Scala analysis: xen13-mclaren-difference-table
9-tone difference table scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 119.443 cents 119.442800 2: 203.910 cents 203.910000 3: 266.870 cents 266.869900 4: 315.641 cents 315.641300 5: 354.547 cents 354.547000 6: 412.745 cents 412.745300 7: 767.923 cents 767.923300 8: 1017.596 cents 1017.596300 9: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 182.4037 cents 182.4037 1: 119.4428 cents 119.4428 2: 84.4672 cents 84.4672 3: 62.9599 cents 62.9599 4: 48.7714 cents 48.7714 5: 38.9057 cents 38.9057 6: 58.1983 cents 58.1983 7: 355.1780 cents 355.1780 8: 249.6730 cents 249.6730 9: 182.4037 cents 182.4037
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 38.90570 cents 1: 1 48.77140 cents 1: 1 58.19830 cents 1: 1 62.95990 cents 1: 1 84.46720 cents 1: 1 119.44280 cents 1: 1 182.40370 cents 1: 1 249.67300 cents 1: 1 355.17800 cents 2: 1 87.67710 cents 2: 1 97.10400 cents 2: 1 111.73130 cents 2: 1 147.42710 cents 2: 1 203.91000 cents 2: 1 301.84650 cents 2: 1 413.37630 cents 2: 1 432.07670 cents 2: 1 604.85100 cents 3: 1 145.87540 cents 3: 1 150.63700 cents 3: 1 196.19850 cents 3: 1 266.86990 cents 3: 1 386.31370 cents 3: 1 452.28200 cents 3: 1 551.51950 cents 3: 1 663.04930 cents 3: 1 787.25470 cents 4: 1 208.83530 cents 4: 1 235.10420 cents 4: 1 315.64130 cents 4: 1 449.27360 cents 4: 1 501.05340 cents 4: 1 635.98670 cents 4: 1 701.95500 cents 4: 1 845.45300 cents 4: 1 906.69750 cents 5: 1 293.30250 cents 5: 1 354.54700 cents 5: 1 498.04500 cents 5: 1 564.01330 cents 5: 1 698.94660 cents 5: 1 750.72640 cents 5: 1 884.35870 cents 5: 1 964.89580 cents 5: 1 991.16470 cents 6: 1 412.74530 cents 6: 1 536.95070 cents 6: 1 648.48050 cents 6: 1 747.71800 cents 6: 1 813.68630 cents 6: 1 933.13010 cents 6: 1 1003.80150 cents 6: 1 1049.36300 cents 6: 1 1054.12460 cents 7: 1 595.14900 cents 7: 1 767.92330 cents 7: 1 786.62370 cents 7: 1 898.15350 cents 7: 1 996.09000 cents 7: 1 1052.57290 cents 7: 1 1088.26870 cents 7: 1 1102.89600 cents 7: 1 1112.32290 cents 8: 1 844.82200 cents 8: 1 950.32700 cents 8: 1 1017.59630 cents 8: 1 1080.55720 cents 8: 1 1115.53280 cents 8: 1 1137.04010 cents 8: 1 1141.80170 cents 8: 1 1151.22860 cents 8: 1 1161.09430 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 : 119.4 203.9 266.9 315.6 354.5 412.7 767.9 1017.6 1200.0 119.4 : 84.5 147.4 196.2 235.1 293.3 648.5 898.2 1080.6 1200.0 203.9 : 63.0 111.7 150.6 208.8 564.0 813.7 996.1 1115.5 1200.0 266.9 : 48.8 87.7 145.9 501.1 750.7 933.1 1052.6 1137.0 1200.0 315.6 : 38.9 97.1 452.3 702.0 884.4 1003.8 1088.3 1151.2 1200.0 354.5 : 58.2 413.4 663.0 845.5 964.9 1049.4 1112.3 1161.1 1200.0 412.7 : 355.2 604.9 787.3 906.7 991.2 1054.1 1102.9 1141.8 1200.0 767.9 : 249.7 432.1 551.5 636.0 698.9 747.7 786.6 844.8 1200.0 1017.6: 182.4 301.8 386.3 449.3 498.0 537.0 595.1 950.