Scala analysis: CD16_09_Morocco
Les lunes m'ont fait souffrir - 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: 202.715 cents 202.715356 2: 500.695 cents 500.695099 3: 697.085 cents 697.085204 4: 901.681 cents 901.680879 5: 997.363 cents 997.363045 6: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 202.6370 cents 202.6370 1: 202.7154 cents 202.7154 2: 297.9797 cents 297.9797 3: 196.3901 cents 196.3901 4: 204.5957 cents 204.5957 5: 95.6822 cents 95.6822 6: 202.6370 cents 202.6370
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 95.68217 cents 1: 1 196.39011 cents 1: 1 202.63695 cents 1: 1 202.71536 cents 1: 1 204.59568 cents 1: 1 297.97974 cents 2: 1 298.31912 cents 2: 1 300.27784 cents 2: 1 400.98578 cents 2: 1 405.35231 cents 2: 1 494.36985 cents 2: 1 500.69510 cents 3: 1 496.66795 cents 3: 1 501.03448 cents 3: 1 502.91480 cents 3: 1 697.08520 cents 3: 1 698.96552 cents 3: 1 703.33205 cents 4: 1 699.30490 cents 4: 1 705.63015 cents 4: 1 794.64769 cents 4: 1 799.01422 cents 4: 1 899.72216 cents 4: 1 901.68088 cents 5: 1 902.02026 cents 5: 1 995.40432 cents 5: 1 997.28464 cents 5: 1 997.36305 cents 5: 1 1003.60989 cents 5: 1 1104.31783 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 : 202.7 500.7 697.1 901.7 997.4 1200.0 202.7 : 298.0 494.4 699.0 794.6 997.3 1200.0 500.7 : 196.4 401.0 496.7 699.3 902.0 1200.0 697.1 : 204.6 300.3 502.9 705.6 1003.6 1200.0 901.7 : 95.7 298.3 501.0 799.0 995.4 1200.0 997.4 : 202.6 405.4 703.3 899.7 1104.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 95.6822 .. 297.9797 cents 202.29758 cents 95.68217 cents 2: 298.3191 .. 500.6951 cents 202.37598 cents 0.33938 cents 3: 496.6679 .. 703.3321 cents 206.66411 cents -4.02715 cents 4: 699.3049 .. 901.6809 cents 202.37598 cents -4.02715 cents 5: 902.0203 .. 1104.3178 cents 202.29758 cents 0.33938 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 95.68217 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 297.97974 cents Average / Smallest step : 2.090254 Largest / Average step : 1.489899 Largest / Smallest step : 3.114266 Median interval of one step : 202.67616 cents, amount: 0 Least squares average step : 209.76813 cents, oct.: 1258.60879 cents Scale is not proper Step pattern alph. order: ABCDEF Step pattern size order : DFBEAC Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 0.33938 cents Scale diversity : 1.341959 Lumma stability : 0.160036 Lumma impropriety factor : 0.006712 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 : 0.07840 cents Number of recognisable fifths : 5, average 700.8636 cents Formal octave complements present : 1 = 16.6667% Limited inverse transpositions with margin 200.4173 cents: 3 -- Rational properties --
FIT/MODE
6: 1 1 1 1 1 1 SP B ME I SD: 70.6144 c. M: 101.6809 c. Whole-tone, Messiaen mode 1, Raga Gopriya, Anhemitonic Hexatonic 7: 1 2 1 1 1 1 P M ME SD: 26.6160 c. M: 44.5380 c. 12: 2 3 2 2 1 2 P G D3 SD: 2.0869 c. M:-2.9148 c. Mixolydian Hexatonic, P'yongjo: Korea, Yosen: Japan, Raga Darbar, Narayani, Suposhini, Andolika, Gorakh Kalyan, Rakta Hauns 77: 13 19 13 13 6 13 P G D3 SD: 2.1076 c. M:-4.2135 c. 89: 15 22 15 15 7 15 P G D3 SD: 1.9512 c. M:-4.0384 c. 100: 17 25 16 17 8 17 N SD: 1.7528 c. M:-3.3049 c. 112: 19 28 18 19 9 19 N SD: 1.4796 c. M:-2.8763 c. 117: 20 29 19 20 9 20 N SD: 1.6545 c. M: 2.4913 c. 124: 21 31 20 21 10 21 N SD: 1.2867 c. M:-2.5307 c. 129: 22 32 21 22 10 22 N SD: 1.3678 c. M: 2.0142 c. 136: 23 34 22 23 11 23 N SD: 1.1557 c. M:-2.2461 c. 141: 24 35 23 24 11 24 N SD: 1.1447 c. M: 1.6184 c. 148: 25 37 24 25 12 25 N SD: 1.0728 c. M:-2.0076 c. 153: 26 38 25 26 12 26 N SD: 0.9743 c. M: 1.2846 c. 165: 28 41 27 28 13 28 N SD: 0.8495 c. M:-1.1231 c. 177: 30 44 29 30 