Scala analysis: CD16_18_Morocco
Parcours le Monde, tu en saisiras les secrets - 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: 213.147 cents 213.146692 2: 504.808 cents 504.808386 3: 705.733 cents 705.733203 4: 908.648 cents 908.647596 5: 994.399 cents 994.398922 6: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 205.6011 cents 205.6011 1: 213.1467 cents 213.1467 2: 291.6617 cents 291.6617 3: 200.9248 cents 200.9248 4: 202.9144 cents 202.9144 5: 85.7513 cents 85.7513 6: 205.6011 cents 205.6011
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 85.75133 cents 1: 1 200.92482 cents 1: 1 202.91439 cents 1: 1 205.60108 cents 1: 1 213.14669 cents 1: 1 291.66169 cents 2: 1 288.66572 cents 2: 1 291.35240 cents 2: 1 403.83921 cents 2: 1 418.74777 cents 2: 1 492.58651 cents 2: 1 504.80839 cents 3: 1 489.59054 cents 3: 1 494.26680 cents 3: 1 504.49910 cents 3: 1 695.50090 cents 3: 1 705.73320 cents 3: 1 710.40946 cents 4: 1 695.19161 cents 4: 1 707.41349 cents 4: 1 781.25223 cents 4: 1 796.16079 cents 4: 1 908.64760 cents 4: 1 911.33428 cents 5: 1 908.33831 cents 5: 1 986.85331 cents 5: 1 994.39892 cents 5: 1 997.08561 cents 5: 1 999.07518 cents 5: 1 1114.24867 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 : 213.1 504.8 705.7 908.6 994.4 1200.0 213.1 : 291.7 492.6 695.5 781.3 986.9 1200.0 504.8 : 200.9 403.8 489.6 695.2 908.3 1200.0 705.7 : 202.9 288.7 494.3 707.4 999.1 1200.0 908.6 : 85.8 291.4 504.5 796.2 997.1 1200.0 994.4 : 205.6 418.7 710.4 911.3 1114.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 85.7513 .. 291.6617 cents 205.91037 cents 85.75133 cents 2: 288.6657 .. 504.8084 cents 216.14267 cents -2.99597 cents 3: 489.5905 .. 710.4095 cents 220.81893 cents -15.21785 cents 4: 695.1916 .. 911.3343 cents 216.14267 cents -15.21785 cents 5: 908.3383 .. 1114.2487 cents 205.91037 cents -2.99597 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 85.75133 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 291.66169 cents Average / Smallest step : 2.332325 Largest / Average step : 1.458308 Largest / Smallest step : 3.401250 Median interval of one step : 204.25774 cents, amount: 0 Least squares average step : 210.40163 cents, oct.: 1262.40976 cents Scale is not proper Step pattern alph. order: ABCDEF Step pattern size order : EFBCAD Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 0.30929 cents Scale diversity : 1.364418 Lumma stability : 0.142919 Lumma impropriety factor : 0.030356 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 : 0.30929 cents Number of recognisable fifths : 5, average 702.8497 cents Formal octave complements present : 1 = 16.6667% Limited inverse transpositions with margin 216.1427 cents: 3 -- Rational properties --
