Scala analysis: CD03_10_Egypt
Suite - Aziz 'Uthmân (nahawand, Egypt)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 96.862 cents 96.861862 2: 311.486 cents 311.486269 3: 401.078 cents 401.077705 4: 497.637 cents 497.637451 5: 610.580 cents 610.580247 6: 722.094 cents 722.094217 7: 889.125 cents 889.124620 8: 1002.975 cents 1002.975151 9: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 197.0248 cents 197.0248 1: 96.8619 cents 96.8619 2: 214.6244 cents 214.6244 3: 89.5914 cents 89.5914 4: 96.5597 cents 96.5597 5: 112.9428 cents 112.9428 6: 111.5140 cents 111.5140 7: 167.0304 cents 167.0304 8: 113.8505 cents 113.8505 9: 197.0248 cents 197.0248
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 89.59144 cents 1: 1 96.55975 cents 1: 1 96.86186 cents 1: 1 111.51397 cents 1: 1 112.94280 cents 1: 1 113.85053 cents 1: 1 167.03040 cents 1: 1 197.02485 cents 1: 1 214.62441 cents 2: 1 186.15118 cents 2: 1 209.50254 cents 2: 1 224.45677 cents 2: 1 278.54437 cents 2: 1 280.88093 cents 2: 1 293.88671 cents 2: 1 304.21584 cents 2: 1 310.87538 cents 2: 1 311.48627 cents 3: 1 299.09398 cents 3: 1 321.01651 cents 3: 1 391.48717 cents 3: 1 392.39490 cents 3: 1 400.77559 cents 3: 1 401.07770 cents 3: 1 407.73724 cents 3: 1 477.90578 cents 3: 1 508.51112 cents 4: 1 410.60795 cents 4: 1 488.04691 cents 4: 1 497.63745 cents 4: 1 505.33770 cents 4: 1 513.71839 cents 4: 1 574.76765 cents 4: 1 589.41975 cents 4: 1 598.10255 cents 4: 1 622.36165 cents 5: 1 577.63835 cents 5: 1 601.89745 cents 5: 1 610.58025 cents 5: 1 625.23235 cents 5: 1 686.28161 cents 5: 1 694.66230 cents 5: 1 702.36255 cents 5: 1 711.95308 cents 5: 1 789.39205 cents 6: 1 691.48888 cents 6: 1 722.09422 cents 6: 1 792.26276 cents 6: 1 798.92230 cents 6: 1 799.22441 cents 6: 1 807.60510 cents 6: 1 808.51283 cents 6: 1 878.98349 cents 6: 1 900.90602 cents 7: 1 888.51373 cents 7: 1 889.12462 cents 7: 1 895.78416 cents 7: 1 906.11329 cents 7: 1 919.11907 cents 7: 1 921.45563 cents 7: 1 975.54323 cents 7: 1 990.49746 cents 7: 1 1013.84882 cents 8: 1 985.37559 cents 8: 1 1002.97515 cents 8: 1 1032.96960 cents 8: 1 1086.14947 cents 8: 1 1087.05720 cents 8: 1 1088.48603 cents 8: 1 1103.13814 cents 8: 1 1103.44025 cents 8: 1 1110.40856 cents Highest number of different intervals for one interval class: 9 Average number of different intervals per interval class: 9.00000 = 9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 0.0 : 96.9 311.5 401.1 497.6 610.6 722.1 889.1 1003.0 1200.0 96.9 : 214.6 304.2 400.8 513.7 625.2 792.3 906.1 1103.1 1200.0 311.5 : 89.6 186.2 299.1 410.6 577.6 691.5 888.5 985.4 1200.0 401.1 : 96.6 209.5 321.0 488.0 601.9 798.9 895.8 1110.4 1200.0 497.6 : 112.9 224.5 391.5 505.3 702.4 799.2 1013.8 1103.4 1200.0 610.6 : 111.5 278.5 392.4 589.4 686.3 900.9 990.5 1087.1 1200.0 722.1 : 167.0 280.9 477.9 574.8 789.4 879.0 975.5 1088.5 1200.0 889.1 : 113.9 310.9 407.7 622.4 712.0 808.5 921.5 1033.0 1200.0 1003.0: 197.0 293.9 508.5 598.1 694.7 807.6 919.1 1086.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 89.5914 .. 214.6244 cents 125.03297 cents 89.59144 cents 2: 186.1512 .. 311.4863 cents 125.33509 cents -28.47323 cents 3: 299.0940 .. 508.5111 cents 209.41714 cents -12.39229 cents 4: 410.6079 .. 622.3616 cents 211.75370 cents -97.90317 cents 5: 577.6384 .. 