Scala analysis: CD01_20_rast_Egypt
L'argent fut incrusté d'hyacinthe / Toi qui te refuses à moi / Je me sacrifierais pour lui et le secourrais - Darwîsh Muhammad al-Harîrî (rast, Egypt)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 224.784 cents 224.784400 2: 360.275 cents 360.275262 3: 502.387 cents 502.387405 4: 702.790 cents 702.789662 5: 804.643 cents 804.642948 6: 908.323 cents 908.322633 7: 1055.114 cents 1055.113884 8: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 144.8861 cents 144.8861 1: 224.7844 cents 224.7844 2: 135.4909 cents 135.4909 3: 142.1121 cents 142.1121 4: 200.4023 cents 200.4023 5: 101.8533 cents 101.8533 6: 103.6797 cents 103.6797 7: 146.7913 cents 146.7913 8: 144.8861 cents 144.8861
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 101.85329 cents 1: 1 103.67968 cents 1: 1 135.49086 cents 1: 1 142.11214 cents 1: 1 144.88612 cents 1: 1 146.79125 cents 1: 1 200.40226 cents 1: 1 224.78440 cents 2: 1 205.53297 cents 2: 1 250.47094 cents 2: 1 277.60300 cents 2: 1 291.67737 cents 2: 1 302.25554 cents 2: 1 342.51440 cents 2: 1 360.27526 cents 2: 1 369.67052 cents 3: 1 352.32422 cents 3: 1 395.35705 cents 3: 1 405.93523 cents 3: 1 444.36769 cents 3: 1 478.00526 cents 3: 1 502.38740 cents 3: 1 505.16138 cents 3: 1 516.46177 cents 4: 1 497.21034 cents 4: 1 548.04737 cents 4: 1 552.72648 cents 4: 1 579.85855 cents 4: 1 620.14145 cents 4: 1 647.27352 cents 4: 1 651.95263 cents 4: 1 702.78966 cents 5: 1 683.53823 cents 5: 1 694.83862 cents 5: 1 697.61260 cents 5: 1 721.99474 cents 5: 1 755.63231 cents 5: 1 794.06477 cents 5: 1 804.64295 cents 5: 1 847.67578 cents 6: 1 830.32948 cents 6: 1 839.72474 cents 6: 1 857.48560 cents 6: 1 897.74446 cents 6: 1 908.32263 cents 6: 1 922.39700 cents 6: 1 949.52906 cents 6: 1 994.46703 cents 7: 1 975.21560 cents 7: 1 999.59774 cents 7: 1 1053.20875 cents 7: 1 1055.11388 cents 7: 1 1057.88786 cents 7: 1 1064.50914 cents 7: 1 1096.32031 cents 7: 1 1098.14671 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 : 224.8 360.3 502.4 702.8 804.6 908.3 1055.1 1200.0 224.8 : 135.5 277.6 478.0 579.9 683.5 830.3 975.2 1200.0 360.3 : 142.1 342.5 444.4 548.0 694.8 839.7 1064.5 1200.0 502.4 : 200.4 302.3 405.9 552.7 697.6 922.4 1057.9 1200.0 702.8 : 101.9 205.5 352.3 497.2 722.0 857.5 999.6 1200.0 804.6 : 103.7 250.5 395.4 620.1 755.6 897.7 1098.1 1200.0 908.3 : 146.8 291.7 516.5 652.0 794.1 994.5 1096.3 1200.0 1055.1: 144.9 369.7 505.2 647.3 847.7 949.5 1053.