Scala analysis: CD16_16_Morocco
La pléïade s'est détournée / Comment se reposerait-il ? - 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: 212.913 cents 212.912598 2: 418.824 cents 418.824395 3: 507.437 cents 507.437216 4: 714.391 cents 714.390746 5: 911.472 cents 911.471529 6: 1012.995 cents 1012.995494 7: 1103.007 cents 1103.007447 8: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 96.9926 cents 96.9926 1: 212.9126 cents 212.9126 2: 205.9118 cents 205.9118 3: 88.6128 cents 88.6128 4: 206.9535 cents 206.9535 5: 197.0808 cents 197.0808 6: 101.5240 cents 101.5240 7: 90.0120 cents 90.0120 8: 96.9926 cents 96.9926
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 88.61282 cents 1: 1 90.01195 cents 1: 1 96.99255 cents 1: 1 101.52397 cents 1: 1 197.08078 cents 1: 1 205.91180 cents 1: 1 206.95353 cents 1: 1 212.91260 cents 2: 1 187.00451 cents 2: 1 191.53592 cents 2: 1 294.52462 cents 2: 1 295.56635 cents 2: 1 298.60475 cents 2: 1 309.90515 cents 2: 1 404.03431 cents 2: 1 418.82439 cents 3: 1 288.52847 cents 3: 1 388.61670 cents 3: 1 399.91710 cents 3: 1 492.64713 cents 3: 1 501.47815 cents 3: 1 505.55828 cents 3: 1 507.43722 cents 3: 1 515.81695 cents 4: 1 485.60925 cents 4: 1 501.44107 cents 4: 1 594.17110 cents 4: 1 595.57023 cents 4: 1 604.42977 cents 4: 1 605.82890 cents 4: 1 698.55893 cents 4: 1 714.39075 cents 5: 1 684.18305 cents 5: 1 692.56278 cents 5: 1 694.44172 cents 5: 1 698.52185 cents 5: 1 707.35287 cents 5: 1 800.08290 cents 5: 1 811.38330 cents 5: 1 911.47153 cents 6: 1 781.17561 cents 6: 1 795.96569 cents 6: 1 890.09485 cents 6: 1 901.39525 cents 6: 1 904.43365 cents 6: 1 905.47538 cents 6: 1 1008.46408 cents 6: 1 1012.99549 cents 7: 1 987.08740 cents 7: 1 993.04647 cents 7: 1 994.08820 cents 7: 1 1002.91922 cents 7: 1 1098.47603 cents 7: 1 1103.00745 cents 7: 1 1109.98805 cents 7: 1 1111.38718 cents Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 8.00000 = 8
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 212.9 418.8 507.4 714.4 911.5 1013.0 1103.0 1200.0 212.9 : 205.9 294.5 501.5 698.6 800.1 890.1 987.1 1200.0 418.8 : 88.6 295.6 492.6 594.2 684.2 781.2 994.1 1200.0 507.4 : 207.0 404.0 505.6 595.6 692.6 905.5 1111.4 1200.0 714.4 : 197.1 298.6 388.6 485.6 698.5 904.4 993.0 1200.0 911.5 : 101.5 191.5 288.5 501.4 707.4 796.0 1002.9 1200.0 1013.0: 90.0 187.0 399.9 605.8 694.4 901.4 1098.5 1200.0 1103.0: 97.0 309.9 515.8 604.4 811.4 1008.5 1110.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 88.6128 .. 212.9126 cents 124.29978 cents 88.61282 cents 2: 187.0045 .. 418.8244 cents 231.81989 cents -25.90809 cents 3: 288.5285 .. 515.8169 cents 227.28848 cents -130.29592 cents 4: 485.6093 .. 714.3907 cents 228.78149 cents -30.20769 cents 5: 684.1831 .. 