FIT/MODE
6: 1 1 1 1 1 1 SP B ME I SD: 75.4683 c. M: 108.6476 c. Whole-tone, Messiaen mode 1, Raga Gopriya, Anhemitonic Hexatonic 7: 1 2 1 1 1 1 P M ME SD: 31.7581 c. M: 51.5047 c. 10: 2 2 2 2 0 2 P M DE SD: 29.8899 c. M:-51.3524 c. 12: 2 3 2 2 1 2 P G D3 SD: 7.4719 c. M: 13.1467 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: 6.2611 c. M: 10.6907 c. 29: 5 7 5 5 2 5 P G D3 SD: 4.4162 c. M: 8.2567 c. 41: 7 10 7 7 3 7 P G D3 SD: 4.7265 c. M: 8.2686 c. 54: 10 13 9 9 4 9 N SD: 5.6044 c. M:-9.0755 c. 57: 10 14 9 10 4 10 N SD: 5.2234 c. M: 10.9964 c. 61: 11 15 10 10 5 10 N SD: 5.0633 c. M:-8.8798 c. 62: 11 15 10 11 4 11 N SD: 4.7821 c. M: 8.9590 c. 66: 12 16 11 11 5 11 N SD: 3.7977 c. M:-5.6011 c. 71: 13 17 12 12 5 12 N SD: 3.8553 c. M:-6.5716 c. 78: 14 19 13 13 6 13 N SD: 2.8708 c. M:-5.6011 c. 83: 15 20 14 14 6 14 N SD: 2.5041 c. M:-3.7208 c. 95: 17 23 16 16 7 16 N SD: 1.7470 c. M:-3.4958 c. 100: 18 24 17 17 7 17 N SD: 2.1500 c. M:-3.3524 c. 107: 19 26 18 18 8 18 N SD: 1.5631 c. M:-3.7319 c. 111: 20 27 18 19 8 19 N SD: 2.2295 c. M:-3.2997 c. 112: 20 27 19 19 8 19 N SD: 1.4835 c. M:-2.0667 c. 124: 22 30 21 21 9 21 N SD: 1.2769 c. M:-2.3753 c. 157: 28 38 26 27 11 27 N SD: 1.2096 c. M: 2.5485 c. 169: 30 41 28 29 12 29 N SD: 1.1769 c. M: 2.7746 c. 180: 32 44 30 30 13 31 N SD: 1.2529 c. M: 1.9809 c. 185: 33 45 31 31 13 32 N SD: 1.1510 c. M: 1.9665 c. 197: 35 48 33 33 14 34 N SD: 0.8839 c. M: 1.5055 c. 209: 37 51 35 35 15 36 N SD: 0.8476 c. M: 1.4706 c. 214: 38 52 36 36 15 37 N SD: 0.8416 c. M: 1.8756 c. 226: 40 55 38 38 16 39 N SD: 0.7731 c. M: 1.4786 c. 235: 42 57 39 40 17 40 N SD: 0.9373 c. M:-1.3458 c. 238: 42 58 40 40 17 41 N SD: 0.8883 c. M: 1.3820 c. 247: 44 60 41 42 18 42 N SD: 0.8812 c. M:-1.5525 c. 252: 45 61 42 43 18 43 N SD: 0.7869 c. M:-1.1390 c. 264: 47 64 44 45 19 45 N SD: 0.7107 c. M: 1.1877 c. 281: 50 68 47 48 20 48 N SD: 0.7607 c. M: 1.1069 c. 292: 52 71 49 49 21 50 N SD: 0.6054 c. M:-1.1161 c. 304: 54 74 51 51 22 52 N SD: 0.5169 c. M:-0.8457 c. 309: 55 75 52 52 22 53 N SD: 0.4811 c. M:-1.0629 c. 321: 57 78 54 54 23 55 N SD: 0.3494 c. M:-0.8089 c. 333: 59 81 56 56 24 57 N SD: 0.4154 c. M:-0.5731 c. 444: 79 108 74 75 32 76 N SD: 0.3932 c. M:-0.5970 c. 449: 80 109 75 76 32 77 N SD: 0.3166 c. M:-0.6618 c. 461: 82 112 77 78 33 79 N SD: 0.2070 c. M: 0.3102 c. 478: 85 116 80 81 34 82 N SD: 0.2132 c. M: 0.2939 c. 490: 87 119 82 83 35 84 N SD: 0.2272 c. M: 0.4271 c. 585: 104 142 98 99 42 100 N SD: 0.2270 c. M:-0.4729 c. 770: 137 187 129 130 55 132 N SD: 0.1924 c. M:-0.3598 c. 782: 