P M ME SD: 24.1083 c. M: 33.3097 c. 12: 2 3 2 2 1 2 P G D3 SD: 7.8047 c. M:-13.0202 c. Mixolydian Hexatonic, P'yongjo: Korea, Yosen: Japan, Raga Darbar, Narayani, Suposhini, Andolika, Gorakh Kalyan, Rakta Hauns 37: 6 9 7 5 4 6 N SD: 7.8229 c. M: 11.5689 c. 39: 7 9 7 6 4 6 P SD: 6.9889 c. M:-10.6464 c. 41: 7 10 7 6 4 7 P SD: 6.7541 c. M: 10.2246 c. 42: 7 10 8 6 4 7 N SD: 5.9263 c. M: 12.3411 c. 49: 8 12 9 7 5 8 N SD: 5.4622 c. M: 8.8199 c. 51: 9 12 9 8 5 8 P SD: 5.6715 c. M:-7.1378 c. 54: 9 13 10 8 5 9 N SD: 4.8183 c. M: 9.1665 c. 57: 10 14 10 8 6 9 N SD: 4.7475 c. M:-7.2077 c. 61: 10 15 11 9 6 10 N SD: 4.5499 c. M: 8.0169 c. 62: 11 15 11 9 6 10 N SD: 4.5433 c. M:-8.1650 c. 69: 12 17 12 10 7 11 N SD: 3.3622 c. M:-6.2924 c. 72: 12 18 13 10 7 12 N SD: 3.8950 c. M: 5.3465 c. 74: 13 18 13 11 7 12 N SD: 3.7699 c. M:-6.0726 c. 81: 14 20 14 12 8 13 N SD: 2.8140 c. M:-5.6483 c. 93: 16 23 16 14 9 15 N SD: 2.7963 c. M:-5.1704 c. 99: 17 24 18 14 10 16 N SD: 1.7645 c. M:-3.2713 c. 111: 19 27 20 16 11 18 N SD: 0.8098 c. M:-1.6333 c. 123: 21 30 22 18 12 20 N SD: 0.4589 c. M:-0.8251 c. 241: 41 59 43 35 24 39 N SD: 0.4191 c. M: 0.6727 c. 253: 43 62 45 37 25 41 N SD: 0.3716 c. M: 0.7857 c. 352: 60 86 63 51 35 57 N SD: 0.4125 c. M:-0.6198 c. 364: 62 89 65 53 36 59 N SD: 0.2138 c. M: 0.3426 c. 487: 83 119 87 71 48 79 N SD: 0.1869 c. M: 0.3141 c. 851: 145 208 152 124 84 138 N SD: 0.1877 c. M: 0.2881 c. 863: 147 211 154 126 85 140 N SD: 0.1855 c. M: 0.3350 c. 932: 159 228 166 136 92 151 N SD: 0.1561 c. M:-0.2329 c. 1055: 180 258 188 154 104 171 N SD: 0.1405 c. M:-0.2240 c. 1185: 202 290 211 173 117 192 N SD: 0.1441 c. M:-0.2231 c. 1207: 206 295 215 176 119 196 N SD: 0.1114 c. M: 0.2098 c. 1296: 221 317 231 189 128 210 N SD: 0.1238 c. M:-0.2090 c. 1308: 223 320 233 191 129 212 N SD: 0.1245 c. M:-0.1762 c. 1330: 227 325 237 194 131 216 N SD: 0.1034 c. M: 0.2337 c. 1419: 242 347 253 207 140 230 N SD: 0.1128 c. M:-0.1705 c. 1448: 247 354 258 211 143 235 N SD: 0.1071 c. M: 0.2395 c. 1460: 249 357 260 213 144 237 N SD: 0.0949 c. M: 0.1411 c. 1571: 268 384 280 229 155 255 N SD: 0.0843 c. M: 0.1561 c. 1583: 270 387 282 231 156 257 N SD: 0.0813 c. M: 0.1665 c. 1694: 289 414 302 247 167 275 N SD: 0.0778 c. M: 0.1517 c. 1824: 311 446 325 266 180 296 N SD: 0.0875 c. M: 0.1377 c. 1898: 324 464 338 277 187 308 N SD: 0.0872 c. M:-0.1532 c. 1947: 332 476 347 284 192 316 N SD: 0.0759 c. M: 0.1157 c. 2016: 344 493 359 294 199 327 N SD: 0.0732 c. M:-0.1589 c. 2021: 345 494 360 295 199 328 N SD: 0.0901 c. M:-0.1138 c. 2028: 346 496 361 296 200 329 N SD: 0.0722 c. M:-0.1694 c. 2058: 351 503 367 300 203 334 N SD: 0.0813 c. M: 0.0993 c. 2070: 353 506 369 302 204 336 N SD: 0.0758 c. M: 0.1291 c. 2139: 365 523 381 312 211 347 N SD: 0.0550 c. M:-0.1213 c. 2262: 386 553 403 330 223 367 N SD: 0.0490 c. M:-0.0878 c. 2385: 407 583 425 348 235 387 N SD: 0.0549 c. M:-0.0695 c. 2392: 408 585 426 349 236 388 N SD: 0.0497 c. M:-0.1051 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x 4 S SD: 4.9626 cents 3 x 4 x 5 x 6 S SD: 0.8737 cents 4 x 5:6 x 7:8 S SD: 29.4941 cents 5:6:7 x 8:9:10 S SD: 31.5939 cents 6:7:8:9:10:11:12 H SD: 12.8055 cents 9:10:12:14:15:16:18 S SD: 9.7242 cents 14:16:19:21:23:25:28 SD: 8.3267 cents 15:17:20:23:25:27:30 SD: 5.5044 cents 18:20:24:27:30:32:36 S SD: 4.3776 cents 24:27:32:36:40:43:48 SD: 1.8547 cents 33:37:44:50:55:59:66 SD: 1.7280 cents 39:44:52:59:65:70:78 SD: 1.6685 cents 57:64:76:86:95:102:114 SD: 0.8973 cents 102:115:136:154:170:182:204 SD: 0.8461 cents 112:126:149:169:187:200:224 SD: 0.7161 cents 126:142:168:190:210:225:252 SD: 0.6416 cents 136:153:181:205:227:243:272 SD: 0.6081 cents 151:170:201:228:252:270:302 SD: 0.5630 cents 159:179:212:240:265:284:318 SD: 0.5030 cents 175:197:233:264:292:313:350 SD: 0.4762 cents 183:206:244:276:305:327:366 SD: 0.4512 cents 216:243:288:326:361:386:432 SD: 0.4097 cents 230:259:307:347:384:411:460 SD: 0.3529 cents 240:270:320:362:401:429:480 SD: 0.3218 cents 279:314:372:421:466:499:558 SD: 0.2776 cents 287:323:383:433:479:513:574 SD: 0.2550 cents 342:385:456:516:571:611:684 SD: 0.1517 cents 366:412:488:552:611:654:732 SD: 0.1184 cents 399:449:532:602:666:713:798 SD: 0.0847 cents