911.4715 cents 227.28848 cents -30.20769 cents 6: 781.1756 .. 1012.9955 cents 231.81989 cents -130.29592 cents 7: 987.0874 .. 1111.3872 cents 124.29978 cents -25.90809 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 88.61282 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 212.91260 cents Average / Smallest step : 1.692757 Largest / Average step : 1.419417 Largest / Smallest step : 2.402729 Median interval of one step : 149.30237 cents, amount: 0 Least squares average step : 163.66088 cents, oct.: 1309.28701 cents Scale is not proper Step pattern alph. order: ABCDEFGH Step pattern size order : HFAGEDBC Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 0.03708 cents Scale diversity : 1.405803 Lumma stability : 0.147688 Lumma impropriety factor : 0.310686 Rothenberg efficiency : 0.250000 redundancy: 0.750000 Efficiency x scale size : 2.000000 Number of different interval sizes : 56 = 8.00000 / class Number of one step interval sizes : 8 Highest interval variety : 8 Mean interval variety : 8.00000 = 8 Median interval variety : 8 Lowest interval variety : 8 Smallest interval difference : 0.03708 cents Number of recognisable fifths : 6, average 700.9715 cents Number of appreciable fifths : 5, average 698.2876 cents Formal octave complements present : 1 = 12.5000% Limited inverse transpositions with margin 227.2885 cents: 5 -- Rational properties --
FIT/MODE
8: 1 2 0 2 1 1 0 1 N T3 SD: 41.5447 c. M: 62.9126 c. 9: 2 1 1 1 2 1 0 1 N D3 SD: 36.8633 c. M:-53.7541 c. 10: 2 1 1 2 1 1 1 1 P D3 S SD: 40.9639 c. M: 71.4715 c. 11: 2 2 1 2 1 1 1 1 N SD: 29.2091 c. M:-49.2456 c. 12: 2 2 1 2 2 1 1 1 N D3 SD: 11.6888 c. M: 18.8244 c. Genus diatonicum, Dominant Bebop, Raga Khamaj, Alhaiya Bilaval, Bihagara, Desh Malhar (Des), Devagandhari, Lankeshree, Malagunji, Nat Bihag, Nat Malhar, Maqam Shawq Awir, Gregorian nr.6, Chinese Eight-Tone, Rast: Greece, Ionian/Mixolydian mixed 25: 4 5 2 4 4 2 2 2 N SD: 11.6803 c. M: 20.9126 c. 26: 5 4 2 5 4 2 2 2 N SD: 11.5785 c. M:-24.0708 c. 28: 5 5 2 5 4 3 2 2 N SD: 10.2852 c. M:-15.5759 c. 33: 6 6 2 6 5 3 2 3 N SD: 9.2399 c. M:-17.5392 c. 34: 6 6 2 6 6 3 2 3 N SD: 7.9167 c. M: 13.3196 c. 37: 7 6 3 6 6 3 3 3 N SD: 7.1472 c. M:-14.1144 c. 38: 7 6 3 7 6 3 3 3 N SD: 6.2438 c. M:-11.9250 c. 40: 7 7 3 7 6 4 3 3 N SD: 5.8891 c. M: 11.4715 c. 45: 8 8 3 8 7 4 3 4 N SD: 5.1299 c. M: 9.6741 c. 49: 9 8 4 8 8 4 4 4 N SD: 5.4297 c. M: 8.9139 c. 50: 9 8 4 9 8 4 4 4 N SD: 4.9522 c. M: 10.8244 c. 52: 9 9 4 9 8 5 4 4 N SD: 4.9923 c. M: 11.4715 c. 54: 10 9 4 9 9 5 4 4 N SD: 5.8459 c. M:-9.3096 c. 57: 10 10 4 10 9 5 4 5 N SD: 4.0371 c. M: 8.2706 c. 62: 11 11 4 11 10 5 5 5 N SD: 3.8012 c. M:-6.9821 c. 66: 12 11 5 11 11 6 5 5 N SD: 4.0090 c. M:-6.0835 c. 