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 101.8533 .. 224.7844 cents 122.93111 cents 101.85329 cents 2: 205.5330 .. 369.6705 cents 164.13755 cents -19.25143 cents 3: 352.3242 .. 516.4618 cents 164.13754 cents -17.34629 cents 4: 497.2103 .. 702.7897 cents 205.57932 cents -19.25143 cents 5: 683.5382 .. 847.6758 cents 164.13755 cents -19.25143 cents 6: 830.3295 .. 994.4670 cents 164.13755 cents -17.34629 cents 7: 975.2156 .. 1098.1467 cents 122.93111 cents -19.25143 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 101.85329 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 224.78440 cents Average / Smallest step : 1.472707 Largest / Average step : 1.498563 Largest / Smallest step : 2.206943 Median interval of one step : 143.49913 cents, amount: 0 Least squares average step : 155.50296 cents, oct.: 1244.02367 cents Scale is not proper Step pattern alph. order: ABCDEFGH Step pattern size order : HCDGABFE Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 5.13071 cents Scale diversity : 1.620475 Lumma stability : 0.169755 Lumma impropriety factor : 0.093082 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 : 1.82640 cents Number of recognisable fifths : 3, average 698.4136 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: 56.5876 c. M: 102.7897 c. 9: 2 1 1 1 1 1 1 1 P M ME SD: 28.2295 c. M:-41.8823 c. 10: 2 1 1 2 1 1 1 1 P D3 S SD: 26.3841 c. M:-51.6774 c. 12: 2 2 1 2 1 1 2 1 P D3 S SD: 23.2147 c. M:-44.8861 c. Major Bebop, Altered Mixolydian 15: 3 2 1 3 1 1 2 2 N SD: 21.3867 c. M:-39.7247 c. 16: 3 2 2 2 2 1 2 2 P T3 SD: 15.8520 c. M: 27.7897 c. 17: 3 2 2 3 1 2 2 2 P SD: 12.2252 c. M: 28.1724 c. 20: 4 2 2 4 1 2 3 2 N SD: 17.0471 c. M:-24.8861 c. 21: 4 2 3 3 2 2 2 3 N SD: 13.7499 c. M: 26.5425 c. 22: 4 3 2 4 2 2 2 3 N SD: 14.0229 c. M:-21.5429 c. 24: 4 3 3 4 2 2 3 3 P SD: 10.3096 c. M: 24.7844 c. 26: 5 3 3 4 2 3 3 3 P SD: 10.6894 c. M: 20.0276 c. 27: 5 3 3 5 2 2 4 3 N SD: 10.0809 c. M: 19.4337 c. 28: 5 3 4 4 3 2 4 3 P SD: 12.6252 c. M: 17.4181 c. 31: 6 3 4 5 3 2 4 4 N SD: 9.5221 c. M: 18.0001 c. 33: 6 4 4 5 3 3 4 4 P SD: 5.7385 c. M: 11.8806 c. 36: 7 4 4 6 3 3 5 4 N SD: 6.6305 c. M:-11.5528 c. 43: 8 5 5 7 4 4 5 5 P SD: 5.5242 c. M:-12.6076 c. 48: 9 5 6 8 4 4 6 6 N SD: 5.4324 c. M: 10.2753 c. 53: 10 6 6 9 5 4 7 6 N SD: 5.2878 c. M:-10.4514 c. 57: 11 6 7 9 5 5 7 7 N SD: 4.5004 c. M: 8.0528 c. 58: 11 6 7 10 5 5 7 7 N SD: 3.9470 c. M: 8.5511 c. 63: 12 7 7 11 5 6 7 8 N SD: 4.8126 c. M: 7.4948 c. 66: 12 8 8 11 5 6 8 8 N SD: 4.5001 