Scala analysis: xen18-ayers-table-28
7 Iterated Second Subcontraries to Geometric 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: 259.681 cents 259.681000 2: 461.945 cents 461.945000 3: 629.974 cents 629.974000 4: 771.578 cents 771.578000 5: 899.057 cents 899.057000 6: 1010.614 cents 1010.614000 7: 1110.343 cents 1110.343000 8: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 89.6570 cents 89.6570 1: 259.6810 cents 259.6810 2: 202.2640 cents 202.2640 3: 168.0290 cents 168.0290 4: 141.6040 cents 141.6040 5: 127.4790 cents 127.4790 6: 111.5570 cents 111.5570 7: 99.7290 cents 99.7290 8: 89.6570 cents 89.6570
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 89.65700 cents 1: 1 99.72900 cents 1: 1 111.55700 cents 1: 1 127.47900 cents 1: 1 141.60400 cents 1: 1 168.02900 cents 1: 1 202.26400 cents 1: 1 259.68100 cents 2: 1 189.38600 cents 2: 1 211.28600 cents 2: 1 239.03600 cents 2: 1 269.08300 cents 2: 1 309.63300 cents 2: 1 349.33800 cents 2: 1 370.29300 cents 2: 1 461.94500 cents 3: 1 300.94300 cents 3: 1 338.76500 cents 3: 1 380.64000 cents 3: 1 437.11200 cents 3: 1 449.06700 cents 3: 1 511.89700 cents 3: 1 551.60200 cents 3: 1 629.97400 cents 4: 1 428.42200 cents 4: 1 480.36900 cents 4: 1 548.66900 cents 4: 1 560.62400 cents 4: 1 639.37600 cents 4: 1 651.33100 cents 4: 1 719.63100 cents 4: 1 771.57800 cents 5: 1 570.02600 cents 5: 1 648.39800 cents 5: 1 688.10300 cents 5: 1 750.93300 cents 5: 1 762.88800 cents 5: 1 819.36000 cents 5: 1 861.23500 cents 5: 1 899.05700 cents 6: 1 738.05500 cents 6: 1 829.70700 cents 6: 1 850.66200 cents 6: 1 890.36700 cents 6: 1 930.91700 cents 6: 1 960.96400 cents 6: 1 988.71400 cents 6: 1 1010.61400 cents 7: 1 940.31900 cents 7: 1 997.73600 cents 7: 1 1031.97100 cents 7: 1 1058.39600 cents 7: 1 1072.52100 cents 7: 1 1088.44300 cents 7: 1 1100.27100 cents 7: 1 1110.34300 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 : 259.7 461.9 630.0 771.6 899.1 1010.6 1110.3 1200.0 259.7 : 202.3 370.3 511.9 639.4 750.9 850.7 940.3 1200.0 461.9 : 168.0 309.6 437.1 548.7 648.4 738.1 997.7 1200.0 630.0 : 141.6 269.1 380.6 480.4 570.0 829.7 1032.0 1200.0 771.6 : 127.5 239.0 338.8 428.4 688.1 890.4 1058.4 1200.0 899.1 : 111.6 211.3 300.9 560.6 762.9 930.9 1072.5 1200.0 1010.6: 99.7 189.4 449.1 651.3 819.4 961.0 1088.4 1200.0 1110.3: 89.7 349.3 551.6 719.6 861.2 988.7 1100.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 89.6570 .. 259.6810 cents 170.02400 cents 89.65700 cents 2: 189.3860 .. 461.9450 cents 272.55900 cents -70.29500 cents 3: 300.9430 .. 