69: 12 12 5 12 11 6 5 6 N SD: 4.3950 c. M: 7.3553 c. 71: 13 12 5 12 12 6 5 6 N SD: 3.5867 c. M:-6.8057 c. 75: 13 13 6 13 12 6 6 6 N SD: 3.7184 c. M:-5.6093 c. 78: 14 13 6 13 13 7 6 6 N SD: 3.6197 c. M: 6.6984 c. 83: 15 14 6 14 14 7 6 7 N SD: 3.0076 c. M: 5.9570 c. 88: 16 15 6 15 15 7 7 7 N SD: 3.5663 c. M: 5.2998 c. 89: 16 15 7 15 15 7 7 7 N SD: 2.9961 c. M:-5.3824 c. 94: 17 16 7 16 15 8 7 8 N SD: 3.6361 c. M: 5.1351 c. 95: 17 16 7 16 16 8 7 8 N SD: 3.3142 c. M: 7.0223 c. 96: 17 17 7 16 16 8 7 8 N SD: 3.1198 c. M:-6.1756 c. 97: 17 17 7 17 16 8 7 8 N SD: 2.2854 c. M:-3.9924 c. 101: 18 17 8 17 17 8 8 8 N SD: 2.4701 c. M:-3.4539 c. 109: 19 19 8 19 18 9 8 9 N SD: 1.8138 c. M: 3.7383 c. 111: 20 19 8 19 18 10 8 9 N SD: 2.2841 c. M: 3.3634 c. 121: 21 21 9 21 20 10 9 10 N SD: 2.1611 c. M: 4.6481 c. 123: 22 21 9 21 20 11 9 10 N SD: 1.8888 c. M: 4.1545 c. 128: 23 22 9 22 21 11 10 10 N SD: 2.1448 c. M:-3.2426 c. 134: 24 23 10 23 22 11 10 11 N SD: 1.8963 c. M:-3.0105 c. 140: 25 24 10 24 23 12 11 11 N SD: 2.0373 c. M: 2.9622 c. 141: 25 24 11 24 23 12 11 11 N SD: 1.7998 c. M:-3.3755 c. 146: 26 25 11 25 24 12 11 12 N SD: 1.2941 c. M:-2.1518 c. 163: 29 28 12 28 27 14 12 13 N SD: 1.3108 c. M:-2.9554 c. 175: 31 30 13 30 29 15 13 14 N SD: 0.9147 c. M:-1.8616 c. 220: 39 38 16 38 36 19 16 18 N SD: 0.8367 c. M:-1.5500 c. 232: 41 40 17 40 38 20 17 19 N SD: 0.7853 c. M: 1.2833 c. 237: 42 41 17 41 39 20 18 19 N SD: 0.7328 c. M:-1.4288 c. 270: 48 46 20 47 44 23 20 22 N SD: 0.7145 c. M:-1.1648 c. 309: 55 53 23 53 51 26 23 25 N SD: 0.7265 c. M:-1.3006 c. 321: 57 55 24 55 53 27 24 26 N SD: 0.4532 c. M:-0.9740 c. 333: 59 57 25 57 55 28 25 27 N SD: 0.5312 c. M: 0.8772 c. 383: 68 66 28 66 63 32 29 31 N SD: 0.5176 c. M:-1.0189 c. 412: 73 71 30 71 68 35 31 33 N SD: 0.5745 c. M:-0.8760 c. 423: 75 73 31 73 69 36 32 34 N SD: 0.5604 c. M:-1.0338 c. 435: 77 75 32 75 71 37 33 35 N SD: 0.5383 c. M: 1.1267 c. 445: 79 76 33 77 73 38 33 36 N SD: 0.4855 c. M:-0.9371 c. 469: 83 81 34 81 77 40 35 38 N SD: 0.5425 c. M: 0.8274 c. 470: 83 81 35 81 77 40 35 38 N SD: 0.5081 c. M: 0.9977 c. 487: 86 84 36 84 80 41 37 39 N SD: 0.4994 c. M: 1.0029 c. 492: 87 85 36 85 81 41 37 40 N SD: 0.5644 c. M: 0.8004 c. 494: 88 84 37 85 81 42 37 40 N SD: 0.5227 c. M: 1.0106 c. 495: 88 85 36 86 81 42 37 40 N SD: 0.4731 c. M: 0.7705 c. 496: 88 85 37 85 82 42 37 40 N SD: 0.4851 c. M:-0.7142 c. 507: 90 87 37 88 83 43 38 41 N SD: 0.3712 c. M: 0.9283 c. 541: 96 93 40 93 89 46 40 44 N SD: 0.4044 c. M:-0.6829 c. 546: 97 94 40 94 90 46 41 44 N SD: 0.4423 c. M:-0.9558 c. 553: 98 95 41 95 91 47 41 45 N SD: 0.3507 c. M: 0.6566 c. 558: 99 96 41 96 92 47 42 45 N SD: 0.2834 c. M:-0.5304 c. 608: 108 104 45 105 100 51 46 49 N SD: 0.3025 c. M: 0.4955 c. 653: 