Scala analysis: bihex540
Bihexany in 540/539 tempering
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 101.621 cents 101.621102 2: 267.824 cents 267.824229 3: 386.257 cents 386.256798 4: 417.216 cents 417.215888 5: 535.648 cents 535.648458 6: 701.852 cents 701.851584 7: 803.473 cents 803.472686 8: 884.228 cents 884.228421 9: 969.676 cents 969.675813 10: 1033.620 cents 1033.620081 11: 1119.067 cents 1119.067472 12: 1199.823 cents 1199.823207
SHOW/INTERVAL
0: 80.7557 cents 80.7557 1: 101.6211 cents 101.6211 2: 166.2031 cents 166.2031 3: 118.4326 cents 118.4326 4: 30.9591 cents 30.9591 5: 118.4326 cents 118.4326 6: 166.2031 cents 166.2031 7: 101.6211 cents 101.6211 8: 80.7557 cents 80.7557 9: 85.4474 cents 85.4474 10: 63.9443 cents 63.9443 11: 85.4474 cents 85.4474 12: 80.7557 cents 80.7557
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 30.95909 cents 1: 1 63.94427 cents 1: 2 80.75574 cents 1: 2 85.44739 cents 1: 2 101.62110 cents 1: 2 118.43257 cents 1: 2 166.20313 cents 2: 4 149.39166 cents 2: 2 166.20313 cents 2: 2 182.37684 cents 2: 2 267.82423 cents 2: 2 284.63570 cents 3: 2 230.14740 cents 3: 1 234.83905 cents 3: 3 267.82423 cents 3: 2 315.59479 cents 3: 2 348.57996 cents 3: 2 386.25680 cents 4: 2 315.59479 cents 4: 2 331.76850 cents 4: 2 417.21589 cents 4: 4 434.02736 cents 4: 2 467.01253 cents 5: 1 396.35052 cents 5: 2 417.21589 cents 5: 4 497.97162 cents 5: 2 535.64846 cents 5: 2 552.45993 cents 5: 1 600.23048 cents 6: 2 497.97162 cents 6: 4 583.41901 cents 6: 4 616.40419 cents 6: 2 701.85158 cents 7: 1 599.59272 cents 7: 2 647.36328 cents 7: 2 664.17475 cents 7: 4 701.85158 cents 7: 2 782.60732 cents 7: 1 803.47269 cents 8: 2 732.81067 cents 8: 4 765.79585 cents 8: 2 782.60732 cents 8: 2 868.05471 cents 8: 2 884.22842 cents 9: 2 813.56641 cents 9: 2 851.24324 cents 9: 2 884.22842 cents 9: 3 931.99898 cents 9: 1 964.98416 cents 9: 2 969.67581 cents 10: 2 915.18751 cents 10: 2 931.99898 cents 10: 2 1017.44637 cents 10: 2 1033.62008 cents 10: 4 1050.43155 cents 11: 2 1033.62008 cents 11: 2 1081.39064 cents 11: 2 1098.20210 cents 11: 2 1114.37581 cents 11: 2 1119.06747 cents 11: 1 1135.87894 cents 11: 1 1168.86412 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 5.63636 = 62/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 101.6 267.8 386.3 417.2 535.6 701.9 803.5 884.2 969.7 1033.6 1119.1 1199.8 101.6 : 166.2 284.6 315.6 434.0 600.2 701.9 782.6 868.1 932.0 1017.4 1098.2 1199.8 267.8 : 118.4 149.4 267.8 434.0 535.6 616.4 701.9 765.8 851.2 932.0 1033.6 1199.8 386.3 : 31.0 149.4 315.6 417.2 498.0 