Scala analysis: CD12_14_Iraq
Neuf rythmes de l'école de Bagdad, Dumbakk - Ensemble de Muhammad Al-Qubbbânjî (unknown maqam, Iraq)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 110.077 cents 110.076923 2: 526.046 cents 526.045599 3: 717.092 cents 717.091743 4: 788.000 cents 788.000000 5: 919.632 cents 919.631579 6: 1007.317 cents 1007.317460 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 192.6825 cents 192.6825 1: 110.0769 cents 110.0769 2: 415.9687 cents 415.9687 3: 191.0461 cents 191.0461 4: 70.9083 cents 70.9083 5: 131.6316 cents 131.6316 6: 87.6859 cents 87.6859 7: 192.6825 cents 192.6825
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 70.90826 cents 1: 1 87.68588 cents 1: 1 110.07692 cents 1: 1 131.63158 cents 1: 1 191.04614 cents 1: 1 192.68254 cents 1: 1 415.96868 cents 2: 1 202.53984 cents 2: 1 219.31746 cents 2: 1 261.95440 cents 2: 1 280.36842 cents 2: 1 302.75946 cents 2: 1 526.04560 cents 2: 1 607.01482 cents 3: 1 290.22572 cents 3: 1 390.44534 cents 3: 1 393.58598 cents 3: 1 412.00000 cents 3: 1 677.92308 cents 3: 1 717.09174 cents 3: 1 718.72814 cents 4: 1 481.27186 cents 4: 1 482.90826 cents 4: 1 522.07692 cents 4: 1 788.00000 cents 4: 1 806.41402 cents 4: 1 809.55466 cents 4: 1 909.77428 cents 5: 1 592.98518 cents 5: 1 673.95440 cents 5: 1 897.24054 cents 5: 1 919.63158 cents 5: 1 938.04560 cents 5: 1 980.68254 cents 5: 1 997.46016 cents 6: 1 784.03132 cents 6: 1 1007.31746 cents 6: 1 1008.95386 cents 6: 1 1068.36842 cents 6: 1 1089.92308 cents 6: 1 1112.31412 cents 6: 1 1129.09174 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 : 110.1 526.0 717.1 788.0 919.6 1007.3 1200.0 110.1 : 416.0 607.0 677.9 809.6 897.2 1089.9 1200.0 526.0 : 191.0 262.0 393.6 481.3 674.0 784.0 1200.0 717.1 : 70.9 202.5 290.2 482.9 593.0 1009.0 1200.0 788.0 : 131.6 219.3 412.0 522.1 938.0 1129.1 1200.0 919.6 : 87.7 280.4 390.4 806.4 997.5 1068.4 1200.0 1007.3: 192.7 302.8 718.7 909.8 980.7 1112.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.9083 .. 415.9687 cents 345.06042 cents 70.90826 cents 2: 202.5398 .. 607.0148 cents 404.47498 cents -213.42884 cents 3: 290.2257 .. 718.7281 cents 428.50242 cents -316.78910 cents 4: 481.2719 .. 909.7743 cents 428.50242 cents -237.45628 cents 5: 592.9852 .. 997.4602 cents 404.47498 cents -316.78910 cents 6: 784.0313 .. 