Scala analysis: xen18-mitchell-fractal-2
Geordan's Scale, Erv Wilson's calculation
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 57.200 cents 57.199720 2: 177.218 cents 177.217785 3: 306.180 cents 306.180025 4: 445.528 cents 445.527668 5: 597.081 cents 597.081063 6: 714.116 cents 714.116253 7: 839.641 cents 839.640632 8: 974.983 cents 974.982722 9: 1121.810 cents 1121.809590 10: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 78.1904 cents 78.1904 1: 57.1997 cents 57.1997 2: 120.0181 cents 120.0181 3: 128.9622 cents 128.9622 4: 139.3476 cents 139.3476 5: 151.5534 cents 151.5534 6: 117.0352 cents 117.0352 7: 125.5244 cents 125.5244 8: 135.3421 cents 135.3421 9: 146.8269 cents 146.8269 10: 78.1904 cents 78.1904
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 57.19972 cents 1: 1 78.19041 cents 1: 1 117.03519 cents 1: 1 120.01807 cents 1: 1 125.52438 cents 1: 1 128.96224 cents 1: 1 135.34209 cents 1: 1 139.34764 cents 1: 1 146.82687 cents 1: 1 151.55339 cents 2: 1 135.39013 cents 2: 1 177.21778 cents 2: 1 225.01728 cents 2: 1 242.55957 cents 2: 1 248.98031 cents 2: 1 260.86647 cents 2: 1 268.30988 cents 2: 1 268.58859 cents 2: 1 282.16896 cents 2: 1 290.90104 cents 3: 1 255.40819 cents 3: 1 282.21700 cents 3: 1 306.18002 cents 3: 1 360.35937 cents 3: 1 377.90166 cents 3: 1 388.32795 cents 3: 1 394.11296 cents 3: 1 407.69334 cents 3: 1 407.93623 cents 3: 1 419.86328 cents 4: 1 384.37043 cents 4: 1 402.23506 cents 4: 1 417.55909 cents 4: 1 445.52767 cents 4: 1 485.88375 cents 4: 1 524.72853 cents 4: 1 529.45505 cents 4: 1 533.46061 cents 4: 1 536.89847 cents 4: 1 539.88134 cents 5: 1 523.71808 cents 5: 1 531.19730 cents 5: 1 537.57715 cents 5: 1 543.08347 cents 5: 1 597.08106 cents 5: 1 602.91894 cents 5: 1 656.91653 cents 5: 1 662.42285 cents 5: 1 668.80270 cents 5: 1 676.28192 cents 6: 1 660.11866 cents 6: 1 663.10153 cents 6: 1 666.53939 cents 6: 1 670.54495 cents 6: 1 675.27147 cents 6: 1 714.11625 cents 6: 1 754.47233 cents 6: 1 782.44091 cents 6: 1 797.76494 cents 6: 1 815.62957 cents 7: 1 780.13672 cents 7: 1 792.06377 cents 7: 1 792.30666 cents 7: 1 805.88704 cents 7: 1 811.67205 cents 7: 1 822.09834 cents 7: 1 839.64063 cents 7: 1 893.81998 cents 7: 1 917.78300 cents 7: 1 944.59181 cents 8: 1 909.09896 cents 8: 1 917.83104 cents 8: 1 931.41142 cents 8: 1 931.69012 cents 8: 1 939.13353 cents 8: 1 951.01969 cents 8: 1 957.44043 cents 8: 1 974.98272 cents 8: 1 1022.78222 cents 8: 1 1064.60987 cents 9: 1 1048.44661 cents 9: 1 1053.17313 cents 9: 1 1060.65236 cents 9: 1 1064.65791 cents 9: 1 1071.03776 cents 9: 1 1074.47562 cents 9: 1 1079.98194 cents 9: 1 1082.96481 cents 9: 1 1121.80959 cents 9: 1 1142.80028 cents Highest number of different intervals for one interval class: 10 Average number of different intervals per interval class: 10.00000 = 10
