Scala analysis: xen03-wilson-partch

Harry Partch's Scale on the Bosanquet keyboard

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

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:         81/80             21.506290 syntonic comma, Didymus comma
  2:         33/32             53.272943 undecimal comma, al-Farabi's 1/4-tone
  3:         21/20             84.467193 minor semitone
  4:         16/15            111.731285 minor diatonic semitone
  5:         12/11            150.637059 undecimal neutral second, 3/4-tone
  6:         11/10            165.004228 Ptolemy's second, 4/5-tone
  7:          9/8             203.910002 major whole tone
  8:          8/7             231.174094 septimal whole tone
  9:          7/6             266.870906 septimal minor third
 10:         32/27            294.134997 Pythagorean minor third
 11:          6/5             315.641287 minor third
 12:         11/9             347.407941 undecimal neutral third
 13:          5/4             386.313714 major third
 14:         14/11            417.507964 undecimal diminished fourth or major third
 15:          9/7             435.084095 septimal major third, BP third
 16:         21/16            470.780907 narrow fourth
 17:          4/3             498.044999 perfect fourth
 18:         27/20            519.551289 acute fourth
 19:         11/8             551.317942 undecimal semi-augmented fourth
 20:          7/5             582.512193 septimal or Huygens' tritone, BP fourth
 21:         10/7             617.487807 Euler's tritone
 22:         16/11            648.682058 undecimal semi-diminished fifth
 23:         40/27            680.448711 grave fifth
 24:          3/2             701.955001 perfect fifth
 25:         32/21            729.219093 wide fifth
 26:         14/9             764.915905 septimal minor sixth
 27:         11/7             782.492036 undecimal augmented fifth
 28:          8/5             813.686286 minor sixth
 29:         18/11            852.592059 undecimal neutral sixth
 30:          5/3             884.358713 major sixth, BP sixth
 31:         27/16            905.865003 Pythagorean major sixth
 32:         12/7             933.129094 septimal major sixth
 33:          7/4             968.825906 harmonic seventh
 34:         16/9             996.089998 Pythagorean minor seventh
 35:          9/5            1017.596288 just minor seventh, BP seventh
 36:         11/6            1049.362941 undecimal neutral seventh, 21/4-tone
 37:         15/8            1088.268715 classic major seventh
 38:         40/21           1115.532807 acute major seventh
 39:         64/33           1146.727057 33rd subharmonic
 40:        160/81           1178.493710 octave - syntonic comma
 41:          2/1            1200.000000 octave
SHOW/INTERVAL
  0:         81/80             21.5063 syntonic comma, Didymus comma
  1:         81/80             21.5063 syntonic comma, Didymus comma
  2:         55/54             31.7667 telepathma
  3:         56/55             31.1943 undecimal diesis, konbini comma
  4:         64/63             27.2641 septimal comma, Archytas' comma
  5:         45/44             38.9058 1/5-tone
  6:        121/120            14.3672 undecimal seconds comma, biyatisma
  7:         45/44             38.9058 1/5-tone
  8:         64/63             27.2641 septimal comma, Archytas' comma
  9:         49/48             35.6968 slendro diesis, septimal 1/6-tone
 10:         64/63             27.2641 septimal comma, Archytas' comma
 11:         81/80             21.5063 syntonic comma, Didymus comma
 12:         55/54             31.7667 telepathma
 13:         45/44             38.9058 1/5-tone
 14:         56/55             31.1943 undecimal diesis, konbini comma
 15:         99/98             17.5761 small undecimal comma
 16:         49/48             35.6968 slendro diesis, septimal 1/6-tone
 17:         64/63             27.2641 septimal comma, Archytas' comma
