Scala analysis: xen18-ayers-table-34
7 Iterated Root Mean Squares 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: 275.659 cents 275.659000 2: 484.413 cents 484.413000 3: 652.478 cents 652.478000 4: 793.157 cents 793.157000 5: 914.137 cents 914.137000 6: 1020.264 cents 1020.264000 7: 1114.789 cents 1114.789000 8: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 85.2110 cents 85.2110 1: 275.6590 cents 275.6590 2: 208.7540 cents 208.7540 3: 168.0650 cents 168.0650 4: 140.6790 cents 140.6790 5: 120.9800 cents 120.9800 6: 106.1270 cents 106.1270 7: 94.5250 cents 94.5250 8: 85.2110 cents 85.2110
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 85.21100 cents 1: 1 94.52500 cents 1: 1 106.12700 cents 1: 1 120.98000 cents 1: 1 140.67900 cents 1: 1 168.06500 cents 1: 1 208.75400 cents 1: 1 275.65900 cents 2: 1 179.73600 cents 2: 1 200.65200 cents 2: 1 227.10700 cents 2: 1 261.65900 cents 2: 1 308.74400 cents 2: 1 360.87000 cents 2: 1 376.81900 cents 2: 1 484.41300 cents 3: 1 285.86300 cents 3: 1 321.63200 cents 3: 1 367.78600 cents 3: 1 429.72400 cents 3: 1 455.39500 cents 3: 1 517.49800 cents 3: 1 569.62400 cents 3: 1 652.47800 cents 4: 1 406.84300 cents 4: 1 462.31100 cents 4: 1 535.85100 cents 4: 1 561.52200 cents 4: 1 638.47800 cents 4: 1 664.14900 cents 4: 1 737.68900 cents 4: 1 793.15700 cents 5: 1 547.52200 cents 5: 1 630.37600 cents 5: 1 682.50200 cents 5: 1 744.60500 cents 5: 1 770.27600 cents 5: 1 832.21400 cents 5: 1 878.36800 cents 5: 1 914.13700 cents 6: 1 715.58700 cents 6: 1 823.18100 cents 6: 1 839.13000 cents 6: 1 891.25600 cents 6: 1 938.34100 cents 6: 1 972.89300 cents 6: 1 999.34800 cents 6: 1 1020.26400 cents 7: 1 924.34100 cents 7: 1 991.24600 cents 7: 1 1031.93500 cents 7: 1 1059.32100 cents 7: 1 1079.02000 cents 7: 1 1093.87300 cents 7: 1 1105.47500 cents 7: 1 1114.78900 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 : 275.7 484.4 652.5 793.2 914.1 1020.3 1114.8 1200.0 275.7 : 208.8 376.8 517.5 638.5 744.6 839.1 924.3 1200.0 484.4 : 168.1 308.7 429.7 535.9 630.4 715.6 991.2 1200.0 652.5 : 140.7 261.7 367.8 462.3 547.5 823.2 1031.9 1200.0 793.2 : 121.0 227.1 321.6 406.8 682.5 891.3 1059.3 1200.0 914.1 : 106.1 200.7 285.9 561.5 770.3 938.3 1079.0 1200.0 1020.3: 94.5 179.7 455.4 664.1 832.2 972.9 1093.9 1200.0 1114.8: 85.2 360.9 569.6 737.7 878.4 999.3 1105.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 85.2110 .. 275.6590 cents 190.44800 cents 85.21100 cents 2: 179.7360 .. 484.4130 cents 304.67700 cents -95.92300 cents 3: 285.8630 .. 652.4780 cents 366.61500 cents -198.55000 cents 4: 406.8430 .. 793.1570 cents 386.31400 cents -245.63500 cents 5: 547.5220 .. 914.1370 cents 366.61500 cents -245.63500 cents 6: 715.5870 .. 