Scala analysis: O3-ri24

Rational intonation version of O3 (24), subdivision of 896:891

Generated by Scala: https://www.huygens-fokker.org/scala/

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:         91/88             58.035626
  2:       1764/1639          127.241648
  3:      40131/36058         185.277274
  4:        168/149           207.778683
  5:       1911/1639          265.814309
  6:        176/149           288.315718
  7:        182/149           346.351344
  8:        567/446           415.566030
  9:      51597/39248         473.601656
 10:        297/223           496.103065
 11:       2457/1784          554.138691
 12:      14112/9845          623.351226
 13:     160524/108295        681.386852
 14:       1344/895           703.888261
 15:      15288/9845          761.923887
 16:      15876/9823          831.134236
 17:     361179/216106        889.169862
 18:       1512/893           911.671271
 19:      17199/9823          969.706897
 20:       1584/893           992.208306
 21:       1638/893          1050.243932
 22:         21/11           1119.462965 undecimal major seventh
 23:       1911/968          1177.498591
 24:          2/1            1200.000000 octave
SHOW/INTERVAL
  0:       1936/1911           22.5014 
  1:         91/88             58.0356 
  2:       2016/1937           69.2060 
  3:         91/88             58.0356 
  4:       1936/1911           22.5014 
  5:         91/88             58.0356 
  6:       1936/1911           22.5014 
  7:         91/88             58.0356 
  8:      12069/11596          69.2147 
  9:         91/88             58.0356 
 10:       1936/1911           22.5014 
 11:         91/88             58.0356 
 12:     399616/383955         69.2125 
 13:         91/88             58.0356 
 14:       1936/1911           22.5014 
 15:         91/88             58.0356 
 16:      24165/23218          69.2103 
 17:         91/88             58.0356 
 18:       1936/1911           22.5014 
 19:         91/88             58.0356 
 20:       1936/1911           22.5014 
 21:         91/88             58.0356 
 22:        893/858            69.2190 
 23:         91/88             58.0356 
 24:       1936/1911           22.5014 
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   7 1936/1911           22.501 cents   
  1:  12 91/88               58.036 cents   
  1:   1 2016/1937           69.206 cents   
  1:   1 24165/23218         69.210 cents   
  1:   1 399616/383955       69.213 cents   
  1:   1 12069/11596         69.215 cents   
  1:   1 893/858             69.219 cents   
  2:  14 22/21               80.537 cents   undecimal minor semitone
  2:   2 1764/1639           127.242 cents  
  2:   2 169155/157168       127.246 cents  
  2:   2 349664/324885       127.248 cents  
  2:   2 84483/78496         127.250 cents  
  2:   2 6251/5808           127.255 cents  
  3:   2 42592/40131         103.038 cents  
  3:   7 13/12               138.573 cents  tridecimal 2/3-tone
  3:   2 2112/1937           149.743 cents  
  3:   2 88605/81263         149.747 cents  
  3:   2 114176/104715       149.750 cents  
  3:   2 44253/40586         149.752 cents  
  3:   2 893/819             149.756 cents  
  3:   1 40131/36058         185.277 cents  
  3:   1 15393105/13830784   185.282 cents  
  3:   1 3977428/3573735     185.284 cents  
  3:   1 7687953/6907648     185.286 cents  
  3:   1 568841/511104       185.290 cents  
  4:   4 484/441             161.074 cents  two (undecimal minor semitone)
  4:   4 168/149             207.779 cents  
  4:   4 8055/7144           207.783 cents  
  4:   4 99904/88605         207.785 cents  
  4:   4 4023/3568           207.787 cents  
  4:   4 893/792             207.792 cents  
  5:   2 143/126             219.110 cents  
  5:   2 15488/13559         230.280 cents  
  5:   2 649770/568841       230.284 cents  
  5:   1 2511872/2199015     230.287 cents  
  5:   2 162261/142051       230.289 cents  
  5:   2 19646/17199         230.293 cents  
  5:   2 1911/1639           265.814 cents  
  5:   2 733005/628672       265.819 cents  
  5:   2 1136408/974655      265.821 cents  
  5:   2 366093/313984       265.823 cents  
  5:   2 81263/69696         265.827 cents  
  5:   1 149856/127699       276.996 cents  
  5:   1 25004/21307         276.998 cents  
  5:   1 150192/127985       277.000 cents  
  6:   4 176/149             288.316 cents  
  6:   4 29535/25004         288.320 cents  
  6:   2 28544/24165         288.322 cents  
  6:   4 14751/12488         288.324 cents  
  6:   4 893/756             288.329 cents  
  6:   2 131124/108053       335.031 cents  
  6:   2 43757/36058         335.033 cents  