 18:         81/80             21.5063 syntonic comma, Didymus comma
 19:         55/54             31.7667 telepathma
 20:         56/55             31.1943 undecimal diesis, konbini comma
 21:         50/49             34.9756 Erlich's decatonic comma, tritonic diesis
 22:         56/55             31.1943 undecimal diesis, konbini comma
 23:         55/54             31.7667 telepathma
 24:         81/80             21.5063 syntonic comma, Didymus comma
 25:         64/63             27.2641 septimal comma, Archytas' comma
 26:         49/48             35.6968 slendro diesis, septimal 1/6-tone
 27:         99/98             17.5761 small undecimal comma
 28:         56/55             31.1943 undecimal diesis, konbini comma
 29:         45/44             38.9058 1/5-tone
 30:         55/54             31.7667 telepathma
 31:         81/80             21.5063 syntonic comma, Didymus comma
 32:         64/63             27.2641 septimal comma, Archytas' comma
 33:         49/48             35.6968 slendro diesis, septimal 1/6-tone
 34:         64/63             27.2641 septimal comma, Archytas' comma
 35:         81/80             21.5063 syntonic comma, Didymus comma
 36:         55/54             31.7667 telepathma
 37:         45/44             38.9058 1/5-tone
 38:         64/63             27.2641 septimal comma, Archytas' comma
 39:         56/55             31.1943 undecimal diesis, konbini comma
 40:         55/54             31.7667 telepathma
 41:         81/80             21.5063 syntonic comma, Didymus comma
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   1 121/120             14.367 cents   undecimal seconds comma, biyatisma
  1:   2 99/98               17.576 cents   small undecimal comma
  1:   7 81/80               21.506 cents   syntonic comma, Didymus comma
  1:   8 64/63               27.264 cents   septimal comma, Archytas' comma
  1:   6 56/55               31.194 cents   undecimal diesis, konbini comma
  1:   7 55/54               31.767 cents   telepathma
  1:   1 50/49               34.976 cents   Erlich's decatonic comma, tritonic diesis
  1:   4 49/48               35.697 cents   slendro diesis, septimal 1/6-tone
  1:   5 45/44               38.906 cents   1/5-tone
  2:   1 6561/6400           43.013 cents   Mathieu superdiesis
  2:   7 36/35               48.770 cents   septimal diesis, 1/4-tone
  2:  11 33/32               53.273 cents   undecimal comma, al-Farabi's 1/4-tone
  2:   2 512/495             58.458 cents   
  2:  10 28/27               62.961 cents   Archytas' 1/3-tone
  2:   5 80/77               66.170 cents   
  2:   2 126/121             70.100 cents   
  2:   3 25/24               70.672 cents   classic chromatic semitone, minor chroma
  3:   2 2673/2560           74.779 cents   
  3:   9 22/21               80.537 cents   undecimal minor semitone
  3:  11 21/20               84.467 cents   minor semitone
  3:   2 81/77               87.676 cents   
  3:   4 256/243             90.225 cents   limma, Pythagorean minor second
  3:   4 135/128             92.179 cents   major chroma, major limma
  3:   3 128/121             97.364 cents   undecimal semitone
  3:   3 200/189             97.937 cents   
  3:   3 35/33               101.867 cents  
  4:   2 297/280             102.043 cents  
  4:   2 1701/1600           105.973 cents  
  4:   1 1089/1024           106.546 cents  two (undecimal comma, al-Farabi's 1/4-tone)
  4:  10 16/15               111.731 cents  minor diatonic semitone
  4:   6 77/72               116.234 cents  undecimal secor
  4:  10 15/14               119.443 cents  major diatonic semitone
  4:   4 189/176             123.373 cents  
  4:   6 320/297             129.131 cents  
  5:   5 27/25               133.238 cents  large limma, BP small semitone, Zarlino semitone
  5:   2 121/112             133.810 cents  
  5:   2 693/640             137.740 cents  
  5:   2 243/224             140.949 cents  Archytas' 2/3-tone
  5:   5 88/81               143.498 cents  2nd undecimal neutral second
