Scala analysis: CD06_07_Egypt
Qu'y-a-t-il donc mon amour, que t'ai-je donc fait ? - Muhammad Awad Al-Arabî (unknown maqam, Egypt)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 129.737 cents 129.736656 2: 273.564 cents 273.563828 3: 468.042 cents 468.041860 4: 616.584 cents 616.584353 5: 832.562 cents 832.562269 6: 974.926 cents 974.926461 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 225.0735 cents 225.0735 1: 129.7367 cents 129.7367 2: 143.8272 cents 143.8272 3: 194.4780 cents 194.4780 4: 148.5425 cents 148.5425 5: 215.9779 cents 215.9779 6: 142.3642 cents 142.3642 7: 225.0735 cents 225.0735
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 129.73666 cents 1: 1 142.36419 cents 1: 1 143.82717 cents 1: 1 148.54249 cents 1: 1 194.47803 cents 1: 1 215.97792 cents 1: 1 225.07354 cents 2: 1 273.56383 cents 2: 1 338.30520 cents 2: 1 343.02053 cents 2: 1 354.81020 cents 2: 1 358.34211 cents 2: 1 364.52041 cents 2: 1 367.43773 cents 3: 1 468.04186 cents 3: 1 486.84770 cents 3: 1 497.17439 cents 3: 1 498.63737 cents 3: 1 506.88460 cents 3: 1 558.99844 cents 3: 1 583.41565 cents 4: 1 616.58435 cents 4: 1 641.00156 cents 4: 1 693.11540 cents 4: 1 701.36263 cents 4: 1 702.82561 cents 4: 1 713.15230 cents 4: 1 731.95814 cents 5: 1 832.56227 cents 5: 1 835.47959 cents 5: 1 841.65789 cents 5: 1 845.18980 cents 5: 1 856.97947 cents 5: 1 861.69480 cents 5: 1 926.43617 cents 6: 1 974.92646 cents 6: 1 984.02208 cents 6: 1 1005.52197 cents 6: 1 1051.45751 cents 6: 1 1056.17283 cents 6: 1 1057.63581 cents 6: 1 1070.26334 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 : 129.7 273.6 468.0 616.6 832.6 974.9 1200.0 129.7 : 143.8 338.3 486.8 702.8 845.2 1070.3 1200.0 273.6 : 194.5 343.0 559.0 701.4 926.4 1056.2 1200.0 468.0 : 148.5 364.5 506.9 732.0 861.7 1005.5 1200.0 616.6 : 216.0 358.3 583.4 713.2 857.0 1051.5 1200.0 832.6 : 142.4 367.4 497.2 641.0 835.5 984.0 1200.0 974.9 : 225.1 354.8 498.6 693.1 841.7 1057.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 129.7367 .. 225.0735 cents 95.33688 cents 129.73666 cents 2: 273.5638 .. 367.4377 cents 93.87390 cents 48.49029 cents 3: 468.0419 .. 583.4156 cents 115.37379 cents 100.60413 cents 4: 616.5844 .. 731.9581 cents 115.37379 cents 33.16871 cents 5: 832.5623 .. 926.4362 cents 93.87390 cents 100.60413 cents 6: 974.9265 .. 1070.2633 cents 95.33688 cents 48.49029 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 129.73666 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 225.07354 cents Average / Smallest step : 1.321358 Largest / Average step : 1.312929 Largest / Smallest step : 1.734849 Median interval of one step : 148.54249 cents, amount: 1 Least squares average step : 163.99784 cents, oct.: 1147.98487 cents Scale is strictly proper Step pattern alph. order: ABCDEFG Step pattern size order : ACEDFBG Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 33.16871 cents Scale diversity : 1.473327 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.492359 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 : 1.46298 cents Number of recognisable fifths : 4, average 702.6140 cents Best fifths form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 14.2857% -- Rational properties --