1020.2640 cents 304.67700 cents -198.55000 cents 7: 924.3410 .. 1114.7890 cents 190.44800 cents -95.92300 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 85.21100 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 275.65900 cents Average / Smallest step : 1.760336 Largest / Average step : 1.837727 Largest / Smallest step : 3.235017 Median interval of one step : 130.82950 cents, amount: 0 Least squares average step : 168.97225 cents, oct.: 1351.77800 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 6.91600 cents Scale diversity : 1.724156 Lumma stability : 0.142018 Lumma impropriety factor : 0.683433 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 : 6.91600 cents Number of recognisable fifths : 1, average 715.5870 cents Number of appreciable fifths : 0 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: 38.2016 c. M: 64.7890 c. 9: 2 2 1 1 1 1 0 1 N SD: 30.7402 c. M:-48.9203 c. 11: 2 2 2 1 1 1 1 1 N SD: 35.7967 c. M: 57.4772 c. 12: 3 2 2 1 1 1 1 1 N SD: 22.2761 c. M:-47.5220 c. 13: 3 2 2 2 1 1 1 1 N SD: 16.3310 c. M:-37.6122 c. 14: 3 3 2 1 2 1 1 1 N SD: 21.5236 c. M:-33.2363 c. 15: 3 3 2 2 1 2 1 1 N SD: 19.6073 c. M: 35.6590 c. 17: 4 3 2 2 2 1 2 1 N SD: 15.6712 c. M: 32.0287 c. 18: 4 3 3 2 2 1 2 1 N SD: 14.8617 c. M: 20.2640 c. 20: 5 3 3 2 2 2 2 1 N SD: 14.4791 c. M:-25.2110 c. 22: 5 4 3 3 2 2 2 1 N SD: 16.0212 c. M:-30.6655 c. 26: 6 4 4 3 3 2 2 2 N SD: 9.9492 c. M: 22.8745 c. 27: 6 5 4 3 3 2 2 2 N SD: 9.5845 c. M:-19.1963 c. 29: 7 5 4 3 3 3 2 2 N SD: 9.3948 c. M:-14.2188 c. 30: 7 5 4 4 3 3 2 2 N SD: 9.2998 c. M:-19.7360 c. 33: 8 5 5 4 3 3 3 2 N SD: 8.7025 c. M:-15.2501 c. 35: 8 6 5 4 4 3 3 2 N SD: 8.0887 c. M:-16.6396 c. 38: 9 6 6 4 4 3 3 3 N SD: 7.9385 c. M: 10.7288 c. 39: 9 7 5 5 4 3 3 3 N SD: 6.1729 c. M:-8.9399 c. 42: 10 7 6 5 4 4 3 3 N SD: 5.4850 c. M:-10.0553 c. 53: 12 9 8 6 5 5 4 4 N SD: 5.1917 c. M: 8.9413 c. 55: 13 9 8 6 6 5 4 4 N SD: 4.7810 c. M:-7.9774 c. 59: 14 10 8 7 6 5 5 4 N SD: 3.9716 c. M:-9.0868 c. 60: 14 10 9 7 6 5 5 4 N SD: 5.0414 c. M:-7.5220 c. 62: 14 11 9 7 6 6 5 4 N SD: 4.5412 c. M:-7.7916 c. 66: 15 12 9 8 6 6 5 5 N SD: 4.5299 c. M:-6.8430 c. 67: 15 12 9 8 7 6 5 5 N SD: 4.3984 c. M: 7.7019 c. 68: 16 11 10 8 7 6 5 5 N SD: 4.2006 c. M: 7.9424 c. 70: 16 12 10 8 7 6 6 5 N SD: 4.3701 c. M: 8.8354 c. 71: 16 13 10 8 7 6 6 5 N SD: 4.2879 c. M:-6.6769 c. 72: 17 12 10 9 7 6 6 5 N SD: 4.1215 c. M:-7.6743 c. 74: 17 13 10 9 7 7 6 5 N SD: 3.0878 c. M: 6.0289 c. 79: 18 14 11 9 8 7 6 6 N SD: 2.9194 c. M: 5.9282 c. 92: 21 16 13 11 9 8 7 7 N SD: 2.7203 c. M: 6.0933 c. 94: 22 16 13 11 10 8 7 7 N SD: 3.0739 c. M:-5.1921 c. 95: 22 16 14 11 9 9 7 7 N SD: 3.3703 c. M: 4.6633 c. 96: 22 17 13 11 10 9 7 7 N SD: 3.1316 c. M: 5.6570 c. 97: 22 17 14 11 10 8 8 7 N SD: 2.8682 c. M: 5.8310 c. 100: 23 17 