Scala analysis: CD13_04_Iraq
Suite - Ensemble de Muhammad Al-Qubbbânjî (dukah, Iraq)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 166.815 cents 166.814872 2: 362.675 cents 362.675361 3: 564.790 cents 564.789742 4: 700.755 cents 700.755344 5: 846.844 cents 846.844107 6: 1061.359 cents 1061.358964 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 138.6410 cents 138.6410 1: 166.8149 cents 166.8149 2: 195.8605 cents 195.8605 3: 202.1144 cents 202.1144 4: 135.9656 cents 135.9656 5: 146.0888 cents 146.0888 6: 214.5149 cents 214.5149 7: 138.6410 cents 138.6410
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 135.96560 cents 1: 1 138.64104 cents 1: 1 146.08876 cents 1: 1 166.81487 cents 1: 1 195.86049 cents 1: 1 202.11438 cents 1: 1 214.51486 cents 2: 1 282.05436 cents 2: 1 305.45591 cents 2: 1 338.07998 cents 2: 1 353.15589 cents 2: 1 360.60362 cents 2: 1 362.67536 cents 2: 1 397.97487 cents 3: 1 484.16875 cents 3: 1 496.56922 cents 3: 1 499.24466 cents 3: 1 501.31640 cents 3: 1 519.97077 cents 3: 1 533.94047 cents 3: 1 564.78974 cents 4: 1 635.21026 cents 4: 1 666.05953 cents 4: 1 680.02923 cents 4: 1 698.68360 cents 4: 1 700.75534 cents 4: 1 703.43078 cents 4: 1 715.83125 cents 5: 1 802.02513 cents 5: 1 837.32464 cents 5: 1 839.39638 cents 5: 1 846.84411 cents 5: 1 861.92002 cents 5: 1 894.54409 cents 5: 1 917.94564 cents 6: 1 985.48514 cents 6: 1 997.88562 cents 6: 1 1004.13951 cents 6: 1 1033.18513 cents 6: 1 1053.91124 cents 6: 1 1061.35896 cents 6: 1 1064.03440 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 7.00000 = 7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 166.8 362.7 564.8 700.8 846.8 1061.4 1200.0 166.8 : 195.9 398.0 533.9 680.0 894.5 1033.2 1200.0 362.7 : 202.1 338.1 484.2 698.7 837.3 1004.1 1200.0 564.8 : 136.0 282.1 496.6 635.2 802.0 997.9 1200.0 700.8 : 146.1 360.6 499.2 666.1 861.9 1064.0 1200.0 846.8 : 214.5 353.2 520.0 715.8 917.9 1053.9 1200.0 1061.4: 138.6 305.5 501.3 703.4 839.4 985.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 135.9656 .. 214.5149 cents 78.54926 cents 135.96560 cents 2: 282.0544 .. 397.9749 cents 115.92051 cents 67.53951 cents 3: 484.1687 .. 564.7897 cents 80.62100 cents 86.19388 cents 4: 635.2103 .. 715.8313 cents 80.62100 cents 70.42052 cents 5: 802.0251 .. 917.9456 cents 115.92051 cents 86.19388 cents 6: 985.4851 .. 