FIT/MODE
7: 0 1 1 1 1 1 2 N T3 SD: 112.6542 c. M: 146.8480 c. 8: 1 1 1 1 2 1 1 P M ME S SD: 41.2205 c. M:-75.0735 c. 9: 1 1 1 1 2 1 2 N D3 S SD: 45.3734 c. M: 83.2510 c. 10: 1 1 2 1 2 1 2 P M ME S SD: 16.5507 c. M: 33.5638 c. 12: 1 2 2 1 2 2 2 P M ME S SD: 25.5468 c. M: 32.5623 c. G.Mixolydian, G.Hyperdorian, M.Hypophrygian, M.Locrian, G.M.Hyperaeolian, Rut biscale descending, Pien chih: China, Makam Lami, Yishtabach: Jewish 13: 1 2 2 2 2 2 2 SP M ME S SD: 23.8116 c. M:-40.4582 c. Zo-Kalarian 16: 2 2 2 2 3 2 3 P D3 S SD: 15.8890 c. M:-26.4362 c. 17: 2 2 3 2 3 2 3 SP M ME S SD: 15.2381 c. M:-26.0758 c. Safi al-Din's maqam Higazi 20: 2 3 3 2 4 2 4 P D3 S SD: 14.5888 c. M:-26.4362 c. 21: 2 3 3 3 4 2 4 SP T3 SD: 13.4445 c. M:-24.5806 c. 23: 2 3 4 3 4 3 4 SP T3 SD: 12.9368 c. M: 25.3888 c. 25: 3 3 4 3 4 3 5 SP T3 SD: 12.5752 c. M: 16.5623 c. 26: 3 3 4 3 5 3 5 P SD: 7.9318 c. M: 16.5844 c. 35: 4 4 6 4 6 4 7 SP SD: 8.5830 c. M: 14.9265 c. 36: 4 4 6 4 7 4 7 P SD: 7.6182 c. M: 16.5844 c. 37: 4 4 6 5 7 4 7 SP SD: 8.5576 c. M: 14.1044 c. 39: 4 5 6 5 7 5 7 SP SD: 5.2977 c. M:-9.6889 c. 43: 5 5 7 5 8 5 8 SP SD: 5.3292 c. M:-9.7982 c. 48: 5 6 8 6 8 6 9 SP SD: 5.3576 c. M:-8.4156 c. 49: 5 6 8 6 9 6 9 SP SD: 4.1168 c. M: 7.2877 c. 62: 7 7 10 8 11 7 12 SP SD: 3.9926 c. M: 7.1845 c. 66: 7 8 11 8 12 8 12 SP SD: 3.6493 c. M:-6.8917 c. 74: 8 9 12 9 13 9 14 SP SD: 2.5076 c. M: 5.5352 c. 82: 9 10 13 10 15 10 15 SP SD: 2.9593 c. M:-5.5613 c. 84: 9 10 14 10 15 10 16 SP SD: 2.6948 c. M: 3.9908 c. 92: 10 11 15 11 17 11 17 SP SD: 2.1219 c. M: 3.5409 c. 101: 11 12 16 13 18 12 19 SP SD: 1.9129 c. M: 4.6755 c. 111: 12 13 18 14 20 13 21 SP SD: 1.8864 c. M: 3.2936 c. 118: 13 14 19 15 21 14 22 SP SD: 1.8845 c. M:-3.7546 c. 123: 13 15 20 15 22 15 23 SP SD: 1.8436 c. M: 3.2940 c. 128: 14 15 21 16 23 15 24 SP SD: 1.3952 c. M:-2.1656 c. 154: 17 18 25 19 28 18 29 SP SD: 1.2916 c. M:-2.7309 c. 166: 18 20 27 20 30 20 31 SP SD: 1.2994 c. M: 2.1265 c. 167: 18 20 27 21 30 20 31 SP SD: 1.1706 c. M:-2.3190 c. 185: 20 22 30 23 33 22 35 SP SD: 1.2826 c. M: 2.2920 c. 187: 20 23 30 23 34 22 35 SP SD: 1.2546 c. M:-2.3720 c. 193: 21 23 31 24 35 23 36 SP SD: 0.9733 c. M: 1.7206 c. 202: 22 24 33 25 36 24 38 SP SD: 0.8746 c. M:-1.2651 c. 241: 26 29 39 30 43 29 45 SP SD: 0.6484 c. M: 1.0270 c. 251: 27 30 41 31 45 30 47 SP SD: 0.5865 c. M: 1.0539 c. 277: 30 33 45 34 50 33 52 SP SD: 0.6740 c. M: 1.4219 c. 294: 32 35 48 36 53 35 55 SP SD: 0.6549 c. M:-1.3459 c. 298: 32 36 48 37 54 35 56 SP SD: 0.6656 c. M:-0.9948 c. 346: 37 42 56 43 62 41 65 SP SD: 0.6485 c. M: 1.4130 c. 352: 38 42 57 44 63 42 66 SP SD: 0.5977 c. M: 0.9964 c. 369: 40 44 60 46 66 44 69 SP SD: 0.5976 c. M:-1.3018 c. 372: 40 45 60 46 67 44 70 SP SD: 0.5099 c. M: 0.7329 c. 389: 42 47 63 48 70 46 73 SP SD: 0.5356 c. M:-0.9863 c. 395: 43 