14 12 10 9 8 7 N SD: 2.4260 c. M: 4.4780 c. 101: 23 18 14 12 10 9 8 7 N SD: 1.9160 c. M:-2.8826 c. 114: 26 20 16 13 12 10 9 8 N SD: 1.6540 c. M: 3.6833 c. 127: 29 22 18 15 13 11 10 9 N SD: 1.3896 c. M: 2.5232 c. 156: 36 27 22 18 16 14 12 11 N SD: 1.3255 c. M:-2.8129 c. 169: 39 29 24 20 17 15 13 12 N SD: 1.4765 c. M:-2.2212 c. 171: 39 30 24 20 17 15 14 12 N SD: 1.4072 c. M: 2.7201 c. 180: 41 32 25 21 18 16 14 13 N SD: 1.3269 c. M: 2.3257 c. 186: 43 32 26 22 19 16 15 13 N SD: 1.1664 c. M:-1.9920 c. 201: 46 35 28 24 20 18 16 14 N SD: 1.0645 c. M: 1.7317 c. 213: 49 37 30 25 21 19 17 15 N SD: 0.8400 c. M: 1.4609 c. 248: 57 43 35 29 25 22 19 18 N SD: 0.8080 c. M: 1.8858 c. 265: 61 46 37 31 27 23 21 19 N SD: 0.7037 c. M: 1.3961 c. 280: 64 49 39 33 28 25 22 20 N SD: 0.7949 c. M: 1.3733 c. 307: 71 53 43 36 31 27 24 22 N SD: 0.7614 c. M:-1.8654 c. 312: 72 54 44 36 32 27 25 22 N SD: 0.9494 c. M:-1.3682 c. 313: 72 54 44 37 31 28 25 22 N SD: 0.8979 c. M: 1.6769 c. 315: 72 55 44 37 32 28 25 22 N SD: 0.8954 c. M:-1.4015 c. 322: 74 56 45 38 32 29 25 23 N SD: 0.5796 c. M: 1.0935 c. 327: 75 57 46 38 33 29 26 23 N SD: 0.4701 c. M:-0.8073 c. 366: 84 64 51 43 37 32 29 26 N SD: 0.4430 c. M:-0.8329 c. 419: 96 73 59 49 42 37 33 30 N SD: 0.5276 c. M: 0.7187 c. 421: 97 73 59 49 43 37 33 30 N SD: 0.5176 c. M:-0.8274 c. 436: 100 76 61 51 44 39 34 31 N SD: 0.4060 c. M:-0.8369 c. 449: 103 78 63 53 45 40 35 32 N SD: 0.4548 c. M:-0.6714 c. 466: 107 81 65 55 47 41 37 33 N SD: 0.4154 c. M: 0.9759 c. 495: 114 86 69 58 50 44 39 35 N SD: 0.4009 c. M:-0.7046 c. 508: 117 88 71 60 51 45 40 36 N SD: 0.3828 c. M:-0.7190 c. 522: 120 91 73 61 53 46 41 37 N SD: 0.4286 c. M:-0.8055 c. 567: 130 99 79 67 57 50 45 40 N SD: 0.4074 c. M: 0.6261 c. 575: 132 100 81 67 58 51 45 41 N SD: 0.3248 c. M:-0.7394 c. 579: 133 101 81 68 58 51 46 41 N SD: 0.3957 c. M:-0.6254 c. 587: 135 102 82 69 59 52 46 42 N SD: 0.3151 c. M: 0.6493 c. 622: 143 108 87 73 63 55 49 44 N SD: 0.2732 c. M: 0.3880 c. 634: 146 110 89 74 64 56 50 45 N SD: 0.3104 c. M:-0.6817 c. 688: 158 120 96 81 69 61 54 49 N SD: 0.2638 c. M:-0.4707 c. 701: 161 122 98 82 71 62 55 50 N SD: 0.2625 c. M: 0.5750 c. 761: 175 132 107 89 77 67 60 54 N SD: 0.2527 c. M:-0.4491 c. 802: 184 140 112 94 81 71 63 57 N SD: 0.2057 c. M:-0.3750 c. 835: 192 145 117 98 84 74 66 59 N SD: 0.1948 c. M:-0.4206 c. 914: 210 159 128 107 92 81 72 65 N SD: 0.1540 c. M: 0.3514 c. 1015: 233 177 142 119 102 90 80 72 N SD: 0.1745 c. M:-0.3161 c. 1041: 239 181 146 122 105 92 82 74 N SD: 0.1206 c. M: 0.2631 c. 1083: 249 188 152 127 109 96 85 77 N SD: 0.1686 c. M:-0.2413 c. 1100: 253 191 154 129 111 97 87 78 N SD: 0.1667 c. M:-0.3410 c. 1142: 262 199 160 134 115 101 90 81 N SD: 0.1491 c. M: 0.3525 c. 1280: 294 223 179 150 129 