c. M:-6.7035 c. 67: 13 7 8 11 6 6 8 8 N SD: 3.8516 c. M:-8.0514 c. 70: 13 8 8 12 6 6 9 8 N SD: 3.3998 c. M:-7.7433 c. 74: 14 8 9 12 7 6 9 9 N SD: 3.2956 c. M:-6.1679 c. 83: 16 9 10 14 7 7 10 10 N SD: 3.8833 c. M:-6.5409 c. 84: 16 9 10 14 7 8 10 10 N SD: 3.5155 c. M:-5.9631 c. 86: 16 10 10 14 8 7 11 10 N SD: 3.2975 c. M:-5.3512 c. 89: 17 10 10 15 8 7 11 11 N SD: 3.6071 c. M: 4.9518 c. 90: 17 10 11 15 7 8 11 11 N SD: 2.8379 c. M: 4.6429 c. 91: 17 10 11 15 8 8 11 11 N SD: 2.1680 c. M: 4.2313 c. 107: 20 12 13 18 9 9 13 13 N SD: 1.9479 c. M:-3.7524 c. 116: 22 13 14 19 10 10 14 14 N SD: 2.2640 c. M:-4.5091 c. 119: 22 14 14 20 10 10 15 14 N SD: 2.4418 c. M:-3.7096 c. 124: 23 14 15 21 10 11 15 15 N SD: 1.8633 c. M:-3.6620 c. 127: 24 14 15 21 11 11 16 15 N SD: 2.0766 c. M: 3.5771 c. 133: 25 15 16 22 11 12 16 16 N SD: 1.6544 c. M:-2.9556 c. 140: 26 16 17 23 12 12 17 17 N SD: 1.4473 c. M:-3.3269 c. 143: 27 16 17 24 12 12 18 17 N SD: 1.5480 c. M:-2.2288 c. 160: 30 18 19 27 13 14 20 19 N SD: 1.4135 c. M:-2.3861 c. 176: 33 20 21 29 15 15 22 21 N SD: 1.1902 c. M:-2.1580 c. 198: 37 22 24 33 17 17 24 24 N SD: 1.1713 c. M: 2.6995 c. 201: 38 22 24 34 17 17 25 24 N SD: 1.4714 c. M:-2.0813 c. 203: 38 23 24 34 17 18 24 25 N SD: 1.3009 c. M: 2.8971 c. 207: 39 23 25 34 18 18 25 25 N SD: 1.2611 c. M:-1.9604 c. 210: 39 24 25 35 18 18 26 25 N SD: 1.0806 c. M:-2.0290 c. 213: 40 24 25 36 18 18 26 26 N SD: 1.0358 c. M: 1.5928 c. 230: 43 26 27 39 19 20 28 28 N SD: 1.0027 c. M:-1.5582 c. 234: 44 26 28 39 20 20 29 28 N SD: 0.7763 c. M: 1.3009 c. 239: 45 27 28 40 20 21 29 29 N SD: 0.8196 c. M: 1.2957 c. 246: 46 28 29 41 21 21 30 30 N SD: 0.7032 c. M: 1.4553 c. 263: 49 30 31 44 22 23 32 32 N SD: 0.8430 c. M: 1.6011 c. 267: 50 30 32 44 23 23 33 32 N SD: 0.8396 c. M: 1.6661 c. 273: 51 31 32 46 23 24 33 33 N SD: 0.7795 c. M:-1.5675 c. 289: 54 33 34 48 25 25 35 35 N SD: 0.7430 c. M: 1.0596 c. 304: 57 34 36 51 26 26 37 37 N SD: 0.7316 c. M: 1.1665 c. 316: 59 36 37 53 27 27 39 38 N SD: 0.6268 c. M: 1.1216 c. 330: 62 37 39 55 28 29 40 40 N SD: 0.6818 c. M: 1.0066 c. 337: 63 38 40 56 29 29 41 41 N SD: 0.6837 c. M: 1.3060 c. 346: 65 39 41 58 29 30 42 42 N SD: 0.6281 c. M:-1.2566 c. 379: 71 43 45 63 32 33 46 46 N SD: 0.5544 c. M:-1.0427 c. 406: 76 46 48 68 34 35 50 49 N SD: 0.4913 c. M: 0.9335 c. 416: 78 47 49 70 35 36 51 50 N SD: 0.5044 c. M:-1.0565 c. 432: 81 49 51 72 37 37 53 52 N SD: 0.4906 c. M:-0.9126 c. 437: 82 49 52 73 37 38 53 53 N SD: 0.4023 c. M: 0.6516 c. 449: 