Scala analysis: xen18-ayers-table-32
7 Iterated Counter-Logarithmic Means between 1/1 and 2/1
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 279.960 cents 279.960000 2: 490.809 cents 490.809000 3: 659.173 cents 659.173000 4: 800.000 cents 800.000000 5: 918.673 cents 918.673000 6: 1023.000 cents 1023.000000 7: 1116.020 cents 1116.020000 8: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 83.9800 cents 83.9800 1: 279.9600 cents 279.9600 2: 210.8490 cents 210.8490 3: 168.3640 cents 168.3640 4: 140.8270 cents 140.8270 5: 118.6730 cents 118.6730 6: 104.3270 cents 104.3270 7: 93.0200 cents 93.0200 8: 83.9800 cents 83.9800
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 83.98000 cents 1: 1 93.02000 cents 1: 1 104.32700 cents 1: 1 118.67300 cents 1: 1 140.82700 cents 1: 1 168.36400 cents 1: 1 210.84900 cents 1: 1 279.96000 cents 2: 1 177.00000 cents 2: 1 197.34700 cents 2: 1 223.00000 cents 2: 1 259.50000 cents 2: 1 309.19100 cents 2: 1 363.94000 cents 2: 1 379.21300 cents 2: 1 490.80900 cents 3: 1 281.32700 cents 3: 1 316.02000 cents 3: 1 363.82700 cents 3: 1 427.86400 cents 3: 1 456.96000 cents 3: 1 520.04000 cents 3: 1 574.78900 cents 3: 1 659.17300 cents 4: 1 400.00000 cents 4: 1 456.84700 cents 4: 1 532.19100 cents 4: 1 561.28700 cents 4: 1 638.71300 cents 4: 1 667.80900 cents 4: 1 743.15300 cents 4: 1 800.00000 cents 5: 1 540.82700 cents 5: 1 625.21100 cents 5: 1 679.96000 cents 5: 1 743.04000 cents 5: 1 772.13600 cents 5: 1 836.17300 cents 5: 1 883.98000 cents 5: 1 918.67300 cents 6: 1 709.19100 cents 6: 1 820.78700 cents 6: 1 836.06000 cents 6: 1 890.80900 cents 6: 1 940.50000 cents 6: 1 977.00000 cents 6: 1 1002.65300 cents 6: 1 1023.00000 cents 7: 1 920.04000 cents 7: 1 989.15100 cents 7: 1 1031.63600 cents 7: 1 1059.17300 cents 7: 1 1081.32700 cents 7: 1 1095.67300 cents 7: 1 1106.98000 cents 7: 1 1116.02000 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 : 280.0 490.8 659.2 800.0 918.7 1023.0 1116.0 1200.0 280.0 : 210.8 379.2 520.0 638.7 743.0 836.1 920.0 1200.0 490.8 : 168.4 309.2 427.9 532.2 625.2 709.2 989.2 1200.0 659.2 : 140.8 259.5 363.8 456.8 540.8 820.8 1031.6 1200.0 800.0 : 118.7 223.0 316.0 400.0 680.0 890.8 1059.2 1200.0 918.7 : 104.3 197.3 281.3 561.3 772.1 940.5 1081.3 1200.0 1023.0: 93.0 177.0 457.0 667.8 836.2 977.0 1095.7 1200.0 1116.0: 84.0 363.9 574.8 743.2 884.0 1002.7 1107.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 83.9800 .. 279.9600 cents 195.98000 cents 83.98000 cents 2: 177.0000 .. 490.8090 cents 313.80900 cents -102.96000 cents 3: 281.3270 .. 