629.9740 cents 329.03100 cents -161.00200 cents 4: 428.4220 .. 771.5780 cents 343.15600 cents -201.55200 cents 5: 570.0260 .. 899.0570 cents 329.03100 cents -201.55200 cents 6: 738.0550 .. 1010.6140 cents 272.55900 cents -161.00200 cents 7: 940.3190 .. 1110.3430 cents 170.02400 cents -70.29500 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 89.65700 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 259.68100 cents Average / Smallest step : 1.673043 Largest / Average step : 1.731207 Largest / Smallest step : 2.896383 Median interval of one step : 134.54150 cents, amount: 0 Least squares average step : 167.11360 cents, oct.: 1336.90882 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 2.93300 cents Scale diversity : 1.692018 Lumma stability : 0.149428 Lumma impropriety factor : 0.615587 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 : 2.93300 cents Number of recognisable fifths : 2, average 703.8670 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: 32.2602 c. M: 60.3430 c. 10: 2 2 1 1 1 1 1 1 N D3 S SD: 37.4871 c. M: 59.0570 c. 11: 2 2 2 1 1 1 1 1 N SD: 24.8585 c. M: 41.4992 c. 12: 3 2 1 2 1 1 1 1 N SD: 25.0014 c. M:-40.3190 c. 13: 3 2 2 1 2 1 1 1 N SD: 16.8177 c. M: 33.1165 c. 15: 3 3 2 2 1 2 1 1 N SD: 19.1756 c. M:-29.3860 c. 17: 4 3 2 2 2 1 2 1 N SD: 18.7462 c. M:-32.1726 c. 19: 4 3 3 2 2 2 1 2 N SD: 16.5734 c. M: 36.6588 c. 23: 5 4 3 3 2 2 2 2 N SD: 10.7899 c. M: 19.3097 c. 26: 6 4 4 3 3 2 2 2 N SD: 12.9226 c. M:-24.0199 c. 27: 6 4 4 3 3 3 2 2 N SD: 10.6689 c. M: 17.5006 c. 28: 6 5 4 3 3 3 2 2 N SD: 8.6695 c. M:-17.9574 c. 31: 7 5 4 4 3 3 3 2 N SD: 7.8818 c. M:-12.2376 c. 36: 8 6 5 4 4 3 3 3 N SD: 6.3936 c. M: 10.6140 c. 42: 9 7 6 5 4 4 4 3 N SD: 6.4973 c. M: 13.3427 c. 44: 10 7 6 5 5 4 4 3 N SD: 6.2057 c. M:-13.0463 c. 45: 10 7 7 5 5 4 4 3 N SD: 6.9383 c. M:-10.0260 c. 50: 11 8 7 6 5 5 4 4 N SD: 5.8289 c. M: 11.0570 c. 51: 11 9 7 6 5 5 4 4 N SD: 4.6543 c. M:-8.6432 c. 55: 12 9 8 6 6 5 5 4 N SD: 4.5291 c. M: 7.9416 c. 57: 12 10 8 7 6 5 5 4 N SD: 4.6936 c. M:-7.3694 c. 59: 13 10 8 7 6 6 5 4 N SD: 4.8057 c. M:-8.3011 c. 64: 14 11 9 7 7 6 5 5 N SD: 4.1847 c. M:-7.5260 c. 65: 14 11 9 8 7 6 5 5 N SD: 3.2021 c. M:-5.5584 c. 68: 15 11 10 8 7 6 6 5 N SD: 3.7506 c. M:-5.3201 c. 70: 15 12 10 8 7 7 6 5 N SD: 3.5406 c. M: 7.6284 c. 75: 16 13 10 9 8 7 6 6 N SD: 3.9159 c. M: 6.3430 c. 76: 16 13 11 9 8 7 6 6 N SD: 3.5322 c. M: 7.0494 c. 78: 17 13 11 9 8 8 6 6 N SD: 3.2614 c. M: 6.7493 c. 83: 18 14 12 9 9 8 7 6 N SD: 3.2553 c. M:-6.1706 c. 