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.9057 .. 355.1780 cents 316.27230 cents 38.90570 cents 2: 87.6771 .. 604.8510 cents 517.17390 cents -267.50090 cents 3: 145.8754 .. 787.2547 cents 641.37930 cents -458.97560 cents 4: 208.8353 .. 906.6975 cents 697.86220 cents -578.41940 cents 5: 293.3025 .. 991.1647 cents 697.86220 cents -613.39500 cents 6: 412.7453 .. 1054.1246 cents 641.37930 cents -578.41940 cents 7: 595.1490 .. 1112.3229 cents 517.17390 cents -458.97560 cents 8: 844.8220 .. 1161.0943 cents 316.27230 cents -267.50090 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 38.90570 cents, class 1 Average step (divided formal octave): 133.3333 cents Largest one step interval : 355.17800 cents Average / Smallest step : 3.427090 Largest / Average step : 2.663835 Largest / Smallest step : 9.129202 Median interval of one step : 84.46720 cents, amount: 1 Least squares average step : 109.31887 cents, oct.: 983.86983 cents Scale is not proper Step pattern alph. order: ABCDEFGHI Step pattern size order : FEDBACIHG Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 0.63100 cents Scale diversity : 1.752074 Lumma stability : 0.064843 Lumma impropriety factor : 0.853871 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 : 0.63100 cents Number of recognisable fifths : 2, average 700.4508 cents Formal octave complements present : 1 = 11.1111% -- Rational properties --
FIT/MODE
9: 1 1 0 0 1 0 3 2 1 N SD: 36.8105 c. M:-62.7567 c. 11: 1 1 0 1 0 1 3 2 2 N SD: 24.5330 c. M: 48.6881 c. 12: 1 1 1 0 1 0 4 2 2 N SD: 24.2728 c. M:-45.4530 c. 13: 1 1 1 0 1 0 4 3 2 N SD: 25.1457 c. M: 43.5145 c. 14: 1 1 1 1 0 1 4 3 2 N SD: 19.8546 c. M: 33.7285 c. 17: 2 1 1 0 1 1 5 3 3 N SD: 18.0613 c. M: 33.2884 c. 18: 2 1 1 1 0 1 6 3 3 N SD: 16.5740 c. M:-32.0767 c. 19: 2 1 1 1 1 1 5 4 3 N SD: 15.1523 c. M:-29.3600 c. 20: 2 1 1 1 1 1 6 4 3 N SD: 14.0342 c. M: 26.8699 c. 22: 2 2 1 1 1 1 6 5 3 N SD: 15.4653 c. M:-27.2712 c. 23: 2 2 1 1 1 1 7 5 3 N SD: 12.0853 c. M:-25.8820 c. 24: 2 2 1 1 1 1 7 5 4 N SD: 13.8906 c. M: 19.4428 c. 27: 3 2 1 1 1 1 8 6 4 N SD: 9.9257 c. M:-18.3122 c. 28: 3 2 1 1 1 2 8 6 4 N SD: 10.8018 c. M:-15.8261 c. 30: 3 2 2 1 1 1 9 6 5 N SD: 9.2591 c. M: 17.5963 c. 31: 3 2 2 1 1 2 9 6 5 N SD: 7.7658 c. M:-13.0612 c. 37: 4 2 2 2 1 2 11 7 6 N SD: 8.5927 c. M: 12.1909 c. 38: 4 2 2 2 1 2 11 8 6 N SD: 8.5985 c. M: 