Scala analysis: xen18-ayers-table-26
7 Iterated First 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: 306.278 cents 306.278000 2: 526.813 cents 526.813000 3: 694.073 cents 694.073000 4: 833.090 cents 833.090000 5: 941.201 cents 941.201000 6: 1036.963 cents 1036.963000 7: 1122.409 cents 1122.409000 8: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 77.5910 cents 77.5910 1: 306.2780 cents 306.2780 2: 220.5350 cents 220.5350 3: 167.2600 cents 167.2600 4: 139.0170 cents 139.0170 5: 108.1110 cents 108.1110 6: 95.7620 cents 95.7620 7: 85.4460 cents 85.4460 8: 77.5910 cents 77.5910
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 77.59100 cents 1: 1 85.44600 cents 1: 1 95.76200 cents 1: 1 108.11100 cents 1: 1 139.01700 cents 1: 1 167.26000 cents 1: 1 220.53500 cents 1: 1 306.27800 cents 2: 1 163.03700 cents 2: 1 181.20800 cents 2: 1 203.87300 cents 2: 1 247.12800 cents 2: 1 306.27700 cents 2: 1 383.86900 cents 2: 1 387.79500 cents 2: 1 526.81300 cents 3: 1 258.79900 cents 3: 1 289.31900 cents 3: 1 342.89000 cents 3: 1 414.38800 cents 3: 1 469.31500 cents 3: 1 526.81200 cents 3: 1 604.40400 cents 3: 1 694.07300 cents 4: 1 366.91000 cents 4: 1 428.33600 cents 4: 1 510.15000 cents 4: 1 565.07700 cents 4: 1 634.92300 cents 4: 1 689.85000 cents 4: 1 771.66400 cents 4: 1 833.09000 cents 5: 1 505.92700 cents 5: 1 595.59600 cents 5: 1 673.18800 cents 5: 1 730.68500 cents 5: 1 785.61200 cents 5: 1 857.11000 cents 5: 1 910.68100 cents 5: 1 941.20100 cents 6: 1 673.18700 cents 6: 1 812.20500 cents 6: 1 816.13100 cents 6: 1 893.72300 cents 6: 1 952.87200 cents 6: 1 996.12700 cents 6: 1 1018.79200 cents 6: 1 1036.96300 cents 7: 1 893.72200 cents 7: 1 979.46500 cents 7: 1 1032.74000 cents 7: 1 1060.98300 cents 7: 1 1091.88900 cents 7: 1 1104.23800 cents 7: 1 1114.55400 cents 7: 1 1122.40900 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 : 306.3 526.8 694.1 833.1 941.2 1037.0 1122.4 1200.0 306.3 : 220.5 387.8 526.8 634.9 730.7 816.1 893.7 1200.0 526.8 : 167.3 306.3 414.4 510.2 595.6 673.2 979.5 1200.0 694.1 : 139.0 247.1 342.9 428.3 505.9 812.2 1032.7 1200.0 833.1 : 108.1 203.9 289.3 366.9 673.2 893.7 1061.0 1200.0 941.2 : 95.8 181.2 258.8 565.1 785.6 952.9 1091.9 1200.0 1037.0: 85.4 163.0 469.3 689.9 857.1 996.1 1104.2 1200.0 1122.4: 77.6 383.9 604.4 771.7 910.7 1018.8 1114.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 77.5910 .. 306.2780 cents 228.68700 cents 77.59100 cents 2: 163.0370 .. 526.8130 cents 363.77600 cents -143.24100 cents 3: 258.7990 .. 