Scala analysis: xen18-ayers-table-30
7 Iterated 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: 83.979 cents 83.979000 2: 176.997 cents 176.997000 3: 281.327 cents 281.327000 4: 400.000 cents 400.000000 5: 540.827 cents 540.827000 6: 709.191 cents 709.191000 7: 920.040 cents 920.040000 8: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 279.9600 cents 279.9600 1: 83.9790 cents 83.9790 2: 93.0180 cents 93.0180 3: 104.3300 cents 104.3300 4: 118.6730 cents 118.6730 5: 140.8270 cents 140.8270 6: 168.3640 cents 168.3640 7: 210.8490 cents 210.8490 8: 279.9600 cents 279.9600
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 83.97900 cents 1: 1 93.01800 cents 1: 1 104.33000 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: 1 176.99700 cents 2: 1 197.34800 cents 2: 1 223.00300 cents 2: 1 259.50000 cents 2: 1 309.19100 cents 2: 1 363.93900 cents 2: 1 379.21300 cents 2: 1 490.80900 cents 3: 1 281.32700 cents 3: 1 316.02100 cents 3: 1 363.83000 cents 3: 1 427.86400 cents 3: 1 456.95700 cents 3: 1 520.04000 cents 3: 1 574.78800 cents 3: 1 659.17300 cents 4: 1 400.00000 cents 4: 1 456.84800 cents 4: 1 532.19400 cents 4: 1 561.28700 cents 4: 1 638.71300 cents 4: 1 667.80600 cents 4: 1 743.15200 cents 4: 1 800.00000 cents 5: 1 540.82700 cents 5: 1 625.21200 cents 5: 1 679.96000 cents 5: 1 743.04300 cents 5: 1 772.13600 cents 5: 1 836.17000 cents 5: 1 883.97900 cents 5: 1 918.67300 cents 6: 1 709.19100 cents 6: 1 820.78700 cents 6: 1 836.06100 cents 6: 1 890.80900 cents 6: 1 940.50000 cents 6: 1 976.99700 cents 6: 1 1002.65200 cents 6: 1 1023.00300 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 1095.67000 cents 7: 1 1106.98200 cents 7: 1 1116.02100 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 : 84.0 177.0 281.3 400.0 540.8 709.2 920.0 1200.0 84.0 : 93.0 197.3 316.0 456.8 625.2 836.1 1116.0 1200.0 177.0 : 104.3 223.0 363.8 532.2 743.0 1023.0 1107.0 1200.0 281.3 : 118.7 259.5 427.9 638.7 918.7 1002.7 1095.7 1200.0 400.0 : 140.8 309.2 520.0 800.0 884.0 977.0 1081.3 1200.0 540.8 : 168.4 379.2 659.2 743.2 836.2 940.5 1059.2 1200.0 709.2 : 210.8 490.8 574.8 667.8 772.1 890.8 1031.6 1200.0 920.0 : 280.0 363.9 457.0 561.3 680.0 820.8 989.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 83.9790 .. 279.9600 cents 195.98100 cents 83.97900 cents 2: 176.9970 .. 490.8090 cents 313.81200 cents -102.96300 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 .. 1023.0030 cents 313.81200 cents -209.48200 cents 7: 920.0400 .. 1116.0210 cents 195.98100 cents -102.96300 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 83.97900 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 279.96000 cents Average / Smallest step : 1.786161 Largest / Average step : 1.866400 Largest / Smallest step : 3.333691 Median interval of one step : 129.75000 cents, amount: 0 Least squares average step : 126.87017 cents, oct.: 1014.96137 cents Scale is not proper Step pattern alph. order: ABCDEFGH Step pattern size order : ABCDEFGH Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 0.10900 cents Scale diversity : 1.705057 Lumma stability : 0.139965 Lumma impropriety factor : 0.702727 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 : 0.10900 cents Number of recognisable fifths : 1, average 709.1910 cents Steps are strictly increasing Formal octave complements present : 1 = 12.5000% -- Rational properties --
