Scala analysis: CD05_04_bayati_Egypt
Suite - ‘Abduh al-Ḥāmūlī (bayati, Egypt)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 149.350 cents 149.350450 2: 303.441 cents 303.440689 3: 505.510 cents 505.509906 4: 619.631 cents 619.630614 5: 876.575 cents 876.575448 6: 994.799 cents 994.798875 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 205.2011 cents 205.2011 1: 149.3505 cents 149.3505 2: 154.0902 cents 154.0902 3: 202.0692 cents 202.0692 4: 114.1207 cents 114.1207 5: 256.9448 cents 256.9448 6: 118.2234 cents 118.2234 7: 205.2011 cents 205.2011
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 114.12071 cents 1: 1 118.22343 cents 1: 1 149.35045 cents 1: 1 154.09024 cents 1: 1 202.06922 cents 1: 1 205.20113 cents 1: 1 256.94483 cents 2: 1 303.44069 cents 2: 1 316.18992 cents 2: 1 323.42455 cents 2: 1 354.55158 cents 2: 1 356.15946 cents 2: 1 371.06554 cents 2: 1 375.16826 cents 3: 1 470.28016 cents 3: 1 472.77500 cents 3: 1 489.28897 cents 3: 1 505.50991 cents 3: 1 508.64181 cents 3: 1 573.13476 cents 3: 1 580.36939 cents 4: 1 619.63061 cents 4: 1 626.86524 cents 4: 1 691.35819 cents 4: 1 694.49009 cents 4: 1 710.71103 cents 4: 1 727.22500 cents 4: 1 729.71984 cents 5: 1 824.83174 cents 5: 1 828.93446 cents 5: 1 843.84054 cents 5: 1 845.44842 cents 5: 1 876.57545 cents 5: 1 883.81008 cents 5: 1 896.55931 cents 6: 1 943.05517 cents 6: 1 994.79887 cents 6: 1 997.93078 cents 6: 1 1045.90976 cents 6: 1 1050.64955 cents 6: 1 1081.77657 cents 6: 1 1085.87929 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 : 149.4 303.4 505.5 619.6 876.6 994.8 1200.0 149.4 : 154.1 356.2 470.3 727.2 845.4 1050.6 1200.0 303.4 : 202.1 316.2 573.1 691.4 896.6 1045.9 1200.0 505.5 : 114.1 371.1 489.3 694.5 843.8 997.9 1200.0 619.6 : 256.9 375.2 580.4 729.7 883.8 1085.9 1200.0 876.6 : 118.2 323.4 472.8 626.9 828.9 943.1 1200.0 994.8 : 205.2 354.6 508.6 710.7 824.8 1081.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 114.1207 .. 256.9448 cents 142.82413 cents 114.12071 cents 2: 303.4407 .. 375.1683 cents 71.72757 cents 46.49586 cents 3: 470.2802 .. 580.3694 cents 110.08922 cents 95.11190 cents 4: 619.6306 .. 729.7198 cents 110.08922 cents 39.26123 cents 5: 824.8317 .. 896.5593 cents 71.72757 cents 95.11190 cents 6: 943.0552 .. 1085.8793 cents 142.82413 cents 46.49586 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 114.12071 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 256.94483 cents Average / Smallest step : 1.502169 Largest / Average step : 1.498845 Largest / Smallest step : 2.251518 Median interval of one step : 154.09024 cents, amount: 1 Least squares average step : 167.87825 cents, oct.: 1175.14772 cents Scale is strictly proper Step pattern alph. order: ABCDEFG