  5:   4 160/147             146.707 cents  
  5:   2 49/45               147.428 cents  BP minor semitone
  5:  11 12/11               150.637 cents  undecimal neutral second, 3/4-tone
  5:   6 35/32               155.140 cents  septimal neutral second
  5:   2 800/729             160.897 cents  grave whole tone
  6:  10 11/10               165.004 cents  Ptolemy's second, 4/5-tone
  6:   2 54/49               168.213 cents  Zalzal's mujannab
  6:   1 441/400             168.934 cents  two (minor semitone)
  6:   4 243/220             172.143 cents  
  6:   2 567/512             176.646 cents  
  6:   4 256/231             177.901 cents  
  6:  16 10/9                182.404 cents  minor whole tone
  6:   2 49/44               186.334 cents  undecimal minor whole tone
  7:   1 891/800             186.511 cents  
  7:   4 28/25               196.198 cents  middle second
  7:   2 121/108             196.771 cents  
  7:   2 55/49               199.980 cents  quasi-equal major second
  7:  19 9/8                 203.910 cents  major whole tone
  7:   6 640/567             209.668 cents  
  7:   6 112/99              213.598 cents  
  7:   1 25/22               221.309 cents  undecimal acute whole tone
  8:   1 363/320             218.277 cents  
  8:   1 256/225             223.463 cents  Neapolitan diminished third
  8:   4 729/640             225.416 cents  acute major second
  8:  14 8/7                 231.174 cents  septimal whole tone
  8:   5 63/55               235.104 cents  
  8:   7 55/48               235.677 cents  undecimal semi-augmented whole tone
  8:   2 147/128             239.607 cents  
  8:   2 1024/891            240.862 cents  
  8:   4 280/243             245.365 cents  
  8:   1 140/121             252.504 cents  
  9:   1 231/200             249.471 cents  5/4-tone
  9:   5 81/70               252.680 cents  Al-Hwarizmi's lute middle finger
  9:   4 297/256             257.183 cents  
  9:   1 512/441             258.438 cents  
  9:   6 64/55               262.368 cents  
  9:   4 220/189             262.941 cents  
  9:  13 7/6                 266.871 cents  septimal minor third
  9:   3 90/77               270.080 cents  
  9:   2 2560/2187           272.629 cents  grave minor third
  9:   2 75/64               274.582 cents  classic augmented second
 10:   1 88/75               276.736 cents  
 10:   8 33/28               284.447 cents  undecimal minor third
 10:   9 189/160             288.377 cents  
 10:  13 32/27               294.135 cents  Pythagorean minor third
 10:   3 144/121             301.274 cents  two (undecimal neutral second, 3/4-tone)
 10:   4 25/21               301.847 cents  BP second, quasi-equal minor third
 10:   3 105/88              305.777 cents  
 11:   2 176/147             311.711 cents  
 11:  16 6/5                 315.641 cents  minor third
 11:   6 77/64               320.144 cents  Keemun minor third
 11:   4 135/112             323.353 cents  septimal wide minor third
 11:   2 880/729             325.902 cents  
 11:   1 98/81               329.832 cents  
 11:  10 40/33               333.041 cents  
 12:   3 243/200             337.148 cents  acute minor third
 12:   4 128/105             342.905 cents  septimal neutral third
 12:  11 11/9                347.408 cents  undecimal neutral third
 12:   4 60/49               350.617 cents  smaller approximation to neutral third
 12:   4 49/40               351.338 cents  larger approximation to neutral third
 12:   7 27/22               354.547 cents  neutral third, Zalzal wosta of al-Farabi
 12:   2 315/256             359.050 cents  
 12:   2 448/363             364.235 cents  
 12:   4 100/81              364.807 cents  grave major third
 13:   1 121/98              364.984 cents  
 13:   8 99/80               368.914 cents  
 13:   8 56/45               378.602 cents  septimal narrow major third
 13:   8 96/77               381.811 cents  
 13:  14 5/4                 386.314 cents  major third