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 57.2 177.2 306.2 445.5 597.1 714.1 839.6 975.0 1121.8 1200.0 57.2 : 120.0 249.0 388.3 539.9 656.9 782.4 917.8 1064.6 1142.8 1200.0 177.2 : 129.0 268.3 419.9 536.9 662.4 797.8 944.6 1022.8 1080.0 1200.0 306.2 : 139.3 290.9 407.9 533.5 668.8 815.6 893.8 951.0 1071.0 1200.0 445.5 : 151.6 268.6 394.1 529.5 676.3 754.5 811.7 931.7 1060.7 1200.0 597.1 : 117.0 242.6 377.9 524.7 602.9 660.1 780.1 909.1 1048.4 1200.0 714.1 : 125.5 260.9 407.7 485.9 543.1 663.1 792.1 931.4 1083.0 1200.0 839.6 : 135.3 282.2 360.4 417.6 537.6 666.5 805.9 957.4 1074.5 1200.0 975.0 : 146.8 225.0 282.2 402.2 531.2 670.5 822.1 939.1 1064.7 1200.0 1121.8: 78.2 135.4 255.4 384.4 523.7 675.3 792.3 917.8 1053.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 57.1997 .. 151.5534 cents 94.35368 cents 57.19972 cents 2: 135.3901 .. 290.9010 cents 155.51091 cents -16.16326 cents 3: 255.4082 .. 419.8633 cents 164.45508 cents -35.49284 cents 4: 384.3704 .. 539.8813 cents 155.51091 cents -35.49284 cents 5: 523.7181 .. 676.2819 cents 152.56384 cents -16.16327 cents 6: 660.1187 .. 815.6296 cents 155.51091 cents -16.16327 cents 7: 780.1367 .. 944.5918 cents 164.45508 cents -35.49284 cents 8: 909.0990 .. 1064.6099 cents 155.51091 cents -35.49284 cents 9: 1048.4466 .. 1142.8003 cents 94.35368 cents -16.16327 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 57.19972 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 151.55339 cents Average / Smallest step : 2.097912 Largest / Average step : 1.262945 Largest / Smallest step : 2.649548 Median interval of one step : 127.24331 cents, amount: 0 Least squares average step : 119.88577 cents, oct.: 1198.85770 cents Scale is not proper Step pattern alph. order: ABCDEFGHIJ Step pattern size order : ADFHJCEGIB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 0.04804 cents Scale diversity : 1.566008 Lumma stability : 0.095333 Lumma impropriety factor : 0.172187 Rothenberg efficiency : 0.200000 redundancy: 0.800000 Efficiency x scale size : 2.000000 Number of different interval sizes : 90 = 10.00000 / class Number of one step interval sizes : 10 Highest interval variety : 10 Mean interval variety : 10.00000 = 10 Median interval variety : 10 Lowest interval variety : 10 Smallest interval difference : 0.04804 cents Number of recognisable fifths : 1, average 714.1163 cents Formal octave complements present : 1 = 10.0000% -- Rational properties --
FIT/MODE