139 190 131 132 56 134 N SD: 0.1238 c. M: 0.2077 c. 799: 142 194 134 135 57 137 N SD: 0.1243 c. M: 0.1776 c. 811: 144 197 136 137 58 139 N SD: 0.1257 c. M: 0.2461 c. 1243: 221 302 208 210 89 213 N SD: 0.1256 c. M:-0.2081 c. 1255: 223 305 210 212 90 215 N SD: 0.1255 c. M: 0.2811 c. 1260: 224 306 211 213 90 216 N SD: 0.0966 c. M:-0.1866 c. 1272: 226 309 213 215 91 218 N SD: 0.0871 c. M: 0.1570 c. 1581: 281 384 265 267 113 271 N SD: 0.1042 c. M:-0.1491 c. 1593: 283 387 267 269 114 273 N SD: 0.0954 c. M: 0.1730 c. 1750: 311 425 293 296 125 300 N SD: 0.1030 c. M: 0.1332 c. 1780: 316 433 298 301 127 305 N SD: 0.0974 c. M:-0.1354 c. 1845: 328 448 309 312 132 316 N SD: 0.0926 c. M:-0.1866 c. 1857: 330 451 311 314 133 318 N SD: 0.0918 c. M: 0.1234 c. 2054: 365 499 344 347 147 352 N SD: 0.0856 c. M: 0.1763 c. 2071: 368 503 347 350 148 355 N SD: 0.0839 c. M: 0.1247 c. 2083: 370 506 349 352 149 357 N SD: 0.0914 c. M: 0.1516 c. 2166: 385 526 363 366 155 371 N SD: 0.0882 c. M:-0.1497 c. 2178: 387 529 365 368 156 373 N SD: 0.0858 c. M: 0.1252 c. 2241: 398 545 375 379 160 384 N SD: 0.0653 c. M:-0.1448 c. 2253: 400 548 377 381 161 386 N SD: 0.0628 c. M:-0.1184 c. 2270: 403 552 380 384 162 389 N SD: 0.0576 c. M: 0.1070 c. 2365: 420 575 396 400 169 405 N SD: 0.0706 c. M:-0.1050 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x 4 S SD: 1.8891 cents 3 x 4 x 5 x 6 S SD: 8.4043 cents 4 x 5:6 x 7:8 S SD: 30.3204 cents 5:6:7 x 8:9:10 S SD: 32.3102 cents 6:7:8:9:10:11:12 H SD: 13.4962 cents 7:8:9:11:12 x 14 SD: 21.6127 cents 8:9:11:12 x 14:16 SD: 10.8013 cents 12:14:16:18:20:21:24 S SD: 10.7887 cents 14:16:19:21:24:25:28 SD: 6.6608 cents 22:25:29:33:37:39:44 SD: 4.9175 cents 23:26:31:35:39:41:46 SD: 4.2881 cents 30:34:40:45:51:53:60 SD: 2.6687 cents 32:36:43:48:54:57:64 SD: 2.2239 cents 44:50:59:66:74:78:88 SD: 2.2046 cents 45:51:60:68:76:80:90 SD: 1.9997 cents 53:60:71:80:90:94:106 SD: 1.8671 cents 54:61:72:81:91:96:108 SD: 1.6160 cents 62:70:83:93:105:110:124 SD: 1.0336 cents 68:77:91:102:115:121:136 SD: 0.9182 cents 106:120:142:159:179:188:212 SD: 0.8664 cents 107:121:143:161:181:190:214 SD: 0.5812 cents 139:157:186:209:235:247:278 SD: 0.4377 cents 175:198:234:263:296:311:350 SD: 0.4298 cents 183:207:245:275:309:325:366 SD: 0.3136 cents 236:267:316:355:399:419:472 SD: 0.2575 cents 268:303:359:403:453:476:536 SD: 0.2568 cents 290:328:388:436:490:515:580 SD: 0.1704 cents 419:474:561:630:708:744:838 SD: 0.1536 cents 443:501:593:666:749:787:886 SD: 0.1242 cents 481:544:644:723:813:854:962 SD: 0.1211 cents 558:631:747:839:943:991:1116 SD: 0.0948 cents 594:672:795:893:1004:1055:1188 SD: 0.0858 cents