  6:   2 131418/108295       335.036 cents  
  7:   1 340736/284739       310.817 cents  
  7:   1 4764980/3981887     310.821 cents  
  7:   1 1189914/994357      310.826 cents  
  7:   1 432212/361179       310.830 cents  
  7:   2 182/149             346.351 cents  
  7:   2 34905/28576         346.356 cents  
  7:   1 324688/265815       346.358 cents  
  7:   2 17433/14272         346.360 cents  
  7:   2 11609/9504          346.364 cents  
  7:   1 3564/2899           357.530 cents  
  7:   2 14272/11609         357.533 cents  
  7:   2 7144/5811           357.535 cents  
  7:   2 14304/11635         357.537 cents  
  7:   1 895/728             357.539 cents  
  7:   1 2983071/2377166     393.067 cents  
  7:   1 3981887/3173104     393.069 cents  
  7:   1 5979519/4764980     393.071 cents  
  8:   2 3872/3129           368.853 cents  
  8:   2 108295/87514        368.857 cents  
  8:   2 54087/43708         368.861 cents  
  8:   2 9823/7938           368.866 cents  
  8:   2 567/446             415.566 cents  
  8:   4 12488/9823          415.568 cents  
  8:   4 6251/4917           415.570 cents  
  8:   4 12516/9845          415.573 cents  
  8:   2 895/704             415.575 cents  
  9:   1 572/447             426.888 cents  
  9:   1 127985/100016       426.893 cents  
  9:   1 63921/49952         426.897 cents  
  9:   1 11609/9072          426.901 cents  
  9:   2 26136/20293         438.067 cents  
  9:   2 313984/243789       438.070 cents  
  9:   3 157168/122031       438.072 cents  
  9:   2 104896/81445        438.074 cents  
  9:   2 9845/7644           438.076 cents  
  9:   1 51597/39248         473.602 cents  
  9:   2 142051/108053       473.604 cents  
  9:   2 568841/432696       473.606 cents  
  9:   2 284739/216590       473.608 cents  
  9:   1 81445/61952         473.610 cents  
  9:   1 168966/127699       484.783 cents  
 10:   4 297/223             496.103 cents  
 10:   4 3568/2679           496.105 cents  
 10:   6 1786/1341           496.107 cents  
 10:   4 1192/895            496.110 cents  
 10:   4 895/672             496.112 cents  
 10:   2 591381/432212       542.819 cents  
 11:   1 191664/142051       518.604 cents  
 11:   1 6907648/5119569     518.607 cents  
 11:   2 3457696/2562651     518.609 cents  
 11:   1 2307712/1710345     518.611 cents  
 11:   1 108295/80262        518.613 cents  
 11:   2 2457/1784           554.139 cents  
 11:   2 40586/29469         554.141 cents  
 11:   3 81263/59004         554.143 cents  
 11:   2 13559/9845          554.145 cents  
 11:   2 11635/8448          554.147 cents  
 11:   1 16128/11635         565.316 cents  
 11:   1 2685/1937           565.318 cents  
 11:   2 16092/11609         565.320 cents  
 11:   1 8037/5798           565.322 cents  
 11:   1 1784/1287           565.324 cents  
 11:   1 53815671/38034656   600.854 cents  
 12:   2 2178/1561           576.640 cents  
 12:   2 78496/56259         576.642 cents  
 12:   4 39292/28161         576.644 cents  
 12:   2 26224/18795         576.647 cents  
 12:   2 9845/7056           576.649 cents  
 12:   2 14112/9845          623.351 cents  
 12:   2 18795/13112         623.353 cents  
 12:   4 28161/19646         623.356 cents  
 12:   2 56259/39248         623.358 cents  
 12:   2 1561/1089           623.360 cents  
 13:   1 76069312/53815671   599.146 cents  
 13:   1 1287/892            634.676 cents  
 13:   1 11596/8037          634.678 cents  
 13:   2 11609/8046          634.680 cents  
 13:   1 3874/2685           634.682 cents  
 13:   1 11635/8064          634.684 cents  
 13:   2 16896/11635         645.853 cents  
 13:   2 19690/13559         645.855 cents  
 13:   3 118008/81263        645.857 cents  
 13:   2 29469/20293         645.859 cents  
 13:   2 3568/2457           645.861 cents  
 13:   1 160524/108295       681.387 cents  
 13:   1 1710345/1153856     681.389 cents  
 13:   2 2562651/1728848     681.391 cents  
 13:   1 5119569/3453824     681.393 cents  
 13:   1 142051/95832        681.396 cents  
 14:   2 864424/591381       657.181 cents  
 14:   4 1344/895            703.888 cents  
 14:   4 895/596             703.890 cents  
 14:   6 1341/893            703.893 cents  
 14:   4 2679/1784           703.895 cents  
 14:   4 446/297             703.897 cents  
 15:   1 127699/84483        715.217 cents  
 15:   1 123904/81445        726.390 cents  
 15:   2 433180/284739       726.392 cents  
 15:   2 865392/568841       726.394 cents  
 15:   2 216106/142051       726.396 cents  
 15:   1 78496/51597         726.398 cents  
 15:   2 15288/9845          761.924 cents  
 15:   2 81445/52448         761.926 cents  