116 112 48 113 107 55 49 53 N SD: 0.3003 c. M:-0.4638 c. 665: 118 114 49 115 109 56 50 54 N SD: 0.3334 c. M: 0.6647 c. 682: 121 117 50 118 112 58 51 55 N SD: 0.3115 c. M: 0.6923 c. 719: 128 123 53 124 118 61 54 58 N SD: 0.2777 c. M:-0.7174 c. 731: 130 125 54 126 120 62 55 59 N SD: 0.2756 c. M:-0.4937 c. 756: 134 130 56 130 124 64 57 61 N SD: 0.2743 c. M:-0.4993 c. 771: 137 132 57 133 127 65 58 62 N SD: 0.3107 c. M:-0.5907 c. 778: 138 134 57 134 128 66 58 63 N SD: 0.3073 c. M:-0.7129 c. 783: 139 134 58 135 129 66 59 63 N SD: 0.2810 c. M:-0.4408 c. 790: 140 136 58 136 130 67 59 64 N SD: 0.2620 c. M: 0.4667 c. 816: 145 140 60 141 134 69 61 66 N SD: 0.2357 c. M:-0.3227 c. 828: 147 142 61 143 136 70 62 67 N SD: 0.1081 c. M: 0.1908 c. 1584: 281 272 117 273 260 134 119 128 N SD: 0.0861 c. M:-0.1385 c. 1759: 312 302 130 303 289 149 132 142 N SD: 0.0861 c. M:-0.1239 c. 2017: 358 346 149 348 331 171 151 163 N SD: 0.0899 c. M:-0.1924 c. 2029: 360 348 150 350 333 172 152 164 N SD: 0.0636 c. M:-0.1144 c. 2266: 402 389 167 391 372 192 170 183 N SD: 0.0668 c. M: 0.1115 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x x 4 S SD: 6.2179 cents 3 x x 4 x 5 x x 6 S SD: 9.5645 cents 4 x 5 x 6 x 7 x 8 S SD: 14.0591 cents 5:6 x 7 x 8:9 x 10 S SD: 32.1077 cents 6:7 x 8:9:10:11 x 12 S SD: 12.0324 cents 7:8:9 x 11:12 x 13:14 SD: 13.6267 cents 8:9:10:11:12 x 14:15:16 S SD: 10.4845 cents 10:11:13 x 15:17:18:19:20 SD: 8.8548 cents 13:15 x 17:20:22:23:25:26 SD: 10.6261 cents 14:16:18:19:21:24:25:26:28 SD: 6.5404 cents 15:17:19:20:23:25:27:28:30 SD: 5.7427 cents 21:24:27:28:32:36:38:40:42 S SD: 5.1850 cents 23:26:29:31:35:39:41:43:46 SD: 4.1404 cents 26:29:33:35:39:44:47:49:52 SD: 3.9354 cents 29:33:37:39:44:49:52:55:58 SD: 1.9766 cents 45:51:57:60:68:76:81:85:90 SD: 1.9238 cents 47:53:60:63:71:80:84:89:94 SD: 1.7326 cents 55:62:70:74:83:93:99:104:110 SD: 1.2562 cents 62:70:79:83:94:105:111:117:124 SD: 1.1655 cents 84:95:107:113:127:142:151:159:168 SD: 0.9033 cents 92:104:117:123:139:156:165:174:184 SD: 0.7900 cents 114:129:145:153:172:193:205:216:228 SD: 0.7527 cents 117:132:149:157:177:198:210:221:234 SD: 0.6754 cents 121:137:154:162:183:205:217:229:242 SD: 0.5751 cents 146:165:186:196:221:247:262:276:292 SD: 0.5652 cents 147:166:187:197:222:249:264:278:294 SD: 0.4491 cents 153:173:195:205:231:259:275:289:306 SD: 0.4275 cents 176:199:224:236:266:298:316:333:352 SD: 0.2285 cents 329:372:419:441:497:557:591:622:658 SD: 0.1553 cents 358:405:456:480:541:606:643:677:716 SD: 0.1483 cents 405:458:516:543:612:686:727:766:810 SD: 0.1423 cents 505:571:643:677:763:855:907:955:1010 SD: 0.1280 cents 566:640:721:759:855:958:1016:1070:1132 SD: 0.1169 cents 596:674:759:799:900:1009:1070:1127:1192 SD: 0.1135 cents