694.0730 cents 435.27400 cents -268.01400 cents 4: 366.9100 .. 833.0900 cents 466.18000 cents -327.16300 cents 5: 505.9270 .. 941.2010 cents 435.27400 cents -327.16300 cents 6: 673.1870 .. 1036.9630 cents 363.77600 cents -268.01400 cents 7: 893.7220 .. 1122.4090 cents 228.68700 cents -143.24100 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 77.59100 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 306.27800 cents Average / Smallest step : 1.933214 Largest / Average step : 2.041853 Largest / Smallest step : 3.947339 Median interval of one step : 123.56400 cents, amount: 0 Least squares average step : 172.34867 cents, oct.: 1378.78937 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 0.00100 cents Scale diversity : 1.727876 Lumma stability : 0.129318 Lumma impropriety factor : 0.728272 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 : 0.00100 cents Number of recognisable fifths : 2, average 691.9615 cents Steps are strictly decreasing Formal octave complements present : 1 = 12.5000% -- Rational properties --
FIT/MODE
8: 2 1 1 1 1 0 1 1 N T3 SD: 76.9682 c. M: 136.9630 c. 9: 2 2 1 1 1 1 0 1 N SD: 30.6371 c. M: 55.7423 c. 10: 3 1 2 1 1 1 0 1 N SD: 35.0028 c. M:-53.7220 c. 12: 3 2 2 1 1 1 1 1 N SD: 26.1112 c. M: 41.2010 c. 14: 4 2 2 2 1 1 1 1 N SD: 16.8913 c. M:-36.5791 c. 16: 4 3 2 2 2 1 1 1 N SD: 14.9624 c. M:-33.7990 c. 17: 4 3 3 2 1 2 1 1 N SD: 19.5502 c. M: 32.6954 c. 19: 5 3 3 2 2 1 2 1 N SD: 14.3416 c. M: 26.4367 c. 20: 5 4 3 2 2 1 2 1 N SD: 15.3454 c. M:-25.9270 c. 23: 6 4 3 3 2 2 2 1 N SD: 11.2759 c. M:-25.4171 c. 25: 6 5 3 3 3 2 1 2 N SD: 16.4677 c. M: 22.0730 c. 26: 6 5 4 3 2 2 2 2 N SD: 16.7575 c. M: 29.3549 c. 27: 7 5 4 3 2 2 2 2 N SD: 10.5589 c. M:-17.0381 c. 28: 7 5 4 3 3 2 2 2 N SD: 9.7402 c. M: 18.8043 c. 29: 7 6 4 3 3 2 2 2 N SD: 9.0947 c. M: 16.6228 c. 32: 8 6 5 3 3 3 2 2 N SD: 8.9308 c. M:-18.4270 c. 36: 9 7 5 4 3 3 3 2 N SD: 6.2403 c. M:-10.9243 c. 43: 11 8 6 5 4 3 3 3 N SD: 4.4358 c. M:-7.6362 c. 50: 13 9 7 6 4 4 4 3 N SD: 4.5901 c. M:-6.9100 c. 52: 13 10 7 6 5 4 4 3 N SD: 4.4754 c. M:-8.3602 c. 59: 15 11 8 7 5 5 4 4 N SD: 2.6995 c. M: 5.6078 c. 66: 17 12 9 8 6 5 5 4 N SD: 2.9782 c. M:-4.8637 c. 75: 19 14 10 9 7 6 5 5 N SD: 2.9054 c. M: 6.0730 c. 78: 20 14 11 9 7 6 6 5 N SD: 2.9744 c. M: 6.1938 c. 79: 20 15 11 9 7 6 6 5 N SD: 3.0864 c. M:-4.8326 c. 87: 22 16 12 10 8 7 6 6 N SD: 3.6831 c. M: 5.5038 c. 88: 22 17 12 10 8 7 6 6 N SD: 3.2845 c. M: 6.2780 c. 89: 23 16 12 11 8 7 6 6 N SD: 3.2513 c. M: 6.4326 c. 93: 24 17 