 15:   3 122031/78584        761.928 cents  
 15:   2 243789/156992       761.930 cents  
 15:   2 20293/13068         761.933 cents  
 15:   1 18144/11609         773.099 cents  
 15:   1 99904/63921         773.103 cents  
 15:   1 200032/127985       773.107 cents  
 15:   1 447/286             773.112 cents  
 16:   2 1408/895            784.425 cents  
 16:   4 9845/6258           784.427 cents  
 16:   4 9834/6251           784.430 cents  
 16:   4 9823/6244           784.432 cents  
 16:   2 892/567             784.434 cents  
 16:   2 15876/9823          831.134 cents  
 16:   2 87416/54087         831.139 cents  
 16:   2 175028/108295       831.143 cents  
 16:   2 3129/1936           831.147 cents  
 17:   1 9529960/5979519     806.929 cents  
 17:   1 6346208/3981887     806.931 cents  
 17:   1 4754332/2983071     806.933 cents  
 17:   1 1456/895            842.461 cents  
 17:   2 11635/7152          842.463 cents  
 17:   2 5811/3572           842.465 cents  
 17:   2 11609/7136          842.467 cents  
 17:   1 2899/1782           842.470 cents  
 17:   2 19008/11609         853.636 cents  
 17:   2 28544/17433         853.640 cents  
 17:   1 265815/162344       853.642 cents  
 17:   2 57152/34905         853.644 cents  
 17:   2 149/91              853.649 cents  
 17:   1 361179/216106       889.170 cents  
 17:   1 994357/594957       889.174 cents  
 17:   1 3981887/2382490     889.179 cents  
 17:   1 284739/170368       889.183 cents  
 18:   2 108295/65709        864.964 cents  
 18:   2 72116/43757         864.967 cents  
 18:   2 108053/65562        864.969 cents  
 18:   4 1512/893            911.671 cents  
 18:   4 24976/14751         911.676 cents  
 18:   2 24165/14272         911.678 cents  
 18:   4 50008/29535         911.680 cents  
 18:   4 149/88              911.684 cents  
 19:   1 127985/75096        923.000 cents  
 19:   1 21307/12502         923.002 cents  
 19:   1 127699/74928        923.004 cents  
 19:   2 139392/81263        934.173 cents  
 19:   2 627968/366093       934.177 cents  
 19:   2 974655/568204       934.179 cents  
 19:   2 1257344/733005      934.181 cents  
 19:   2 3278/1911           934.186 cents  
 19:   2 17199/9823          969.707 cents  
 19:   2 284102/162261       969.711 cents  
 19:   1 2199015/1255936     969.713 cents  
 19:   2 568841/324885       969.716 cents  
 19:   2 13559/7744          969.720 cents  
 19:   2 252/143             980.890 cents  
 20:   4 1584/893            992.208 cents  
 20:   4 7136/4023           992.213 cents  
 20:   4 88605/49952         992.215 cents  
 20:   4 14288/8055          992.217 cents  
 20:   4 149/84              992.221 cents  
 20:   4 441/242             1038.926 cents 
 21:   1 1022208/568841      1014.710 cents 
 21:   1 13815296/7687953    1014.714 cents 
 21:   1 3573735/1988714     1014.716 cents 
 21:   1 27661568/15393105   1014.718 cents 
 21:   1 72116/40131         1014.723 cents 
 21:   2 1638/893            1050.244 cents 
 21:   2 81172/44253         1050.248 cents 
 21:   2 104715/57088        1050.250 cents 
 21:   2 162526/88605        1050.253 cents 
 21:   2 1937/1056           1050.257 cents 
 21:   7 24/13               1061.427 cents tridecimal neutral seventh
 21:   2 40131/21296         1096.962 cents 
 22:   2 11616/6251          1072.745 cents 
 22:   2 156992/84483        1072.750 cents 
 22:   2 324885/174832       1072.752 cents 
 22:   2 314336/169155       1072.754 cents 
 22:   2 1639/882            1072.758 cents 
 22:  14 21/11               1119.463 cents undecimal major seventh
 23:   1 1716/893            1130.781 cents 
 23:   1 23192/12069         1130.785 cents 
 23:   1 383955/199808       1130.787 cents 
 23:   1 46436/24165         1130.790 cents 
 23:   1 1937/1008           1130.794 cents 
 23:  12 176/91              1141.964 cents 
 23:   7 1911/968            1177.499 cents 
Highest number of different intervals for one interval class: 17
Average number of different intervals per interval class: 10.52174 = 242/23
SHOW/LINE/CENTS INTERVALS
         1    2     3     4     5     6     7     8     9     10    11    12    13    14    15    16    17    18    19    20    
 21     22     23     24    
 0.0   : 58.0 127.2 185.3 207.8 265.8 288.3 346.4 415.6 473.6 496.1 554.1 623.4 681.4 703.9 761.9 831.1 889.2 911.7 969.7 992.2 
 1050.2 1119.5 1177.5 1200.0
 58.0  : 69.2 127.2 149.7 207.8 230.3 288.3 357.5 415.6 438.1 496.1 565.3 623.4 645.9 703.9 773.1 831.1 853.6 911.7 934.2 992.2 
 1061.4 1119.5 1142.0 1200.0
 127.2 : 58.0 80.5  138.6 161.1 219.1 288.3 346.4 368.9 426.9 496.1 554.1 576.6 634.7 703.9 761.9 784.4 842.5 865.0 923.0 992.2 