 13:   2 1120/891            396.002 cents  
 14:   3 44/35               396.178 cents  
 14:   3 63/50               400.108 cents  quasi-equal major third
 14:   4 121/96              400.681 cents  
 14:   2 512/405             405.866 cents  narrow diminished fourth
 14:   7 81/64               407.820 cents  Pythagorean major third
 14:  11 80/63               413.578 cents  wide major third
 14:  11 14/11               417.508 cents  undecimal diminished fourth or major third
 15:   3 32/25               427.373 cents  classic diminished fourth
 15:   5 77/60               431.875 cents  
 15:  13 9/7                 435.084 cents  septimal major third, BP third
 15:   2 567/440             439.014 cents  
 15:   4 165/128             439.587 cents  
 15:   6 128/99              444.772 cents  
 15:   7 35/27               449.275 cents  septimal semi-diminished fourth, 9/4-tone
 15:   1 100/77              452.484 cents  
 16:   2 729/560             456.590 cents  
 16:   3 176/135             459.139 cents  
 16:   3 64/49               462.348 cents  2 septatones or septatonic major third
 16:   7 72/55               466.278 cents  undecimal semi-diminished fourth
 16:   6 55/42               466.851 cents  
 16:  14 21/16               470.781 cents  narrow fourth
 16:   5 320/243             476.539 cents  grave fourth
 16:   1 160/121             483.678 cents  
 17:   1 33/25               480.646 cents  2 pentatones
 17:   4 297/224             488.357 cents  
 17:   2 1701/1280           492.287 cents  
 17:  28 4/3                 498.045 cents  perfect fourth
 17:   2 147/110             501.975 cents  
 17:   1 162/121             505.184 cents  
 17:   2 75/56               505.757 cents  marvelous fourth
 17:   1 400/297             515.444 cents  
 18:   1 121/90              512.412 cents  
 18:   2 66/49               515.621 cents  
 18:  11 27/20               519.551 cents  acute fourth
 18:   2 693/512             524.054 cents  
 18:   4 256/189             525.309 cents  
 18:   4 224/165             529.239 cents  
 18:   5 110/81              529.812 cents  
 18:   2 200/147             533.021 cents  
 18:   3 49/36               533.742 cents  Arabic lute acute fourth
 18:   7 15/11               536.951 cents  undecimal augmented fourth
 19:   2 2187/1600           541.058 cents  
 19:   7 48/35               546.815 cents  septimal semi-augmented fourth
 19:  11 11/8                551.318 cents  undecimal semi-augmented fourth
 19:   2 441/320             555.248 cents  
 19:   2 243/176             558.457 cents  
 19:   6 112/81              561.006 cents  
 19:   5 320/231             564.215 cents  
 19:   2 168/121             568.145 cents  
 19:   4 25/18               568.717 cents  classic augmented fourth
 20:   4 891/640             572.824 cents  
 20:   6 88/63               578.582 cents  
 20:  12 7/5                 582.512 cents  septimal or Huygens' tritone, BP fourth
 20:   4 108/77              585.721 cents  
 20:   1 1024/729            588.270 cents  Pythagorean diminished fifth
 20:   6 45/32               590.224 cents  diatonic tritone
 20:   2 512/363             595.409 cents  
 20:   4 800/567             595.982 cents  
 20:   2 140/99              599.912 cents  quasi-equal tritone
 21:   2 99/70               600.088 cents  2nd quasi-equal tritone
 21:   4 567/400             604.018 cents  
 21:   2 363/256             604.591 cents  
 21:   6 64/45               609.776 cents  2nd tritone
 21:   1 729/512             611.730 cents  Pythagorean tritone
 21:   4 77/54               614.279 cents  
 21:  12 10/7                617.488 cents  Euler's tritone
 21:   6 63/44               621.418 cents  
 21:   4 1280/891            627.176 cents  
 22:   4 36/25               631.283 cents  classic diminished fifth
 22:   2 121/84              631.855 cents  
 22:   5 231/160             635.785 cents  
 22:   6 81/56               638.994 cents  
