Scala analysis: CD06_02_rast_Egypt
Suite - Muhammad al-Bahr (rast, Egypt)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 225.253 cents 225.252809 2: 352.552 cents 352.551660 3: 500.994 cents 500.994246 4: 711.018 cents 711.017515 5: 896.364 cents 896.364258 6: 1069.602 cents 1069.602001 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 130.3980 cents 130.3980 1: 225.2528 cents 225.2528 2: 127.2989 cents 127.2989 3: 148.4426 cents 148.4426 4: 210.0233 cents 210.0233 5: 185.3467 cents 185.3467 6: 173.2377 cents 173.2377 7: 130.3980 cents 130.3980
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 127.29885 cents 1: 1 130.39800 cents 1: 1 148.44259 cents 1: 1 173.23774 cents 1: 1 185.34674 cents 1: 1 210.02327 cents 1: 1 225.25281 cents 2: 1 275.74144 cents 2: 1 303.63574 cents 2: 1 352.55166 cents 2: 1 355.65081 cents 2: 1 358.46586 cents 2: 1 358.58449 cents 2: 1 395.37001 cents 3: 1 482.94966 cents 3: 1 485.76471 cents 3: 1 488.98248 cents 3: 1 500.99425 cents 3: 1 528.88855 cents 3: 1 543.81260 cents 3: 1 568.60775 cents 4: 1 631.39225 cents 4: 1 656.18740 cents 4: 1 671.11145 cents 4: 1 699.00575 cents 4: 1 711.01752 cents 4: 1 714.23529 cents 4: 1 717.05034 cents 5: 1 804.62999 cents 5: 1 841.41551 cents 5: 1 841.53414 cents 5: 1 844.34919 cents 5: 1 847.44834 cents 5: 1 896.36426 cents 5: 1 924.25856 cents 6: 1 974.74719 cents 6: 1 989.97673 cents 6: 1 1014.65326 cents 6: 1 1026.76226 cents 6: 1 1051.55741 cents 6: 1 1069.60200 cents 6: 1 1072.70115 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 : 225.3 352.6 501.0 711.0 896.4 1069.6 1200.0 225.3 : 127.3 275.7 485.8 671.1 844.3 974.7 1200.0 352.6 : 148.4 358.5 543.8 717.1 847.4 1072.7 1200.0 501.0 : 210.0 395.4 568.6 699.0 924.3 1051.6 1200.0 711.0 : 185.3 358.6 489.0 714.2 841.5 990.0 1200.0 896.4 : 173.2 303.6 528.9 656.2 804.6 1014.7 1200.0 1069.6: 130.4 355.7 482.9 631.4 841.4 1026.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 127.2989 .. 225.2528 cents 97.95396 cents 127.29885 cents 2: 275.7414 .. 395.3700 cents 119.62857 cents 50.48863 cents 3: 482.9497 .. 568.6078 cents 85.65810 cents 87.57965 cents 4: 631.3922 .. 717.0503 cents 85.65810 cents 62.78449 cents 5: 804.6300 .. 924.2586 cents 119.62857 cents 87.57965 cents 6: 974.7472 .. 1072.7011 cents 97.95396 cents 50.48863 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 127.29885 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 225.25281 cents Average / Smallest step : 1.346662 Largest / Average step : 1.313975 Largest / Smallest step : 1.769480 Median interval of one step : 173.23774 cents, amount: 1 Least squares average step : 175.54887 cents, oct.: 1228.84211 cents Scale is strictly proper Step pattern alph. order: ABCDEFG Step pattern size order : GACFEDB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 