113 101 91 N SD: 0.1430 c. M:-0.2745 c. 1310: 301 228 183 154 132 116 103 93 N SD: 0.1413 c. M: 0.2643 c. 1368: 314 238 192 160 138 121 108 97 N SD: 0.1488 c. M: 0.2204 c. 1407: 323 245 197 165 142 124 111 100 N SD: 0.1176 c. M: 0.2214 c. 1449: 333 252 203 170 146 128 114 103 N SD: 0.1159 c. M:-0.2177 c. 1481: 340 258 207 174 149 131 117 105 N SD: 0.1426 c. M: 0.2160 c. 1536: 353 267 215 180 155 136 121 109 N SD: 0.1005 c. M: 0.1883 c. 1637: 376 285 229 192 165 145 129 116 N SD: 0.0963 c. M:-0.1774 c. 1729: 397 301 242 203 174 153 136 123 N SD: 0.0948 c. M: 0.1563 c. 1776: 408 309 249 208 179 157 140 126 N SD: 0.0928 c. M:-0.2247 c. 1876: 431 326 263 220 189 166 148 133 N SD: 0.0878 c. M: 0.1913 c. 1885: 433 328 264 221 190 167 148 134 N SD: 0.0878 c. M:-0.2135 c. 1902: 437 331 266 223 192 168 150 135 N SD: 0.0804 c. M:-0.1296 c. 2056: 472 358 288 241 207 182 162 146 N SD: 0.0804 c. M: 0.1726 c. 2115: 486 368 296 248 213 187 167 150 N SD: 0.0860 c. M:-0.1260 c. 2150: 494 374 301 252 217 190 169 153 N SD: 0.0804 c. M: 0.1843 c. 2242: 515 390 314 263 226 198 177 159 N SD: 0.0612 c. M:-0.1084 c. 2363: 543 411 331 277 238 209 186 168 N SD: 0.0687 c. M: 0.1043 c. 2398: 551 417 336 281 242 212 189 170 N SD: 0.0807 c. M:-0.1401 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: 24.7385 cents 3 x 4 x x 5 x x 6 S SD: 10.9167 cents 4 x 5:6 x x 7 x 8 S SD: 30.3287 cents 5:6 x 7:8 x 9 x 10 S SD: 16.6402 cents 6:7:8:9 x 10:11 x 12 S SD: 11.1112 cents 7:8:9:10:11:12 x 13:14 S SD: 12.7516 cents 8:9:11:12:13 x 14:15:16 SD: 18.9873 cents 9:11:12:13:14:15:16:17:18 SD: 11.2103 cents 10:12:13:15:16:17:18:19:20 SD: 9.2028 cents 12:14:16:18:19:20:22:23:24 S SD: 8.4625 cents 13:15:17:19:21:22:23:25:26 SD: 7.8497 cents 15:18:20:22:24:25:27:29:30 SD: 7.8210 cents 16:19:21:23:25:27:29:30:32 SD: 6.2864 cents 19:22:25:28:30:32:34:36:38 SD: 4.4985 cents 22:26:29:32:35:37:40:42:44 SD: 3.5081 cents 24:28:32:35:38:41:43:46:48 SD: 3.2716 cents 29:34:38:42:46:49:52:55:58 SD: 3.0573 cents 31:36:41:45:49:53:56:59:62 SD: 2.9410 cents 35:41:46:51:55:59:63:67:70 SD: 2.6269 cents 40:47:53:58:63:68:72:76:80 SD: 1.7265 cents 46:54:61:67:73:78:83:88:92 SD: 1.4485 cents 52:61:69:76:82:88:94:99:104 SD: 1.2722 cents 65:76:86:95:103:110:117:124:130 SD: 1.1834 cents 81:95:107:118:128:137:146:154:162 SD: 0.7210 cents 105:123:139:153:166:178:189:200:210 SD: 0.4480 cents 168:197:222:245:266:285:303:320:336 SD: 0.4283 cents 186:218:246:271:294:315:335:354:372 SD: 0.3819 cents 198:232:262:289:313:336:357:377:396 SD: 0.3750 cents 208:244:275:303:329:353:375:396:416 SD: 0.3010 cents 260:305:344:379:411:441:469:495:520 SD: 0.1823 cents 325:381:430:474:514:551:586:619:650 SD: 0.1623 cents 365:428:483:532:577:619:658:695:730 SD: 0.0962 cents