789.3921 cents 211.75370 cents -44.72330 cents 6: 691.4889 .. 900.9060 cents 209.41714 cents -97.90317 cents 7: 888.5137 .. 1013.8488 cents 125.33509 cents -12.39229 cents 8: 985.3756 .. 1110.4086 cents 125.03297 cents -28.47323 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 89.59144 cents, class 1 Average step (divided formal octave): 133.3333 cents Largest one step interval : 214.62441 cents Average / Smallest step : 1.488237 Largest / Average step : 1.609683 Largest / Smallest step : 2.395591 Median interval of one step : 112.94280 cents, amount: 1 Least squares average step : 127.53248 cents, oct.: 1147.79234 cents Scale is not proper Step pattern alph. order: ABCDEFGHI Step pattern size order : CIABEDGFH Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 2.87071 cents Scale diversity : 1.461210 Lumma stability : 0.149319 Lumma impropriety factor : 0.268551 Rothenberg efficiency : 0.222222 redundancy: 0.777778 Efficiency x scale size : 2.000000 Number of different interval sizes : 72 = 9.00000 / class Number of one step interval sizes : 9 Highest interval variety : 9 Mean interval variety : 9.00000 = 9 Median interval variety : 9 Lowest interval variety : 9 Smallest interval difference : 0.30212 cents Number of recognisable fifths : 5, average 697.3497 cents Number of appreciable fifths : 4, average 700.1167 cents Formal octave complements present : 1 = 11.1111% -- Rational properties --
FIT/MODE
9: 0 2 0 1 1 1 1 1 2 N T3 SD: 82.2077 c. M: 134.4110 c. 10: 1 1 1 1 1 1 1 1 2 P M ME S SD: 36.5461 c. M: 71.4863 c. 11: 1 2 1 1 1 1 1 1 2 N D3 S SD: 30.3782 c. M:-47.8171 c. 12: 1 2 1 1 1 1 2 1 2 N D3 S SD: 9.8643 c. M: 22.0942 c. 22: 2 4 1 2 2 2 3 2 4 N SD: 14.1911 c. M: 21.1570 c. 23: 2 4 2 2 2 2 3 2 4 N SD: 12.2765 c. M:-24.1017 c. 26: 2 5 2 2 2 3 3 3 4 N SD: 11.2723 c. M:-16.3673 c. 27: 2 5 2 2 3 2 4 3 4 N SD: 9.2381 c. M:-19.2471 c. 30: 2 6 2 2 3 3 4 3 5 N SD: 9.8741 c. M: 17.6375 c. 31: 3 5 2 3 3 3 4 3 5 N SD: 9.8375 c. M:-19.2672 c. 35: 3 6 3 3 3 3 5 3 6 N SD: 7.8670 c. M:-16.6483 c. 36: 3 6 3 3 3 4 5 3 6 N SD: 7.5565 c. M: 11.4863 c. 38: 3 7 3 3 3 4 5 4 6 N SD: 6.5098 c. M: 10.5802 c. 42: 3 8 3 3 4 4 6 4 7 N SD: 7.2175 c. M: 11.9232 c. 43: 3 8 3 4 4 4 6 4 7 N SD: 6.3621 c. M: 13.1409 c. 45: 4 8 3 4 4 4 6 5 7 N SD: 7.1010 c. M:-10.3582 c. 47: 4 8 4 3 5 4 7 4 8 N SD: 6.6260 c. M: 12.5311 c. 50: 4 9 4 4 4 5 7 5 8 N SD: 5.0799 c. M: 10.5802 c. 51: 4 9 4 4 5 5 7 5 8 N SD: 4.8261 c. M:-8.7896 c. 53: 4 10 4 4 5 5 7 5 9 N SD: 4.7283 c. M: 6.7487 c. 61: 5 11 4 5 6 6 8 6 10 N SD: 4.1405 c. M: 7.6351 c. 63: 5 11 5 5 6 6 9 6 10 N SD: 3.9312 c. M: 6.7244 c. 65: 5 12 5 5 6 6 9 6 11 N SD: 3.4061 c. M: 6.0521 c. 73: 6 13 5 6 7 7 10 7 12 N SD: 2.9084 c. M: 6.5572 c. 77: 6 14 6 6 7 7 11 7 13 N SD: 3.2664 c. M: 5.5726 c. 78: 6 14 6 6 8 7 11 7 13 N SD: 3.4598 c. M: 5.3298 c. 84: 7 15 6 7 8 8 11 8 14 N SD: 3.3432 c. M:-6.4772 c. 85: 7 15 6 7 8 8 12 8 14 N SD: 2.7437 c. M: 5.7836 c. 86: 7 15 7 7 8 8 12 8 14 N SD: 3.2879 c. M:-4.6881 c. 90: 7 16 7 7 9 8 13 8 15 N SD: 3.2300 c. M: 4.8196 c. 92: 7 17 7 7 9 8 13 9 15 N SD: 3.0316 c. M: 5.5575 c. 96: 8 17 7 8 9 9 13 9 16 N SD: 2.1406 c. M:-3.1381 c. 108: 9 19 8 9 10 10 15 10 18 N SD: 1.6976 c. M:-3.1381 c. 123: 10 22 9 10 12 11 17 12 20 N SD: 1.6322 c. M:-4.0539 c. 128: 10 23 10 10 12 12 18 12 21 N SD: 