Scala analysis: CD13_21_Turkey
Prélude, puis danse - Mesut Cemil Bey (unknown maqam, Turkey)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 211.157 cents 211.157060 2: 298.172 cents 298.171793 3: 369.720 cents 369.720284 4: 498.212 cents 498.211607 5: 705.911 cents 705.911296 6: 799.987 cents 799.987488 7: 1087.969 cents 1087.969339 8: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 112.0307 cents 112.0307 1: 211.1571 cents 211.1571 2: 87.0147 cents 87.0147 3: 71.5485 cents 71.5485 4: 128.4913 cents 128.4913 5: 207.6997 cents 207.6997 6: 94.0762 cents 94.0762 7: 287.9819 cents 287.9819 8: 112.0307 cents 112.0307
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 71.54849 cents 1: 1 87.01473 cents 1: 1 94.07619 cents 1: 1 112.03066 cents 1: 1 128.49132 cents 1: 1 207.69969 cents 1: 1 211.15706 cents 1: 1 287.98185 cents 2: 1 158.56322 cents 2: 1 200.03981 cents 2: 1 298.17179 cents 2: 1 301.77588 cents 2: 1 323.18772 cents 2: 1 336.19101 cents 2: 1 382.05804 cents 2: 1 400.01251 cents 3: 1 287.05455 cents 3: 1 369.72028 cents 3: 1 407.73950 cents 3: 1 410.20245 cents 3: 1 430.26720 cents 3: 1 494.08870 cents 3: 1 589.75773 cents 3: 1 611.16957 cents 4: 1 481.75094 cents 4: 1 494.75424 cents 4: 1 498.21161 cents 4: 1 501.81570 cents 4: 1 698.18430 cents 4: 1 701.78839 cents 4: 1 705.24576 cents 4: 1 718.24905 cents 5: 1 588.83043 cents 5: 1 610.24227 cents 5: 1 705.91130 cents 5: 1 769.73280 cents 5: 1 789.79755 cents 5: 1 792.26050 cents 5: 1 830.27972 cents 5: 1 912.94545 cents 6: 1 799.98749 cents 6: 1 817.94196 cents 6: 1 863.80899 cents 6: 1 876.81228 cents 6: 1 898.22412 cents 6: 1 901.82821 cents 6: 1 999.96019 cents 6: 1 1041.43678 cents 7: 1 912.01815 cents 7: 1 988.84294 cents 7: 1 992.30031 cents 7: 1 1071.50868 cents 7: 1 1087.96934 cents 7: 1 1105.92381 cents 7: 1 1112.98527 cents 7: 1 1128.45151 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 : 211.2 298.2 369.7 498.2 705.9 800.0 1088.0 1200.0 211.2 : 87.0 158.6 287.1 494.8 588.8 876.8 988.8 1200.0 298.2 : 71.5 200.0 407.7 501.8 789.8 901.8 1113.0 1200.0 369.7 : 128.5 336.2 430.3 718.2 830.3 1041.4 1128.5 1200.0 498.2 : 207.7 301.8 589.8 701.8 912.9 1000.0 1071.5 1200.0 705.9 : 94.1 382.1 494.1 705.2 792.3 863.8 992.3 1200.0 800.0 : 288.0 400.0 611.2 698.2 769.7 898.2 1105.9 1200.0 1088.0: 112.0 323.2 410.2 481.8 610.2 817.9 912.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 71.5485 .. 287.9819 cents 216.43336 cents 71.54849 cents 2: 158.5632 .. 400.0125 cents 241.44929 cents -129.41863 cents 3: 287.0545 .. 611.1696 cents 324.11503 cents -112.95797 cents 4: 481.7509 .. 718.2491 cents 236.49811 cents -129.41863 cents 5: 588.8304 .. 912.9455 cents 324.11503 cents -129.41863 cents 6: 799.9875 .. 