583.4 647.4 732.8 813.6 915.2 1081.4 1199.8 417.2 : 118.4 284.6 386.3 467.0 552.5 616.4 701.9 782.6 884.2 1050.4 1168.9 1199.8 535.6 : 166.2 267.8 348.6 434.0 498.0 583.4 664.2 765.8 932.0 1050.4 1081.4 1199.8 701.9 : 101.6 182.4 267.8 331.8 417.2 498.0 599.6 765.8 884.2 915.2 1033.6 1199.8 803.5 : 80.8 166.2 230.1 315.6 396.4 498.0 664.2 782.6 813.6 932.0 1098.2 1199.8 884.2 : 85.4 149.4 234.8 315.6 417.2 583.4 701.9 732.8 851.2 1017.4 1119.1 1199.8 969.7 : 63.9 149.4 230.1 331.8 498.0 616.4 647.4 765.8 932.0 1033.6 1114.4 1199.8 1033.6: 85.4 166.2 267.8 434.0 552.5 583.4 701.9 868.1 969.7 1050.4 1135.9 1199.8 1119.1: 80.8 182.4 348.6 467.0 498.0 616.4 782.6 884.2 965.0 1050.4 1114.4 1199.8 1199.8
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 30.9591 .. 166.2031 cents 135.24404 cents 30.95909 cents 2: 149.3917 .. 284.6357 cents 135.24404 cents -16.81147 cents 3: 230.1474 .. 386.2568 cents 156.10940 cents -54.48830 cents 4: 315.5948 .. 467.0125 cents 151.41775 cents -70.66201 cents 5: 396.3505 .. 600.2305 cents 203.87996 cents -70.66201 cents 6: 497.9716 .. 701.8516 cents 203.87996 cents -102.25886 cents 7: 599.5927 .. 803.4727 cents 203.87996 cents -102.25886 cents 8: 732.8107 .. 884.2284 cents 151.41775 cents -70.66201 cents 9: 813.5664 .. 969.6758 cents 156.10940 cents -70.66201 cents 10: 915.1875 .. 1050.4315 cents 135.24404 cents -54.48830 cents 11: 1033.6201 .. 1168.8641 cents 135.24404 cents -16.81147 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 30.95909 cents, class 1 Average step (divided formal octave): 99.9853 cents Largest one step interval : 166.20313 cents Average / Smallest step : 3.229593 Largest / Average step : 1.662276 Largest / Smallest step : 5.368476 Median interval of one step : 93.53425 cents, amount: 0 Least squares average step : 105.88199 cents, oct.: 1270.58391 cents Scale is not proper Step pattern alph. order: ABCDCBAEFGFE Step pattern size order : EGFAFGECDBDC Scale is not a Constant Structure Scale diversity : 1.512682 Lumma stability : 0.051606 Lumma impropriety factor : 0.524350 Rothenberg efficiency : 0.290458 redundancy: 0.709542 Efficiency x scale size : 3.485498 Number of different interval sizes : 52 = 4.72727 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 5.63636 = 62/11 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 0.63776 cents Most common intervals : 497.97162 cents & inv., amount: 6 Most common triad is 0.0 701.852 1168.864 cents, amount: 1 Number of recognisable fifths : 6, average 701.8516 cents Number of recognisable fourths : 6, average 497.9716 cents Formal octave complements present : 1 = 8.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 9-10 -- Rational properties --