1064.0344 cents 78.54926 cents 67.53951 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 135.96560 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 214.51486 cents Average / Smallest step : 1.260823 Largest / Average step : 1.251337 Largest / Smallest step : 1.577714 Median interval of one step : 166.81487 cents, amount: 1 Least squares average step : 174.22808 cents, oct.: 1219.59653 cents Scale is strictly proper Step pattern alph. order: ABCDEFG Step pattern size order : DEFACGB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 67.53951 cents Scale diversity : 1.494548 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.541515 Rothenberg efficiency : 0.285714 redundancy: 0.714286 Efficiency x scale size : 2.000000 Number of different interval sizes : 42 = 7.00000 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 7.00000 = 7 Median interval variety : 7 Lowest interval variety : 7 Smallest interval difference : 2.07174 cents Number of recognisable fifths : 4, average 704.6752 cents Number of appreciable fifths : 3, average 700.9566 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 14.2857% -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 24.9915 c. M: 50.5040 c. Lebeng 9: 1 2 1 1 1 2 1 P M ME I SD: 31.3693 c. M: 46.8441 c. 10: 1 2 2 1 1 2 1 P D3 S SD: 24.5043 c. M: 46.8149 c. 13: 2 2 2 2 1 2 2 SP M ME S SD: 24.7080 c. M: 45.9743 c. Glacial-7, Lobonian 14: 2 2 3 1 2 2 2 P T3 SD: 20.9118 c. M:-35.2103 c. 16: 2 3 2 2 2 3 2 SP M ME I SD: 21.6709 c. M: 39.7897 c. Armodue-7, Antidorian 17: 2 3 3 2 2 3 2 SP D3 S SD: 10.5887 c. M: 25.6384 c. 20: 3 3 3 3 2 4 2 SP D3 S SD: 14.9295 c. M: 24.7897 c. 21: 3 3 4 2 3 4 2 SP T3 SD: 14.0591 c. M:-24.3553 c. 23: 3 4 4 2 3 4 3 SP SD: 12.9109 c. M: 22.4945 c. 24: 3 4 4 3 3 4 3 SP D3 S SD: 10.7018 c. M: 16.8149 c. Maqam Sikah (Segah), Neutral Diatonic Hypolydian 27: 4 4 5 3 3 5 3 SP SD: 8.2872 c. M:-12.9880 c. 34: 5 5 6 4 4 6 4 SP SD: 5.6157 c. M: 9.7342 c. 43: 6 7 7 5 5 8 5 SP SD: 4.5943 c. M: 9.6348 c. 44: 6 7 8 5 5 8 5 SP SD: 5.5524 c. M:-8.3356 c. 51: 7 8 9 6 6 9 6 SP SD: 4.3420 c. M: 9.7342 c. 55: 8 9 9 6 7 10 6 SP SD: 5.5633 c. M:-8.2337 c. 57: 8 9 10 6 7 10 7 SP SD: 4.9780 c. M: 8.7274 c. 60: 8 10 10 7 7 11 7 SP SD: 4.2393 c. M: 6.8441 c. 70: 10 11 12 8 8 13 8 SP SD: 3.4393 c. M: 6.8441 c. 72: 10 12 12 8 9 13 8 SP SD: 2.8829 c. M:-5.3077 c. 77: 11 12 13 9 9 14 9 SP SD: 3.4669 c. M: 5.2857 c. 79: 11 13 13 9 10 14 9 SP SD: 2.1854 c. M:-3.7888 c. 106: 15 17 18 12 13 19 12 SP SD: 1.8775 c. M:-2.9964 c. 113: 16 18 19 13 14 20 13 SP SD: 1.8420 c. M:-3.0966 c. 115: 16 19 19 13 14 21 13 SP SD: 1.7897 c. M:-2.9889 c. 123: 17 20 21 14 15 22 14 SP SD: 1.5002 c. M:-2.0557 c. 149: 21 24 25 17 18 27 17 SP SD: 1.2495 c. M:-2.3126 c. 166: 23 27 28 19 20 30 19 SP SD: 0.9010 c. M:-1.2916 c. 245: 34 40 41 28 30 44 28 SP SD: 0.8514 c. M: 1.5244 c. 259: 36 42 44 29 32 46 30 