Scala analysis: CD05_05_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: 150.743 cents 150.742665 2: 308.360 cents 308.359701 3: 507.884 cents 507.883913 4: 609.952 cents 609.952415 5: 717.929 cents 717.929125 6: 950.396 cents 950.395792 7: 984.769 cents 984.769308 8: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 215.2307 cents 215.2307 1: 150.7427 cents 150.7427 2: 157.6170 cents 157.6170 3: 199.5242 cents 199.5242 4: 102.0685 cents 102.0685 5: 107.9767 cents 107.9767 6: 232.4667 cents 232.4667 7: 34.3735 cents 34.3735 8: 215.2307 cents 215.2307
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 34.37352 cents 1: 1 102.06850 cents 1: 1 107.97671 cents 1: 1 150.74267 cents 1: 1 157.61704 cents 1: 1 199.52421 cents 1: 1 215.23069 cents 1: 1 232.46667 cents 2: 1 210.04521 cents 2: 1 249.60421 cents 2: 1 266.84018 cents 2: 1 301.59271 cents 2: 1 308.35970 cents 2: 1 340.44338 cents 2: 1 357.14125 cents 2: 1 365.97336 cents 3: 1 374.81689 cents 3: 1 400.34687 cents 3: 1 409.56942 cents 3: 1 442.51188 cents 3: 1 459.20975 cents 3: 1 482.07088 cents 3: 1 507.88391 cents 3: 1 523.59039 cents 4: 1 476.88540 cents 4: 1 557.96391 cents 4: 1 567.18646 cents 4: 1 590.04758 cents 4: 1 609.95241 cents 4: 1 632.81354 cents 4: 1 642.03609 cents 4: 1 723.11460 cents 5: 1 676.40961 cents 5: 1 692.11609 cents 5: 1 717.92912 cents 5: 1 740.79025 cents 5: 1 757.48812 cents 5: 1 790.43058 cents 5: 1 799.65313 cents 5: 1 825.18311 cents 6: 1 834.02664 cents 6: 1 842.85875 cents 6: 1 859.55662 cents 6: 1 891.64030 cents 6: 1 898.40729 cents 6: 1 933.15982 cents 6: 1 950.39579 cents 6: 1 989.95479 cents 7: 1 967.53333 cents 7: 1 984.76931 cents 7: 1 1000.47579 cents 7: 1 1042.38296 cents 7: 1 1049.25733 cents 7: 1 1092.02329 cents 7: 1 1097.93150 cents 7: 1 1165.62648 cents Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 8.00000 = 8
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 150.7 308.4 507.9 610.0 717.9 950.4 984.8 1200.0 150.7 : 157.6 357.1 459.2 567.2 799.7 834.0 1049.3 1200.0 308.4 : 199.5 301.6 409.6 642.0 676.4 891.6 1042.4 1200.0 507.9 : 102.1 210.0 442.5 476.9 692.1 842.9 1000.5 1200.0 610.0 : 108.0 340.4 374.8 590.0 740.8 898.4 1097.9 1200.0 717.9 : 232.5 266.8 482.1 632.8 790.4 990.0 1092.0 1200.0 950.4 : 34.4 249.6 400.3 558.0 757.5 859.6 967.5 1200.0 984.8 : 215.2 366.0 523.6 723.1 825.2 933.2 1165.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 34.3735 .. 232.4667 cents 198.09315 cents 34.37352 cents 2: 210.0452 .. 365.9734 cents 155.92814 cents -22.42145 cents 3: 374.8169 .. 