Scala analysis: CD07_09_Egypt
Introduction instrumentale - Taha Abû Mandûr (unknown maqam, Egypt)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 187.606 cents 187.606180 2: 381.895 cents 381.894737 3: 504.027 cents 504.026551 4: 702.824 cents 702.824252 5: 856.765 cents 856.765325 6: 968.590 cents 968.590389 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 231.4096 cents 231.4096 1: 187.6062 cents 187.6062 2: 194.2886 cents 194.2886 3: 122.1318 cents 122.1318 4: 198.7977 cents 198.7977 5: 153.9411 cents 153.9411 6: 111.8251 cents 111.8251 7: 231.4096 cents 231.4096
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 111.82506 cents 1: 1 122.13181 cents 1: 1 153.94107 cents 1: 1 187.60618 cents 1: 1 194.28856 cents 1: 1 198.79770 cents 1: 1 231.40961 cents 2: 1 265.76614 cents 2: 1 316.42037 cents 2: 1 320.92952 cents 2: 1 343.23468 cents 2: 1 352.73877 cents 2: 1 381.89474 cents 2: 1 419.01579 cents 3: 1 464.56384 cents 3: 1 474.87059 cents 3: 1 497.17575 cents 3: 1 504.02655 cents 3: 1 515.21807 cents 3: 1 530.84085 cents 3: 1 613.30435 cents 4: 1 586.69565 cents 4: 1 669.15915 cents 4: 1 684.78193 cents 4: 1 695.97345 cents 4: 1 702.82425 cents 4: 1 725.12941 cents 4: 1 735.43616 cents 5: 1 780.98421 cents 5: 1 818.10526 cents 5: 1 847.26123 cents 5: 1 856.76532 cents 5: 1 879.07048 cents 5: 1 883.57963 cents 5: 1 934.23386 cents 6: 1 968.59039 cents 6: 1 1001.20230 cents 6: 1 1005.71144 cents 6: 1 1012.39382 cents 6: 1 1046.05893 cents 6: 1 1077.86819 cents 6: 1 1088.17494 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 : 187.6 381.9 504.0 702.8 856.8 968.6 1200.0 187.6 : 194.3 316.4 515.2 669.2 781.0 1012.4 1200.0 381.9 : 122.1 320.9 474.9 586.7 818.1 1005.7 1200.0 504.0 : 198.8 352.7 464.6 696.0 883.6 1077.9 1200.0 702.8 : 153.9 265.8 497.2 684.8 879.1 1001.2 1200.0 856.8 : 111.8 343.2 530.8 725.1 847.3 1046.1 1200.0 968.6 : 231.4 419.0 613.3 735.4 934.2 1088.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.8251 .. 231.4096 cents 119.58455 cents 111.82506 cents 2: 265.7661 .. 419.0158 cents 153.24965 cents 34.35653 cents 3: 464.5638 .. 613.3043 cents 148.74051 cents 45.54805 cents 4: 586.6957 .. 735.4362 cents 148.74051 cents -26.60870 cents 5: 780.9842 .. 934.2339 cents 153.24965 cents 45.54805 cents 6: 968.5904 .. 1088.1749 cents 119.58455 cents 34.35653 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 111.82506 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 231.40961 cents Average / Smallest step : 1.533007 Largest / Average step : 1.349889 Largest / Smallest step : 2.069389 Median interval of one step : 187.60618 cents, amount: 1 Least squares average step : 169.78672 cents, oct.: 1188.50706 cents Scale