Scala analysis: xen18-ayers-table-39
7 Iterated Root Harmonic Square 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: 85.211 cents 85.211400 2: 179.736 cents 179.736000 3: 285.863 cents 285.863000 4: 406.843 cents 406.843000 5: 547.522 cents 547.522000 6: 715.587 cents 715.587000 7: 924.341 cents 924.341000 8: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 275.6590 cents 275.6590 1: 85.2114 cents 85.2114 2: 94.5246 cents 94.5246 3: 106.1270 cents 106.1270 4: 120.9800 cents 120.9800 5: 140.6790 cents 140.6790 6: 168.0650 cents 168.0650 7: 208.7540 cents 208.7540 8: 275.6590 cents 275.6590
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 85.21140 cents 1: 1 94.52460 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: 1 200.65160 cents 2: 1 227.10700 cents 2: 1 261.65900 cents 2: 1 308.74400 cents 2: 1 360.87040 cents 2: 1 376.81900 cents 2: 1 484.41300 cents 3: 1 285.86300 cents 3: 1 321.63160 cents 3: 1 367.78600 cents 3: 1 429.72400 cents 3: 1 455.39500 cents 3: 1 517.49800 cents 3: 1 569.62440 cents 3: 1 652.47800 cents 4: 1 406.84300 cents 4: 1 462.31060 cents 4: 1 535.85100 cents 4: 1 561.52200 cents 4: 1 638.47800 cents 4: 1 664.14900 cents 4: 1 737.68940 cents 4: 1 793.15700 cents 5: 1 547.52200 cents 5: 1 630.37560 cents 5: 1 682.50200 cents 5: 1 744.60500 cents 5: 1 770.27600 cents 5: 1 832.21400 cents 5: 1 878.36840 cents 5: 1 914.13700 cents 6: 1 715.58700 cents 6: 1 823.18100 cents 6: 1 839.12960 cents 6: 1 891.25600 cents 6: 1 938.34100 cents 6: 1 972.89300 cents 6: 1 999.34840 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 1105.47540 cents 7: 1 1114.78860 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 : 85.2 179.7 285.9 406.8 547.5 715.6 924.3 1200.0 85.2 : 94.5 200.7 321.6 462.3 630.4 839.1 1114.8 1200.0 179.7 : 106.1 227.1 367.8 535.9 744.6 1020.3 1105.5 1200.0 285.9 : 121.0 261.7 429.7 638.5 914.1 999.3 1093.9 1200.0 406.8 : 140.7 308.7 517.5 793.2 878.4 972.9 1079.0 1200.0 547.5 : 168.1 376.8 652.5 737.7 832.2 938.3 1059.3 1200.0 715.6 : 208.8 484.4 569.6 664.1 770.3 891.3 1031.9 1200.0 924.3 : 275.7 360.9 455.4 561.5 682.5 823.2 991.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 85.2114 .. 275.6590 cents 190.44760 cents 85.21140 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 .. 1114.7886 cents 190.44760 cents -95.92300 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 85.21140 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 275.65900 cents Average / Smallest step : 1.760328 Largest / Average step : 1.837727 Largest / Smallest step : 3.235001 Median interval of one step : 130.82950 cents, amount: 0 Least squares average step : 127.60374 cents, oct.: 1020.82994 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 6.91560 cents Scale