84 51 53 75 38 39 55 54 N SD: 0.3281 c. M:-0.5654 c. 497: 93 56 59 83 42 43 61 60 N SD: 0.3523 c. M: 0.6188 c. 613: 115 69 73 102 52 53 75 74 N SD: 0.2816 c. M:-0.7121 c. 647: 121 73 77 108 55 56 79 78 N SD: 0.3164 c. M:-0.4873 c. 662: 124 75 78 111 56 57 81 80 N SD: 0.2833 c. M:-0.5336 c. 695: 130 79 82 116 59 60 85 84 N SD: 0.2490 c. M:-0.5880 c. 753: 141 85 89 126 64 65 92 91 N SD: 0.1641 c. M: 0.3954 c. 893: 167 101 106 149 76 77 109 108 N SD: 0.2060 c. M: 0.3723 c. 896: 168 101 106 150 76 77 110 108 N SD: 0.2226 c. M:-0.3353 c. 929: 174 105 110 155 79 80 114 112 N SD: 0.1359 c. M: 0.2494 c. 1202: 225 136 142 201 102 104 147 145 N SD: 0.1302 c. M: 0.2243 c. 1366: 256 154 162 228 116 118 167 165 N SD: 0.0687 c. M:-0.1058 c. 1815: 340 205 215 303 154 157 222 219 N SD: 0.0635 c. M:-0.1071 c. 2119: 397 239 251 354 180 183 259 256 N SD: 0.0639 c. M: 0.1054 c. 2295: 430 259 272 383 195 198 281 277 N SD: 0.0594 c. M:-0.0963 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x x 4 S SD: 0.4173 cents 3 x x 4 x x 5 x 6 S SD: 8.1181 cents 4 x 5 x 6 x 7 x 8 S SD: 16.4684 cents 5 x 6:7 x 8 x 9:10 S SD: 19.9013 cents 6:7 x 8:9 x 10:11:12 S SD: 8.1619 cents 7:8 x 9 x 11:12:13:14 SD: 12.8579 cents 8:9:10:11:12:13:14:15:16 H SD: 12.2195 cents 9:10:11:12 x 14:15:17:18 SD: 11.2873 cents 12:14:15:16:18:19:20:22:24 S SD: 7.0253 cents 14:16:17:19:21:22:24:26:28 SD: 6.4921 cents 20:23:25:27:30:32:34:37:40 SD: 4.9291 cents 22:25:27:29:33:35:37:40:44 SD: 4.1495 cents 26:30:32:35:39:41:44:48:52 SD: 3.9195 cents 29:33:36:39:44:46:49:53:58 SD: 3.5993 cents 30:34:37:40:45:48:51:55:60 SD: 2.2161 cents 42:48:52:56:63:67:71:77:84 SD: 1.7615 cents 44:50:54:59:66:70:74:81:88 SD: 1.5150 cents 56:64:69:75:84:89:95:103:112 SD: 1.2837 cents 74:84:91:99:111:118:125:136:148 SD: 0.8803 cents 86:98:106:115:129:137:145:158:172 SD: 0.6624 cents 116:132:143:155:174:185:196:213:232 SD: 0.6537 cents 122:139:150:163:183:194:206:224:244 SD: 0.6100 cents 130:148:160:174:195:207:220:239:260 SD: 0.4701 cents 152:173:187:203:228:242:257:280:304 SD: 0.4536 cents 181:206:223:242:272:288:306:333:362 SD: 0.3594 cents 216:246:266:289:324:344:365:397:432 SD: 0.3203 cents 238:271:293:318:357:379:402:438:476 SD: 0.2324 cents 294:335:362:393:441:468:497:541:588 SD: 0.2180 cents 368:419:453:492:552:586:622:677:736 SD: 0.1712 cents 419:477:516:560:629:667:708:771:838 SD: 0.1237 cents 519:591:639:694:779:826:877:955:1038 SD: 0.1221 cents 541:616:666:723:812:861:914:995:1082 SD: 0.0985 cents