523.5904 cents 148.77350 cents 8.84354 cents 4: 476.8854 .. 723.1146 cents 246.22921 cents -46.70500 cents 5: 676.4096 .. 825.1831 cents 148.77350 cents -46.70500 cents 6: 834.0266 .. 989.9548 cents 155.92814 cents 8.84354 cents 7: 967.5333 .. 1165.6265 cents 198.09315 cents -22.42146 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 34.37352 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 232.46667 cents Average / Smallest step : 4.363825 Largest / Average step : 1.549778 Largest / Smallest step : 6.762959 Median interval of one step : 154.17985 cents, amount: 0 Least squares average step : 149.58985 cents, oct.: 1196.71878 cents Scale is not proper Step pattern alph. order: ABCDEFGH Step pattern size order : DEFBCHAG Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 5.18548 cents Scale diversity : 1.760402 Lumma stability : 0.072028 Lumma impropriety factor : 0.115211 Rothenberg efficiency : 0.250000 redundancy: 0.750000 Efficiency x scale size : 2.000000 Number of different interval sizes : 56 = 8.00000 / class Number of one step interval sizes : 8 Highest interval variety : 8 Mean interval variety : 8.00000 = 8 Median interval variety : 8 Lowest interval variety : 8 Smallest interval difference : 5.18548 cents Number of recognisable fifths : 2, average 705.0226 cents Number of appreciable fifths : 1, average 692.1161 cents Formal octave complements present : 1 = 12.5000% -- Rational properties --
FIT/MODE
8: 1 1 1 1 1 1 1 1 SP B ME I SD: 37.6553 c. M:-65.2307 c. 9: 1 1 2 0 1 2 0 2 N SD: 42.0181 c. M: 76.6191 c. 10: 1 1 2 1 1 2 0 2 P D3 SD: 30.0099 c. M: 68.3597 c. 12: 2 1 2 1 1 3 0 2 N SD: 26.6256 c. M:-49.6042 c. 15: 2 2 2 2 1 3 0 3 N SD: 18.0680 c. M:-30.0476 c. 16: 2 2 3 1 2 3 0 3 N SD: 16.5522 c. M:-32.0709 c. 18: 2 3 3 1 2 3 1 3 N SD: 17.4423 c. M:-25.4494 c. 19: 2 3 3 2 1 4 1 3 N SD: 17.0914 c. M:-25.7570 c. 20: 2 3 3 2 2 4 0 4 N SD: 18.0333 c. M: 30.7427 c. 22: 3 3 3 2 2 4 1 4 N SD: 13.8413 c. M: 23.1231 c. 23: 3 3 4 2 2 4 1 4 N SD: 10.2080 c. M:-16.1345 c. 24: 3 3 4 2 2 5 1 4 N SD: 9.9072 c. M: 17.9291 c. 30: 4 4 5 2 3 6 1 5 N SD: 9.9721 c. M:-15.2307 c. 32: 4 4 5 3 3 6 1 6 N SD: 10.4655 c. M: 20.3839 c. 33: 4 4 6 3 3 6 1 6 N SD: 8.0785 c. M: 17.4506 c. 34: 4 5 5 3 3 7 1 6 N SD: 8.8737 c. M: 13.7663 c. 35: 4 5 6 3 3 7 1 6 N SD: 7.6221 c. M: 13.5998 c. 38: 5 5 6 3 4 7 1 7 N SD: 6.3803 c. M: 9.9524 c. 40: 5 5 7 3 4 8 1 7 N SD: 6.1018 c. M: 9.9524 c. 43: 5 6 7 4 4 8 1 8 N SD: 6.1219 c. M: 11.2078 c. 45: 6 6 7 4 4 9 1 8 N SD: 6.4637 c. M:-11.6403 c. 47: 6 6 8 4 4 9 2 8 N SD: 4.8443 c. M:-10.9754 