14 30 N SD: 0.7648 c. M:-1.2199 c. 189: 32 47 31 32 15 32 N SD: 0.7150 c. M:-1.3275 c. 201: 34 50 33 34 16 34 N SD: 0.6938 c. M:-1.4223 c. 314: 53 78 51 54 25 53 N SD: 0.6423 c. M: 1.5438 c. 326: 55 81 53 56 26 55 N SD: 0.5827 c. M: 1.3797 c. 331: 56 82 54 57 26 56 N SD: 0.6454 c. M:-1.0382 c. 338: 57 84 55 58 27 57 N SD: 0.5354 c. M: 1.2272 c. 343: 58 85 56 59 27 58 N SD: 0.5680 c. M:-0.9430 c. 350: 59 87 57 60 28 59 N SD: 0.5003 c. M: 1.0852 c. 355: 60 88 58 61 28 60 N SD: 0.5003 c. M:-0.8543 c. 362: 61 90 59 62 29 61 N SD: 0.4772 c. M: 0.9526 c. 367: 62 91 60 63 29 62 N SD: 0.4426 c. M:-0.7714 c. 374: 63 93 61 64 30 63 N SD: 0.4651 c. M: 0.8285 c. 379: 64 94 62 65 30 64 N SD: 0.3955 c. M:-0.6938 c. 391: 66 97 64 67 31 66 N SD: 0.3601 c. M:-0.6209 c. 403: 68 100 66 69 32 68 N SD: 0.3368 c. M:-0.5524 c. 415: 70 103 68 71 33 70 N SD: 0.3258 c. M:-0.4878 c. 427: 72 106 70 73 34 72 N SD: 0.3261 c. M: 0.4609 c. 491: 83 122 80 84 39 83 N SD: 0.2863 c. M: 0.5475 c. 503: 85 125 82 86 40 85 N SD: 0.2392 c. M: 0.4649 c. 515: 87 128 84 88 41 87 N SD: 0.1984 c. M: 0.3862 c. 527: 89 131 86 90 42 89 N SD: 0.1662 c. M: 0.3110 c. 539: 91 134 88 92 43 91 N SD: 0.1454 c. M: 0.2392 c. 551: 93 137 90 94 44 93 N SD: 0.1391 c. M:-0.2123 c. 1095: 185 272 179 187 87 185 N SD: 0.1246 c. M:-0.2369 c. 1107: 187 275 181 189 88 187 N SD: 0.1083 c. M:-0.2161 c. 1114: 188 277 182 190 89 188 N SD: 0.1415 c. M:-0.2026 c. 1119: 189 278 183 191 89 189 N SD: 0.0954 c. M:-0.1958 c. 1131: 191 281 185 193 90 191 N SD: 0.0869 c. M:-0.1759 c. 1143: 193 284 187 195 91 193 N SD: 0.0838 c. M:-0.1564 c. 1155: 195 287 189 197 92 195 N SD: 0.0863 c. M:-0.1373 c. 1682: 284 418 275 287 134 284 N SD: 0.0847 c. M:-0.1372 c. 1694: 286 421 277 289 135 286 N SD: 0.0839 c. M:-0.1313 c. 1930: 326 479 316 329 154 326 N SD: 0.0993 c. M: 0.1770 c. 1942: 328 482 318 331 155 328 N SD: 0.0993 c. M: 0.1802 c. 2059: 348 511 337 351 164 348 N SD: 0.0959 c. M: 0.1799 c. 2071: 350 514 339 353 165 350 N SD: 0.0887 c. M: 0.1636 c. 2083: 352 517 341 355 166 352 N SD: 0.0828 c. M: 0.1475 c. 2095: 354 520 343 357 167 354 N SD: 0.0784 c. M: 0.1315 c. 2107: 356 523 345 359 168 356 N SD: 0.0758 c. M: 0.1158 c. 2119: 358 526 347 361 169 358 N SD: 0.0750 c. M: 0.1235 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x 4 S SD: 2.4349 cents 3 x 4 x 5 x 6 S SD: 5.8412 cents 4 x 5:6 x 7:8 S SD: 29.4970 cents 5:6:7 x 8:9:10 S SD: 33.2257 cents 6:7:8:9:10:11:12 H SD: 14.0937 cents 7:8:9:10:12 x 14 S SD: 22.3064 cents 8:9:11:12:13:14:16 SD: 14.0850 cents 9:10:12:13:15:16:18 SD: 11.0272 cents 10:11:13:15:17:18:20 SD: 10.9334 cents 14:16:19:21:24:25:28 SD: 8.5758 cents 15:17:20:22:25:27:30 SD: 7.5831 cents 16:18:21:24:27:28:32 S SD: 6.9759 cents 18:20:24:27:30:32:36 S SD: 4.5491 cents 24:27:32:36:40:43:48 SD: 3.6555 cents 32:36:43:48:54:57:64 SD: 2.1357 cents 41:46:55:61:69:73:82 SD: 2.1226 cents 48:54:64:72:81:85:96 SD: 1.7831 cents 54:61:72:81:91:96:108 SD: 1.7045 cents 57:64:76:85:96:101:114 SD: 1.5727 cents 63:71:84:94:106:112:126 SD: 1.1318 cents 72:81:96:108:121:128:144 SD: 1.0868 cents 81:91:108:121:136:144:162 SD: 0.9979 cents 89:100:119:133:150:158:178 SD: 0.8543 cents 95:107:127:142:160:169:190 SD: 0.6690 cents 113:127:151:169:190:201:226 SD: 0.4110 cents 200:225:267:299:337:356:400 SD: 0.4049 cents 208:234:278:311:350:370:416 SD: 0.3649 cents 218:245:291:326:367:388:436 SD: 0.2018 cents 313:352:418:468:527:557:626 SD: 0.1738 cents 331:372:442:495:557:589:662 SD: 0.1677 cents 379:426:506:567:638:674:758 SD: 0.1515 cents 426:479:569:637:717:758:852 SD: 0.1422 cents 474:533:633:709:798:843:948 SD: 0.1196 cents 587:660:784:878:988:1044:1174 SD: 0.1193 cents 597:671:797:893:1005:1062:1194 SD: 0.1101 cents