659.1730 cents 377.84600 cents -209.48200 cents 4: 400.0000 .. 800.0000 cents 400.00000 cents -259.17300 cents 5: 540.8270 .. 918.6730 cents 377.84600 cents -259.17300 cents 6: 709.1910 .. 1023.0000 cents 313.80900 cents -209.48200 cents 7: 920.0400 .. 1116.0200 cents 195.98000 cents -102.96000 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 83.98000 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 279.96000 cents Average / Smallest step : 1.786140 Largest / Average step : 1.866400 Largest / Smallest step : 3.333651 Median interval of one step : 129.75000 cents, amount: 0 Least squares average step : 169.52256 cents, oct.: 1356.18047 cents Scale is not proper Step pattern alph. order: ABCDEFGH Step pattern size order : HGFEDCBA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 0.11300 cents Scale diversity : 1.705066 Lumma stability : 0.139967 Lumma impropriety factor : 0.702722 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 : 0.11300 cents Number of recognisable fifths : 1, average 709.1910 cents Steps are strictly decreasing Formal octave complements present : 1 = 12.5000% -- Rational properties --
FIT/MODE
8: 2 1 1 1 1 1 0 1 N T3 SD: 41.0864 c. M: 66.0200 c. 9: 2 2 1 1 1 1 0 1 N SD: 28.7199 c. M: 49.3533 c. 12: 3 2 2 1 1 1 1 1 N SD: 20.2708 c. M:-40.8270 c. 13: 3 2 2 2 1 1 1 1 N SD: 16.3132 c. M:-30.7692 c. 14: 3 3 2 1 2 1 1 1 N SD: 20.0358 c. M: 28.5714 c. 17: 4 3 2 2 2 1 2 1 N SD: 17.7816 c. M: 34.7647 c. 18: 4 3 3 2 2 1 2 1 N SD: 15.2455 c. M: 24.1423 c. 20: 5 3 3 2 2 2 2 1 N SD: 15.2145 c. M:-23.9800 c. 21: 5 4 3 2 2 2 2 1 N SD: 16.0438 c. M:-26.8371 c. 22: 5 4 3 3 2 2 1 2 N SD: 12.6857 c. M: 25.1109 c. 23: 5 4 4 2 3 2 1 2 N SD: 18.4907 c. M: 21.2438 c. 24: 5 5 3 3 2 2 2 2 N SD: 16.5852 c. M: 29.9600 c. 25: 6 4 4 3 2 2 2 2 N SD: 11.2695 c. M:-16.0000 c. 26: 6 4 4 3 3 2 2 2 N SD: 13.3178 c. M: 29.2705 c. 27: 6 5 4 3 3 2 2 2 N SD: 7.7151 c. M:-14.6603 c. 29: 7 5 4 3 3 3 2 2 N SD: 8.1265 c. M: 13.7931 c. 34: 8 6 5 4 3 3 3 2 N SD: 7.6327 c. M:-13.3918 c. 39: 9 7 5 5 4 3 3 3 N SD: 6.4003 c. M: 13.0192 c. 40: 9 7 6 5 4 3 3 3 N SD: 7.8283 c. M:-11.3270 c. 42: 10 7 6 5 4 4 3 3 N SD: 3.8159 c. M:-5.7543 c. 60: 14 11 8 7 6 5 5 4 N SD: 3.7377 c. M:-9.1910 c. 68: 16 12 9 8 7 6 5 5 N SD: 3.7005 c. M: 6.2318 c. 69: 16 12 10 8 7 6 5 5 N SD: 2.4596 c. M: 3.8525 c. 86: 20 15 12 10 9 7 7 6 N SD: 2.8313 c. M: 4.6512 c. 95: 22 17 13 11 10 8 7 7 N SD: 2.7901 c. M: 4.4411 c. 98: 23 17 14 11 10 9 7 7 N SD: 2.7119 c. M:-5.5714 c. 102: 24 18 14 12 10 9 8 7 N SD: 1.6115 c. M:-3.3086 