SP SD: 0.7892 c. M: 1.2854 c. 295: 41 48 50 33 36 53 34 SP SD: 0.6183 c. M: 1.0943 c. 337: 47 55 57 38 41 60 39 SP SD: 0.7044 c. M:-1.3824 c. 344: 48 56 58 39 42 61 40 SP SD: 0.5564 c. M: 0.8938 c. 380: 53 62 64 43 46 68 44 SP SD: 0.4183 c. M:-0.5535 c. 397: 55 65 67 45 48 71 46 SP SD: 0.4121 c. M: 0.5680 c. 404: 56 66 68 46 49 72 47 SP SD: 0.4757 c. M: 0.9629 c. 459: 64 75 77 52 56 82 53 SP SD: 0.3481 c. M:-0.7233 c. 476: 66 78 80 54 58 85 55 SP SD: 0.2288 c. M: 0.4283 c. 510: 71 83 86 58 62 91 59 SP SD: 0.2471 c. M:-0.4211 c. 625: 87 102 105 71 76 112 72 SP SD: 0.2289 c. M:-0.4010 c. 771: 107 126 130 87 94 138 89 SP SD: 0.2021 c. M: 0.3662 c. 805: 112 131 136 91 98 144 93 SP SD: 0.2006 c. M: 0.4393 c. 856: 119 140 144 97 104 153 99 SP SD: 0.1927 c. M:-0.4088 c. 884: 123 144 149 100 108 158 102 SP SD: 0.1906 c. M: 0.3029 c. 969: 135 158 163 110 118 173 112 SP SD: 0.1897 c. M:-0.3678 c. 986: 137 161 166 112 120 176 114 SP SD: 0.1399 c. M:-0.2589 c. 1115: 155 182 188 126 136 199 129 SP SD: 0.1367 c. M:-0.2327 c. 1264: 176 206 213 143 154 226 146 SP SD: 0.1186 c. M:-0.2737 c. 1281: 178 209 216 145 156 229 148 SP SD: 0.0714 c. M: 0.1461 c. 1740: 242 284 293 197 212 311 201 SP SD: 0.0567 c. M:-0.0833 c. 2382: 331 389 401 270 290 426 275 SP SD: 0.0529 c. M:-0.1020 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 0.5998 cents 3 x x 4 x 5 x 6 S SD: 25.5217 cents 4 x 5 x 6 x 7:8 S SD: 23.8780 cents 5 x 6:7 x 8:9:10 S SD: 14.8874 cents 6 x 7:8:9:10:11:12 S SD: 20.5386 cents 7:8:9:10 x 11:13:14 SD: 21.3505 cents 8:9:10:11:12:13:15:16 SD: 7.6689 cents 18:20:22:25:27:29:33:36 SD: 4.7064 cents 26:29:32:36:39:42:48:52 SD: 3.9983 cents 30:33:37:42:45:49:55:60 SD: 3.0948 cents 38:42:47:53:57:62:70:76 SD: 2.0763 cents 52:57:64:72:78:85:96:104 SD: 1.3619 cents 60:66:74:83:90:98:111:120 SD: 0.8314 cents 78:86:96:108:117:127:144:156 SD: 0.7430 cents 98:108:121:136:147:160:181:196 SD: 0.6226 cents 130:143:160:180:195:212:240:260 SD: 0.5889 cents 138:152:170:191:207:225:255:276 SD: 0.4892 cents 168:185:207:233:252:274:310:336 SD: 0.3439 cents 176:194:217:244:264:287:325:352 SD: 0.3341 cents 228:251:281:316:342:372:421:456 SD: 0.2475 cents 317:349:391:439:475:517:585:634 SD: 0.2207 cents 347:382:428:481:520:566:641:694 SD: 0.2144 cents 365:402:450:506:547:595:674:730 SD: 0.1891 cents 407:448:502:564:610:664:751:814 SD: 0.1862 cents 415:457:512:575:622:677:766:830 SD: 0.1616 cents 425:468:524:589:637:693:785:850 SD: 0.1471 cents 485:534:598:672:727:791:895:970 SD: 0.1056 cents 493:543:608:683:739:804:910:986 SD: 0.1033 cents 583:642:719:808:874:951:1076:1166 SD: 0.0989 cents