14.4363 c. 40: 4 3 2 2 1 2 12 8 6 N SD: 7.3587 c. M:-14.3587 c. 41: 4 3 2 2 1 2 12 9 6 N SD: 4.3810 c. M: 6.9477 c. 53: 5 4 3 2 2 2 16 11 8 N SD: 4.1601 c. M:-7.7172 c. 58: 6 4 3 2 2 3 17 12 9 N SD: 3.2098 c. M: 5.2965 c. 72: 7 5 4 3 2 4 21 15 11 N SD: 2.6370 c. M: 4.5470 c. 91: 9 6 5 4 3 4 27 19 14 N SD: 2.9948 c. M: 6.1078 c. 94: 9 7 5 4 3 4 28 20 14 N SD: 2.9504 c. M: 4.5492 c. 98: 10 7 5 4 3 5 29 20 15 N SD: 2.7473 c. M:-4.2533 c. 99: 10 7 5 4 3 5 29 21 15 N SD: 2.0094 c. M: 4.2869 c. 111: 11 8 6 4 4 5 33 23 17 N SD: 1.8030 c. M:-3.4004 c. 122: 12 9 6 5 4 6 36 25 19 N SD: 1.8971 c. M: 4.4815 c. 125: 12 9 7 5 4 6 37 26 19 N SD: 1.7901 c. M: 4.2428 c. 139: 14 10 7 6 4 7 41 29 21 N SD: 1.8898 c. M:-3.7832 c. 149: 15 10 8 6 5 7 44 31 23 N SD: 1.8884 c. M: 2.8312 c. 152: 15 11 8 6 5 7 45 32 23 N SD: 1.3322 c. M: 2.2190 c. 172: 17 12 9 7 6 8 51 36 26 N SD: 1.2129 c. M: 1.7536 c. 183: 18 13 10 7 6 9 54 38 28 N SD: 1.0216 c. M:-1.9826 c. 224: 22 16 12 9 7 11 66 47 34 N SD: 0.9602 c. M: 1.8519 c. 230: 23 16 12 9 8 11 68 48 35 N SD: 1.0120 c. M: 2.5978 c. 244: 24 17 13 10 8 12 72 51 37 N SD: 1.0875 c. M: 2.2707 c. 247: 25 17 13 10 8 12 73 51 38 N SD: 1.0142 c. M: 2.2117 c. 261: 26 18 14 11 8 13 77 54 40 N SD: 0.9918 c. M: 1.6111 c. 270: 27 19 14 11 9 13 80 56 41 N SD: 0.5747 c. M:-1.0086 c. 311: 31 22 16 13 10 15 92 65 47 N SD: 0.5449 c. M:-1.0532 c. 342: 34 24 18 14 11 17 101 71 52 N SD: 0.4927 c. M:-1.2898 c. 369: 37 26 19 15 12 18 109 77 56 N SD: 0.4888 c. M:-0.9680 c. 383: 38 27 20 16 12 19 113 80 58 N SD: 0.5439 c. M:-0.8317 c. 422: 42 30 22 17 14 20 125 88 64 N SD: 0.4784 c. M:-0.9032 c. 441: 44 31 23 18 14 22 130 92 67 N SD: 0.4572 c. M:-0.8601 c. 453: 45 32 24 18 15 22 134 94 69 N SD: 0.3862 c. M:-0.6798 c. 494: 49 35 26 20 16 24 146 103 75 N SD: 0.2419 c. M: 0.4145 c. 742: 74 52 39 30 24 36 220 154 113 N SD: 0.2581 c. M: 0.3691 c. 764: 76 54 40 31 25 37 226 159 116 N SD: 0.2285 c. M:-0.4268 c. 913: 91 64 48 37 30 44 270 190 139 N SD: 0.2147 c. M: 0.3439 c. 995: 99 70 52 41 32 48 295 207 151 N SD: 0.2372 c. M:-0.3386 c. 1012: 101 71 53 41 33 49 300 210 154 N SD: 0.2160 c. M:-0.4561 c. 1052: 105 74 55 43 34 51 311 219 160 N SD: 0.2208 c. M:-0.3291 c. 1053: 105 74 55 43 34 51 312 219 160 N SD: 0.1447 c. M:-0.2153 c. 1178: 117 83 62 48 38 57 349 245 179 N SD: 0.1428 c. M: 0.2577 c. 1236: 123 87 65 50 40 60 366 257 188 N SD: 0.1002 c. M: 0.1781 c. 1506: 150 106 79 61 49 73 446 313 229 N SD: 0.0905 c. M:-0.2042 c. 1547: 154 109 81 63 50 75 458 322 235 N SD: 0.0644 c. M:-0.1154 c. 2000: 199 141 105 81 65 97 592 416 304 N SD: 0.0669 c. M:-0.1301 c.