is not proper Step pattern alph. order: ABCDEFG Step pattern size order : DEBFCAG Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 26.60870 cents Scale diversity : 1.649988 Lumma stability : 0.319549 Lumma impropriety factor : 0.022174 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 : 4.50914 cents Number of recognisable fifths : 2, average 699.3989 cents Best fifths 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: 28.7390 c. M:-59.9810 c. Lebeng 9: 1 2 1 1 1 1 2 N D3 S SD: 37.6164 c. M: 56.7653 c. 10: 2 1 1 2 1 1 2 P D3 I SD: 25.2180 c. M:-52.3938 c. 12: 2 2 1 2 2 1 2 P M ME S SD: 21.9135 c. M:-43.2347 c. G.Hypophrygian, G.Ionian (Iastian), M.Mixolydian, G.M.Hypoionian, Hypermixolydian, Mischung 3, Khamaj That, Mela Harikambhoji, Raga Balahamsa, Bhim, Devamanohari, Harini, Janjhuti, Kaamaai, Khambhavati, Surati, Gregorian nr.7, Enharmonic Byzantine Liturgical, Rast descending: Greece, Ching, Shang: China 14: 2 2 2 2 2 1 3 P T3 SD: 20.1636 c. M: 39.0376 c. 15: 2 3 1 3 2 1 3 N T3 SD: 19.1827 c. M: 27.6062 c. 17: 3 2 2 3 2 2 3 SP D3 I SD: 16.9437 c. M: 28.9536 c. Safi al-Din's maqam Rast 19: 3 3 2 3 3 1 4 N SD: 13.5368 c. M:-27.4452 c. 21: 3 4 2 3 3 2 4 N T3 S SD: 11.9266 c. M:-18.1053 c. 24: 4 4 2 4 3 2 5 N SD: 11.3198 c. M: 18.5904 c. 25: 4 4 3 4 3 2 5 N SD: 12.0689 c. M:-23.9734 c. 26: 4 4 3 4 4 2 5 P SD: 10.0007 c. M:-20.1578 c. 28: 4 5 3 4 4 3 5 P T3 S SD: 11.7575 c. M:-17.1239 c. 31: 5 5 3 5 4 3 6 N SD: 4.2575 c. M: 6.0501 c. 53: 8 9 5 9 7 5 10 N SD: 4.2227 c. M: 6.4741 c. 57: 9 9 6 9 8 5 11 N SD: 4.1405 c. M: 8.0874 c. 60: 9 10 6 10 8 5 12 N SD: 4.9265 c. M: 8.5904 c. 63: 10 10 6 11 8 6 12 N SD: 3.7477 c. M: 8.7885 c. 67: 10 11 7 11 9 6 13 N SD: 4.4936 c. M: 8.5017 c. 69: 11 11 7 11 9 7 13 N SD: 4.0557 c. M: 7.1721 c. 72: 11 12 7 12 9 7 14 N SD: 3.6642 c. M: 6.7653 c. 78: 12 13 8 13 10 7 15 N SD: 3.3096 c. M:-4.8681 c. 84: 13 14 8 14 11 8 16 N SD: 2.6874 c. M: 4.0266 c. 97: 15 16 10 16 12 9 19 N SD: 2.5520 c. M: 3.6419 c. 98: 15 16 10 16 13 9 19 N SD: 2.6745 c. M: 4.8651 c. 104: 16 17 11 17 13 10 20 N SD: 2.1917 c. M:-3.6658 c. 109: 17 18 11 18 14 10 21 N SD: 1.8761 c. M:-3.4264 c. 123: 19 20 13 20 16 11 24 N SD: 2.0214 c. M:-3.2905 c. 126: 20 20 13 21 16 12 24 N SD: 1.7574 c. M:-2.8700 c. 135: 21 22 14 22 17 13 26 N SD: 1.6983 c. M: 3.4320 c. 140: 22 23 14 23 18 13 27 N SD: 1.6263 c. M:-3.8195 c. 147: 23 24 15 24 19 14 28 N SD: 1.5302 c. M:-2.8382 c. 154: 24 25 16 25 20 14 30 N SD: 1.4376 c. M:-2.4670 c. 160: 25 26 16 27 20 15 31 N SD: 1.2954 c. M:-2.1757 c. 167: 26 27 17 28 21 16 32 N SD: 1.1727 c. M: 1.6755 c. 186: 29 30 19 31 24 17 36 N SD: 0.8478 c. M:-1.2992 c. 217: 34 35 22 36 28 20 42 N SD: 0.5414 c. M: 0.8485 c. 321: 