84: 18 14 12 10 9 8 7 6 N SD: 2.7706 c. M: 4.8021 c. 89: 19 15 13 10 10 8 7 7 N SD: 3.3379 c. M: 4.7250 c. 93: 20 16 13 11 10 8 8 7 N SD: 2.6559 c. M:-4.1688 c. 96: 21 16 13 12 10 9 8 7 N SD: 2.5934 c. M: 4.9740 c. 101: 22 17 14 12 11 9 8 8 N SD: 2.5098 c. M: 5.3925 c. 103: 22 18 14 12 11 10 8 8 N SD: 2.7616 c. M:-4.0744 c. 106: 23 18 15 12 11 10 9 8 N SD: 2.6661 c. M: 4.7174 c. 107: 23 18 15 13 11 10 9 8 N SD: 1.6381 c. M:-2.2538 c. 120: 26 20 17 14 13 11 10 9 N SD: 0.9849 c. M: 1.9450 c. 171: 37 29 24 20 18 16 14 13 N SD: 0.9556 c. M:-1.6049 c. 227: 49 38 32 27 24 21 19 17 N SD: 0.8983 c. M: 2.0331 c. 255: 55 43 36 30 27 24 21 19 N SD: 0.6302 c. M:-1.1507 c. 291: 63 49 41 34 31 27 24 22 N SD: 0.5433 c. M: 1.0646 c. 348: 75 59 49 41 37 32 29 26 N SD: 0.7004 c. M:-1.0605 c. 350: 76 59 49 41 37 33 29 26 N SD: 0.7027 c. M:-0.9121 c. 356: 77 60 50 42 38 33 29 27 N SD: 0.6510 c. M: 1.3542 c. 375: 81 63 53 44 40 35 31 28 N SD: 0.5284 c. M: 1.1450 c. 379: 82 64 53 45 40 35 32 28 N SD: 0.5540 c. M:-1.0026 c. 387: 84 65 54 46 41 36 32 29 N SD: 0.4043 c. M:-0.7841 c. 431: 93 73 60 51 46 40 36 32 N SD: 0.4561 c. M: 0.7483 c. 457: 99 77 64 54 48 43 38 34 N SD: 0.4528 c. M: 1.0264 c. 470: 102 79 66 55 50 44 39 35 N SD: 0.4602 c. M:-0.7445 c. 499: 108 84 70 59 53 46 42 37 N SD: 0.3746 c. M:-0.6790 c. 507: 110 85 71 60 54 47 42 38 N SD: 0.3493 c. M:-0.6740 c. 551: 119 93 77 65 59 51 46 41 N SD: 0.4078 c. M: 0.6161 c. 558: 121 94 78 66 59 52 46 42 N SD: 0.3834 c. M: 0.6656 c. 577: 125 97 81 68 61 54 48 43 N SD: 0.2795 c. M: 0.6168 c. 602: 130 102 84 71 64 56 50 45 N SD: 0.2723 c. M: 0.5448 c. 642: 139 108 90 76 68 60 53 48 N SD: 0.2748 c. M:-0.6010 c. 670: 145 113 94 79 71 62 56 50 N SD: 0.2753 c. M:-0.4738 c. 722: 156 122 101 85 77 67 60 54 N SD: 0.2103 c. M: 0.4012 c. 893: 193 151 125 105 95 83 74 67 N SD: 0.2480 c. M: 0.3766 c. 901: 195 152 126 106 96 84 75 67 N SD: 0.2461 c. M: 0.4348 c. 914: 198 154 128 108 97 85 76 68 N SD: 0.2891 c. M:-0.4132 c. 924: 200 156 129 109 98 86 77 69 N SD: 0.2150 c. M:-0.3927 c. 933: 202 157 131 110 99 87 77 70 N SD: 0.2182 c. M: 0.3752 c. 989: 214 167 138 117 105 92 82 74 N SD: 0.1653 c. M:-0.3401 c. 1044: 226 176 146 123 111 97 87 78 N SD: 0.1749 c. M: 0.3136 c. 1101: 238 186 154 130 117 102 92 82 N SD: 0.1877 c. M:-0.2837 c. 1109: 240 187 155 131 118 103 92 83 N SD: 0.1134 c. M: 0.2175 c. 1299: 281 219 182 153 138 121 108 97 N SD: 0.1163 c. M: 0.2154 c. 1364: 295 230 191 161 145 127 113 102 N SD: 0.1105 c. M:-0.2364 c. 1432: 310 241 201 169 152 133 