c. 115: 27 20 16 14 11 10 9 8 N SD: 1.5473 c. M:-3.4783 c. 124: 29 22 17 15 12 11 9 9 N SD: 2.1698 c. M:-3.2258 c. 128: 30 22 18 15 13 11 10 9 N SD: 2.0109 c. M: 3.3090 c. 129: 30 23 18 15 13 11 10 9 N SD: 1.2546 c. M:-2.2572 c. 171: 40 30 24 20 17 15 13 12 N SD: 0.6923 c. M:-1.5614 c. 257: 60 45 36 30 26 22 20 18 N SD: 0.7877 c. M: 1.5564 c. 269: 63 47 38 31 27 23 21 19 N SD: 0.9520 c. M: 1.4870 c. 273: 64 48 38 32 27 24 21 19 N SD: 0.8454 c. M:-1.4987 c. 286: 67 50 40 34 28 25 22 20 N SD: 0.7198 c. M:-1.3986 c. 291: 68 51 41 34 29 25 23 20 N SD: 0.6895 c. M:-1.5058 c. 299: 70 52 42 35 30 26 23 21 N SD: 0.8291 c. M: 1.3378 c. 300: 70 53 42 35 30 26 23 21 N SD: 0.7799 c. M:-1.3270 c. 313: 73 55 44 37 31 27 24 22 N SD: 0.7392 c. M:-1.4548 c. 317: 74 56 44 37 32 27 25 22 N SD: 0.8905 c. M:-1.3046 c. 318: 74 56 45 37 31 28 25 22 N SD: 0.8613 c. M: 1.6919 c. 330: 77 58 46 39 33 28 26 23 N SD: 0.7306 c. M:-1.3270 c. 333: 78 58 47 39 33 29 26 23 N SD: 0.6422 c. M:-1.1211 c. 357: 83 63 50 42 35 31 28 25 N SD: 0.6561 c. M: 1.1513 c. 359: 84 63 50 42 36 31 28 25 N SD: 0.6302 c. M: 1.1142 c. 372: 87 65 52 44 37 32 29 26 N SD: 0.5687 c. M: 1.1085 c. 381: 89 67 53 45 38 33 29 27 N SD: 0.6855 c. M: 1.0594 c. 384: 90 67 54 45 38 33 30 27 N SD: 0.6291 c. M:-1.2900 c. 399: 93 70 56 47 39 35 31 28 N SD: 0.5957 c. M: 1.3798 c. 413: 96 73 58 48 41 36 32 29 N SD: 0.5697 c. M: 1.0254 c. 415: 97 73 58 49 41 36 32 29 N SD: 0.6013 c. M:-0.9639 c. 426: 99 75 60 50 42 37 33 30 N SD: 0.5307 c. M: 1.0868 c. 428: 100 75 60 50 43 37 33 30 N SD: 0.5261 c. M:-0.9532 c. 432: 101 76 60 51 43 37 34 30 N SD: 0.6532 c. M:-0.8577 c. 440: 103 77 62 51 44 38 34 31 N SD: 0.6113 c. M:-0.9491 c. 441: 103 77 62 52 44 38 34 31 N SD: 0.5960 c. M:-1.0549 c. 453: 106 79 64 53 45 39 35 32 N SD: 0.5669 c. M:-0.8347 c. 455: 106 80 64 53 45 40 35 32 N SD: 0.5058 c. M: 0.8791 c. 462: 108 81 65 54 46 40 36 32 N SD: 0.5225 c. M:-0.8631 c. 486: 113 86 68 57 48 42 38 34 N SD: 0.4791 c. M: 0.9477 c. 501: 117 88 70 59 50 43 39 35 N SD: 0.4510 c. M:-1.0875 c. 502: 117 88 71 59 49 44 39 35 N SD: 0.5379 c. M:-0.7968 c. 513: 120 90 72 60 51 44 40 36 N SD: 0.5002 c. M: 0.7778 c. 515: 120 91 72 60 51 45 40 36 N SD: 0.4857 c. M:-0.8415 c. 524: 122 92 74 61 52 46 40 37 N SD: 0.5824 c. M: 0.7634 c. 528: 123 93 74 62 52 46 41 37 N SD: 0.2541 c. M: 0.4912 c. 699: 163 123 98 82 69 61 54 49 N SD: 0.1370 c. M: 0.2181 c. 990: 231 174 139 116 98 86 77 69 N SD: 0.1552 c. M:-0.3436 c. 1071: 250 188 150 126 106 93 83 75 N SD: 0.1418 c. M: 0.3495 c. 1389: 324 244 195 163 137 