Step pattern size order : CDEAGBF Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 39.26123 cents Scale diversity : 1.522807 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.458932 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 : 1.60788 cents Number of recognisable fifths : 3, average 698.8531 cents Best fifths form a closed circle Best major thirds form a closed circle Formal octave complements present : 1 = 14.2857% Limited inverse transpositions with margin 110.0892 cents: 2 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 33.8133 c. M:-66.0837 c. Lebeng 8: 1 1 1 1 2 1 1 P M ME S SD: 31.7914 c. M: 55.5099 c. 10: 1 1 2 1 2 1 2 P M ME S SD: 34.7871 c. M: 63.4407 c. 11: 1 2 2 1 2 1 2 P M ME S SD: 27.2206 c. M: 40.2595 c. Orgone-7 12: 1 2 2 1 3 1 2 P D3 SD: 22.1643 c. M: 49.3505 c. Locrian natural 6, Maqam Tarznauyn 14: 2 2 2 1 3 2 2 P T3 SD: 23.9693 c. M:-39.4165 c. 15: 2 2 2 2 3 1 3 SP D3 S SD: 19.5521 c. M: 34.7989 c. 16: 2 2 3 1 4 1 3 P S SD: 15.6670 c. M:-23.4246 c. 17: 2 2 3 2 3 2 3 SP M ME S SD: 16.0399 c. M: 29.5166 c. Safi al-Din's maqam Higazi 19: 2 3 3 2 4 2 3 SP D3 SD: 12.7142 c. M: 23.0347 c. 23: 3 3 4 2 5 2 4 SP S SD: 9.0134 c. M:-16.2292 c. 29: 4 3 5 3 6 3 5 SP SD: 9.2084 c. M:-16.1668 c. 31: 4 4 5 3 7 3 5 SP S SD: 7.5506 c. M:-13.7471 c. 33: 4 4 6 3 7 3 6 SP S SD: 7.2747 c. M: 12.9807 c. 40: 5 5 7 4 8 4 7 SP S SD: 5.4276 c. M:-10.3694 c. 41: 5 5 7 4 9 4 7 SP S SD: 5.5447 c. M: 10.7578 c. 47: 6 6 8 4 10 5 8 SP SD: 4.9254 c. M: 8.4903 c. 48: 6 6 8 5 10 5 8 SP S SD: 3.7982 c. M: 5.5099 c. 64: 8 8 11 6 14 6 11 SP S SD: 2.2846 c. M:-4.6746 c. 99: 12 13 17 9 21 10 17 SP SD: 2.5584 c. M: 3.8959 c. 104: 13 13 18 10 22 10 18 SP S SD: 2.2433 c. M:-3.4463 c. 111: 14 14 19 10 24 11 19 SP SD: 1.8442 c. M: 3.4144 c. 118: 15 15 20 11 25 12 20 SP SD: 2.0515 c. M:-3.1919 c. 122: 15 16 20 12 26 12 21 SP SD: 1.8376 c. M: 3.8706 c. 130: 16 17 22 12 28 13 22 SP SD: 1.4586 c. M:-2.1824 c. 145: 18 19 24 14 31 14 25 SP SD: 1.3472 c. M:-2.7662 c. 159: 20 20 27 15 34 16 27 SP SD: 1.1220 c. M:-1.5929 c. 182: 23 23 31 17 39 18 31 SP SD: 1.2453 c. M:-2.2979 c. 186: 23 24 31 18 40 18 32 SP SD: 1.1047 c. M: 2.2841 c. 209: 26 27 35 20 45 20 36 SP SD: 0.9898 c. M:-1.8935 c. 233: 29 30 39 22 50 23 40 SP SD: 0.8542 c. M: 1.6049 c. 240: 30 31 40 23 51 24 41 SP SD: 0.9081 c. M: 1.5754 c. 256: 32 33 43 24 55 25 44 SP SD: 0.7928 c. M:-1.2468 c. 281: 35 36 47 27 60 28 48 SP SD: 0.7665 c. M: 1.5953 c. 297: 37 38 50 28 64 29 51 SP SD: 0.6840 c. M: 1.4488 c. 304: 38 39 51 29 65 30 52 SP SD: 0.3427 c. M:-0.6495 c. 498: 62 64 84 47 107 49 85 SP SD: 0.3488 c. M:-0.5330 c. 515: 64 66 87 49 110 51 88 SP SD: 0.2948 c. M: 0.5281 c. 620: 77 80 104 59 133 61 106 SP SD: 0.2739 c. M:-0.4303 