Scala analysis: CD05_16_Egypt
Gens de beauté et de pureté - ‘Abduh al-Ḥāmūlī (bayati, Egypt)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 206.684 cents 206.684207 2: 356.847 cents 356.847267 3: 515.040 cents 515.039739 4: 708.380 cents 708.380281 5: 896.628 cents 896.627604 6: 1060.369 cents 1060.369428 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 139.6306 cents 139.6306 1: 206.6842 cents 206.6842 2: 150.1631 cents 150.1631 3: 158.1925 cents 158.1925 4: 193.3405 cents 193.3405 5: 188.2473 cents 188.2473 6: 163.7418 cents 163.7418 7: 139.6306 cents 139.6306
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 139.63057 cents 1: 1 150.16306 cents 1: 1 158.19247 cents 1: 1 163.74182 cents 1: 1 188.24732 cents 1: 1 193.34054 cents 1: 1 206.68421 cents 2: 1 303.37240 cents 2: 1 308.35553 cents 2: 1 346.31478 cents 2: 1 351.53301 cents 2: 1 351.98915 cents 2: 1 356.84727 cents 2: 1 381.58786 cents 3: 1 491.61972 cents 3: 1 496.47784 cents 3: 1 501.69607 cents 3: 1 510.05660 cents 3: 1 515.03974 cents 3: 1 539.78034 cents 3: 1 545.32969 cents 4: 1 654.67031 cents 4: 1 660.21966 cents 4: 1 684.96026 cents 4: 1 689.94340 cents 4: 1 698.30393 cents 4: 1 703.52216 cents 4: 1 708.38028 cents 5: 1 818.41214 cents 5: 1 843.15273 cents 5: 1 848.01085 cents 5: 1 848.46699 cents 5: 1 853.68522 cents 5: 1 891.64447 cents 5: 1 896.62760 cents 6: 1 993.31579 cents 6: 1 1006.65946 cents 6: 1 1011.75268 cents 6: 1 1036.25818 cents 6: 1 1041.80753 cents 6: 1 1049.83694 cents 6: 1 1060.36943 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 : 206.7 356.8 515.0 708.4 896.6 1060.4 1200.0 206.7 : 150.2 308.4 501.7 689.9 853.7 993.3 1200.0 356.8 : 158.2 351.5 539.8 703.5 843.2 1049.8 1200.0 515.0 : 193.3 381.6 545.3 685.0 891.6 1041.8 1200.0 708.4 : 188.2 352.0 491.6 698.3 848.5 1006.7 1200.0 896.6 : 163.7 303.4 510.1 660.2 818.4 1011.8 1200.0 1060.4: 139.6 346.3 496.5 654.7 848.0 1036.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 139.6306 .. 206.6842 cents 67.05363 cents 139.63057 cents 2: 303.3724 .. 381.5879 cents 78.21547 cents 96.68819 cents 3: 491.6197 .. 545.3297 cents 53.70997 cents 110.03185 cents 4: 654.6703 .. 708.3803 cents 53.70997 cents 109.34062 cents 5: 818.4121 .. 896.6276 cents 78.21547 cents 110.03185 cents 6: 993.3158 .. 1060.3694 cents 67.05363 cents 96.68819 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 139.63057 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 206.68421 cents Average / Smallest step : 1.227729 Largest / Average step : 1.205658 Largest / Smallest step : 1.480222 Median interval of one step : 163.74182 cents, amount: 1 Least squares average step : 175.31695 cents, oct.: 1227.21868 cents Scale is strictly proper Step