1.5877 c. M: 3.1119 c. 135: 11 24 10 11 13 12 19 13 22 N SD: 1.3474 c. M:-2.7531 c. 159: 13 28 12 13 15 15 22 15 26 N SD: 1.3480 c. M:-2.4341 c. 171: 14 30 13 14 16 16 24 16 28 N SD: 1.3347 c. M: 2.7143 c. 173: 14 31 13 14 16 16 24 17 28 N SD: 1.2992 c. M:-2.8052 c. 185: 15 33 14 15 17 17 26 18 30 N SD: 1.3311 c. M:-2.4303 c. 188: 15 34 14 15 18 17 26 18 31 N SD: 1.2375 c. M:-2.1857 c. 200: 16 36 15 16 19 18 28 19 33 N SD: 1.0856 c. M: 2.0942 c. 201: 16 36 15 16 19 19 28 19 33 N SD: 1.1263 c. M: 2.1151 c. 209: 17 37 16 17 19 20 29 20 34 N SD: 1.3552 c. M: 1.9678 c. 212: 17 38 16 17 20 20 29 20 35 N SD: 1.0093 c. M:-2.4341 c. 224: 18 40 17 18 21 21 31 21 37 N SD: 0.6937 c. M: 1.1894 c. 273: 22 49 20 22 26 25 38 26 45 N SD: 0.8259 c. M: 1.2151 c. 297: 24 53 22 24 28 28 41 28 49 N SD: 0.6874 c. M:-1.1381 c. 309: 25 55 23 25 29 29 43 29 51 N SD: 0.6739 c. M: 1.0777 c. 347: 28 62 26 28 33 32 48 33 57 N SD: 0.5870 c. M:-1.5235 c. 359: 29 64 27 29 34 33 50 34 59 N SD: 0.4547 c. M:-1.1189 c. 371: 30 66 28 30 35 34 52 35 61 N SD: 0.5379 c. M: 0.9741 c. 401: 32 72 30 32 38 37 56 38 66 N SD: 0.5991 c. M: 1.1013 c. 409: 33 73 31 33 38 38 57 39 67 N SD: 0.5509 c. M:-1.1401 c. 425: 34 76 32 34 40 40 59 40 70 N SD: 0.6273 c. M: 0.8980 c. 432: 35 77 32 35 41 40 60 41 71 N SD: 0.4711 c. M: 1.0777 c. 470: 38 84 35 38 44 44 65 45 77 N SD: 0.3397 c. M: 0.6140 c. 482: 39 86 36 39 45 45 67 46 79 N SD: 0.3166 c. M: 0.6217 c. 548: 44 98 41 44 52 51 76 52 90 N SD: 0.3959 c. M: 0.5572 c. 560: 45 100 42 45 53 52 78 53 92 N SD: 0.3683 c. M: 0.7720 c. 598: 48 107 45 48 56 56 83 57 98 N SD: 0.3532 c. M: 0.5468 c. 646: 52 116 48 52 61 60 90 61 106 N SD: 0.4090 c. M:-0.6587 c. 656: 53 117 49 53 62 61 91 62 108 N SD: 0.3598 c. M: 0.5361 c. 658: 53 118 49 53 62 61 92 62 108 N SD: 0.3512 c. M:-0.8450 c. 670: 54 120 50 54 63 62 93 64 110 N SD: 0.3056 c. M: 0.7664 c. 694: 56 124 52 56 65 65 96 66 114 N SD: 0.3023 c. M:-0.6724 c. 706: 57 126 53 57 66 66 98 67 116 N SD: 0.2618 c. M: 0.4381 c. 829: 67 148 62 67 78 77 115 79 136 N SD: 0.2275 c. M: 0.3430 c. 841: 68 150 63 68 79 78 117 80 138 N SD: 0.2145 c. M: 0.4280 c. 979: 79 175 73 79 92 91 136 93 161 N SD: 0.2238 c. M: 0.4627 c. 1030: 83 184 77 83 97 96 143 98 169 N SD: 0.2204 c. M: 0.4183 c. 1107: 89 198 83 89 104 103 154 105 182 N SD: 0.2405 c. M: 0.3849 c. 1116: 90 200 83 90 105 104 155 106 183 N SD: 0.2389 c. M:-0.4864 c. 1128: 91 202 84 91 106 105 157 107 185 N SD: 0.1738 c. M:-0.2462 c. 1140: 92 204 85 92 107 106 159 108 187 N SD: 0.1613 c. M:-0.3491 c. 1278: 103 229 95 103 120 119 178 121 210 N SD: 0.1489 c. M: 0.2516 c. 1401: 113 251 104 113 132 130 195 133 230 N SD: 0.1330 c. M:-0.2910 c. 1413: 114 253 105 114 133 131 197 134 232 N SD: 0.1274 c. M: 0.2284 c. 1529: 123 274 114 123 144 142 213 145 251 N SD: 0.1208 c. M: 0.3282 c. 1625: 131 291 121 131 153 151 226 154 267 N SD: 0.1076 c. M:-0.1445 c. 1637: 132 293 122 132 154 152 228 155 269 N SD: 0.0877 c. M: 0.1651 c. 1645: 133 294 123 132 155 153 229 156 270 N SD: 0.0987 c. M:-0.1594 c. 2011: 162 360 150 162 189 187 280 191 330 N SD: 0.0943 c. M: 0.1935 c. 2107: 170 377 157 170 198 196 293 200 346 N SD: 0.0771 c. M:-0.1319 c. 2119: 171 379 158 171 199 197 295 201 348 N SD: 0.0793 c. M:-0.1445 c. 2315: 187 414 173 186 218 215 322 220 380 N SD: 0.0740 c. M: 0.1397 c.