1041.4368 cents 241.44929 cents -112.95797 cents 7: 912.0181 .. 1128.4515 cents 216.43336 cents -129.41863 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 71.54849 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 287.98185 cents Average / Smallest step : 2.096480 Largest / Average step : 1.919879 Largest / Smallest step : 4.024988 Median interval of one step : 120.26099 cents, amount: 0 Least squares average step : 144.38615 cents, oct.: 1155.08920 cents Scale is not proper Step pattern alph. order: ABCDEFGH Step pattern size order : GBAEFCHD Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 0.66553 cents Scale diversity : 1.563564 Lumma stability : 0.119247 Lumma impropriety factor : 0.599497 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 : 0.66553 cents Number of recognisable fifths : 5, average 705.8758 cents Number of appreciable fifths : 4, average 702.7824 cents Formal octave complements present : 1 = 12.5000% -- Rational properties --
FIT/MODE
8: 1 1 0 1 1 1 2 1 N D3 SD: 57.1034 c. M: 105.9113 c. 9: 2 0 1 1 1 1 2 1 N SD: 32.0512 c. M:-55.5096 c. 10: 2 0 1 1 2 1 2 1 N SD: 28.5154 c. M: 58.1718 c. 11: 2 1 0 2 1 1 3 1 N SD: 33.3512 c. M: 51.3658 c. 12: 2 1 1 1 2 1 3 1 N SD: 12.3873 c. M:-30.2797 c. 17: 3 1 1 2 3 1 4 2 N SD: 15.6182 c. M: 29.1458 c. 19: 3 2 1 2 3 2 4 2 N SD: 14.5262 c. M: 21.6834 c. 22: 4 1 2 2 4 2 5 2 N SD: 12.4812 c. M: 25.4445 c. 24: 4 2 1 3 4 2 6 2 N SD: 9.3514 c. M: 19.7203 c. 29: 5 2 2 3 5 2 7 3 N SD: 7.4436 c. M: 13.7806 c. 36: 6 3 2 4 6 3 9 3 N SD: 6.3248 c. M:-12.0307 c. 39: 7 3 2 4 7 3 9 4 N SD: 5.7966 c. M: 11.0463 c. 50: 9 3 3 6 8 4 12 5 N SD: 7.7496 c. M: 10.1718 c. 51: 9 4 3 5 9 4 12 5 N SD: 4.3831 c. M:-7.7106 c. 53: 9 4 3 6 9 4 13 5 N SD: 4.9895 c. M: 7.5347 c. 56: 10 4 3 6 10 4 14 5 N SD: 4.2951 c. M: 7.1303 c. 61: 11 4 4 6 11 5 14 6 N SD: 4.7282 c. M:-6.5699 c. 63: 11 5 3 7 11 5 15 6 N SD: 3.9120 c. M: 7.8155 c. 68: 12 5 4 7 12 5 17 6 N SD: 3.4184 c. M:-6.1483 c. 72: 13 5 4 8 12 6 17 7 N SD: 3.5822 c. M: 5.9113 c. 75: 13 6 4 8 13 6 18 7 N SD: 2.6325 c. M:-5.8282 c. 85: 15 6 5 9 15 7 20 8 N SD: 2.5050 c. M:-4.7184 c. 97: 17 7 6 10 17 8 23 9 N SD: 2.0557 c. M:-4.1362 c. 104: 18 8 6 11 18 8 25 10 N SD: 2.5008 c. M: 3.8336 c. 108: 19 8 6 12 19 8 26 10 N SD: 2.3386 c. M:-5.1998 c. 114: 20 8 7 12 20 9 27 11 N SD: 2.2502 c. M: 3.7588 c. 120: 21 9 7 13 21 9 29 11 N SD: 1.8973 c. M:-4.0887 c. 121: 21 9 7 13 21 10 29 11 N SD: 2.3670 c. M:-3.3183 c. 126: 22 9 8 13 22 10 30 12 N SD: 1.9184 c. M: 2.9735 c. 149: 26 11 9 16 26 11 36 14 N SD: 1.6016 c. M:-2.8135 c. 150: 26 11 9 16 26 12 36 14 N SD: 1.8093 c. M: 3.1571 c. 153: 27 11 9 17 26 12 37 14 N SD: 1.6046 c. M:-3.7492 c. 178: 31 