pattern alph. order: ABCDEFG Step pattern size order : GBCFEDA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 96.68819 cents Scale diversity : 1.361940 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.668368 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 : 0.45613 cents Number of recognisable fifths : 4, average 700.0374 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 14.2857% Limited inverse transpositions with margin 78.2155 cents: 1 5 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 25.4198 c. M: 39.4847 c. Lebeng 12: 2 2 1 2 2 2 1 P M ME S SD: 23.2539 c. M:-43.1527 c. G.Lydian, M.Ionian, M.Hypolydian, Major, Bilaval That, Mela Shankarabharanam, Raga Atana, Ghana Heptatonic, Peruvian Major, Matzore, Rast ascending: Greece, 4th plagal Byzantine, Ararai: Ethiopia, Makam Cargah, Ajam Ashiran, Dastgah-e Mahur, Dastgah-e Rast Panjgah, Xin: China, DS2, Heptatonia prima 16: 3 2 2 2 3 2 2 SP M ME S SD: 16.8918 c. M: 33.3803 c. Antiphrygian 17: 3 2 2 3 3 2 2 SP D3 S SD: 11.5217 c. M:-21.0195 c. Pseudo Rast 24: 4 3 3 4 4 3 3 SP D3 S SD: 8.5095 c. M: 15.0397 c. Arabic Diatonic, Maqam Rast, Quasi-equal Heptatonic, Neutral Diatonic Phrygian 34: 6 4 5 5 5 5 4 SP D3 S SD: 8.1066 c. M:-14.3720 c. 35: 6 4 5 6 5 5 4 SP T3 SD: 7.2256 c. M: 13.9901 c. 37: 6 5 5 6 6 5 4 SP SD: 7.7219 c. M: 12.0896 c. 40: 7 5 5 7 6 5 5 SP SD: 6.5493 c. M:-11.6197 c. 44: 8 5 6 7 7 6 5 SP S SD: 4.9269 c. M:-11.4976 c. 46: 8 6 6 7 7 7 5 SP SD: 6.6905 c. M: 9.6711 c. 47: 8 6 6 8 7 7 5 SP SD: 5.6115 c. M:-11.9710 c. 51: 9 6 7 8 8 7 6 SP S SD: 2.9951 c. M:-5.0805 c. 75: 13 9 10 12 12 10 9 SP S SD: 3.2324 c. M: 4.8473 c. 86: 15 11 11 14 13 12 10 SP SD: 3.0998 c. M:-5.9434 c. 87: 15 11 11 14 14 12 10 SP SD: 2.7373 c. M: 4.9320 c. 88: 15 11 12 14 14 12 10 SP SD: 2.4581 c. M:-3.3724 c. 95: 16 12 13 15 15 13 11 SP SD: 2.4101 c. M: 4.5789 c. 103: 18 13 13 17 16 14 12 SP SD: 2.3655 c. M:-4.3178 c. 110: 19 14 14 18 17 15 13 SP SD: 1.8996 c. M:-3.1527 c. 122: 21 15 16 20 19 17 14 SP SD: 1.9423 c. M: 3.5643 c. 135: 23 17 18 22 21 18 16 SP SD: 1.7908 c. M:-2.7308 c. 139: 24 17 19 22 22 19 16 SP SD: 1.7418 c. M:-2.9459 c. 147: 25 19 19 24 23 20 17 SP SD: 1.6314 c. M: 2.6026 c. 151: 26 19 20 24 24 20 18 SP SD: 1.5894 c. M: 3.4158 c. 158: 27 20 21 25 25 22 18 SP SD: 1.5843 c. M:-2.9217 c. 161: 28 20 21 26 25 22 19 SP SD: 1.4345 c. M: 2.2177 c. 174: 30 22 23 28 27 24 20 SP SD: 1.4536 c. M:-2.2016 c. 179: 31 22 24 29 28 24 21 SP SD: 1.4247 c. M:-2.2342 c. 181: 31 23 24 29 28 25 21 SP SD: 1.2423 c. M:-2.0873 c. 191: 33 24 25 31 30 26 22 SP SD: 1.1795 c. M:-1.8017 c. 198: 34 25 26 32 31 27 23 SP SD: 0.4796 c. M:-0.7285 c. 249: 43 31 33 40 39 34 29 SP SD: 0.3405 c. M:-0.6229 c. 447: 77 56 59 72 70 61 52 SP