50.48863 cents Scale diversity : 1.530271 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.494599 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 : 0.11863 cents Number of recognisable fifths : 4, average 710.3272 cents Number of appreciable fifths : 3, average 708.0862 cents Best fifths form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 14.2857% Limited inverse transpositions with margin 97.9540 cents: 1 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 31.6900 c. M: 53.8242 c. Lebeng 9: 2 1 1 1 2 1 1 P M ME S SD: 34.5473 c. M:-47.4483 c. 10: 2 1 1 2 1 2 1 P M ME S SD: 24.1408 c. M: 56.3643 c. Sethares Neutral, Beatles-7, Dichotic-7 12: 2 2 1 2 2 2 1 P M ME S SD: 23.7507 c. M:-47.4483 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 14: 3 1 2 2 2 2 2 P T3 SD: 27.1233 c. M: 41.0306 c. 15: 3 1 2 3 2 2 2 P D3 SD: 20.5030 c. M: 32.5517 c. 16: 3 2 2 2 3 2 2 SP M ME S SD: 19.9105 c. M: 36.0175 c. Antiphrygian 17: 3 2 2 3 3 2 2 SP D3 S SD: 10.8554 c. M:-21.2828 c. Pseudo Rast 20: 4 2 2 4 3 3 2 P SD: 11.4376 c. M: 20.9942 c. 24: 4 3 3 4 4 3 3 SP D3 S SD: 12.8954 c. M: 25.2528 c. Arabic Diatonic, Maqam Rast, Quasi-equal Heptatonic, Neutral Diatonic Phrygian 26: 5 3 3 4 4 4 3 SP T3 SD: 12.7980 c. M: 19.4412 c. 27: 5 3 3 5 4 4 3 SP SD: 5.7228 c. M: 12.1054 c. 44: 8 5 5 8 7 6 5 SP SD: 5.4538 c. M: 10.0852 c. 47: 9 5 6 8 7 7 5 SP SD: 4.8932 c. M:-9.6441 c. 52: 10 5 7 9 8 7 6 SP SD: 5.5232 c. M: 8.0635 c. 55: 10 6 7 10 8 8 6 SP SD: 4.5812 c. M:-8.9825 c. 57: 11 6 7 10 9 8 6 SP SD: 5.4171 c. M:-8.8989 c. 58: 11 6 7 10 9 9 6 SP SD: 4.8896 c. M: 7.5692 c. 62: 12 6 8 11 9 9 7 SP SD: 4.7793 c. M:-7.0053 c. 64: 12 7 8 11 10 9 7 SP SD: 2.8662 c. M:-5.2558 c. 74: 14 8 9 13 11 11 8 SP SD: 2.6840 c. M: 4.4724 c. 84: 16 9 10 15 13 12 9 SP SD: 2.9354 c. M:-4.5912 c. 86: 16 9 11 15 13 13 9 SP SD: 2.7850 c. M:-4.8166 c. 91: 17 10 11 16 14 13 10 SP SD: 1.5487 c. M:-3.4923 c. 118: 22 13 14 21 18 17 13 SP SD: 1.9661 c. M:-3.3805 c. 122: 23 13 15 21 19 18 13 SP SD: 1.6801 c. M: 2.8208 c. 139: 26 15 17 24 22 20 15 SP SD: 1.4788 c. M: 3.1038 c. 149: 28 16 18 26 23 22 16 SP SD: 1.6700 c. M: 2.4045 c. 150: 28 16 19 26 23 22 16 SP SD: 1.5927 c. M:-3.0058 c. 154: 29 16 19 27 24 22 17 SP SD: 1.5793 c. M: 2.2929 c. 166: 31 18 20 29 26 24 18 SP SD: 1.4976 c. M: 2.5838 c. 167: 31 18 21 29 26 24 18 SP SD: 1.4676 c. M: 2.4983 c. 174: 33 18 22 30 27 25 19 SP SD: 1.3651 c. M:-2.4540 c. 177: 33 19 22 31 27 26 19 SP SD: 1.0784 c. M:-1.5844 c. 187: 35 20 23 33 29 27 20 SP SD: 1.2414 c. M:-2.0558 c. 194: 36 21 24 34 30 28 21 SP SD: 1.0191 c. M: 2.5724 c. 201: 38 21 25 35 31 29 22 SP SD: 0.8345 c. M:-1.6129 c. 218: 41 23 27 38 34 31 24 SP SD: 0.8307 c. M: 1.7121 c. 246: 46 26 31 43 38 35 27 SP SD: 1.1426 c. M:-1.4448 c. 249: 47 26 31 44 38 36 27 SP SD: 