13 11 19 31 14 42 17 N SD: 1.7400 c. M: 2.5761 c. 180: 32 13 10 20 31 14 43 17 N SD: 1.6908 c. M: 3.0536 c. 181: 32 13 11 19 31 15 43 17 N SD: 1.5688 c. M: 3.1489 c. 185: 33 13 11 20 32 14 45 17 N SD: 1.5394 c. M:-2.8970 c. 192: 34 14 11 21 33 15 46 18 N SD: 1.0966 c. M:-1.8282 c. 204: 36 15 12 22 35 16 49 19 N SD: 0.9833 c. M:-1.8282 c. 233: 41 17 14 25 40 18 56 22 N SD: 0.9986 c. M: 1.7042 c. 234: 41 17 14 25 41 18 56 22 N SD: 0.8653 c. M:-1.7810 c. 238: 42 17 14 26 41 19 57 22 N SD: 1.0351 c. M:-1.6932 c. 243: 43 17 15 26 42 19 58 23 N SD: 1.0081 c. M: 1.8755 c. 246: 43 18 15 26 43 19 59 23 N SD: 0.8504 c. M:-1.4058 c. 267: 47 19 16 29 46 21 64 25 N SD: 0.7430 c. M: 1.5426 c. 279: 49 20 17 30 48 22 67 26 N SD: 0.6106 c. M: 1.3976 c. 289: 51 21 17 31 50 23 69 27 N SD: 0.6107 c. M:-1.3966 c. 301: 53 22 18 32 52 24 72 28 N SD: 0.6935 c. M:-1.3414 c. 311: 55 22 19 33 54 24 75 29 N SD: 0.7618 c. M: 1.2737 c. 318: 56 23 19 34 55 25 76 30 N SD: 0.4325 c. M: 1.1769 c. 345: 61 25 20 37 60 27 83 32 N SD: 0.7275 c. M: 1.0246 c. 347: 61 25 21 37 60 27 84 32 N SD: 0.7191 c. M:-1.3678 c. 354: 62 26 21 38 61 28 85 33 N SD: 0.4697 c. M: 0.9876 c. 410: 72 30 24 44 71 32 99 38 N SD: 0.6618 c. M: 0.9631 c. 415: 73 30 25 44 72 33 99 39 N SD: 0.5769 c. M:-0.9764 c. 426: 75 31 25 46 74 33 102 40 N SD: 0.5621 c. M:-1.1310 c. 438: 77 32 26 47 76 34 105 41 N SD: 0.4204 c. M:-0.9380 c. 462: 81 34 27 50 80 36 111 43 N SD: 0.5427 c. M: 0.8891 c. 471: 83 34 28 51 81 37 113 44 N SD: 0.4403 c. M:-1.1515 c. 484: 85 35 29 52 84 38 116 45 N SD: 0.5134 c. M:-0.8390 c. 496: 87 36 30 53 86 39 119 46 N SD: 0.5633 c. M:-0.8190 c. 503: 89 36 30 54 87 39 121 47 N SD: 0.5261 c. M:-1.1690 c. 506: 89 37 30 54 88 39 122 47 N SD: 0.5117 c. M:-0.8081 c. 510: 90 37 30 55 88 40 122 48 N SD: 0.5116 c. M: 0.9105 c. 513: 90 37 31 55 89 40 123 48 N SD: 0.4938 c. M: 1.0958 c. 522: 92 38 31 56 90 41 125 49 N SD: 0.4389 c. M:-0.6788 c. 535: 94 39 32 57 93 42 128 50 N SD: 0.4065 c. M:-0.7602 c. 568: 100 41 34 61 98 45 136 53 N SD: 0.3224 c. M:-0.7167 c. 587: 103 43 35 63 101 46 141 55 N SD: 0.4864 c. M: 0.6689 c. 588: 103 43 35 63 102 46 141 55 N SD: 0.3902 c. M: 0.9530 c. 597: 105 43 36 64 103 47 143 56 N SD: 0.3544 c. M: 0.6844 c. 600: 106 43 36 64 104 47 144 56 N SD: 0.3302 c. M:-0.8429 c. 619: 109 45 37 66 107 49 148 58 N SD: 0.3771 c. M:-0.6587 c. 621: 109 45 37 67 107 49 149 58 N SD: 0.4339 c. M: 0.6382 c. 624: 110 45 37 67 108 49 150 58 N SD: 0.2904 c. M:-0.4922 c. 636: 112 46 38 68 110 50 153 59 N SD: 0.2773 c. M:-0.7099 c. 653: 115 47 39 70 113 51 157 61 N SD: 0.3235 c. M: 0.6000 c. 665: 117 48 40 71 115 52 160 62 N SD: 0.3049 c. M: 0.5890 c. 672: 118 49 40 72 116 53 161 63 N SD: 0.3024 c. M: 0.5542 