c. 660: 82 85 111 63 141 65 113 SP SD: 0.2250 c. M:-0.3694 c. 724: 90 93 122 69 155 71 124 SP SD: 0.1958 c. M: 0.3237 c. 802: 100 103 135 76 172 79 137 SP SD: 0.2232 c. M:-0.3000 c. 819: 102 105 138 78 175 81 140 SP SD: 0.1719 c. M: 0.3850 c. 883: 110 113 149 84 189 87 151 SP SD: 0.1576 c. M: 0.3829 c. 964: 120 124 162 92 206 95 165 SP SD: 0.1968 c. M:-0.2938 c. 988: 123 127 166 94 212 97 169 SP SD: 0.1955 c. M:-0.3476 c. 1013: 126 130 171 96 217 100 173 SP SD: 0.1769 c. M:-0.3144 c. 1028: 128 132 173 98 220 101 176 SP SD: 0.1334 c. M: 0.2463 c. 1135: 141 146 191 108 243 112 194 SP SD: 0.1296 c. M: 0.2756 c. 1158: 144 149 195 110 248 114 198 SP SD: 0.1210 c. M:-0.1896 c. 1317: 164 169 222 125 282 130 225 SP SD: 0.1071 c. M:-0.1897 c. 1439: 179 185 242 137 308 142 246 SP SD: 0.0962 c. M: 0.1590 c. 1462: 182 188 246 139 313 144 250 SP SD: 0.1073 c. M:-0.2529 c. 1503: 187 193 253 143 322 148 257 SP SD: 0.0647 c. M: 0.1207 c. 1807: 225 232 304 172 387 178 309 SP SD: 0.0641 c. M: 0.1419 c. 1977: 246 254 333 188 423 195 338 SP SD: 0.0704 c. M:-0.1047 c. 2041: 254 262 344 194 437 201 349 SP SD: 0.0615 c. M:-0.1246 c. 2274: 283 292 383 216 487 224 389 SP SD: 0.0554 c. M: 0.1055 c. 2322: 289 298 391 221 497 229 397 SP SD: 0.0571 c. M: 0.0897 c. 2345: 292 301 395 223 502 231 401 SP SD: 0.0488 c. M:-0.0764 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: 41.1622 cents 3 x x 4 x 5 x 6 S SD: 3.5948 cents 4 x 5 x 6 x 7:8 S SD: 29.9164 cents 5 x 6 x 7:8:9:10 S SD: 15.4937 cents 6 x 7:8:9:10:11:12 S SD: 17.6448 cents 7 x 8:9:10:12 x 14 S SD: 23.1389 cents 8:9:10:11 x 13:14:16 SD: 19.6618 cents 9:10:11:12:13:15:16:18 SD: 8.3692 cents 12:13:14:16:17:20:21:24 SD: 7.1728 cents 20:22:24:27:29:33:36:40 SD: 5.9962 cents 21:23:25:28:30:35:37:42 SD: 2.8299 cents 32:35:38:43:46:53:57:64 SD: 2.0736 cents 47:51:56:63:67:78:83:94 SD: 2.0479 cents 53:58:63:71:76:88:94:106 SD: 1.3694 cents 67:73:80:90:96:111:119:134 SD: 1.0935 cents 68:74:81:91:97:113:121:136 SD: 0.9882 cents 79:86:94:106:113:131:140:158 SD: 0.9291 cents 88:96:105:118:126:146:156:176 SD: 0.7696 cents 100:109:119:134:143:166:178:200 SD: 0.6298 cents 121:132:144:162:173:201:215:242 SD: 0.4808 cents 156:170:186:209:223:259:277:312 SD: 0.3223 cents 188:205:224:252:269:312:334:376 SD: 0.2785 cents 256:279:305:343:366:425:455:512 SD: 0.2693 cents 277:302:330:371:396:460:492:554 SD: 0.2663 cents 334:364:398:447:478:554:593:668 SD: 0.2620 cents 344:375:410:461:492:571:611:688 SD: 0.2276 cents 402:438:479:538:575:667:714:804 SD: 0.1967 cents 434:473:517:581:621:720:771:868 SD: 0.1488 cents 511:557:609:684:731:848:908:1022 SD: 0.1390 cents 569:620:678:762:814:944:1011:1138 SD: 0.1268 cents 590:643:703:790:844:979:1048:1180 SD: 0.0780 cents