diversity : 1.724155 Lumma stability : 0.142019 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 : 6.91560 cents Number of recognisable fifths : 1, average 715.5870 cents Number of appreciable fifths : 0 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: 38.2015 c. M:-64.7886 c. 9: 1 0 1 1 1 1 2 2 N SD: 30.7401 c. M: 48.9203 c. 12: 1 1 1 1 1 2 2 3 N SD: 22.2761 c. M: 47.5220 c. 13: 1 1 1 1 2 2 2 3 N SD: 16.3310 c. M: 37.6122 c. 14: 1 1 1 2 1 2 3 3 N SD: 21.5236 c. M: 33.2363 c. 15: 1 1 2 1 2 2 3 3 N SD: 19.6073 c. M:-35.6590 c. 17: 1 2 1 2 2 2 3 4 N SD: 15.6713 c. M:-32.0287 c. 18: 1 2 1 2 2 3 3 4 N SD: 14.8618 c. M:-20.2640 c. 20: 1 2 2 2 2 3 3 5 N SD: 14.4792 c. M: 25.2114 c. 22: 1 2 2 2 3 3 4 5 N SD: 16.0213 c. M: 30.6659 c. 24: 2 2 2 2 3 3 4 6 N SD: 14.6526 c. M: 24.3410 c. 25: 2 2 2 2 3 4 4 6 N SD: 12.9714 c. M: 22.8430 c. 26: 2 2 2 3 3 4 4 6 N SD: 9.9491 c. M:-22.8745 c. 27: 2 2 2 3 3 4 5 6 N SD: 9.5845 c. M: 19.1963 c. 29: 2 2 3 3 3 4 5 7 N SD: 9.3948 c. M: 14.2188 c. 30: 2 2 3 3 4 4 5 7 N SD: 9.2998 c. M: 19.7360 c. 33: 2 3 3 3 4 5 5 8 N SD: 8.7025 c. M: 15.2501 c. 35: 2 3 3 4 4 5 6 8 N SD: 8.0888 c. M: 16.6400 c. 38: 3 3 3 4 4 6 6 9 N SD: 7.9384 c. M:-10.7288 c. 39: 3 3 3 4 5 5 7 9 N SD: 6.1729 c. M: 8.9399 c. 42: 3 3 4 4 5 6 7 10 N SD: 5.4850 c. M: 10.0553 c. 52: 4 4 4 6 6 7 9 12 N SD: 5.7953 c. M: 8.9399 c. 53: 4 4 5 5 6 8 9 12 N SD: 5.1917 c. M:-8.9413 c. 55: 4 4 5 6 6 8 9 13 N SD: 4.7810 c. M: 7.9774 c. 59: 4 5 5 6 7 8 10 14 N SD: 3.9716 c. M: 9.0868 c. 60: 4 5 5 6 7 9 10 14 N SD: 5.0414 c. M: 7.5220 c. 62: 4 5 6 6 7 9 11 14 N SD: 4.5413 c. M: 7.7920 c. 66: 5 5 6 6 8 9 12 15 N SD: 4.5299 c. M: 6.8430 c. 67: 5 5 6 7 8 9 12 15 N SD: 4.3983 c. M:-7.7019 c. 70: 5 6 6 7 8 10 12 16 N SD: 4.3701 c. M:-8.8354 c. 71: 5 6 6 7 8 10 13 16 N SD: 4.2879 c. M: 6.6769 c. 72: 5 6 6 7 9 10 12 17 N SD: 4.1215 c. M: 7.6743 c. 74: 5 6 7 7 9 10 13 17 N SD: 3.0879 c. M:-6.0289 c. 79: 6 6 7 8 9 11 14 18 N SD: 2.9193 c. M:-5.9278 c. 92: 7 7 8 9 11 13 16 21 N SD: 2.7202 c. M:-6.0929 c. 94: 7 7 8 10 11 13 16 22 N SD: 3.0739 c. M: 5.1921 c. 97: 7 8 8 10 11 14 17 22 N SD: 2.8682 c. M:-5.8310 c. 100: 7 8 9 10 12 14 17 23 N SD: 2.4261 c. M:-4.4780 c. 101: 7 8 9 10 12 14 18 23 N SD: 1.9160 c. M: 2.8826 c. 114: 8 9 10 12 13 16 20 26 N SD: 1.6540 c. M:-3.6833 c. 127: 9 10 11 13 15 18 22 29 N SD: 1.3896 c. M:-2.5232 c. 156: 11 12 14 16 18 22 27 36 N SD: 1.3255 c. M: 2.8129 c. 169: 12 13 15 17 20 24 29 39 N SD: 1.4765 c. M: 2.2212 c. 171: 12 14 15 17 20 24 30 39 N SD: 1.4072 c. M:-2.7201 c. 180: 13 14 16 18 21 25 32 41 N SD: 1.3268 c. M:-2.3257 c. 186: 13 15 16 19 22 26 32 43 N SD: 1.1665 c. M: 1.9920 c. 201: 14 16 18 20 24 28 35 46 N SD: 1.0645 c. M:-1.7317 c. 213: 15 17 19 21 25 30 37 49 N SD: 0.8400 c. M:-1.4609 c. 248: 