 22:   2 352/243             641.543 cents  
 22:   2 640/441             644.752 cents  
 22:  11 16/11               648.682 cents  undecimal semi-diminished fifth
 22:   7 35/24               653.185 cents  septimal semi-diminished fifth
 22:   2 3200/2187           658.942 cents  
 23:   7 22/15               663.049 cents  undecimal diminished fifth
 23:   3 72/49               666.258 cents  Arabic lute grave fifth
 23:   2 147/100             666.979 cents  
 23:   5 81/55               670.188 cents  
 23:   4 165/112             670.761 cents  
 23:   4 189/128             674.691 cents  
 23:   2 1024/693            675.946 cents  
 23:  11 40/27               680.449 cents  grave fifth
 23:   2 49/33               684.379 cents  
 23:   1 180/121             687.588 cents  
 24:   1 297/200             684.556 cents  
 24:   2 112/75              694.243 cents  marvelous fifth
 24:   1 121/81              694.816 cents  two (undecimal neutral third)
 24:   2 220/147             698.025 cents  
 24:  28 3/2                 701.955 cents  perfect fifth
 24:   2 2560/1701           707.713 cents  
 24:   4 448/297             711.643 cents  
 24:   1 50/33               719.354 cents  3 pentatones
 25:   1 121/80              716.322 cents  
 25:   5 243/160             723.461 cents  acute fifth
 25:  14 32/21               729.219 cents  wide fifth
 25:   6 84/55               733.149 cents  
 25:   7 55/36               733.722 cents  undecimal semi-augmented fifth
 25:   3 49/32               737.652 cents  
 25:   3 135/88              740.861 cents  
 25:   2 1120/729            743.410 cents  
 26:   1 77/50               747.516 cents  
 26:   7 54/35               750.725 cents  septimal semi-augmented fifth
 26:   6 99/64               755.228 cents  
 26:   4 256/165             760.413 cents  
 26:   2 880/567             760.986 cents  
 26:  13 14/9                764.916 cents  septimal minor sixth
 26:   5 120/77              768.125 cents  
 26:   3 25/16               772.627 cents  classic augmented fifth
 27:  11 11/7                782.492 cents  undecimal augmented fifth
 27:  11 63/40               786.422 cents  narrow minor sixth
 27:   7 128/81              792.180 cents  Pythagorean minor sixth
 27:   2 405/256             794.134 cents  wide augmented fifth
 27:   4 192/121             799.319 cents  
 27:   3 100/63              799.892 cents  quasi-equal minor sixth
 27:   3 35/22               803.822 cents  
 28:   2 891/560             803.998 cents  
 28:  14 8/5                 813.686 cents  minor sixth
 28:   8 77/48               818.189 cents  
 28:   8 45/28               821.398 cents  septimale wide minor sixth
 28:   8 160/99              831.086 cents  
 28:   1 196/121             835.016 cents  two (undecimal diminished fourth or major third)
 29:   4 81/50               835.193 cents  acute minor sixth
 29:   2 363/224             835.765 cents  
 29:   2 512/315             840.950 cents  
 29:   7 44/27               845.453 cents  neutral sixth
 29:   4 80/49               848.662 cents  smaller approximation to neutral sixth
 29:   4 49/30               849.383 cents  larger approximation to neutral sixth
 29:  11 18/11               852.592 cents  undecimal neutral sixth
 29:   4 105/64              857.095 cents  septimal neutral sixth
 29:   3 400/243             862.852 cents  grave major sixth
 30:  10 33/20               866.959 cents  
 30:   1 81/49               870.168 cents  two (septimal major third, BP third)
 30:   2 729/440             874.098 cents  
 30:   4 224/135             876.647 cents  narrow septimal major sixth
 30:   6 128/77              879.856 cents  
 30:  16 5/3                 884.359 cents  major sixth, BP sixth
 30:   2 147/88              888.289 cents  
 31:   3 176/105             894.223 cents  
 31:   4 42/25               898.153 cents  quasi-equal major sixth
 31:   3 121/72              898.726 cents  