50 52 33 53 41 30 62 N SD: 0.5140 c. M: 0.6906 c. 333: 52 54 34 55 43 31 64 N SD: 0.4931 c. M:-0.8923 c. 364: 57 59 37 60 47 34 70 N SD: 0.4548 c. M:-0.6404 c. 493: 77 80 50 82 63 46 95 N SD: 0.2798 c. M:-0.6240 c. 524: 82 85 53 87 67 49 101 N SD: 0.2721 c. M:-0.5480 c. 538: 84 87 55 89 69 50 104 N SD: 0.3224 c. M: 0.5606 c. 550: 86 89 56 91 71 51 106 N SD: 0.2876 c. M:-0.6892 c. 647: 101 105 66 107 83 60 125 N SD: 0.2744 c. M:-0.4557 c. 678: 106 110 69 112 87 63 131 N SD: 0.2854 c. M: 0.4488 c. 685: 107 111 70 113 88 64 132 N SD: 0.2495 c. M:-0.4990 c. 710: 111 115 72 118 91 66 137 N SD: 0.1898 c. M: 0.3646 c. 857: 134 139 87 142 110 80 165 N SD: 0.2131 c. M:-0.3711 c. 871: 136 141 89 144 112 81 168 N SD: 0.1863 c. M: 0.2644 c. 902: 141 146 92 149 116 84 174 N SD: 0.1670 c. M: 0.3852 c. 1031: 161 167 105 171 132 96 199 N SD: 0.1501 c. M: 0.2153 c. 1062: 166 172 108 176 136 99 205 N SD: 0.1370 c. M: 0.2681 c. 1178: 184 191 120 195 151 110 227 N SD: 0.1333 c. M:-0.2179 c. 1286: 201 208 131 213 165 120 248 N SD: 0.1409 c. M: 0.2462 c. 1364: 213 221 139 226 175 127 263 N SD: 0.1118 c. M: 0.2162 c. 1395: 218 226 142 231 179 130 269 N SD: 0.0423 c. M: 0.0793 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: 0.4346 cents 3 x x 4 x 5 x 6 S SD: 9.4114 cents 4 x 5 x 6 x 7:8 S SD: 1.1275 cents 5 x 6:7 x 8:9:10 S SD: 24.3367 cents 6:7 x 8:9:10:11:12 S SD: 19.4401 cents 7:8:9 x x 11:12:14 SD: 21.4488 cents 8:9:10:11:12:13:14:16 S SD: 7.5408 cents 16:18:20:21:24:26:28:32 S SD: 5.8118 cents 20:22:25:27:30:33:35:40 SD: 4.2285 cents 24:27:30:32:36:39:42:48 S SD: 3.4570 cents 33:37:41:44:50:54:58:66 SD: 3.2973 cents 36:40:45:48:54:59:63:72 SD: 1.3205 cents 44:49:55:59:66:72:77:88 SD: 1.0500 cents 80:89:100:107:120:131:140:160 SD: 0.8892 cents 106:118:132:142:159:174:185:212 SD: 0.8453 cents 122:136:152:163:183:200:213:244 SD: 0.7025 cents 130:145:162:174:195:213:227:260 SD: 0.6502 cents 142:158:177:190:213:233:248:284 SD: 0.6311 cents 166:185:207:222:249:272:290:332 SD: 0.5032 cents 175:195:218:234:263:287:306:350 SD: 0.4709 cents 183:204:228:245:275:300:320:366 SD: 0.4635 cents 192:214:239:257:288:315:336:384 SD: 0.4390 cents 219:244:273:293:329:359:383:438 SD: 0.3336 cents 228:254:284:305:342:374:399:456 SD: 0.2893 cents 272:303:339:364:408:446:476:544 SD: 0.2208 cents 340:379:424:455:510:558:595:680 SD: 0.2044 cents 376:419:469:503:564:617:658:752 SD: 0.1962 cents 429:478:535:574:644:704:751:858 SD: 0.1880 cents 453:505:565:606:680:743:793:906 SD: 0.1740 cents 479:534:597:641:719:786:838:958 SD: 0.1724 cents 515:574:642:689:773:845:901:1030 SD: 0.0999 cents 551:614:687:737:827:904:964:1102 SD: 0.0991 cents 559:623:697:748:839:917:978:1118 SD: 0.0523 cents