SD: 0.2131 c. M:-0.3965 c. 720: 124 90 95 116 113 98 84 SP SD: 0.1580 c. M: 0.3694 c. 783: 135 98 103 126 123 107 91 SP SD: 0.1920 c. M: 0.3343 c. 918: 158 115 121 148 144 125 107 SP SD: 0.1217 c. M: 0.2387 c. 1116: 192 140 147 180 175 152 130 SP SD: 0.1554 c. M: 0.2326 c. 1160: 200 145 153 187 182 158 135 SP SD: 0.1673 c. M:-0.2689 c. 1167: 201 146 154 188 183 159 136 SP SD: 0.1037 c. M: 0.2152 c. 1230: 212 154 162 198 193 168 143 SP SD: 0.1209 c. M:-0.2259 c. 1365: 235 171 180 220 214 186 159 SP SD: 0.1161 c. M:-0.1911 c. 1428: 246 179 188 230 224 195 166 SP SD: 0.1282 c. M:-0.2956 c. 1452: 250 182 191 234 228 198 169 SP SD: 0.1089 c. M:-0.1775 c. 1503: 259 188 198 242 236 205 175 SP SD: 0.0956 c. M: 0.1966 c. 1591: 274 199 210 256 250 217 185 SP SD: 0.1061 c. M:-0.1669 c. 1677: 289 210 221 270 263 229 195 SP SD: 0.1189 c. M:-0.2189 c. 1684: 290 211 222 271 264 230 196 SP SD: 0.1166 c. M: 0.1905 c. 1701: 293 213 224 274 267 232 198 SP SD: 0.0636 c. M:-0.1192 c. 1950: 336 244 257 314 306 266 227 SP SD: 0.0580 c. M:-0.0850 c. 2148: 370 269 283 346 337 293 250 SP SD: 0.0566 c. M:-0.1360 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: 3.2126 cents 3 x x 4 x 5 x 6 S SD: 6.9869 cents 4 x 5 x 6:7 x 8 S SD: 19.5610 cents 5 x 6:7 x 8:9:10 S SD: 24.4616 cents 6:7 x 8:9:10:11:12 S SD: 10.8323 cents 7:8:9 x 11:12:13:14 SD: 19.4894 cents 8:9:10:11:12:13:15:16 SD: 11.2113 cents 9:10:11:12:14:15:17:18 SD: 11.0369 cents 12:14:15:16:18:20:22:24 S SD: 10.1945 cents 14:16:17:19:21:24:26:28 SD: 7.4468 cents 17:19:21:23:26:29:31:34 SD: 6.8265 cents 18:20:22:24:27:30:33:36 S SD: 5.1118 cents 22:25:27:30:33:37:41:44 SD: 4.6379 cents 25:28:31:34:38:42:46:50 SD: 4.3986 cents 26:29:32:35:39:44:48:52 SD: 3.3838 cents 31:35:38:42:47:52:57:62 SD: 2.5877 cents 38:43:47:51:57:64:70:76 SD: 2.4445 cents 40:45:49:54:60:67:74:80 SD: 1.6575 cents 57:64:70:77:86:96:105:114 SD: 1.6056 cents 69:78:85:93:104:116:127:138 SD: 1.2784 cents 78:88:96:105:117:131:144:156 SD: 1.0604 cents 87:98:107:117:131:146:161:174 SD: 0.8328 cents 109:123:134:147:164:183:201:218 SD: 0.5815 cents 127:143:156:171:191:213:234:254 SD: 0.5202 cents 174:196:214:234:262:292:321:348 SD: 0.3777 cents 196:221:241:264:295:329:362:392 SD: 0.3531 cents 205:231:252:276:309:344:378:410 SD: 0.3394 cents 214:241:263:288:322:359:395:428 SD: 0.2969 cents 245:276:301:330:369:411:452:490 SD: 0.2090 cents 283:319:348:381:426:475:522:566 SD: 0.2010 cents 323:364:397:435:486:542:596:646 SD: 0.1851 cents 401:452:493:540:604:673:740:802 SD: 0.1834 cents 419:472:515:564:631:703:773:838 SD: 0.1681 cents 433:488:532:583:652:727:799:866 SD: 0.1097 cents 528:595:649:711:795:886:974:1056 SD: 0.1048 cents 560:631:688:754:843:940:1033:1120 SD: 0.0929 cents