10: 0 1 1 1 2 1 1 1 1 1 N T3 SD: 45.0069 c. M: 85.5277 c. 12: 0 2 1 1 2 1 1 2 1 1 N T3 SD: 29.6353 c. M: 57.1997 c. 13: 1 1 1 2 1 2 1 2 1 1 N SD: 26.0228 c. M: 43.2349 c. 14: 1 1 2 1 2 1 2 1 2 1 P D3 SD: 21.6553 c. M:-36.6771 c. 16: 1 1 2 2 2 2 1 2 2 1 N SD: 16.2374 c. M:-35.8837 c. 19: 1 2 2 2 2 2 2 2 3 1 N SD: 16.7951 c. M: 28.6600 c. 20: 1 2 2 2 3 2 2 2 3 1 N SD: 11.4196 c. M: 25.5277 c. 22: 1 2 3 2 3 2 2 3 3 1 N SD: 13.4924 c. M:-23.6450 c. 26: 1 3 3 3 3 2 3 3 3 2 P SD: 12.3037 c. M: 21.8086 c. 27: 1 3 3 3 3 3 3 3 3 2 P SD: 8.4587 c. M: 19.3033 c. 28: 1 3 3 3 4 3 3 3 3 2 N SD: 11.2272 c. M:-17.5022 c. 30: 1 3 4 3 4 3 3 3 4 2 N SD: 10.4156 c. M: 17.2178 c. 32: 2 3 3 4 4 3 3 4 4 2 N SD: 8.4642 c. M:-17.8003 c. 33: 2 3 3 4 4 4 3 4 4 2 N SD: 10.3576 c. M:-15.5276 c. 34: 2 3 4 4 4 3 4 4 4 2 N SD: 9.2350 c. M:-13.3885 c. 40: 2 4 4 5 5 4 4 4 5 3 N SD: 6.9354 c. M: 14.9827 c. 42: 2 4 5 5 5 4 4 5 5 3 N SD: 6.5913 c. M:-11.6152 c. 43: 2 4 5 5 5 4 5 5 5 3 N SD: 7.2855 c. M: 16.4418 c. 44: 2 4 5 5 6 4 5 5 5 3 N SD: 6.6418 c. M: 13.5814 c. 46: 2 5 5 5 6 4 5 5 6 3 N SD: 5.7318 c. M: 9.7684 c. 47: 2 5 5 5 6 5 5 5 6 3 N SD: 5.5065 c. M: 11.4851 c. 54: 3 5 6 6 7 5 6 6 7 3 N SD: 5.4467 c. M:-11.5237 c. 59: 3 6 6 7 7 6 6 7 7 4 N SD: 3.9474 c. M: 7.2506 c. 60: 3 6 6 7 8 6 6 7 7 4 N SD: 3.9503 c. M: 6.1800 c. 62: 3 6 7 7 8 6 6 7 8 4 N SD: 3.7730 c. M: 7.3826 c. 79: 4 8 8 9 10 8 8 9 10 5 N SD: 3.4890 c. M:-5.0607 c. 80: 4 8 9 9 10 8 8 9 10 5 N SD: 4.0844 c. M:-8.8200 c. 81: 4 8 9 9 10 8 9 9 10 5 N SD: 3.2719 c. M:-4.9311 c. 86: 4 9 9 10 11 8 9 10 10 6 N SD: 2.7439 c. M: 5.5305 c. 87: 4 9 9 10 11 9 9 10 10 6 N SD: 3.1838 c. M: 4.5682 c. 89: 4 9 10 10 11 9 9 10 11 6 N SD: 2.8915 c. M: 4.1962 c. 102: 5 10 11 12 13 10 10 12 12 7 N SD: 2.5504 c. M: 4.3465 c. 103: 5 10 11 12 13 10 11 12 12 7 N SD: 2.6707 c. M:-3.6581 c. 106: 5 11 11 12 14 10 11 12 13 7 N SD: 2.1939 c. M: 4.0182 c. 107: 5 11 11 13 13 11 11 12 13 7 N SD: 2.2432 c. M:-3.6408 c. 121: 6 12 13 14 15 12 13 13 15 8 N SD: 1.8772 c. M:-3.3346 c. 124: 6 12 14 14 16 12 13 14 15 8 N SD: 2.1594 c. M:-3.4974 c. 129: 6 13 14 15 16 13 13 15 16 8 N SD: 1.8619 c. M:-3.7718 c. 140: 7 14 15 16 18 13 15 16 17 9 N SD: 2.0730 c. M:-2.9189 c. 143: 7 14 15 17 18 14 15 16 18 9 N SD: 1.8084 c. M: 4.0821 c. 149: 7 15 16 17 19 15 15 17 18 10 N SD: 1.6005 c. M:-2.6623 c. 153: 7 16 16 18 19 15 16 17 19 10 N SD: 1.5846 c. M:-3.1744 c. 165: 8 16 18 19 21 16 17 19 20 11 N SD: 1.6988 c. M: 3.2770 c. 167: 8 17 18 19 21 16 18 19 20 11 N SD: 1.6961 c. M:-2.8020 c. 169: 8 17 18 20 21 17 17 19 21 11 N SD: 1.4799 c. M:-3.0435 c. 181: 9 18 19 21 23 18 19 20 22 12 N SD: 1.5442 c. M:-2.4688 c. 183: 9 18 20 21 23 18 19 21 22 12 N SD: 1.1260 c. M:-2.0665 c. 197: 9 20 