121 108 97 N SD: 0.1385 c. M: 0.3145 c. 1416: 330 249 199 166 140 123 110 99 N SD: 0.1371 c. M: 0.2990 c. 1458: 340 256 205 171 144 127 113 102 N SD: 0.1249 c. M: 0.2740 c. 1484: 346 261 208 174 147 129 115 104 N SD: 0.1378 c. M: 0.2695 c. 1518: 354 267 213 178 150 132 118 106 N SD: 0.1040 c. M:-0.1855 c. 1560: 364 274 219 183 154 136 121 109 N SD: 0.0969 c. M: 0.2115 c. 1599: 373 281 224 188 158 139 124 112 N SD: 0.1100 c. M: 0.2612 c. 1689: 394 297 237 198 167 147 131 118 N SD: 0.0941 c. M:-0.1520 c. 1770: 413 311 248 208 175 154 137 124 N SD: 0.0793 c. M: 0.1899 c. 2061: 481 362 289 242 204 179 160 144 N SD: 0.0754 c. M:-0.1372 c. 2217: 517 390 311 260 219 193 172 155 N SD: 0.0900 c. M: 0.1344 c. 2259: 527 397 317 265 223 197 175 158 N SD: 0.0892 c. M: 0.2135 c. 2286: 533 402 321 268 226 199 177 160 N SD: 0.0872 c. M: 0.1700 c. 2345: 547 412 329 275 232 204 182 164 N SD: 0.0876 c. M: 0.1706 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x x x 4 S SD: 21.3910 cents 3 x 4 x x 5 x x 6 S SD: 11.6896 cents 4 x 5:6 x 7 x x 8 S SD: 30.8878 cents 5:6 x 7:8 x 9 x 10 S SD: 17.1657 cents 6:7:8:9 x 10:11 x 12 S SD: 10.4436 cents 7:8:9:10:11:12 x 13:14 S SD: 14.0717 cents 8:9:11:12:13:14 x 15:16 SD: 18.1845 cents 9:11:12:13:14:15:16:17:18 SD: 11.5021 cents 10:12:13:15:16:17:18:19:20 SD: 8.5535 cents 12:14:16:18:19:20:22:23:24 S SD: 7.9572 cents 15:18:20:22:24:26:27:29:30 SD: 7.2074 cents 17:20:23:25:27:29:31:32:34 SD: 5.4472 cents 19:22:25:28:30:32:34:36:38 SD: 5.2439 cents 21:25:28:31:33:36:38:40:42 SD: 4.4870 cents 22:26:29:32:35:37:40:42:44 SD: 3.6895 cents 24:28:32:35:38:41:43:46:48 SD: 3.1550 cents 30:35:40:44:48:51:54:57:60 S SD: 2.7342 cents 34:40:45:50:54:58:61:65:68 SD: 2.1581 cents 46:54:61:67:73:78:83:88:92 SD: 1.5192 cents 56:66:74:82:89:95:101:107:112 SD: 1.4564 cents 61:72:81:89:97:104:110:116:122 SD: 1.4068 cents 63:74:84:92:100:107:114:120:126 SD: 1.1476 cents 73:86:97:107:116:124:132:139:146 SD: 0.7529 cents 97:114:129:142:154:165:175:185:194 SD: 0.4747 cents 170:200:226:249:270:289:307:324:340 SD: 0.3977 cents 177:208:235:259:281:301:320:337:354 SD: 0.3295 cents 211:248:280:309:335:359:381:402:422 SD: 0.2721 cents 257:302:341:376:408:437:464:490:514 SD: 0.2383 cents 274:322:364:401:435:466:495:522:548 SD: 0.1970 cents 330:388:438:483:524:561:596:629:660 SD: 0.1560 cents 421:495:559:616:668:716:760:802:842 SD: 0.1527 cents 427:502:567:625:678:726:771:814:854 SD: 0.1429 cents 473:556:628:692:751:804:854:901:946 SD: 0.0959 cents 570:670:757:834:905:969:1029:1086:1140 SD: 0.0869 cents