18 19 22 25 29 35 43 57 N SD: 0.8079 c. M:-1.8854 c. 265: 19 21 23 27 31 37 46 61 N SD: 0.7037 c. M:-1.3961 c. 280: 20 22 25 28 33 39 49 64 N SD: 0.7948 c. M:-1.3733 c. 307: 22 24 27 31 36 43 53 71 N SD: 0.7613 c. M: 1.8654 c. 312: 22 25 27 32 36 44 54 72 N SD: 0.9494 c. M: 1.3682 c. 313: 22 25 28 31 37 44 54 72 N SD: 0.8980 c. M:-1.6769 c. 315: 22 25 28 32 37 44 55 72 N SD: 0.8955 c. M: 1.4019 c. 322: 23 25 29 32 38 45 56 74 N SD: 0.5795 c. M:-1.0935 c. 327: 23 26 29 33 38 46 57 75 N SD: 0.4702 c. M: 0.8077 c. 366: 26 29 32 37 43 51 64 84 N SD: 0.4430 c. M: 0.8329 c. 419: 30 33 37 42 49 59 73 96 N SD: 0.5275 c. M:-0.7187 c. 421: 30 33 37 43 49 59 73 97 N SD: 0.5176 c. M: 0.8274 c. 436: 31 34 39 44 51 61 76 100 N SD: 0.4060 c. M: 0.8369 c. 449: 32 35 40 45 53 63 78 103 N SD: 0.4548 c. M: 0.6714 c. 466: 33 37 41 47 55 65 81 107 N SD: 0.4154 c. M:-0.9759 c. 495: 35 39 44 50 58 69 86 114 N SD: 0.4009 c. M: 0.7046 c. 508: 36 40 45 51 60 71 88 117 N SD: 0.3828 c. M: 0.7190 c. 522: 37 41 46 53 61 73 91 120 N SD: 0.4286 c. M: 0.8055 c. 567: 40 45 50 57 67 79 99 130 N SD: 0.4074 c. M:-0.6261 c. 575: 41 45 51 58 67 81 100 132 N SD: 0.3247 c. M: 0.7394 c. 579: 41 46 51 58 68 81 101 133 N SD: 0.3957 c. M: 0.6254 c. 587: 42 46 52 59 69 82 102 135 N SD: 0.3150 c. M:-0.6489 c. 622: 44 49 55 63 73 87 108 143 N SD: 0.2733 c. M:-0.3880 c. 634: 45 50 56 64 74 89 110 146 N SD: 0.3104 c. M: 0.6817 c. 688: 49 54 61 69 81 96 120 158 N SD: 0.2637 c. M: 0.4707 c. 701: 50 55 62 71 82 98 122 161 N SD: 0.2625 c. M:-0.5750 c. 761: 54 60 67 77 89 107 132 175 N SD: 0.2527 c. M: 0.4491 c. 802: 57 63 71 81 94 112 140 184 N SD: 0.2057 c. M: 0.3750 c. 835: 59 66 74 84 98 117 145 192 N SD: 0.1949 c. M: 0.4210 c. 914: 65 72 81 92 107 128 159 210 N SD: 0.1539 c. M:-0.3514 c. 1015: 72 80 90 102 119 142 177 233 N SD: 0.1745 c. M: 0.3161 c. 1041: 74 82 92 105 122 146 181 239 N SD: 0.1205 c. M:-0.2631 c. 1083: 77 85 96 109 127 152 188 249 N SD: 0.1686 c. M: 0.2413 c. 1100: 78 87 97 111 129 154 191 253 N SD: 0.1667 c. M: 0.3410 c. 1142: 81 90 101 115 134 160 199 262 N SD: 0.1491 c. M:-0.3525 c. 1280: 91 101 113 129 150 179 223 294 N SD: 0.1430 c. M: 0.2745 c. 1310: 93 103 116 132 154 183 228 301 N SD: 0.1413 c. M:-0.2643 c. 1368: 97 108 121 138 160 192 238 314 N SD: 0.1488 c. M:-0.2204 c. 1407: 100 111 124 142 165 197 245 323 N SD: 0.1176 c. M:-0.2214 c. 1449: 103 114 128 146 170 203 252 333 N SD: 0.1159 c. M: 0.2177 c. 1481: 105 117 131 149 174 207 258 340 N SD: 0.1427 c. M:-0.2160 c. 1536: 109 121 136 155 180 215 267 353 N SD: 0.1005 c. M:-0.1882 c. 1637: 116 129 145 165 192 229 285 376 N SD: 0.0964 c. M: 0.1778 c. 1729: 123 136 153 174 203 242 301 397 N SD: 0.0947 c. M:-0.1559 c. 1776: 126 140 157 179 208 249 309 408 N SD: 0.0928 c. M: 0.2247 