 1050.3 1072.8 1130.8 1200.0
 185.3 : 22.5 80.5  103.0 161.1 230.3 288.3 310.8 368.9 438.1 496.1 518.6 576.6 645.9 703.9 726.4 784.4 806.9 865.0 934.2 992.2 
 1014.7 1072.8 1142.0 1200.0
 207.8 : 58.0 80.5  138.6 207.8 265.8 288.3 346.4 415.6 473.6 496.1 554.1 623.4 681.4 703.9 761.9 784.4 842.5 911.7 969.7 992.2 
 1050.3 1119.5 1177.5 1200.0
 265.8 : 22.5 80.5  149.8 207.8 230.3 288.3 357.5 415.6 438.1 496.1 565.3 623.4 645.9 703.9 726.4 784.4 853.6 911.7 934.2 992.2 
 1061.4 1119.5 1142.0 1200.0
 288.3 : 58.0 127.3 185.3 207.8 265.8 335.0 393.1 415.6 473.6 542.8 600.9 623.4 681.4 703.9 761.9 831.1 889.2 911.7 969.7 1038.9
 1097.0 1119.5 1177.5 1200.0
 346.4 : 69.2 127.3 149.8 207.8 277.0 335.0 357.5 415.6 484.8 542.8 565.3 623.4 645.9 703.9 773.1 831.1 853.6 911.7 980.9 1038.9
 1061.4 1119.5 1142.0 1200.0
 415.6 : 58.0 80.5  138.6 207.8 265.8 288.3 346.4 415.6 473.6 496.1 554.1 576.6 634.7 703.9 761.9 784.4 842.5 911.7 969.7 992.2 
 1050.2 1072.7 1130.8 1200.0
 473.6 : 22.5 80.5  149.7 207.8 230.3 288.3 357.5 415.6 438.1 496.1 518.6 576.6 645.9 703.9 726.4 784.4 853.6 911.7 934.2 992.2 
 1014.7 1072.7 1142.0 1200.0
 496.1 : 58.0 127.2 185.3 207.8 265.8 335.0 393.1 415.6 473.6 496.1 554.1 623.4 681.4 703.9 761.9 831.1 889.2 911.7 969.7 992.2 
 1050.2 1119.5 1177.5 1200.0
 554.1 : 69.2 127.2 149.7 207.8 277.0 335.0 357.5 415.6 438.1 496.1 565.3 623.4 645.9 703.9 773.1 831.1 853.6 911.7 934.2 992.2 
 1061.4 1119.5 1142.0 1200.0
 623.4 : 58.0 80.5  138.6 207.8 265.8 288.3 346.4 368.9 426.9 496.1 554.1 576.6 634.7 703.9 761.9 784.4 842.5 865.0 923.0 992.2 
 1050.3 1072.8 1130.8 1200.0
 681.4 : 22.5 80.5  149.7 207.8 230.3 288.3 310.8 368.9 438.1 496.1 518.6 576.6 645.9 703.9 726.4 784.4 806.9 865.0 934.2 992.2 
 1014.7 1072.8 1142.0 1200.0
 703.9 : 58.0 127.2 185.3 207.8 265.8 288.3 346.4 415.6 473.6 496.1 554.1 623.4 681.4 703.9 761.9 784.4 842.5 911.7 969.7 992.2 
 1050.3 1119.5 1177.5 1200.0
 761.9 : 69.2 127.2 149.7 207.8 230.3 288.3 357.5 415.6 438.1 496.1 565.3 623.4 645.9 703.9 726.4 784.4 853.6 911.7 934.2 992.2 
 1061.4 1119.5 1142.0 1200.0
 831.1 : 58.0 80.5  138.6 161.1 219.1 288.3 346.4 368.9 426.9 496.1 554.1 576.6 634.7 657.2 715.2 784.4 842.5 865.0 923.0 992.2 
 1050.3 1072.8 1130.8 1200.0
 889.2 : 22.5 80.5  103.0 161.1 230.3 288.3 310.8 368.9 438.1 496.1 518.6 576.6 599.1 657.2 726.4 784.4 806.9 865.0 934.2 992.2 
 1014.7 1072.8 1142.0 1200.0
 911.7 : 58.0 80.5  138.6 207.8 265.8 288.3 346.4 415.6 473.6 496.1 554.1 576.6 634.7 703.9 761.9 784.4 842.5 911.7 969.7 992.2 
 1050.3 1119.5 1177.5 1200.0
 969.7 : 22.5 80.5  149.8 207.8 230.3 288.3 357.5 415.6 438.1 496.1 518.6 576.6 645.9 703.9 726.4 784.4 853.6 911.7 934.2 992.2 
 1061.4 1119.5 1142.0 1200.0
 992.2 : 58.0 127.3 185.3 207.8 265.8 335.0 393.1 415.6 473.6 496.1 554.1 623.4 681.4 703.9 761.9 831.1 889.2 911.7 969.7 1038.9
 1097.0 1119.5 1177.5 1200.0
 1050.2: 69.2 127.3 149.8 207.8 277.0 335.0 357.5 415.6 438.1 496.1 565.3 623.4 645.9 703.9 773.1 831.1 853.6 911.7 980.9 1038.9
 1061.4 1119.5 1142.0 1200.0
 1119.5: 58.0 80.5  138.6 207.8 265.8 288.3 346.4 368.9 426.9 496.1 554.1 576.6 634.7 703.9 761.9 784.4 842.5 911.7 969.7 992.2 
 1050.2 1072.7 1130.8 1200.0
 1177.5: 22.5 80.5  149.7 207.8 230.3 288.3 310.8 368.9 438.1 496.1 518.6 576.6 645.9 703.9 726.4 784.4 853.6 911.7 934.2 992.2 
 1014.7 1072.7 1142.0 1200.0
 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  22.5014   .. 69.2190 cents       43757/42592, 46.7176 cents         1936/1911, 22.5014 cents
  2:  80.5370   .. 127.2547 cents      43757/42592, 46.7176 cents         6292/6251, 11.3180 cents
  3:  103.0384  .. 185.2903 cents      82.25184 cents                     82458112/83619627,-24.2162 cents
  4:  161.0741  .. 207.7917 cents      43757/42592, 46.7176 cents         82458112/83619627,-24.2162 cents
  5:  219.1097  .. 276.9999 cents      18924192/18301855, 57.8902 cents   6292/6251, 11.3180 cents
  6:  288.3157  .. 335.0355 cents      9790641/9529960, 46.7198 cents     1407835/1398663, 11.3158 cents
  7:  310.8171  .. 393.0711 cents      82.25401 cents                    -24.21838 cents
  8:  368.8528  .. 415.5747 cents      2800455/2725888, 46.7220 cents    -24.21838 cents
  9:  426.8884  .. 484.7829 cents      37763901/36521914, 57.8945 cents   402688/400065, 11.3137 cents
 10:  496.1031  .. 542.8185 cents      4884369/4754332, 46.7155 cents     1404689/1395534, 11.3202 cents
 11:  518.6045  .. 600.8541 cents      82.24967 cents                    -24.21404 cents
 12:  576.6401  .. 623.3599 cents      2436721/2371842, 46.7198 cents    -24.21404 cents
 13:  599.1459  .. 681.3955 cents      82.24967 cents                    -24.21404 cents