FIT/MODE
12: 1 2 1 0 1 2 1 1 1 0 1 1 N T3 SD: 21.3674 c. M: 35.7221 c. 14: 1 2 1 1 1 2 1 1 1 1 1 1 N D3 SD: 21.7177 c. M: 43.4502 c. 15: 1 2 2 0 2 2 1 1 1 1 1 1 N SD: 15.3078 c. M: 27.8596 c. 21: 2 3 2 0 2 3 2 1 2 1 2 1 N SD: 15.8862 c. M: 27.2118 c. 22: 2 3 2 1 2 3 2 1 2 1 2 1 N SD: 12.2312 c. M:-26.2183 c. 26: 2 4 2 1 2 4 2 2 2 1 2 2 N SD: 13.6317 c. M: 28.0309 c. 27: 2 4 3 0 3 4 2 2 2 1 2 2 N SD: 9.2877 c. M: 17.2748 c. 31: 3 4 3 1 3 4 3 2 2 2 2 2 N SD: 7.2212 c. M:-14.4908 c. 40: 3 6 4 1 4 5 4 2 3 2 3 3 N SD: 8.8526 c. M: 14.3566 c. 41: 3 6 4 1 4 6 3 3 3 2 3 3 N SD: 7.9164 c. M: 13.8292 c. 42: 4 5 5 1 4 6 3 3 3 2 3 3 N SD: 8.4720 c. M:-13.6843 c. 43: 4 6 4 1 4 6 4 3 3 2 3 3 N SD: 6.1956 c. M:-11.2044 c. 46: 4 6 5 1 5 6 4 3 3 3 3 3 N SD: 5.6836 c. M:-12.0969 c. 49: 4 7 5 1 5 7 4 3 4 2 4 3 N SD: 5.2334 c. M:-9.7717 c. 57: 5 8 5 2 5 8 5 4 4 3 4 4 N SD: 4.8963 c. M: 9.4102 c. 58: 5 8 6 1 6 8 5 4 4 3 4 4 N SD: 3.1619 c. M:-6.7887 c. 72: 6 10 7 2 7 10 6 5 5 4 5 5 N SD: 2.1127 c. M: 3.5905 c. 103: 9 14 10 3 10 14 9 7 7 6 7 7 N SD: 1.9696 c. M:-3.2178 c. 121: 10 17 12 3 12 17 10 8 9 6 9 8 N SD: 1.4893 c. M: 2.4622 c. 130: 11 18 13 3 13 18 11 9 9 7 9 9 N SD: 1.1173 c. M: 2.3089 c. 152: 13 21 15 4 15 21 13 10 11 8 11 10 N SD: 1.0178 c. M:-1.8200 c. 224: 19 31 22 6 22 31 19 15 16 12 16 15 N SD: 0.3103 c. M: 0.5993 c. 354: 30 49 35 9 35 49 30 24 25 19 25 24 N SD: 0.2703 c. M: 0.5882 c. 475: 40 66 47 12 47 66 40 32 34 25 34 32 N SD: 0.3097 c. M: 0.5834 c. 506: 43 70 50 13 50 70 43 34 36 27 36 34 N SD: 0.2104 c. M:-0.3614 c. 578: 49 80 57 15 57 80 49 39 41 31 41 39 N SD: 0.1434 c. M: 0.2685 c. 981: 83 136 97 25 97 136 83 66 70 52 70 66 N SD: 0.1283 c. M:-0.2306 c. 1053: 89 146 104 27 104 146 89 71 75 56 75 71 N SD: 0.1197 c. M: 0.2115 c. 1084: 92 150 107 28 107 150 92 73 77 58 77 73 N SD: 0.1063 c. M:-0.2089 c. 1205: 102 167 119 31 119 167 102 81 86 64 86 81 N SD: 0.0753 c. M:-0.1398 c. 1277: 108 177 126 33 126 177 108 86 91 68 91 86 N SD: 0.0869 c. M: 0.1482 c. 1429: 121 198 141 37 141 198 121 96 102 76 102 96 N SD: 0.0710 c. M:-0.1518 c. 1559: 132 216 154 40 154 216 132 105 111 83 111 105 N SD: 0.0461 c. M:-0.0878 c. 1783: 151 247 176 46 176 247 151 120 127 95 127 120 N SD: 0.0056 c. M: 0.0096 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.1768 cents 2 x x x x x 3 x x x x x 4 S SD: 0.1024 cents 3 x x x x 4 x x 5 x x x 6 S SD: 12.5347 cents 4 x x 5 x x 6 x x 7 x x 8 S SD: 0.2190 cents 5 x 