1129.0917 cents 345.06042 cents -213.42884 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 70.90826 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 415.96868 cents Average / Smallest step : 2.417611 Largest / Average step : 2.426484 Largest / Smallest step : 5.866294 Median interval of one step : 131.63158 cents, amount: 1 Least squares average step : 182.19647 cents, oct.: 1275.37530 cents Scale is not proper Step pattern alph. order: ABCDEFG Step pattern size order : CGEADBF Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 3.96868 cents Scale diversity : 1.615550 Lumma stability : 0.118180 Lumma impropriety factor : 0.662434 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 : 1.63640 cents Number of recognisable fifths : 2, average 717.9099 cents Number of appreciable fifths : 0 Formal octave complements present : 1 = 14.2857% -- Rational properties --
FIT/MODE
7: 1 2 1 1 0 1 1 N T3 SD: 44.7599 c. M:-69.1429 c. 8: 1 3 1 0 1 1 1 N SD: 41.0527 c. M:-73.9544 c. 9: 1 3 1 1 1 1 1 N M DE S SD: 31.6018 c. M:-59.3492 c. 10: 1 3 2 1 1 0 2 N SD: 35.4556 c. M:-52.0000 c. 11: 1 4 1 1 1 1 2 N SD: 33.2384 c. M: 62.5463 c. 12: 1 4 2 1 1 1 2 N SD: 15.3762 c. M: 26.0456 c. 18: 2 6 3 1 2 1 3 N SD: 13.3258 c. M:-23.2564 c. 20: 2 7 3 1 2 2 3 N SD: 11.4136 c. M: 19.6316 c. 23: 2 8 4 1 3 1 4 N SD: 11.3080 c. M:-19.4989 c. 25: 2 9 4 1 3 2 4 N SD: 9.7771 c. M: 20.0000 c. 30: 3 10 5 2 3 2 5 N SD: 6.9812 c. M:-12.0000 c. 32: 3 11 5 2 4 2 5 N SD: 7.3138 c. M:-17.8684 c. 37: 3 13 6 2 4 3 6 N SD: 8.0705 c. M: 12.7796 c. 43: 4 15 7 2 5 3 7 N SD: 4.5423 c. M:-8.4897 c. 44: 4 15 7 3 5 3 7 N SD: 5.3026 c. M: 8.0008 c. 50: 5 17 8 3 5 4 8 N SD: 5.1471 c. M:-9.9231 c. 52: 5 18 8 3 6 4 8 N SD: 4.5009 c. M:-8.0672 c. 55: 5 19 9 3 6 4 9 N SD: 2.5619 c. M: 3.6811 c. 87: 8 30 14 5 10 6 14 N SD: 1.9796 c. M:-4.5064 c. 99: 9 34 16 6 11 7 16 N SD: 2.1445 c. M: 4.8335 c. 107: 10 37 17 6 12 8 17 N SD: 1.6341 c. M: 2.9533 c. 119: 11 41 19 7 13 9 19 N SD: 1.3093 c. M: 1.9845 c. 164: 15 57 26 10 18 12 26 N SD: 1.5621 c. M:-2.4386 c. 166: 15 58 26 10 18 12 27 N SD: 1.5208 c. M: 2.4982 c. 174: 16 60 28 10 19 13 28 N SD: 1.3543 c. M: 2.3902 c. 187: 17 65 30 11 20 14 30 N SD: 1.1530 c. M: 1.9845 c. 198: 18 69 31 12 22 14 32 N SD: 1.2151 c. M: 1.9402 c. 206: 19 71 33 12 23 15 33 N SD: 1.0116 c. M: 1.7738 c. 219: 20 76 35 13 24 16 35 N SD: 0.7059 c. M:-1.0411 c. 274: 25 95 44 16 30 20 44 N SD: 0.5399 c. M:-1.1564 c. 326: 30 113 52 19 36 24 52 N SD: 0.6316 c. M:-1.2715 c. 335: 31 116 53 20 37 24 54 N SD: 0.6720 c. M:-0.9679 c. 338: 31 117 54 20 37 25 54 N SD: 0.4375 c. M:-0.9666 c. 372: 34 129 59 22 41 27 60 N SD: 0.6308 c. M: 0.9627 c. 381: 35 132 61 22 42 28 61 N SD: 0.4982 c. M:-1.0185 c. 393: 36 136 63 23 43 29 63 N SD: 0.4498 c. M: 0.8548 c. 449: 41 156 71 27 49 33 72 N SD: 0.4566 c. M: 0.8334 c. 472: 43 164 75 28 52 34 76 N SD: 0.4550 c. M: 0.7549 c. 492: 45 171 78 29 54 36 79 N SD: 0.3316 c. M:-0.7837 c. 504: 46 175 80 30 55 37 81 N SD: 0.3562 c. M: 0.5840 c. 522: 48 181 83 31 57 38 84 N SD: 0.3136 c. M:-0.5057 c. 547: 50 190 87 32 60 40 88 N SD: 0.3691 c. M:-0.4626 