 14:  657.1815  .. 703.8969 cents      4884369/4754332, 46.7155 cents    -24.21404 cents
 15:  715.2171  .. 773.1116 cents      37763901/36521914, 57.8945 cents   1404689/1395534, 11.3202 cents
 16:  784.4253  .. 831.1472 cents      2800455/2725888, 46.7220 cents     402688/400065, 11.3137 cents
 17:  806.9289  .. 889.1829 cents      82.25401 cents                    -24.21838 cents
 18:  864.9645  .. 911.6843 cents      9790641/9529960, 46.7198 cents    -24.21838 cents
 19:  923.0001  .. 980.8903 cents      18924192/18301855, 57.8902 cents   1407835/1398663, 11.3158 cents
 20:  992.2083  .. 1038.9259 cents     43757/42592, 46.7176 cents         6292/6251, 11.3180 cents
 21:  1014.7097 .. 1096.9616 cents     82.25184 cents                     82458112/83619627,-24.2162 cents
 22:  1072.7453 .. 1119.4630 cents     43757/42592, 46.7176 cents         82458112/83619627,-24.2162 cents
 23:  1130.7810 .. 1177.4986 cents     43757/42592, 46.7176 cents         6292/6251, 11.3180 cents
SHOW DATA
Number of notes                     : 24
-- Interval properties --
Smallest interval                   : 1936/1911, 22.5014 cents, class 1
Average step (divided formal octave): 50.0000 cents
Largest one step interval           : 893/858, 69.2190 cents
Average / Smallest step             : 2.222083
Largest / Average step              : 1.384381
Largest / Smallest step             : 3.076209
Median interval of one step         : 91/88, 58.0356 cents, amount: 12
Most common interval of one step    : 91/88, 58.0356 cents, amount: 12
Least squares average step          : 50.83804 cents, oct.:  1220.11307 cents
Scale is not proper
Step pattern alph. order: ABACACADACAEACAFACACAGAC
Step pattern size order : BCBABABFBABEBABDBABABGBA
Scale is a Constant Structure, by a margin of 1.70829 cents
Scale diversity                     : 1.271328
Lumma stability                     : 0.131812
Lumma impropriety factor            : 0.240739
Number of different interval sizes  : 242 = 10.52174 / class
Number of one step interval sizes   : 7
Highest interval variety            : 17
Mean interval variety               : 10.52174 = 242/23
Median interval variety             : 6
Lowest interval variety             : 6
Smallest interval difference        : 356457915/356457472, 0.0022 cents
Most common intervals               : 22/21, 80.5370 cents & inv., amount: 14
Most common triad is 0.0 80.537 1119.463 cents, amount: 4
Number of recognisable fifths       : 23, average 704.3850 cents
Number of appreciable fifths        : 22, average 703.8926 cents
Formal octave complements present   : 1 = 4.1667%
Limited inverse transpositions      :
 23
Inversional symmetry on intervals   :
 11-12 23-24
-- Rational properties --
Prime limit                         : 223
Odd number limit                    : 53815671 (O: 53815671 U: 53815671)
Highest odd numerator or denominator: 361179
Scale harmonicity                   : 0.005927
Fundamental                         : too low to compute
Guide tone                          : 254270016,  27.9218 octaves, 66523536675.094 Hz.
Exponens Consonantiae               : 1.307273E+22, 73.46898 octaves
Euler's gradus suavitatis           : 695
Sum of Mann's harmonic distance     : 570697.0, average 23779.04167
Mersenne's string divisions         : too high to compute
Sum of van Prooijen's expressibility: 76.12166, average 3.17174
Sum of Tenney's harmonic distance   : 152.77541, average 6.36564
Vogel's harmonic complexity         : too high to compute
Wille's k value                     : too high to compute
Wilson's harmonic complexity        : 701
Rectangular lattice diameter        : 17
Triangular lattice diameter         : 9
Lattice compactness                 : 1307.96624, average 4.35989
Lattice compactness (without 2's)   : 817.12029, average 2.72373
Number of different primes          : 11
Prime exponents' range, average, count, tones@limit:
  2:  -4 .. 6         0.87500   53    1
  3:   0 .. 4         1.91667   46
  5:  -1 .. 0        -0.16667   4
  7:   0 .. 3         1.41667   34
 11:  -2 .. 1        -0.58333   20    1
 13:   0 .. 1         0.50000   12    2
 19:  -1 .. 0        -0.25000   6
 47:  -1 .. 0        -0.25000   6     6
 149: -1 .. 0        -0.25000   6     6
 179: -1 .. 0        -0.16667   4     4
 223: -1 .. 0        -0.16667   4     4
Average exponent except 2's         : 48 / 24 = 2.00000
Average absolute exponent except 2's: 142 / 24 = 5.91667
Scale is weakly epimorphic with val: <24 38 55 66 82 87 100 134 172 179 186|
Scale is weakly epimorphic with val: <24 38 55 66 82 87 101 133 172 179 186|
Scale is weakly epimorphic with val: <24 38 55 66 82 87 102 132 172 179 186|