c. 55: 7 7 9 5 5 11 1 10 N SD: 4.4063 c. M:-9.6042 c. 57: 7 8 9 5 5 11 2 10 N SD: 3.7023 c. M:-7.4298 c. 63: 8 8 11 5 6 12 2 11 N SD: 3.9982 c. M:-6.4018 c. 67: 8 9 11 6 6 13 2 12 N SD: 3.8117 c. M: 7.4591 c. 73: 9 10 12 6 7 14 2 13 N SD: 2.9522 c. M:-5.3585 c. 78: 10 10 13 7 7 15 2 14 N SD: 3.1235 c. M:-5.4322 c. 82: 10 11 14 7 7 16 2 15 N SD: 3.1762 c. M:-4.6817 c. 85: 11 11 14 7 8 16 3 15 N SD: 2.9760 c. M:-4.5515 c. 90: 11 12 15 8 8 17 3 16 N SD: 2.6026 c. M: 4.0760 c. 97: 12 13 16 8 9 19 3 17 N SD: 2.4965 c. M:-4.9214 c. 102: 13 13 17 9 9 20 3 18 N SD: 2.1457 c. M:-3.4660 c. 112: 14 15 18 10 10 22 3 20 N SD: 2.1289 c. M: 4.3125 c. 120: 15 16 20 10 11 23 3 22 N SD: 2.0891 c. M: 4.7693 c. 128: 16 17 21 11 12 24 4 23 N SD: 2.0220 c. M:-3.9459 c. 134: 17 17 23 11 12 26 4 24 N SD: 1.8894 c. M: 3.8821 c. 135: 17 18 22 12 12 26 4 24 N SD: 1.9045 c. M:-3.3809 c. 140: 18 18 23 12 13 27 4 25 N SD: 1.7840 c. M:-3.5430 c. 144: 18 19 24 12 13 28 4 26 N SD: 0.9479 c. M: 1.6191 c. 222: 28 29 37 19 20 43 6 40 N SD: 0.7146 c. M:-0.9898 c. 246: 31 32 41 21 22 48 7 44 N SD: 0.6559 c. M: 1.0426 c. 269: 34 35 45 23 24 52 8 48 N SD: 0.7417 c. M:-1.2000 c. 279: 35 37 46 24 25 54 8 50 N SD: 0.5832 c. M:-1.3177 c. 366: 46 48 61 31 33 71 10 66 N SD: 0.4591 c. M: 1.1628 c. 374: 47 49 62 32 34 72 11 67 N SD: 0.5267 c. M: 0.9320 c. 390: 49 51 65 33 35 76 11 70 N SD: 0.5219 c. M: 1.0060 c. 413: 52 54 69 35 37 80 12 74 N SD: 0.3241 c. M:-0.5907 c. 525: 66 69 87 45 47 102 15 94 N SD: 0.3112 c. M:-0.4614 c. 669: 84 88 111 57 60 130 19 120 N SD: 0.2171 c. M: 0.4403 c. 692: 87 91 115 59 62 134 20 124 N SD: 0.2270 c. M:-0.4522 c. 836: 105 110 139 71 75 162 24 150 N SD: 0.1651 c. M:-0.2527 c. 1082: 136 142 180 92 97 210 31 194 N SD: 0.1417 c. M: 0.3691 c. 1155: 145 152 192 98 104 224 33 207 N SD: 0.1501 c. M:-0.2536 c. 1210: 152 159 201 103 109 234 35 217 N SD: 0.1254 c. M: 0.3131 c. 1299: 163 171 216 110 117 252 37 233 N SD: 0.1657 c. M: 0.2526 c. 1304: 164 171 217 111 117 253 37 234 N SD: 0.1381 c. M:-0.2177 c. 1354: 170 178 225 115 122 262 39 243 N SD: 0.1492 c. M: 0.3219 c. 1361: 171 179 226 116 122 264 39 244 N SD: 0.1402 c. M:-0.2369 c. 1432: 180 188 238 122 129 277 41 257 N SD: 0.1156 c. M:-0.2273 c. 1456: 183 191 242 124 131 282 42 261 N SD: 0.1093 c. M: 0.1916 c. 1529: 192 201 254 130 138 296 44 274 N SD: 0.1177 c. M:-0.1882 c. 1576: 198 207 262 134 142 305 45 283 N SD: 0.1093 c. M: 0.2515 c. 1600: 201 210 266 136 144 310 46 287 N SD: 0.1249 c. M: 0.2024 c. 1623: 204 213 270 138 146 314 47 291 N SD: 0.1184 c. M: 0.3034 c. 1673: 210 