 31:  13 27/16               905.865 cents  Pythagorean major sixth
 31:   9 320/189             911.623 cents  
 31:   8 56/33               915.553 cents  
 31:   1 75/44               923.264 cents  
 32:   2 128/75              925.418 cents  diminished seventh
 32:   2 2187/1280           927.371 cents  acute major sixth
 32:   3 77/45               929.920 cents  
 32:  13 12/7                933.129 cents  septimal major sixth
 32:   4 189/110             937.059 cents  
 32:   6 55/32               937.632 cents  
 32:   1 441/256             941.562 cents  two (narrow fourth)
 32:   4 512/297             942.817 cents  
 32:   5 140/81              947.320 cents  
 32:   1 400/231             950.529 cents  
 33:   1 121/70              947.496 cents  
 33:   4 243/140             954.635 cents  
 33:   2 891/512             959.138 cents  
 33:   2 256/147             960.393 cents  
 33:   7 96/55               964.323 cents  
 33:   5 110/63              964.896 cents  
 33:  14 7/4                 968.826 cents  harmonic seventh
 33:   4 1280/729            974.584 cents  grave minor seventh
 33:   1 225/128             976.537 cents  augmented sixth
 33:   1 640/363             981.723 cents  
 34:   1 44/25               978.691 cents  undecimal grave minor seventh
 34:   6 99/56               986.402 cents  
 34:   6 567/320             990.332 cents  
 34:  19 16/9                996.090 cents  Pythagorean minor seventh
 34:   2 98/55               1000.020 cents quasi-equal minor seventh
 34:   2 216/121             1003.229 cents 
 34:   4 25/14               1003.802 cents middle minor seventh
 34:   1 1600/891            1013.489 cents 
 35:   2 88/49               1013.666 cents undecimal minor seventh
 35:  16 9/5                 1017.596 cents just minor seventh, BP seventh
 35:   4 231/128             1022.099 cents 
 35:   2 1024/567            1023.354 cents 
 35:   4 440/243             1027.857 cents 
 35:   1 800/441             1031.066 cents 
 35:   2 49/27               1031.787 cents 
 35:  10 20/11               1034.996 cents large minor seventh
 36:   2 729/400             1039.103 cents acute minor seventh
 36:   6 64/35               1044.860 cents septimal neutral seventh
 36:  11 11/6                1049.363 cents undecimal neutral seventh, 21/4-tone
 36:   2 90/49               1052.572 cents 
 36:   4 147/80              1053.293 cents 
 36:   5 81/44               1056.502 cents 2nd undecimal neutral seventh
 36:   2 448/243             1059.051 cents 
 36:   2 1280/693            1062.260 cents 
 36:   2 224/121             1066.190 cents 
 36:   5 50/27               1066.762 cents grave major seventh
 37:   6 297/160             1070.869 cents 
 37:   4 352/189             1076.627 cents 
 37:  10 28/15               1080.557 cents grave major seventh
 37:   6 144/77              1083.766 cents 
 37:  10 15/8                1088.269 cents classic major seventh
 37:   1 2048/1089           1093.454 cents 
 37:   2 3200/1701           1094.027 cents 
 37:   2 560/297             1097.957 cents 
 38:   3 66/35               1098.133 cents 
 38:   3 189/100             1102.063 cents 
 38:   3 121/64              1102.636 cents two (undecimal semi-augmented fourth)
 38:   4 256/135             1107.821 cents octave - major chroma
 38:   4 243/128             1109.775 cents Pythagorean major seventh
 38:   2 154/81              1112.324 cents 
 38:  11 40/21               1115.533 cents acute major seventh
 38:   9 21/11               1119.463 cents undecimal major seventh
 38:   2 5120/2673           1125.221 cents 
 39:   3 48/25               1129.328 cents classic diminished octave
 39:   2 121/63              1129.900 cents 
 39:   5 77/40               1133.830 cents 
 39:  10 27/14               1137.039 cents septimal major seventh
 39:   2 495/256             1141.542 cents 
 39:  11 64/33               1146.727 cents 33rd subharmonic