FIT/MODE
8: 1 0 1 1 1 1 1 2 N T3 SD: 41.0864 c. M:-66.0210 c. 9: 1 0 1 1 1 1 2 2 N SD: 28.7195 c. M:-49.3543 c. 12: 1 1 1 1 1 2 2 3 N SD: 20.2713 c. M: 40.8270 c. 13: 1 1 1 1 2 2 2 3 N SD: 16.3135 c. M: 30.7692 c. 14: 1 1 1 2 1 2 3 3 N SD: 20.0357 c. M:-28.5714 c. 17: 1 2 1 2 2 2 3 4 N SD: 17.7822 c. M:-34.7677 c. 18: 1 2 1 2 2 3 3 4 N SD: 15.2459 c. M:-24.1423 c. 20: 1 2 2 2 2 3 3 5 N SD: 15.2143 c. M: 23.9790 c. 21: 1 2 2 2 2 3 4 5 N SD: 16.0435 c. M: 26.8361 c. 22: 1 2 2 2 3 3 4 5 N SD: 13.7981 c. M: 29.4335 c. 24: 2 2 2 2 3 3 4 6 N SD: 14.5976 c. M:-23.0030 c. 25: 2 2 2 2 3 4 4 6 N SD: 11.2702 c. M: 16.0000 c. 26: 2 2 2 3 3 3 5 6 N SD: 10.2911 c. M: 16.8833 c. 27: 2 2 2 3 3 4 5 6 N SD: 7.7152 c. M: 14.6603 c. 29: 2 2 3 3 3 4 5 7 N SD: 8.1259 c. M:-13.7931 c. 34: 2 3 3 3 4 5 6 8 N SD: 7.6324 c. M: 13.3908 c. 39: 3 3 3 4 5 5 7 9 N SD: 6.4009 c. M:-13.0192 c. 40: 3 3 3 4 5 6 7 9 N SD: 7.8286 c. M: 11.3270 c. 42: 3 3 4 4 5 6 7 10 N SD: 3.8154 c. M: 5.7543 c. 60: 4 5 5 6 7 8 11 14 N SD: 3.7378 c. M: 9.1910 c. 68: 5 5 6 7 8 9 12 16 N SD: 3.7006 c. M:-6.2318 c. 69: 5 5 6 7 8 10 12 16 N SD: 2.4593 c. M:-3.8525 c. 86: 6 7 7 9 10 12 15 20 N SD: 2.8318 c. M:-4.6512 c. 95: 7 7 8 10 11 13 17 22 N SD: 2.7903 c. M:-4.4421 c. 98: 7 7 9 10 11 14 17 23 N SD: 2.7112 c. M: 5.5684 c. 102: 7 8 9 10 12 14 18 24 N SD: 1.6113 c. M: 3.3086 c. 115: 8 9 10 11 14 16 20 27 N SD: 1.5473 c. M: 3.4783 c. 124: 9 9 11 12 15 17 22 29 N SD: 2.1695 c. M: 3.2258 c. 128: 9 10 11 13 15 18 22 30 N SD: 2.0112 c. M:-3.3090 c. 129: 9 10 11 13 15 18 23 30 N SD: 1.2545 c. M: 2.2572 c. 171: 12 13 15 17 20 24 30 40 N SD: 0.6915 c. M: 1.5584 c. 257: 18 20 22 26 30 36 45 60 N SD: 0.7879 c. M:-1.5564 c. 269: 19 21 23 27 31 38 47 63 N SD: 0.9526 c. M:-1.4870 c. 273: 19 21 24 27 32 38 48 64 N SD: 0.8448 c. M: 1.4987 c. 286: 20 22 25 28 34 40 50 67 N SD: 0.7194 c. M: 1.3986 c. 291: 20 23 25 29 34 41 51 68 N SD: 0.6894 c. M: 1.5048 c. 299: 21 23 26 30 35 42 52 70 N SD: 0.8289 c. M:-1.3378 c. 300: 21 23 26 30 35 42 53 70 N SD: 0.7794 c. M: 1.3270 c. 313: 22 24 27 31 37 44 55 73 N SD: 0.7390 c. M: 1.4548 c. 317: 22 25 27 32 37 44 56 74 N SD: 0.8907 c. M: 1.3046 c. 318: 22 25 28 31 37 45 56 74 N SD: 0.8613 c. M:-1.6919 c. 330: 23 26 28 33 39 46 58 77 N SD: 0.7311 c. M: 1.3270 c. 333: 23 26 29 33 39 47 58 78 N SD: 0.6417 c. M: 1.1211 c. 357: 25 28 31 35 42 50 63 83 N SD: 0.6568 c. M:-1.1543 c. 359: 25 28 31 36 42 50 63 84 N SD: 0.6303 c. M:-1.1142 c. 372: 26 29 32 37 44 52 65 87 N SD: 0.5690 c. M:-1.1085 c. 381: 27 29 33 38 45 53 67 89 N SD: 0.6854 c. M:-1.0604 c. 384: 27 30 33 38 45 54 67 90 N SD: 0.6299 c. M: 1.2900 c. 399: 28 31 35 39 47 56 70 93 N SD: 0.5961 c. M:-1.3798 c. 413: 29 32 36 41 48 58 73 96 N SD: 0.5699 c. M:-1.0254 c. 415: 29 32 36 41 49 58 73 97 N SD: 0.6009 c. M: 0.9639 c. 426: 30 33 37 42 50 60 75 99 N SD: 0.5312 c. M:-1.0868 c. 428: 30 33 37 43 50 60 75 100 N SD: 0.5259 c. M: 0.9532 c. 432: 30 34 37 43 51 60 76 101 N SD: 0.6535 c. M: 0.8577 c. 440: 31 34 38 44 51 62 77 103 N SD: 0.6116 c. M: 0.9491 c. 441: 31 34 38 44 52 62 77 103 N SD: 0.5960 c. M: 1.0549 