c. 577: 53 200 92 34 63 42 93 N SD: 0.3673 c. M: 0.7317 c. 579: 53 201 92 34 64 42 93 N SD: 0.3213 c. M:-0.5757 c. 586: 54 203 93 35 64 43 94 N SD: 0.3090 c. M:-0.5033 c. 591: 54 205 94 35 65 43 95 N SD: 0.2486 c. M: 0.4323 c. 641: 59 222 102 38 70 47 103 N SD: 0.2346 c. M: 0.4428 c. 728: 67 252 116 43 80 53 117 N SD: 0.1868 c. M:-0.3626 c. 860: 79 298 137 51 94 63 138 N SD: 0.1696 c. M:-0.3721 c. 885: 81 307 141 52 97 65 142 N SD: 0.1925 c. M: 0.3095 c. 915: 84 317 146 54 100 67 147 N SD: 0.1859 c. M: 0.2873 c. 947: 87 328 151 56 104 69 152 N SD: 0.1750 c. M:-0.3262 c. 1002: 92 347 160 59 110 73 161 N SD: 0.1725 c. M: 0.2971 c. 1058: 97 367 168 63 116 77 170 N SD: 0.1969 c. M:-0.2798 c. 1066: 98 369 170 63 117 78 171 N SD: 0.1755 c. M: 0.3420 c. 1113: 102 386 177 66 122 81 179 N SD: 0.1466 c. M: 0.3094 c. 1177: 108 408 187 70 129 86 189 N SD: 0.1411 c. M: 0.3543 c. 1220: 112 423 194 72 134 89 196 N SD: 0.1021 c. M:-0.1839 c. 1232: 113 427 196 73 135 90 198 N SD: 0.1209 c. M: 0.2086 c. 1439: 132 499 229 85 158 105 231 N SD: 0.0953 c. M:-0.1738 c. 1451: 133 503 231 86 159 106 233 N SD: 0.0731 c. M:-0.1461 c. 1558: 143 540 248 92 171 114 250 N SD: 0.0604 c. M:-0.1280 c. 2080: 191 721 331 123 228 152 334 N SD: 0.0675 c. M:-0.1154 c. 2135: 196 740 340 126 234 156 343 N SD: 0.0756 c. M: 0.1043 c. 2149: 197 745 342 127 236 157 345 N SD: 0.0670 c. M: 0.1071 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x x 4 S SD: 7.5684 cents 3 x 4 x x 5 x 6 S SD: 15.0119 cents 4 x 5:6 x x 7:8 S SD: 36.4312 cents 5:6:7 x 8 x 9:10 S SD: 42.9933 cents 6:7:8:9 x 10:11:12 S SD: 28.1906 cents 7:8:9 x 11:12:13:14 SD: 27.5360 cents 8:9:11:12:13 x 14:16 SD: 19.6590 cents 9:10:12 x 14:15:16:18 S SD: 14.8308 cents 10:11:14:15:16:17:18:20 SD: 12.1227 cents 11:12:15 x 17:19:20:22 SD: 11.0762 cents 12:13:16:18:19:20:21:24 SD: 9.6975 cents 13:14:18:20 x 22:23:26 SD: 9.1448 cents 14:15:19:21:22:24:25:28 SD: 3.3463 cents 29:31:39:44:46:49:52:58 SD: 3.1442 cents 31:33:42:47:49:53:55:62 SD: 2.5991 cents 33:35:45:50:52:56:59:66 SD: 2.0734 cents 43:46:58:65:68:73:77:86 SD: 1.7733 cents 47:50:64:71:74:80:84:94 SD: 1.4197 cents 62:66:84:94:98:105:111:124 SD: 1.3883 cents 74:79:100:112:117:126:132:148 SD: 1.3599 cents 76:81:103:115:120:129:136:152 SD: 0.6578 cents 90:96:122:136:142:153:161:180 SD: 0.4955 cents 181:193:245:274:285:308:324:362 SD: 0.4593 cents 200:213:271:303:315:340:358:400 SD: 0.4369 cents 214:228:290:324:337:364:383:428 SD: 0.3057 cents 257:274:348:389:405:437:460:514 SD: 0.2679 cents 290:309:393:439:457:493:519:580 SD: 0.2037 cents 304:324:412:460:479:517:544:608 SD: 0.1400 cents 442:471:599:669:697:752:791:884 SD: 0.1229 cents 532:567:721:805:839:905:952:1064 SD: 0.1137 cents