c. 675: 119 49 40 72 117 53 162 63 N SD: 0.2771 c. M:-0.4949 c. 717: 126 52 43 77 124 56 172 67 N SD: 0.2737 c. M:-0.5332 c. 773: 136 56 46 83 134 60 186 72 N SD: 0.2721 c. M: 0.5050 c. 780: 137 57 46 84 135 61 187 73 N SD: 0.2899 c. M: 0.4895 c. 785: 138 57 47 84 136 61 189 73 N SD: 0.2873 c. M: 0.4970 c. 792: 139 58 47 85 137 62 190 74 N SD: 0.2519 c. M: 0.5510 c. 824: 145 60 49 88 143 64 198 77 N SD: 0.2715 c. M: 0.4729 c. 828: 146 60 49 89 143 65 199 77 N SD: 0.2910 c. M:-0.4371 c. 857: 151 62 51 92 148 67 206 80 N SD: 0.2249 c. M: 0.4542 c. 870: 153 63 52 93 151 68 209 81 N SD: 0.2054 c. M:-0.3065 c. 942: 166 68 56 101 163 74 226 88 N SD: 0.1732 c. M:-0.3079 c. 954: 168 69 57 102 165 75 229 89 N SD: 0.1214 c. M: 0.2509 c. 1188: 209 86 71 127 206 93 285 111 N SD: 0.1244 c. M: 0.2318 c. 1341: 236 97 80 144 232 105 322 125 N SD: 0.1382 c. M:-0.2224 c. 1380: 243 100 82 148 239 108 331 129 N SD: 0.1160 c. M:-0.1757 c. 1392: 245 101 83 149 241 109 334 130 N SD: 0.0756 c. M:-0.1232 c. 2334: 411 169 139 250 404 183 560 218 N SD: 0.0617 c. M:-0.1540 c. 2346: 413 170 140 251 406 184 563 219 N SD: 0.0523 c. M:-0.1007 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: 1.9781 cents 3 x x x 4 x 5 x 6 S SD: 28.1238 cents 4 x x 5 x 6 x x 8 S SD: 5.6862 cents 5 x 6 x 7 x 8:9:10 S SD: 22.4070 cents 6 x 7 x 8:9:10:11:12 S SD: 16.3337 cents 7:8 x x 9 x 11:13:14 SD: 14.0805 cents 8:9 x 10:11:12:13:15:16 SD: 9.9051 cents 9:10 x 11:12 x 14:17:18 SD: 8.7012 cents 10:11:12 x 13:15:16:19:20 SD: 10.2160 cents 11:12:13:14:15 x 17:21:22 SD: 14.7548 cents 12 x 14:15:16:18:19:23:24 SD: 7.5066 cents 13:15 x 16:17:20:21:24:26 SD: 10.8752 cents 14:16 x 17:19:21:22:26:28 SD: 7.8820 cents 15:17:18:19:20:23:24:28:30 SD: 7.1839 cents 16:18:19:20:21:24:25:30:32 S SD: 5.3693 cents 21:24:25:26:28:32:33:39:42 SD: 4.8865 cents 22:25:26:27:29:33:35:41:44 SD: 3.8459 cents 30:34:36:37:40:45:48:56:60 SD: 3.1578 cents 32:36:38:40:43:48:51:60:64 SD: 2.9818 cents 37:42:44:46:49:56:59:69:74 SD: 2.9137 cents 38:43:45:47:51:57:60:71:76 SD: 2.1665 cents 46:52:55:57:61:69:73:86:92 SD: 2.0112 cents 48:54:57:59:64:72:76:90:96 SD: 1.9553 cents 54:61:64:67:72:81:86:101:108 SD: 1.2105 cents 63:71:75:78:84:95:100:118:126 SD: 0.9709 cents 101:114:120:125:135:152:160:189:202 SD: 0.8392 cents 117:132:139:145:156:176:186:219:234 SD: 0.6001 cents 155:175:184:192:207:233:246:291:310 SD: 0.5138 cents 177:200:210:219:236:266:281:332:354 SD: 0.3458 cents 201:227:239:249:268:302:319:377:402 SD: 0.3071 cents 240:271:285:297:320:361:381:450:480 SD: 0.2034 cents 378:427:449:468:504:568:600:709:756 SD: 0.1647 cents 441:498:524:546:588:663:700:827:882 SD: 0.1254 cents 516:583:613:639:688:776:819:967:1032 SD: 0.1181 cents