Scale is weakly epimorphic with val: <24 38 55 66 82 87 103 131 172 179 186|
Scale is weakly epimorphic with val: <24 38 55 66 82 87 104 130 172 179 186|
Scale is JI-epimorphic with val: <24 38 55 66 82 89 100 134 172 179 186|
Scale is JI-epimorphic with val: <24 38 55 66 82 89 101 133 172 179 186|
Scale is JI-epimorphic with val: <24 38 55 66 82 89 102 132 172 179 186|
Scale is JI-epimorphic with val: <24 38 55 66 82 89 103 131 172 179 186|
Scale is JI-epimorphic with val: <24 38 55 66 82 89 104 130 172 179 186|
Scale is weakly epimorphic with val: <24 38 55 66 82 91 100 134 172 179 186|
Scale is weakly epimorphic with val: <24 38 55 66 82 91 101 133 172 179 186|
Scale is weakly epimorphic with val: <24 38 55 66 82 91 102 132 172 179 186|
Scale is weakly epimorphic with val: <24 38 55 66 82 91 103 131 172 179 186|
Scale is weakly epimorphic with val: <24 38 55 66 82 91 104 130 172 179 186|
Scale is weakly epimorphic with val: <24 38 55 67 83 87 100 135 173 180 187|
Scale is weakly epimorphic with val: <24 38 55 67 83 87 101 134 173 180 187|
Scale is weakly epimorphic with val: <24 38 55 67 83 87 102 133 173 180 187|
Scale is weakly epimorphic with val: <24 38 55 67 83 87 103 132 173 180 187|
Scale is weakly epimorphic with val: <24 38 55 67 83 87 104 131 173 180 187|
Scale is JI-epimorphic with val: <24 38 55 67 83 89 100 135 173 180 187|
Scale is JI-epimorphic with val: <24 38 55 67 83 89 101 134 173 180 187|
Scale is JI-epimorphic with val: <24 38 55 67 83 89 102 133 173 180 187|
Scale is JI-epimorphic with val: <24 38 55 67 83 89 103 132 173 180 187|
Scale is JI-epimorphic with val: <24 38 55 67 83 89 104 131 173 180 187|
Scale is weakly epimorphic with val: <24 38 55 67 83 91 100 135 173 180 187|
Scale is weakly epimorphic with val: <24 38 55 67 83 91 101 134 173 180 187|
Scale is weakly epimorphic with val: <24 38 55 67 83 91 102 133 173 180 187|
Scale is weakly epimorphic with val: <24 38 55 67 83 91 103 132 173 180 187|
Scale is weakly epimorphic with val: <24 38 55 67 83 91 104 131 173 180 187|
Scale is weakly epimorphic with val: <24 38 55 68 84 87 100 136 174 181 188|
Scale is weakly epimorphic with val: <24 38 55 68 84 87 101 135 174 181 188|
Scale is weakly epimorphic with val: <24 38 55 68 84 87 102 134 174 181 188|
Scale is weakly epimorphic with val: <24 38 55 68 84 87 103 133 174 181 188|
Scale is weakly epimorphic with val: <24 38 55 68 84 87 104 132 174 181 188|
Scale is JI-epimorphic with val: <24 38 55 68 84 89 100 136 174 181 188|
Scale is JI-epimorphic with val: <24 38 55 68 84 89 101 135 174 181 188|
Scale is JI-epimorphic with val: <24 38 55 68 84 89 102 134 174 181 188|
Scale is JI-epimorphic with val: <24 38 55 68 84 89 103 133 174 181 188|
Scale is JI-epimorphic with val: <24 38 55 68 84 89 104 132 174 181 188|
Scale is weakly epimorphic with val: <24 38 55 68 84 91 100 136 174 181 188|
Scale is weakly epimorphic with val: <24 38 55 68 84 91 101 135 174 181 188|
Scale is weakly epimorphic with val: <24 38 55 68 84 91 102 134 174 181 188|
Scale is weakly epimorphic with val: <24 38 55 68 84 91 103 133 174 181 188|
Scale is weakly epimorphic with val: <24 38 55 68 84 91 104 132 174 181 188|
Scale is weakly epimorphic with val: <24 38 56 67 83 87 100 135 173 179 187|
Scale is weakly epimorphic with val: <24 38 56 67 83 87 101 134 173 179 187|
Scale is weakly epimorphic with val: <24 38 56 67 83 87 102 133 173 179 187|
Scale is weakly epimorphic with val: <24 38 56 67 83 87 103 132 173 179 187|
Scale is weakly epimorphic with val: <24 38 56 67 83 87 104 131 173 179 187|
Scale is JI-epimorphic with val: <24 38 56 67 83 89 100 135 173 179 187|
Scale is JI-epimorphic with val: <24 38 56 67 83 89 101 134 173 179 187|
Scale is JI-epimorphic with val: <24 38 56 67 83 89 102 133 173 179 187|
Scale is JI-epimorphic with val: <24 38 56 67 83 89 103 132 173 179 187|
Scale is JI-epimorphic with val: <24 38 56 67 83 89 104 131 173 179 187|
Scale is weakly epimorphic with val: <24 38 56 67 83 91 100 135 173 179 187|
Scale is weakly epimorphic with val: <24 38 56 67 83 91 101 134 173 179 187|
Scale is weakly epimorphic with val: <24 38 56 67 83 91 102 133 173 179 187|
Scale is weakly epimorphic with val: <24 38 56 67 83 91 103 132 173 179 187|
Scale is weakly epimorphic with val: <24 38 56 67 83 91 104 131 173 179 187|
Scale is weakly epimorphic with val: <24 38 56 68 84 87 100 136 174 180 188|
Scale is weakly epimorphic with val: <24 38 56 68 84 87 101 135 174 180 188|
Scale is weakly epimorphic with val: <24 38 56 68 84 87 102 134 174 180 188|
Scale is weakly epimorphic with val: <24 38 56 68 84 87 103 133 174 180 188|
Scale is weakly epimorphic with val: <24 38 56 68 84 87 104 132 174 180 188|