21 23 25 19 21 22 24 13 N SD: 1.1585 c. M: 2.3774 c. 203: 10 20 22 23 26 20 21 23 25 13 N SD: 1.1500 c. M: 2.1779 c. 229: 11 23 24 27 29 22 24 26 28 15 N SD: 1.0052 c. M: 2.2499 c. 244: 12 24 26 29 30 24 26 27 30 16 N SD: 1.3227 c. M:-2.0133 c. 245: 12 24 27 28 31 24 25 28 30 16 N SD: 1.2126 c. M:-2.3914 c. 246: 12 24 27 28 31 24 26 28 30 16 N SD: 1.2895 c. M: 1.9591 c. 247: 12 25 26 29 31 24 26 28 30 16 N SD: 1.1513 c. M:-2.5393 c. 250: 12 25 27 29 31 25 26 28 31 16 N SD: 0.9603 c. M: 1.8811 c. 251: 12 25 27 29 32 24 27 28 31 16 N SD: 1.0290 c. M:-1.7936 c. 256: 12 26 27 30 32 25 27 29 31 17 N SD: 1.1097 c. M: 1.7686 c. 259: 12 26 28 30 33 25 27 29 32 17 N SD: 1.0371 c. M: 2.0097 c. 266: 13 26 29 31 33 26 28 30 33 17 N SD: 1.1141 c. M: 1.5923 c. 267: 13 26 29 31 34 26 28 30 33 17 N SD: 1.0266 c. M: 1.9369 c. 272: 13 27 29 32 34 27 28 31 33 18 N SD: 0.9877 c. M: 1.7683 c. 277: 13 28 30 32 35 27 29 31 34 18 N SD: 0.7169 c. M:-1.4012 c. 289: 14 29 31 33 37 28 30 33 35 19 N SD: 0.8929 c. M:-1.3289 c. 293: 14 29 32 34 37 28 31 33 36 19 N SD: 0.7865 c. M: 1.4883 c. 326: 16 32 35 38 41 32 34 37 40 21 N SD: 0.7315 c. M:-1.6960 c. 336: 16 34 36 39 42 33 35 38 41 22 N SD: 0.6558 c. M:-1.3536 c. 340: 16 34 37 39 43 33 36 38 42 22 N SD: 0.7392 c. M: 1.1751 c. 353: 17 35 38 41 45 34 37 40 43 23 N SD: 0.5113 c. M:-1.2192 c. 380: 18 38 41 44 48 37 40 43 46 25 N SD: 0.4421 c. M:-0.8068 c. 442: 21 44 48 51 56 43 46 50 54 29 N SD: 0.4489 c. M: 0.7472 c. 506: 24 51 54 59 64 49 53 57 62 33 N SD: 0.3379 c. M:-0.6478 c. 549: 26 55 59 64 69 54 57 62 67 36 N SD: 0.3492 c. M:-0.6378 c. 603: 29 60 65 70 76 59 63 68 74 39 N SD: 0.2994 c. M:-0.5785 c. 689: 33 69 74 80 87 67 72 78 84 45 N SD: 0.2778 c. M:-0.4310 c. 736: 35 74 79 85 93 72 77 83 90 48 N SD: 0.2614 c. M:-0.4996 c. 800: 38 80 86 93 101 78 84 90 98 52 N SD: 0.1750 c. M:-0.3594 c. 902: 43 90 97 105 114 88 94 102 110 59 N SD: 0.2111 c. M: 0.3018 c. 983: 47 98 106 114 124 96 103 111 120 64 N SD: 0.1914 c. M:-0.3988 c. 1089: 52 109 117 126 138 106 114 123 133 71 N SD: 0.1666 c. M: 0.3486 c. 1109: 53 111 119 129 140 108 116 125 136 72 N SD: 0.1704 c. M:-0.2824 c. 1136: 54 114 122 132 143 111 119 128 139 74 N SD: 0.1606 c. M: 0.2501 c. 1212: 58 121 130 141 153 118 127 137 148 79 N SD: 0.1577 c. M:-0.2648 c. 1258: 60 126 135 146 159 123 131 142 154 82 N SD: 0.1520 c. M:-0.3512 c. 1306: 62 131 140 152 165 127 137 147 160 85 N SD: 0.1515 c. M: 0.2319 c. 1455: 69 146 156 169 184 142 152 164 178 95 N SD: 0.1499 c. M: 0.2925 c. 1471: 70 147 158 171 186 143 154 166 180 96 N SD: 0.1772 c. M: 0.3161 c. 1489: 71 149 160 173 188 145 156 168 182 97 N SD: 0.0948 c. M:-0.1684 c. 2038: 97 204 219 237 