47 64 49 71 47 74 SP SD: 0.3726 c. M:-0.8963 c. 490: 53 59 79 61 88 58 92 SP SD: 0.3744 c. M:-0.7219 c. 500: 54 60 81 62 90 59 94 SP SD: 0.2396 c. M: 0.5265 c. 646: 70 77 105 80 116 77 121 SP SD: 0.2889 c. M: 0.4988 c. 666: 72 80 108 82 120 79 125 SP SD: 0.2545 c. M:-0.4266 c. 693: 75 83 112 86 125 82 130 SP SD: 0.2425 c. M: 0.5094 c. 741: 80 89 120 92 133 88 139 SP SD: 0.1910 c. M:-0.4197 c. 751: 81 90 122 93 135 89 141 SP SD: 0.2121 c. M: 0.3281 c. 767: 83 92 124 95 138 91 144 SP SD: 0.1900 c. M: 0.2452 c. 833: 90 100 135 103 150 99 156 SP SD: 0.1587 c. M:-0.3436 c. 944: 102 113 153 117 170 112 177 SP SD: 0.1444 c. M: 0.2587 c. 1018: 110 122 165 126 183 121 191 SP SD: 0.1444 c. M: 0.3422 c. 1146: 124 137 186 142 206 136 215 SP SD: 0.1334 c. M: 0.2654 c. 1238: 134 148 201 153 223 147 232 SP SD: 0.1428 c. M: 0.2197 c. 1333: 144 160 216 165 240 158 250 SP SD: 0.0878 c. M:-0.1459 c. 1600: 173 192 259 198 288 190 300 SP SD: 0.0870 c. M:-0.1862 c. 1610: 174 193 261 199 290 191 302 SP SD: 0.0750 c. M: 0.1868 c. 1728: 187 207 280 214 311 205 324 SP SD: 0.0717 c. M:-0.1245 c. 1979: 214 237 321 245 356 235 371 SP SD: 0.0714 c. M:-0.1114 c. 2100: 227 252 340 260 378 249 394 SP SD: 0.0654 c. M:-0.1505 c. 2267: 245 272 367 281 408 269 425 SP SD: 0.0853 c. M: 0.1107 c. 2277: 246 273 369 282 410 270 427 SP SD: 0.0638 c. M:-0.1123 c. 2351: 254 282 381 291 423 279 441 SP SD: 0.0440 c. M: 0.0897 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: 42.6853 cents 3 x x 4 x 5 x 6 S SD: 19.9529 cents 4 x x 5:6 x 7:8 S SD: 29.5855 cents 5 x 6 x 7:8:9:10 S SD: 14.2947 cents 6 x 7:8:9:10:11:12 S SD: 21.3807 cents 7 x 8:9:10:11:12:14 S SD: 14.0811 cents 8 x 9:10:11:13:14:16 SD: 21.0103 cents 9:10:11:12:13:15:16:18 SD: 16.0732 cents 10:11:12:13:14:16:18:20 S SD: 11.5559 cents 11:12:13:14:16:18:19:22 SD: 10.5871 cents 12:13:14:16:17:19:21:24 SD: 7.3041 cents 13:14:15:17:19:21:23:26 SD: 7.1198 cents 16:17:19:21:23:26:28:32 SD: 5.4069 cents 23:25:27:30:33:37:40:46 SD: 3.8880 cents 28:30:33:37:40:45:49:56 SD: 3.4895 cents 29:31:34:38:41:47:51:58 SD: 3.2472 cents 35:38:41:46:50:57:61:70 SD: 3.1904 cents 36:39:42:47:51:58:63:72 SD: 2.9750 cents 39:42:46:51:56:63:68:78 SD: 2.9288 cents 40:43:47:52:57:65:70:80 SD: 2.6949 cents 42:45:49:55:60:68:74:84 SD: 1.9554 cents 52:56:61:68:74:84:91:104 SD: 1.4196 cents 65:70:76:85:93:105:114:130 SD: 0.9775 cents 94:101:110:123:134:152:165:188 SD: 0.9720 cents 100:108:117:131:143:162:176:200 SD: 0.9441 cents 112:121:131:147:160:181:197:224 SD: 0.9028 cents 115:124:135:151:164:186:202:230 SD: 0.8238 cents 128:138:150:168:183:207:225:256 SD: 0.5822 cents 152:164:178:199:217:246:267:304 SD: 0.3780 cents 180:194:211:236:257:291:316:360 SD: 0.3005 cents 245:264:287:321:350:396:430:490 SD: 0.2867 cents 280:302:328:367:400:453:492:560 SD: 0.2701 cents 309:333:362:405:441:500:543:618 SD: 0.2300 cents 332:358:389:435:474:537:583:664 SD: 0.1621 cents 374:403:438:490:534:605:657:748 SD: 0.1101 cents 554:597:649:726:791:896:973:1108 SD: 0.0867 cents