Scale is JI-epimorphic with val: <24 38 56 68 84 89 100 136 174 180 188|
Scale is JI-epimorphic with val: <24 38 56 68 84 89 101 135 174 180 188|
Scale is JI-epimorphic with val: <24 38 56 68 84 89 102 134 174 180 188|
Scale is JI-epimorphic with val: <24 38 56 68 84 89 103 133 174 180 188|
Scale is JI-epimorphic with val: <24 38 56 68 84 89 104 132 174 180 188|
Scale is weakly epimorphic with val: <24 38 56 68 84 91 100 136 174 180 188|
Scale is weakly epimorphic with val: <24 38 56 68 84 91 101 135 174 180 188|
Scale is weakly epimorphic with val: <24 38 56 68 84 91 102 134 174 180 188|
Scale is weakly epimorphic with val: <24 38 56 68 84 91 103 133 174 180 188|
Scale is weakly epimorphic with val: <24 38 56 68 84 91 104 132 174 180 188|
Scale is weakly epimorphic with val: <24 38 57 68 84 87 100 136 174 179 188|
Scale is weakly epimorphic with val: <24 38 57 68 84 87 101 135 174 179 188|
Scale is weakly epimorphic with val: <24 38 57 68 84 87 102 134 174 179 188|
Scale is weakly epimorphic with val: <24 38 57 68 84 87 103 133 174 179 188|
Scale is weakly epimorphic with val: <24 38 57 68 84 87 104 132 174 179 188|
Scale is JI-epimorphic with val: <24 38 57 68 84 89 100 136 174 179 188|
Scale is JI-epimorphic with val: <24 38 57 68 84 89 101 135 174 179 188|
Scale is JI-epimorphic with val: <24 38 57 68 84 89 102 134 174 179 188|
Scale is JI-epimorphic with val: <24 38 57 68 84 89 103 133 174 179 188|
Scale is JI-epimorphic with val: <24 38 57 68 84 89 104 132 174 179 188|
Scale is weakly epimorphic with val: <24 38 57 68 84 91 100 136 174 179 188|
Scale is weakly epimorphic with val: <24 38 57 68 84 91 101 135 174 179 188|
Scale is weakly epimorphic with val: <24 38 57 68 84 91 102 134 174 179 188|
Scale is weakly epimorphic with val: <24 38 57 68 84 91 103 133 174 179 188|
Scale is weakly epimorphic with val: <24 38 57 68 84 91 104 132 174 179 188|
Scale is weakly epimorphic with val: <24 39 56 68 81 88 101 136 173 181 188|
Scale is weakly epimorphic with val: <24 39 56 68 81 88 102 135 173 181 188|
Scale is weakly epimorphic with val: <24 39 56 68 81 88 103 134 173 181 188|
Scale is weakly epimorphic with val: <24 39 56 68 81 88 104 133 173 181 188|
Scale is weakly epimorphic with val: <24 39 56 68 81 90 101 136 173 181 188|
Scale is weakly epimorphic with val: <24 39 56 68 81 90 102 135 173 181 188|
Scale is weakly epimorphic with val: <24 39 56 68 81 90 103 134 173 181 188|
Scale is weakly epimorphic with val: <24 39 56 68 81 90 104 133 173 181 188|
Scale is weakly epimorphic with val: <24 39 57 68 81 88 101 136 173 180 188|
Scale is weakly epimorphic with val: <24 39 57 68 81 88 102 135 173 180 188|
Scale is weakly epimorphic with val: <24 39 57 68 81 88 103 134 173 180 188|
Scale is weakly epimorphic with val: <24 39 57 68 81 88 104 133 173 180 188|
Scale is weakly epimorphic with val: <24 39 57 68 81 90 101 136 173 180 188|
Scale is weakly epimorphic with val: <24 39 57 68 81 90 102 135 173 180 188|
Scale is weakly epimorphic with val: <24 39 57 68 81 90 103 134 173 180 188|
Scale is weakly epimorphic with val: <24 39 57 68 81 90 104 133 173 180 188|
FIT/MODE
 24:  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 0 1 1 1 1 1 1   N   T3   SD: 18.0715 c. M: 35.2773 c. 
 25:  1 2 1 0 2 0 1 2 1 0 2 1 1 1 1 1 2 0 1 1 1 1 2 0   N        SD: 13.8157 c. M:-22.8301 c. 
 29:  1 2 1 1 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 1 1 2 1 1   P   D3   SD: 12.6774 c. M: 20.2043 c. 
 30:  1 2 2 0 2 0 2 1 2 0 2 2 1 1 1 2 1 1 1 1 1 2 1 1   N        SD: 11.2349 c. M: 18.0356 c. 
 32:  2 1 2 1 1 1 1 2 2 0 2 2 1 1 1 2 2 0 2 0 2 2 1 1   N        SD: 10.6208 c. M:-17.2213 c. 
 35:  2 2 1 1 2 0 2 2 2 0 2 2 2 1 1 2 2 1 1 1 2 2 1 1   N        SD: 9.6176 c. M:-16.1117 c. 
 39:  2 2 2 1 2 0 2 2 2 1 2 2 2 1 2 2 2 1 1 1 2 2 2 1   N        SD: 8.2407 c. M: 15.8607 c. 
 41:  2 2 2 1 2 1 2 2 2 1 2 2 2 1 2 2 2 1 2 1 2 2 2 1   P   D3   SD: 6.0545 c. M: 11.6220 c. 
 46:  2 3 2 1 2 1 2 3 2 1 2 3 2 1 2 3 2 1 2 1 2 3 2 1   N        SD: 3.7758 c. M: 7.2209 c. 
 58:  3 3 3 1 3 1 3 3 3 1 3 3 3 1 3 3 3 1 3 1 3 3 3 1   N   D3   SD: 2.6923 c. M:-5.3728 c. 
 104: 5 6 5 2 5 2 5 6 5 2 5 6 5 2 5 6 5 2 5 2 5 6 5 2   N        SD: 0.3678 c. M: 0.7083 c. 
 433: 21 25 21 8 21 8 21 25 21 8 21 25 21 8 21 25 21 8 21 8 21 25 21 8   N        SD: 0.2211 c. M:-0.4375 c. 
 537: 26 31 26 10 26 10 26 31 26 10 26 31 26 10 26 31 26 10 26 10 26 31 26 10   N        SD: 0.1081 c. M:-0.2156 c. 
 641: 31 37 31 12 31 12 31 37 31 12 31 37 31 12 31 37 31 12 31 12 31 37 31 12   N        SD: 0.0348 c. M:-0.0670 c. 
 745: 36 43 36 14 36 14 36 43 36 14 36 43 36 14 36 43 36 14 36 14 36 43 36 14   N        SD: 0.0316 c. M: 0.0490 c. 