257 199 213 230 249 133 N SD: 0.0924 c. M:-0.2034 c. 2058: 98 206 221 239 260 201 215 232 252 134 N SD: 0.0675 c. M:-0.1695 c. 2348: 112 235 252 273 296 229 246 265 287 153 N SD: 0.1015 c. M: 0.1475 c. 2351: 112 235 253 273 297 229 246 265 288 153 N SD: 0.0713 c. M:-0.1116 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x x 4 S SD: 6.0806 cents 3 x x x 4 x x 5 x x 6 S SD: 22.9922 cents 4 x x x 5 x 6 x 7 x 8 S SD: 15.1907 cents 5 x x 6 x 7 x 8:9 x 10 S SD: 10.5666 cents 6 x x 7:8 x 9:10 x 11:12 S SD: 18.0273 cents 7 x 8 x 9:10 x 11:12:13:14 S SD: 14.9593 cents 8 x 9 x 10:11:12:13:14:15:16 S SD: 10.9149 cents 9 x 10:11:12:13:14:15:16:17:18 S SD: 11.9178 cents 10 x 11:12:13:14:15:16:18:19:20 S SD: 6.3600 cents 11 x 12:13:14:16:17:18:19:21:22 SD: 9.3003 cents 12 x 13:14:16:17:18:19:21:23:24 SD: 9.9264 cents 13 x 14:16:17:18:20:21:23:25:26 SD: 9.9913 cents 14 x 16:17:18:20:21:23:25:27:28 SD: 8.5609 cents 16:17:18:19:21:23:24:26:28:31:32 SD: 7.3519 cents 17:18:19:20:22:24:26:28:30:33:34 S SD: 6.6446 cents 19:20:21:23:25:27:29:31:33:36:38 SD: 6.0101 cents 20:21:22:24:26:28:30:32:35:38:40 SD: 4.7349 cents 21:22:23:25:27:30:32:34:37:40:42 SD: 4.2503 cents 24:25:27:29:31:34:36:39:42:46:48 SD: 4.0021 cents 25:26:28:30:32:35:38:41:44:48:50 SD: 3.9679 cents 26:27:29:31:34:37:39:42:46:50:52 SD: 3.5492 cents 27:28:30:32:35:38:41:44:47:52:54 SD: 2.7668 cents 37:38:41:44:48:52:56:60:65:71:74 SD: 1.7619 cents 55:57:61:66:71:78:83:89:97:105:110 SD: 1.7023 cents 56:58:62:67:72:79:85:91:98:107:112 SD: 1.5870 cents 57:59:63:68:74:80:86:93:100:109:114 SD: 1.5409 cents 58:60:64:69:75:82:88:94:102:111:116 SD: 1.2888 cents 82:85:91:98:106:116:124:133:144:157:164 SD: 0.8336 cents 92:95:102:110:119:130:139:149:162:176:184 SD: 0.7976 cents 112:116:124:134:145:158:169:182:197:214:224 SD: 0.6966 cents 119:123:132:142:154:168:180:193:209:227:238 SD: 0.5605 cents 149:154:165:178:193:210:225:242:262:285:298 SD: 0.4884 cents 177:183:196:211:229:250:267:287:311:338:354 SD: 0.4866 cents 180:186:199:215:233:254:272:292:316:344:360 SD: 0.4713 cents 184:190:204:220:238:260:278:299:323:352:368 SD: 0.4481 cents 202:209:224:241:261:285:305:328:355:386:404 SD: 0.3761 cents 239:247:265:285:309:337:361:388:420:457:478 SD: 0.3460 cents 242:250:268:289:313:342:366:393:425:463:484 SD: 0.3404 cents 259:268:287:309:335:366:391:421:455:495:518 SD: 0.3228 cents 269:278:298:321:348:380:406:437:472:514:538 SD: 0.2563 cents 296:306:328:353:383:418:447:481:520:566:592 SD: 0.2004 cents 362:374:401:432:468:511:547:588:636:692:724 SD: 0.1495 cents 476:492:527:568:616:672:719:773:836:910:952 SD: 0.1365 cents 558:577:618:666:722:788:843:906:980:1067:1116 SD: 0.1348 cents