220 278 142 151 324 48 300 N SD: 0.1116 c. M: 0.2692 c. 1678: 211 220 279 143 151 325 48 301 N SD: 0.0931 c. M:-0.1513 c. 1822: 229 239 303 155 164 353 52 327 N SD: 0.0840 c. M: 0.1370 c. 1942: 244 255 323 165 175 376 56 348 N SD: 0.0833 c. M:-0.1946 c. 2086: 262 274 347 177 188 404 60 374 N SD: 0.0763 c. M: 0.1729 c. 2101: 264 276 349 179 189 407 60 377 N SD: 0.0643 c. M: 0.1257 c. 2308: 290 303 384 196 208 447 66 414 N SD: 0.0583 c. M:-0.0951 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x 4 S SD: 7.9871 cents 3 x x 4 x x 5 x 6 S SD: 22.2553 cents 4 x 5 x x 6 x 7:8 S SD: 20.2888 cents 5 x 6 x 7:8 x 9:10 S SD: 21.0267 cents 6 x 7:8 x 9:10:11:12 S SD: 17.1647 cents 7 x 8:9:10:11:12 x 14 S SD: 20.9369 cents 8:9:10:11 x 12 x 14:16 S SD: 17.7165 cents 9:10:11:12:13:14 x 16:18 S SD: 10.7580 cents 10:11:12:13:14:15:17:18:20 SD: 9.8670 cents 11:12:13:15:16:17:19 x 22 SD: 9.0400 cents 12:13:14:16:17:18 x 21:24 S SD: 7.1770 cents 13:14:16:17:18:20 x 23:26 SD: 12.7442 cents 14:15:17:19:20:21:24:25:28 SD: 7.0222 cents 15:16:18:20:21:23:26 x 30 SD: 7.7137 cents 16:17:19:21:23:24 x 28:32 SD: 9.5146 cents 17:19:20:23:24:26:29:30:34 SD: 7.7674 cents 18:20:22:24:26:27:31:32:36 SD: 7.7099 cents 19:21:23:25:27:29:33:34:38 SD: 6.6477 cents 20:22:24:27:28:30 x 35:40 S SD: 5.8114 cents 21:23:25:28:30:32:36:37:42 SD: 3.2713 cents 24:26:29:32:34:36 x 42:48 SD: 4.8941 cents 26:28:31:35:37:39:45:46:52 SD: 3.5993 cents 30:33:36:40:43:45:52:53:60 SD: 3.5109 cents 31:34:37:42:44:47:54:55:62 SD: 3.0555 cents 33:36:39:44:47:50:57:58:66 SD: 2.9582 cents 35:38:42:47:50:53:61:62:70 SD: 2.3093 cents 41:45:49:55:58:62:71:72:82 SD: 2.1667 cents 45:49:54:60:64:68:78:79:90 SD: 2.1060 cents 47:51:56:63:67:71:81:83:94 SD: 1.7994 cents 52:57:62:70:74:79:90:92:104 SD: 1.6506 cents 55:60:66:74:78:83:95:97:110 SD: 1.6170 cents 56:61:67:75:80:85:97:99:112 SD: 1.2280 cents 76:83:91:102:108:115:132:134:152 SD: 0.9563 cents 97:106:116:130:138:147:168:171:194 SD: 0.6239 cents 123:134:147:165:175:186:213:217:246 SD: 0.4737 cents 164:179:196:220:233:248:284:290:328 SD: 0.4543 cents 175:191:209:235:249:265:303:309:350 SD: 0.3625 cents 220:240:263:295:313:333:381:389:440 SD: 0.2719 cents 261:285:312:350:371:395:452:461:522 SD: 0.2648 cents 308:336:368:413:438:466:533:544:616 SD: 0.1851 cents 317:346:379:425:451:480:549:560:634 SD: 0.1821 cents 364:397:435:488:518:551:630:643:728 SD: 0.1653 cents 405:442:484:543:576:613:701:715:810 SD: 0.1550 cents 440:480:526:590:626:666:762:777:880 SD: 0.1252 cents 595:649:711:798:846:901:1030:1051:1190 SD: 0.1242 cents