c. 1876: 133 148 166 189 220 263 326 431 N SD: 0.0878 c. M:-0.1913 c. 1885: 134 148 167 190 221 264 328 433 N SD: 0.0877 c. M: 0.2135 c. 1902: 135 150 168 192 223 266 331 437 N SD: 0.0805 c. M: 0.1296 c. 2056: 146 162 182 207 241 288 358 472 N SD: 0.0804 c. M:-0.1726 c. 2115: 150 167 187 213 248 296 368 486 N SD: 0.0861 c. M: 0.1260 c. 2150: 153 169 190 217 252 301 374 494 N SD: 0.0803 c. M:-0.1839 c. 2242: 159 177 198 226 263 314 390 515 N SD: 0.0613 c. M: 0.1088 c. 2363: 168 186 209 238 277 331 411 543 N SD: 0.0686 c. M:-0.1039 c. 2398: 170 189 212 242 281 336 417 551 N SD: 0.0808 c. M: 0.1405 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: 6.8160 cents 3 x x x x 4 x 5:6 S SD: 21.2042 cents 4 x x x 5 x 6:7:8 S SD: 12.7136 cents 5 x x 6 x 7:8:9:10 S SD: 28.5875 cents 6 x x 7 x 8:9:10:12 S SD: 13.5545 cents 7 x 8 x 9:10:11:12:14 S SD: 18.9239 cents 8 x 9 x 10:11:12:14:16 S SD: 9.4059 cents 9 x 10 x 11:12:14:15:18 S SD: 16.6829 cents 10 x 11:12:13:14:15:17:20 SD: 9.8875 cents 11 x 12:13:14:15:17:19:22 SD: 7.8362 cents 12 x 13:14:15:16:18:20:24 S SD: 11.7012 cents 13:14 x 15:16:18:20:22:26 SD: 11.8674 cents 14:15:16:17:18:19:21:24:28 SD: 11.0112 cents 15:16:17:18:19:21:23:26:30 SD: 9.3217 cents 16:17:18:19:20:22:24:27:32 SD: 5.6913 cents 18:19:20:21:23:25:27:31:36 SD: 5.0960 cents 26:27:29:31:33:36:39:44:52 SD: 4.8173 cents 27:28:30:32:34:37:41:46:54 SD: 3.2990 cents 35:37:39:41:44:48:53:60:70 SD: 2.8517 cents 37:39:41:44:47:51:56:63:74 SD: 2.4008 cents 38:40:42:45:48:52:57:65:76 SD: 2.2994 cents 45:47:50:53:57:62:68:77:90 SD: 1.7815 cents 56:59:62:66:71:77:85:96:112 SD: 1.7485 cents 57:60:63:67:72:78:86:97:114 SD: 1.5048 cents 72:76:80:85:91:99:109:123:144 SD: 1.3062 cents 83:87:92:98:105:114:125:142:166 SD: 1.2236 cents 84:88:93:99:106:115:127:143:168 SD: 1.1025 cents 94:99:104:111:119:129:142:160:188 SD: 0.9920 cents 99:104:110:117:125:136:150:169:198 SD: 0.8785 cents 102:107:113:120:129:140:154:174:204 SD: 0.7703 cents 118:124:131:139:149:162:178:201:236 SD: 0.7668 cents 121:127:134:143:153:166:183:206:242 SD: 0.7233 cents 139:146:154:164:176:191:210:237:278 SD: 0.5244 cents 156:164:173:184:197:214:236:266:312 SD: 0.4335 cents 201:211:223:237:254:276:304:343:402 SD: 0.3506 cents 256:269:284:302:324:351:387:437:512 SD: 0.2708 cents 295:310:327:348:373:405:446:503:590 SD: 0.2673 cents 301:316:334:355:381:413:455:513:602 SD: 0.2628 cents 336:353:373:396:425:461:508:573:672 SD: 0.2301 cents 373:392:414:440:472:512:564:636:746 SD: 0.2101 cents 401:421:445:473:507:550:606:684:802 SD: 0.2015 cents 412:433:457:486:521:565:623:703:824 SD: 0.1892 cents 438:460:486:517:554:601:662:747:876 SD: 0.1779 cents 457:480:507:539:578:627:691:779:914 SD: 0.1367 cents 578:607:641:682:731:793:874:986:1156 SD: 0.1361 cents