13 11 8 7 7 6 N SD: 3.1238 c. M:-5.6197 c. 94: 24 17 13 11 9 7 7 6 N SD: 2.8802 c. M: 4.7113 c. 98: 25 18 14 11 9 8 7 6 N SD: 2.4994 c. M:-4.1216 c. 102: 26 19 14 12 9 8 7 7 N SD: 2.1573 c. M: 4.7619 c. 105: 27 19 15 12 9 9 7 7 N SD: 2.4702 c. M: 4.0581 c. 111: 28 21 15 13 10 9 8 7 N SD: 1.9796 c. M: 3.5753 c. 121: 31 22 17 14 11 10 8 8 N SD: 1.7940 c. M:-4.3593 c. 125: 32 23 17 15 11 10 9 8 N SD: 1.4044 c. M: 2.8730 c. 157: 40 29 22 18 14 13 11 10 N SD: 1.2076 c. M:-2.5274 c. 171: 44 31 24 20 15 14 12 11 N SD: 1.3439 c. M:-2.4939 c. 176: 45 32 25 20 16 14 13 11 N SD: 1.3352 c. M:-2.5910 c. 185: 47 34 26 21 17 15 13 12 N SD: 1.2841 c. M: 2.8197 c. 189: 48 35 26 22 17 15 14 12 N SD: 1.4409 c. M: 2.0424 c. 199: 51 36 28 23 18 16 14 13 N SD: 1.0339 c. M: 2.1899 c. 200: 51 37 28 23 18 16 14 13 N SD: 0.9943 c. M:-1.9270 c. 219: 56 40 31 25 20 17 16 14 N SD: 1.0294 c. M:-1.8174 c. 223: 57 41 31 26 20 18 16 14 N SD: 1.0833 c. M:-2.2547 c. 228: 58 42 32 26 21 18 16 15 N SD: 0.9133 c. M: 1.5111 c. 235: 60 43 33 27 21 19 17 15 N SD: 0.8087 c. M: 1.6265 c. 251: 64 46 35 29 23 20 18 16 N SD: 0.7881 c. M: 1.2175 c. 278: 71 51 39 32 25 22 20 18 N SD: 0.4877 c. M: 0.9918 c. 344: 88 63 48 40 31 27 25 22 N SD: 0.6016 c. M: 0.9165 c. 353: 90 65 49 41 32 28 25 23 N SD: 0.3684 c. M: 0.5960 c. 501: 128 92 70 58 45 40 36 32 N SD: 0.4374 c. M:-0.9443 c. 510: 130 94 71 59 46 41 36 33 N SD: 0.2985 c. M:-0.6841 c. 524: 134 96 73 61 47 42 37 34 N SD: 0.3371 c. M:-0.5922 c. 529: 135 97 74 61 48 42 38 34 N SD: 0.3473 c. M: 0.5758 c. 553: 141 102 77 64 50 44 39 36 N SD: 0.3815 c. M:-0.5712 c. 560: 143 103 78 65 50 45 40 36 N SD: 0.3314 c. M: 0.4867 c. 576: 147 106 80 67 52 46 41 37 N SD: 0.3536 c. M:-0.5370 c. 588: 150 108 82 68 53 47 42 38 N SD: 0.2585 c. M: 0.4369 c. 631: 161 116 88 73 57 50 45 41 N SD: 0.2409 c. M: 0.5129 c. 788: 201 145 110 91 71 63 56 51 N SD: 0.1545 c. M:-0.3432 c. 854: 218 157 119 99 77 68 61 55 N SD: 0.1612 c. M:-0.3076 c. 913: 233 168 127 106 82 73 65 59 N SD: 0.1289 c. M:-0.2407 c. 1112: 284 204 155 129 100 89 79 72 N SD: 0.1451 c. M:-0.1968 c. 1141: 291 210 159 132 103 91 81 74 N SD: 0.1349 c. M: 0.2355 c. 1191: 304 219 166 138 107 95 85 77 N SD: 0.1217 c. M: 0.1872 c. 1442: 368 265 201 167 130 115 103 93 N SD: 0.0833 c. M:-0.1985 c. 1544: 394 284 215 179 139 123 110 100 N SD: 0.0962 c. M: 0.1754 c. 1642: 419 302 229 190 148 131 117 106 N SD: 0.1036 c. M:-0.2023 c. 1701: 434 313 237 197 153 136 121 110 N SD: 0.0958 c. M:-0.1711 c. 1795: 458 330 250 208 162 