FIT/HARMONIC
1 x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x 4 S SD: 10.0696 cents 3 x x x 4 x x 5 x 6 S SD: 1.5944 cents 4 x x 5 x x 6 x 7:8 S SD: 10.5763 cents 5 x 6 x x 7 x 8:9:10 S SD: 16.3827 cents 6 x 7 x 8 x 9:10:11:12 S SD: 11.2680 cents 7 x 8:9 x 10:11:12:13:14 S SD: 19.1460 cents 8:9 x 10:11 x 12:13:14:16 S SD: 19.4266 cents 9:10:11 x 12:13:14:15:16:18 S SD: 13.2227 cents 10:11:12 x 13:14:15:17:18:20 SD: 11.7425 cents 11:12:13:14:15:16:17:18:20:22 S SD: 11.1168 cents 12:13:14:15:16:17:18:20:21:24 S SD: 8.3151 cents 13:14 x 16:17:19:20:22:23:26 SD: 10.6347 cents 14:15:17:18:19:20:21:23:25:28 SD: 7.5133 cents 15:16:18:19:20:21:23:25:27:30 SD: 4.5138 cents 19:20:23:24:25:27:29:32:34:38 SD: 3.9409 cents 30:32:36:38:40:43:46:50:54:60 SD: 3.5539 cents 31:33:37:39:41:44:47:52:55:62 SD: 2.5435 cents 36:38:43:45:48:51:55:60:64:72 SD: 2.5008 cents 42:44:50:53:56:60:64:70:75:84 SD: 2.4449 cents 45:48:54:57:60:64:68:75:80:90 SD: 2.3046 cents 46:49:55:58:61:65:70:77:82:92 SD: 2.2828 cents 50:53:60:63:67:71:76:84:89:100 SD: 1.7214 cents 54:57:65:68:72:77:82:90:96:108 SD: 1.5308 cents 66:70:79:83:88:94:100:110:118:132 SD: 1.0261 cents 85:90:102:107:113:121:129:142:152:170 SD: 0.8759 cents 106:112:127:134:141:151:161:177:189:212 SD: 0.8013 cents 116:123:139:146:155:165:176:194:207:232 SD: 0.7939 cents 122:129:146:154:163:174:185:204:218:244 SD: 0.7348 cents 126:133:151:159:168:179:191:211:225:252 SD: 0.7095 cents 135:143:162:170:180:192:205:226:241:270 SD: 0.7000 cents 137:145:164:173:183:195:208:229:245:274 SD: 0.6571 cents 141:149:169:178:188:201:214:236:252:282 SD: 0.6499 cents 153:162:183:193:204:218:232:256:273:306 SD: 0.4934 cents 168:178:201:212:224:239:255:281:300:336 SD: 0.4615 cents 177:187:212:223:236:252:269:296:316:354 SD: 0.4162 cents 192:203:230:242:256:273:291:321:343:384 SD: 0.3677 cents 222:235:266:280:296:316:337:371:396:444 SD: 0.3090 cents 265:280:317:334:353:377:402:443:473:530 SD: 0.2829 cents 279:295:334:352:372:397:423:466:498:558 SD: 0.2650 cents 315:333:377:397:420:448:478:526:562:630 SD: 0.2330 cents 334:353:400:421:445:475:507:558:596:668 SD: 0.2250 cents 381:403:456:480:508:542:578:637:680:762 SD: 0.1845 cents 456:482:546:575:608:649:692:762:814:912 SD: 0.1339 cents 487:515:583:614:649:693:739:814:869:974 SD: 0.0808 cents