FIT/HARMONIC
1 x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x 4 S SD: 32.9841 cents 3 x x x x x 4:5 x 6 S SD: 48.1124 cents 4 x x x x x 5:6:7:8 S SD: 21.5479 cents 5 x x x 6 x x 8:9:10 S SD: 11.4407 cents 6 x x 7 x x 8:9:11:12 SD: 22.4829 cents 7 x 8 x x x 9:11:13:14 SD: 13.2393 cents 8 x 9 x x x 10:12:14:16 S SD: 17.2383 cents 9 x 10 x x 11 x 14:16:18 SD: 6.2771 cents 10 x 11 x 12 x 13:16:18:20 SD: 12.1650 cents 11:12 x 13 x x 14:17:20:22 SD: 7.4567 cents 12:13 x 14 x x 15:19:22:24 SD: 8.8778 cents 13:14 x 15 x 16:17:20:23:26 SD: 9.6052 cents 14:15:16 x x 17:18:22:25:28 SD: 6.3633 cents 15:16:17 x 18 x 19:23:27:30 SD: 4.5499 cents 16:17:18 x 19 x 20:25:29:32 SD: 5.3506 cents 17:18:19:20 x 21:22:26:31:34 SD: 7.4666 cents 18:19:20:21 x 22:23:28:32:36 SD: 5.2852 cents 19:20:21:22:23 x 24:30:34:38 SD: 6.8128 cents 20:21 x 23:24 x 25:31:36:40 SD: 7.3221 cents 21:23:24 x 25:26:27:33:38:42 SD: 7.2964 cents 22:24:25:26 x 27:28:34:40:44 SD: 6.0005 cents 23:25:26:27 x 28:29:36:41:46 SD: 4.7989 cents 24:26:27:28:29 x 30:37:43:48 SD: 5.0252 cents 25:27:28:29:30:31:32:39:45:50 SD: 3.3052 cents 27:29:30 x 32:33:34:42:49:54 SD: 4.6622 cents 28:30:32:33 x 34:36:44:50:56 SD: 5.9857 cents 29:31:33:34:35:36:37:45:52:58 SD: 3.7649 cents 30:32:34:35:36:37:38:47:54:60 SD: 2.2068 cents 40:43:45:47:48:49:51:62:72:80 SD: 2.0538 cents 41:44:46:48:49:50:52:64:74:82 SD: 1.8233 cents 55:59:62:64:66:68:70:86:99:110 SD: 1.7859 cents 56:60:63:65:67:69:71:87:101:112 SD: 1.5498 cents 66:71:74:77:79:81:84:103:119:132 SD: 1.3144 cents 70:75:79:82:84:86:89:109:126:140 SD: 1.0757 cents 71:76:80:83:85:87:90:111:128:142 SD: 1.0570 cents 96:103:108:112:115:118:122:150:173:192 SD: 0.8078 cents 114:122:128:133:137:140:145:178:205:228 SD: 0.7991 cents 115:123:129:134:138:141:146:179:207:230 SD: 0.7512 cents 126:135:142:147:151:155:160:196:227:252 SD: 0.7299 cents 144:154:162:168:173:177:183:224:259:288 SD: 0.6762 cents 145:155:163:169:174:178:184:226:261:290 SD: 0.5096 cents 185:198:208:216:222:227:235:288:333:370 SD: 0.3735 cents 215:230:242:251:258:264:273:335:387:430 SD: 0.3634 cents 256:274:288:299:307:314:325:399:461:512 SD: 0.3537 cents 264:283:297:308:317:324:335:411:475:528 SD: 0.2538 cents 294:315:331:343:353:361:373:458:529:588 SD: 0.2385 cents 335:359:377:391:402:411:425:522:603:670 SD: 0.1548 cents 480:514:540:560:576:589:609:748:864:960 SD: 0.1330 cents 505:541:568:589:606:620:641:787:909:1010 SD: 0.1042 cents