1.0173 c. M:-2.2355 c. 256: 48 27 32 45 39 37 28 SP SD: 0.8779 c. M:-1.4825 c. 268: 50 29 33 47 41 39 29 SP SD: 0.8769 c. M: 1.3722 c. 292: 55 31 36 51 45 42 32 SP SD: 0.6504 c. M: 1.1089 c. 297: 56 31 37 52 46 43 32 SP SD: 0.7261 c. M:-1.1051 c. 304: 57 32 38 53 47 44 33 SP SD: 0.5413 c. M: 1.2359 c. 324: 61 34 40 57 50 47 35 SP SD: 0.6018 c. M: 0.9942 c. 331: 62 35 41 58 51 48 36 SP SD: 0.5993 c. M: 0.8960 c. 368: 69 39 46 64 57 53 40 SP SD: 0.5017 c. M:-1.1797 c. 378: 71 40 47 66 58 55 41 SP SD: 0.4980 c. M: 1.1262 c. 388: 73 41 48 68 60 56 42 SP SD: 0.3631 c. M:-0.5430 c. 395: 74 42 49 69 61 57 43 SP SD: 0.2360 c. M: 0.4427 c. 719: 135 76 89 126 111 104 78 SP SD: 0.2111 c. M: 0.3959 c. 766: 144 81 95 134 118 111 83 SP SD: 0.2605 c. M:-0.3719 c. 783: 147 83 97 137 121 113 85 SP SD: 0.1132 c. M:-0.1875 c. 810: 152 86 100 142 125 117 88 SP SD: 0.1100 c. M: 0.2535 c. 1178: 221 125 146 206 182 170 128 SP SD: 0.0977 c. M:-0.1942 c. 1198: 225 127 148 210 185 173 130 SP SD: 0.1307 c. M:-0.1810 c. 1205: 226 128 149 211 186 174 131 SP SD: 0.0902 c. M: 0.1906 c. 1593: 299 169 197 279 246 230 173 SP SD: 0.0552 c. M:-0.0936 c. 1988: 373 211 246 348 307 287 216 SP SD: 0.0458 c. M: 0.1019 c. 2189: 411 232 271 383 338 316 238 SP SD: 0.0529 c. M: 0.0725 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: 4.5313 cents 3 x x 4 x 5 x 6 S SD: 4.1208 cents 4 x 5 x 6:7 x 8 S SD: 20.1133 cents 5 x 6:7 x 8:9:10 S SD: 26.4936 cents 6:7 x 8:9:10:11:12 S SD: 8.1251 cents 7:8 x 9:11:12:13:14 SD: 17.3557 cents 8:9:10:11:12:13:15:16 SD: 12.5162 cents 9:10:11:12:14:15:17:18 SD: 10.9815 cents 11 x 13:15:17:18:20:22 SD: 16.8615 cents 12:14:15:16:18:20:22:24 S SD: 8.4715 cents 13:15:16:17:20:22:24:26 SD: 8.2987 cents 14:16:17:19:21:24:26:28 SD: 7.1569 cents 18:21:22:24:27:30:33:36 S SD: 7.0031 cents 20:23:25:27:30:34:37:40 SD: 6.9440 cents 21:24:26:28:32:35:39:42 SD: 4.0890 cents 22:25:27:29:33:37:41:44 SD: 3.7749 cents 27:31:33:36:41:45:50:54 SD: 3.2870 cents 35:40:43:47:53:59:65:70 SD: 2.2801 cents 44:50:54:59:66:74:82:88 SD: 2.1591 cents 49:56:60:65:74:82:91:98 SD: 2.0911 cents 50:57:61:67:75:84:93:100 SD: 2.0783 cents 53:60:65:71:80:89:98:106 SD: 1.8715 cents 57:65:70:76:86:96:106:114 SD: 1.2869 cents 71:81:87:95:107:119:132:142 SD: 0.9090 cents 102:116:125:136:154:171:189:204 SD: 0.7466 cents 116:132:142:155:175:195:215:232 SD: 0.6333 cents 128:146:157:171:193:215:237:256 SD: 0.6298 cents 137:156:168:183:207:230:254:274 SD: 0.5349 cents 146:166:179:195:220:245:271:292 SD: 0.4918 cents 164:187:201:219:247:275:304:328 SD: 0.4894 cents 173:197:212:231:261:290:321:346 SD: 0.3483 cents 230:262:282:307:347:386:427:460 SD: 0.3038 cents 274:312:336:366:413:460:508:548 SD: 0.2023 cents 345:393:423:461:520:579:640:690 SD: 0.1676 cents 447:509:548:597:674:750:829:894 SD: 0.0938 cents