6 x x 7 x 8 x x 9 x 10 S SD: 13.9195 cents 6 x 7 x x 8:9 x 10 x 11 x 12 S SD: 6.7963 cents 7 x 8 x 9:10 x 11 x 12:13 x 14 S SD: 15.3771 cents 8 x 9:10 x 11:12:13 x 14 x 15:16 S SD: 10.1957 cents 9:10 x 11 x 12 x 14:15:16 x 17:18 S SD: 13.6692 cents 10:11:12 x 13:14:15:16:17 x 18:19:20 S SD: 10.7127 cents 11:12:13 x 14:15 x x 18:19:20:21:22 S SD: 7.3836 cents 12:13:14:15 x 16:18:19:20:21:22:23:24 S SD: 5.0976 cents 14:15:16 x 18:19:21:22:23 x 25:27:28 SD: 6.5536 cents 15:16:18 x 19:20:23:24:25:26:27:29:30 SD: 7.3187 cents 16:17:19:20 x 22:24:25:27:28:29:31:32 SD: 5.1819 cents 18:19:21 x 23:25:27:29:30:32:33:34:36 SD: 4.9567 cents 19:20:22 x 24:26:29:30:32:33:35:36:38 SD: 4.9097 cents 20:21:23:25 x 27:30:32:33:35:36:38:40 SD: 4.0085 cents 22:23:26 x 28:30:33:35:37:39:40:42:44 SD: 3.8366 cents 23:24:27:29 x 31:35:37:38:40:42:44:46 SD: 4.9157 cents 24:25:28:30:31:33:36:38:40:42:44:46:48 SD: 3.9415 cents 26:28:30 x 33:35:39:41:43:46:47:50:52 SD: 4.5880 cents 27:29:32:34 x 37:41:43:45:47:49:52:54 SD: 4.3115 cents 28:30:33:35:36:38:42:45:47:49:51:53:56 SD: 3.4012 cents 30:32:35 x 38:41:45:48:50:53:55:57:60 SD: 2.6495 cents 31:33:36:39 x 42:46:49:52:54:56:59:62 SD: 3.0662 cents 32:34:37:40:41:44:48:51:53:56:58:61:64 SD: 2.3823 cents 34:36:40 x 43:46:51:54:57:60:62:65:68 SD: 2.5774 cents 36:38:42:45:46:49:54:57:60:63:65:69:72 SD: 1.5595 cents 38:40:44 x 48:52:57:60:63:67:69:73:76 SD: 3.0076 cents 39:41:46:49:50:53:58:62:65:68:71:74:78 SD: 2.8924 cents 40:42:47:50:51:55:60:64:67:70:73:76:80 SD: 2.6167 cents 42:45:49 x 53:57:63:67:70:74:76:80:84 SD: 2.5407 cents 44:47:51:55:56:60:66:70:73:77:80:84:88 SD: 1.6082 cents 48:51:56:60:61:65:72:76:80:84:87:92:96 SD: 1.3577 cents 64:68:75:80:81:87:96:102:107:112:116:122:128 SD: 1.2536 cents 66:70:77:82:84:90:99:105:110:116:120:126:132 SD: 1.0491 cents 80:85:93:100:102:109:120:127:133:140:145:153:160 SD: 0.9570 cents 84:89:98:105:107:114:126:134:140:147:153:160:168 SD: 0.8880 cents 88:93:103:110:112:120:132:140:147:154:160:168:176 SD: 0.7374 cents 96:102:112:120:122:131:144:153:160:168:174:183:192 SD: 0.6304 cents 120:127:140:150:153:164:180:191:200:210:218:229:240 SD: 0.6072 cents 132:140:154:165:168:180:198:210:220:231:240:252:264 SD: 0.1991 cents 348:369:406:435:443:474:522:554:580:609:632:664:696 SD: 0.1956 cents 364:386:425:455:463:496:546:579:607:637:661:695:728 SD: 0.1584 cents 480:509:560:600:611:654:720:763:800:840:872:916:960 SD: 0.1515 cents 496:526:579:620:631:676:744:789:827:868:901:947:992 SD: 0.1230 cents 579:614:676:724:737:789:868:921:965:1014:1052:1105:1158 SD: 0.1151 cents