119 107 N SD: 0.1356 c. M: 0.2132 c. 1484: 321 250 208 175 158 138 123 111 N SD: 0.1335 c. M: 0.2199 c. 1488: 322 251 208 176 158 138 124 111 N SD: 0.1300 c. M:-0.1962 c. 1507: 326 254 211 178 160 140 125 113 N SD: 0.1396 c. M: 0.3231 c. 1515: 328 255 212 179 161 141 126 113 N SD: 0.1391 c. M: 0.2710 c. 1535: 332 259 215 181 163 143 127 115 N SD: 0.1330 c. M: 0.2453 c. 1566: 339 264 219 185 166 146 130 117 N SD: 0.1070 c. M: 0.2064 c. 1686: 365 284 236 199 179 157 140 126 N SD: 0.0710 c. M: 0.1246 c. 2034: 440 343 285 240 216 189 169 152 N SD: 0.0674 c. M:-0.1145 c. 2154: 466 363 302 254 229 200 179 161 N SD: 0.0726 c. M:-0.1096 c. 2356: 510 397 330 278 250 219 196 176 N SD: 0.0627 c. M: 0.0877 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x x 4 S SD: 34.8115 cents 3 x 4 x x 5 x x 6 S SD: 12.9925 cents 4 x 5 x 6 x 7 x 8 S SD: 27.7418 cents 5:6 x 7:8 x 9 x 10 S SD: 16.9777 cents 6:7:8 x 9:10:11 x 12 S SD: 14.8322 cents 7:8:9:10:11:12 x 13:14 S SD: 9.5439 cents 8:9:10 x x 13:14:15:16 SD: 20.0622 cents 9:10:12:13:14:15:16:17:18 S SD: 11.0940 cents 10:12:13:14:16:17:18:19:20 S SD: 10.9331 cents 11:13:14:16:17:18:20:21:22 SD: 9.9648 cents 12:14:16:17:19:20:22:23:24 SD: 8.5058 cents 13:15:17:19:20:22:23:25:26 SD: 6.4681 cents 16:19:21:23:25:27:29:30:32 SD: 6.1321 cents 18:21:24:26:28:30:32:34:36 S SD: 5.5295 cents 19:22:25:27:30:32:34:36:38 SD: 4.1092 cents 23:27:30:33:36:39:41:44:46 SD: 3.6512 cents 25:29:33:36:39:42:45:47:50 SD: 3.3457 cents 29:34:38:42:45:49:52:55:58 SD: 3.0988 cents 30:35:39:43:47:50:54:57:60 SD: 2.6641 cents 32:37:42:46:50:54:57:61:64 SD: 2.3879 cents 39:45:51:56:61:66:70:74:78 SD: 2.2147 cents 43:50:56:62:67:72:77:82:86 SD: 1.5344 cents 50:58:65:72:78:84:90:95:100 SD: 1.3819 cents 62:72:81:89:97:104:111:118:124 SD: 0.9827 cents 68:79:89:98:106:114:122:129:136 SD: 0.9532 cents 82:95:107:118:128:138:147:156:164 SD: 0.7914 cents 91:106:119:131:142:153:163:173:182 SD: 0.7306 cents 98:114:128:141:153:165:176:186:196 SD: 0.6058 cents 130:151:170:187:203:219:233:247:260 SD: 0.5911 cents 137:159:179:197:214:230:246:260:274 SD: 0.5514 cents 141:164:184:203:220:237:253:268:282 SD: 0.4410 cents 160:186:209:230:250:269:287:304:320 SD: 0.3334 cents 216:251:282:311:337:363:387:410:432 SD: 0.2959 cents 228:265:298:328:356:383:409:433:456 SD: 0.2921 cents 235:273:307:338:367:395:421:446:470 SD: 0.2450 cents 278:323:363:400:434:467:498:528:556 SD: 0.2222 cents 285:331:372:410:445:479:511:541:570 SD: 0.1655 cents 376:437:491:541:587:632:674:714:752 SD: 0.0971 cents