143 128 116 N SD: 0.0847 c. M: 0.1454 c. 1841: 470 338 257 213 166 147 131 119 N SD: 0.0804 c. M: 0.1427 c. 1900: 485 349 265 220 171 152 135 123 N SD: 0.0778 c. M: 0.1484 c. 1952: 498 359 272 226 176 156 139 126 N SD: 0.0878 c. M:-0.1320 c. 1966: 502 361 274 228 177 157 140 127 N SD: 0.0719 c. M:-0.1310 c. 2194: 560 403 306 254 198 175 156 142 N SD: 0.0669 c. M: 0.1038 c. 2230: 569 410 311 258 201 178 159 144 N SD: 0.0677 c. M:-0.1022 c. 2319: 592 426 323 269 209 185 165 150 N SD: 0.0668 c. M: 0.1532 c. 2355: 601 433 328 273 212 188 168 152 N SD: 0.0641 c. M:-0.1388 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: 3.9410 cents 3 x 4 x 5 x x x 6 S SD: 19.5961 cents 4:5 x 6 x 7 x x 8 S SD: 21.2588 cents 5:6:7 x 8 x 9 x 10 S SD: 12.5565 cents 6:7:8:9:10 x 11 x 12 S SD: 12.0472 cents 7:8 x 10:11:12:13 x 14 S SD: 20.6411 cents 8:10:11:12:13:14 x 15:16 S SD: 13.5920 cents 9:11:12:13:15 x 16:17:18 SD: 14.6913 cents 10:12:14:15:16:17:18:19:20 S SD: 8.5132 cents 11:13:15:16:18:19:20:21:22 SD: 6.6992 cents 16:19:22:24:26:28:29:31:32 SD: 5.7614 cents 20:24:27:30:32:34:36:38:40 S SD: 4.9823 cents 21:25:28:31:34:36:38:40:42 SD: 4.7734 cents 22:26:30:33:36:38:40:42:44 SD: 3.6955 cents 26:31:35:39:42:45:47:50:52 SD: 2.8828 cents 32:38:43:48:52:55:58:61:64 SD: 2.8669 cents 36:43:49:54:58:62:66:69:72 SD: 2.2915 cents 37:44:50:55:60:64:67:71:74 SD: 2.2274 cents 42:50:57:63:68:72:76:80:84 SD: 2.1779 cents 45:54:61:67:73:78:82:86:90 SD: 2.0143 cents 47:56:64:70:76:81:86:90:94 SD: 1.6633 cents 57:68:77:85:92:98:104:109:114 SD: 1.1705 cents 71:85:96:106:115:122:129:136:142 SD: 1.1624 cents 73:87:99:109:118:126:133:140:146 SD: 0.8900 cents 79:94:107:118:128:136:144:151:158 SD: 0.8274 cents 104:124:141:155:168:179:189:199:208 SD: 0.7066 cents 115:137:156:172:186:198:209:220:230 SD: 0.6654 cents 118:141:160:176:191:203:215:226:236 SD: 0.5862 cents 134:160:182:200:217:231:244:256:268 SD: 0.5527 cents 144:172:195:215:233:248:262:275:288 SD: 0.4281 cents 160:191:217:239:259:276:291:306:320 SD: 0.4161 cents 180:215:244:269:291:310:328:344:360 SD: 0.4113 cents 191:228:259:285:309:329:348:365:382 SD: 0.3078 cents 217:259:294:324:351:374:395:415:434 SD: 0.2144 cents 306:365:415:457:495:527:557:585:612 SD: 0.1812 cents 377:450:511:563:610:649:686:721:754 SD: 0.1362 cents 450:537:610:672:728:775:819:861:900 SD: 0.1295 cents 501:598:679:748:811:863:912:958:1002 SD: 0.1254 cents 511:610:693:763:827:880:930:977:1022 SD: 0.1172 cents 568:678:770:848:919:978:1034:1086:1136 SD: 0.0863 cents