c. 453: 32 35 39 45 53 64 79 106 N SD: 0.5674 c. M: 0.8347 c. 455: 32 35 40 45 53 64 80 106 N SD: 0.5057 c. M:-0.8791 c. 462: 32 36 40 46 54 65 81 108 N SD: 0.5220 c. M: 0.8621 c. 486: 34 38 42 48 57 68 86 113 N SD: 0.4797 c. M:-0.9477 c. 501: 35 39 43 50 59 70 88 117 N SD: 0.4511 c. M: 1.0875 c. 502: 35 39 44 49 59 71 88 117 N SD: 0.5378 c. M: 0.7968 c. 513: 36 40 44 51 60 72 90 120 N SD: 0.5008 c. M:-0.7808 c. 515: 36 40 45 51 60 72 91 120 N SD: 0.4858 c. M: 0.8415 c. 524: 37 40 46 52 61 74 92 122 N SD: 0.5821 c. M:-0.7634 c. 528: 37 41 46 52 62 74 93 123 N SD: 0.2546 c. M:-0.4912 c. 699: 49 54 61 69 82 98 123 163 N SD: 0.1367 c. M:-0.2181 c. 990: 69 77 86 98 116 139 174 231 N SD: 0.1548 c. M: 0.3426 c. 1071: 75 83 93 106 126 150 188 250 N SD: 0.1419 c. M:-0.3495 c. 1389: 97 108 121 137 163 195 244 324 N SD: 0.1386 c. M:-0.3145 c. 1416: 99 110 123 140 166 199 249 330 N SD: 0.1373 c. M:-0.2990 c. 1458: 102 113 127 144 171 205 256 340 N SD: 0.1248 c. M:-0.2740 c. 1484: 104 115 129 147 174 208 261 346 N SD: 0.1382 c. M:-0.2695 c. 1518: 106 118 132 150 178 213 267 354 N SD: 0.1041 c. M: 0.1845 c. 1560: 109 121 136 154 183 219 274 364 N SD: 0.0964 c. M:-0.2115 c. 1599: 112 124 139 158 188 224 281 373 N SD: 0.1104 c. M:-0.2612 c. 1689: 118 131 147 167 198 237 297 394 N SD: 0.0936 c. M: 0.1520 c. 1770: 124 137 154 175 208 248 311 413 N SD: 0.0792 c. M:-0.1899 c. 2061: 144 160 179 204 242 289 362 481 N SD: 0.0752 c. M: 0.1362 c. 2217: 155 172 193 219 260 311 390 517 N SD: 0.0898 c. M:-0.1344 c. 2259: 158 175 197 223 265 317 397 527 N SD: 0.0887 c. M:-0.2135 c. 2286: 160 177 199 226 268 321 402 533 N SD: 0.0868 c. M:-0.1700 c. 2345: 164 182 204 232 275 329 412 547 N SD: 0.0878 c. M:-0.1706 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x 4 S SD: 3.6180 cents 3 x x x x 4 x 5:6 S SD: 18.5696 cents 4 x x x 5 x 6:7:8 S SD: 12.7958 cents 5 x x 6 x 7:8:9:10 S SD: 30.5625 cents 6 x x 7 x 8:9:10:12 S SD: 11.6014 cents 7 x x 8:9:10:11:12:14 S SD: 20.5260 cents 8 x 9 x 10:11:12:14:16 S SD: 9.7953 cents 9 x 10 x 11:12:14:15:18 S SD: 15.8148 cents 10 x 11:12:13:14:15:17:20 SD: 11.1139 cents 11 x 12:13:14:15:17:19:22 SD: 8.7343 cents 12 x 13:14:15:16:18:20:24 S SD: 10.1303 cents 13:14 x 15:16:18:20:22:26 SD: 11.6656 cents 14:15 x 16:18:19:21:24:28 SD: 10.4734 cents 16:17:18:19:20:22:24:27:32 SD: 5.5579 cents 19:20:21:22:24:26:29:32:38 SD: 5.0782 cents 22:23:24:26:28:30:33:37:44 SD: 4.9699 cents 24:25:27:28:30:33:36:41:48 SD: 4.8574 cents 27:28:30:32:34:37:41:46:54 SD: 3.6642 cents 35:37:39:41:44:48:53:60:70 SD: 3.1056 cents 38:40:42:45:48:52:57:65:76 SD: 2.2704 cents 46:48:51:54:58:63:69:78:92 SD: 1.8707 cents 57:60:63:67:72:78:86:97:114 SD: 1.0622 cents 85:89:94:100:107:116:128:145:170 SD: 0.9398 cents 101:106:112:119:127:138:152:172:202 SD: 0.6583 cents 120:126:133:141:151:164:181:204:240 SD: 0.5335 cents 158:166:175:186:199:216:238:269:316 SD: 0.2960 cents 204:214:226:240:257:279:307:347:408 SD: 0.2941 cents 261:274:289:307:329:357:393:444:522 SD: 0.2377 cents 324:340:359:381:408:443:488:551:648 SD: 0.2243 cents 362:380:401:426:456:495:545:616:724 SD: 0.1790 cents 466:489:516:548:587:637:702:793:932 SD: 0.1546 cents 482:506:534:567:607:659:726:820:964 SD: 0.1422 cents