 1386: 67 80 67 26 67 26 67 80 67 26 67 80 67 26 67 80 67 26 67 26 67 80 67 26   N        SD: 0.0183 c. M:-0.0346 c. 
FIT/HARMONIC
 1 .. 2  match: 1  H SD: 0.0000 cents
 2 .. 4  match: 2  H SD: 0.9666 cents
 3 .. 6  match: 3  H SD: 1.7294 cents
 4 .. 8  match: 4  H SD: 7.3323 cents
 5 .. 10  match: 5  H SD: 10.0014 cents
 6 .. 12  match: 6  H SD: 0.9509 cents
 7 .. 14  match: 7  H SD: 6.8610 cents
 8 .. 16  match: 8  H SD: 5.5120 cents
 9 .. 18  match: 9  H SD: 2.6655 cents
 10 .. 20  match: 10  H SD: 5.8380 cents
 11 .. 22  match: 11  H SD: 4.8134 cents
 12 .. 24  match: 12  H SD: 4.2572 cents
 13 .. 26  match: 13  H SD: 3.2921 cents
 14 .. 28  match: 14  H SD: 4.7210 cents
 15 .. 30  match: 15  H SD: 4.9011 cents
 16 .. 32  match: 15    SD: 3.5366 cents
 17 .. 34  match: 16  S SD: 5.1692 cents
 18 .. 36  match: 16  S SD: 2.8177 cents
 19 .. 38  match: 18  S SD: 3.8023 cents
 20 .. 40  match: 19    SD: 4.4070 cents
 21 .. 42  match: 20    SD: 3.7310 cents
 22 .. 44  match: 18    SD: 3.1926 cents
 23 .. 46  match: 22  S SD: 2.7139 cents
 24 .. 48  match: 20    SD: 2.6892 cents
 25 .. 50  match: 20  S SD: 3.0591 cents
 26 .. 52  match: 21    SD: 2.3958 cents
 27 .. 54  match: 23    SD: 2.5170 cents
 28 .. 56  match: 20    SD: 2.6434 cents
 29 .. 58  match: 22    SD: 2.3793 cents
 30 .. 60  match: 22    SD: 2.3719 cents
 31 .. 62  match: 21    SD: 2.2228 cents
 32 .. 64  match: 23    SD: 2.0409 cents
 33 .. 66  match: 23    SD: 2.3360 cents
 34 .. 68  match: 20    SD: 2.1612 cents
 35 .. 70  match: 22    SD: 2.0726 cents
 36 .. 72  match: 24    SD: 1.7737 cents
 37 .. 74  match: 23    SD: 1.6759 cents
 38 .. 76  match: 22    SD: 2.0522 cents
 39 .. 78  match: 24    SD: 1.8886 cents
 40 .. 80  match: 21    SD: 1.4782 cents
 41 .. 82  match: 21    SD: 1.7903 cents
 42 .. 84  match: 23    SD: 1.6320 cents
 43 .. 86  match: 22    SD: 1.8236 cents
 44 .. 88  match: 24    SD: 1.6656 cents
 45 .. 90  match: 24    SD: 1.6380 cents
 46 .. 92  match: 23    SD: 1.8252 cents
 47 .. 94  match: 24    SD: 1.7632 cents
 48 .. 96  match: 24    SD: 1.3771 cents
 49 .. 98  match: 23    SD: 1.4147 cents
 50 .. 100  match: 23    SD: 1.4902 cents
 52 .. 104  match: 23    SD: 1.3532 cents
 53 .. 106  match: 24    SD: 1.3042 cents
 54 .. 108  match: 24    SD: 1.0129 cents
 58 .. 116  match: 23    SD: 1.2628 cents
 60 .. 120  match: 24    SD: 1.0519 cents
 63 .. 126  match: 24    SD: 1.0498 cents
 66 .. 132  match: 24    SD: 1.0325 cents
 67 .. 134  match: 24    SD: 0.9694 cents
 72 .. 144  match: 24    SD: 0.9689 cents
 76 .. 152  match: 24    SD: 0.9121 cents
 77 .. 154  match: 24    SD: 0.8847 cents
 78 .. 156  match: 24    SD: 0.7743 cents
 85 .. 170  match: 24    SD: 0.7387 cents
 88 .. 176  match: 24    SD: 0.7128 cents
 89 .. 178  match: 24    SD: 0.7074 cents
 96 .. 192  match: 24    SD: 0.6890 cents
 104 .. 208  match: 24    SD: 0.6678 cents
 108 .. 216  match: 24    SD: 0.5939 cents
 114 .. 228  match: 24    SD: 0.5444 cents
 117 .. 234  match: 24    SD: 0.5318 cents
 121 .. 242  match: 24    SD: 0.5267 cents
 127 .. 254  match: 24    SD: 0.4928 cents
 133 .. 266  match: 24    SD: 0.4582 cents
 141 .. 282  match: 24    SD: 0.4433 cents
 143 .. 286  match: 24    SD: 0.3697 cents
 180 .. 360  match: 24    SD: 0.3436 cents
 195 .. 390  match: 24    SD: 0.3414 cents
 198 .. 396  match: 24    SD: 0.3290 cents
 199 .. 398  match: 24    SD: 0.3009 cents
 211 .. 422  match: 24    SD: 0.2997 cents
 222 .. 444  match: 24    SD: 0.2708 cents
 235 .. 470  match: 24    SD: 0.2427 cents
 265 .. 530  match: 24    SD: 0.1815 cents
 344 .. 688  match: 24    SD: 0.1675 cents
 353 .. 706  match: 24    SD: 0.1421 cents
 416 .. 832  match: 24    SD: 0.1314 cents
 469 .. 938  match: 24    SD: 0.1133 cents
 524 .. 1048  match: 24    SD: 0.1006 cents
 591 .. 1182  match: 24    SD: 0.0932 cents