 39:   7 35/18               1151.230 cents septimal semi-diminished octave
 39:   1 12800/6561          1156.987 cents 
 40:   5 88/45               1161.094 cents 
 40:   4 96/49               1164.303 cents 
 40:   1 49/25               1165.024 cents BP eighth
 40:   7 108/55              1168.233 cents 
 40:   6 55/28               1168.806 cents 
 40:   8 63/32               1172.736 cents octave - septimal comma
 40:   7 160/81              1178.494 cents octave - syntonic comma
 40:   2 196/99              1182.424 cents 
 40:   1 240/121             1185.633 cents 
Highest number of different intervals for one interval class: 10
Average number of different intervals per interval class: 8.40000 = 42/5
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    25    26    27    28    29    30    31    32    33    34     35     36     37     38     39     40    
 41    
 0.0   : 21.5 53.3 84.5  111.7 150.6 165.0 203.9 231.2 266.9 294.1 315.6 347.4 386.3 417.5 435.1 470.8 498.0 519.6 551.3 582.5
 617.5 648.7 680.4 702.0 729.2 764.9 782.5 813.7 852.6 884.4 905.9 933.1 968.8 996.1  1017.6 1049.4 1088.3 1115.5 1146.7 1178.5
 1200.0
 21.5  : 31.8 63.0 90.2  129.1 143.5 182.4 209.7 245.4 272.6 294.1 325.9 364.8 396.0 413.6 449.3 476.5 498.0 529.8 561.0 596.0
 627.2 658.9 680.4 707.7 743.4 761.0 792.2 831.1 862.9 884.4 911.6 947.3 974.6 996.1  1027.9 1066.8 1094.0 1125.2 1157.0 1178.5
 1200.0
 53.3  : 31.2 58.5 97.4  111.7 150.6 177.9 213.6 240.9 262.4 294.1 333.0 364.2 381.8 417.5 444.8 466.3 498.0 529.2 564.2 595.4
 627.2 648.7 675.9 711.6 729.2 760.4 799.3 831.1 852.6 879.9 915.6 942.8 964.3 996.1  1035.0 1062.3 1093.5 1125.2 1146.7 1168.2
 1200.0
 84.5  : 27.3 66.2 80.5  119.4 146.7 182.4 209.7 231.2 262.9 301.8 333.0 350.6 386.3 413.6 435.1 466.9 498.0 533.0 564.2 596.0
 617.5 644.8 680.4 698.0 729.2 768.1 799.9 821.4 848.7 884.4 911.6 933.1 964.9 1003.8 1031.1 1062.3 1094.0 1115.5 1137.0 1168.8
 1200.0
 111.7 : 38.9 53.3 92.2  119.4 155.1 182.4 203.9 235.7 274.6 305.8 323.4 359.0 386.3 407.8 439.6 470.8 505.8 537.0 568.7 590.2
 617.5 653.2 670.8 702.0 740.9 772.6 794.1 821.4 857.1 884.4 905.9 937.6 976.5 1003.8 1035.0 1066.8 1088.3 1109.8 1141.5 1172.7
 1200.0
 150.6 : 14.4 53.3 80.5  116.2 143.5 165.0 196.8 235.7 266.9 284.4 320.1 347.4 368.9 400.7 431.9 466.9 498.0 529.8 551.3 578.6
 614.3 631.9 663.0 702.0 733.7 755.2 782.5 818.2 845.5 867.0 898.7 937.6 964.9 996.1  1027.9 1049.4 1070.9 1102.6 1133.8 1161.1
 1200.0
 165.0 : 38.9 66.2 101.9 129.1 150.6 182.4 221.3 252.5 270.1 305.8 333.0 354.5 386.3 417.5 452.5 483.7 515.4 537.0 564.2 599.9
 617.5 648.7 687.6 719.4 740.9 768.1 803.8 831.1 852.6 884.4 923.3 950.5 981.7 1013.5 1035.0 1056.5 1088.3 1119.5 1146.7 1185.6
 1200.0
 203.9 : 27.3 63.0 90.2  111.7 143.5 182.4 213.6 231.2 266.9 294.1 315.6 347.4 378.6 413.6 444.8 476.5 498.0 525.3 561.0 578.6
 609.8 648.7 680.4 702.0 729.2 764.9 792.2 813.7 845.5 884.4 911.6 942.8 974.6 996.1  1017.6 1049.4 1080.6 1107.8 1146.7 1161.1
 1200.0
 231.2 : 35.7 63.0 84.5  116.2 155.1 186.3 203.9 239.6 266.9 288.4 320.1 351.3 386.3 417.5 449.3 470.8 498.0 533.7 551.3 582.5
 621.4 653.2 674.7 702.0 737.7 764.9 786.4 818.2 857.1 884.4 915.6 947.3 968.8 990.3  1022.1 1053.3 1080.6 1119.5 1133.8 1172.7
 1200.0
 266.9 : 27.3 48.8 80.5  119.4 150.6 168.2 203.9 231.2 252.7 284.4 315.6 350.6 381.8 413.6 435.1 462.3 498.0 515.6 546.8 585.7
 617.5 639.0 666.3 702.0 729.2 750.7 782.5 821.4 848.7 879.9 911.6 933.1 954.6 986.4  1017.6 1044.9 1083.8 1098.1 1137.0 1164.3
 1200.0
 294.1 : 21.5 53.3 92.2  123.4 140.9 176.6 203.9 225.4 257.2 288.4 323.4 354.5 386.3 407.8 435.1 470.8 488.4 519.6 558.5 590.2
 611.7 639.0 674.7 702.0 723.5 755.2 794.1 821.4 852.6 884.4 905.9 927.4 959.1 990.3  1017.6 1056.5 1070.9 1109.8 1137.0 1172.7
 1200.0
 315.6 : 31.8 70.7 101.9 119.4 155.1 182.4 203.9 235.7 266.9 301.8 333.0 364.8 386.3 413.6 449.3 466.9 498.0 537.0 568.7 590.2
 617.5 653.2 680.4 702.0 733.7 772.6 799.9 831.1 862.9 884.4 905.9 937.6 968.8 996.1  1035.0 1049.4 1088.3 1115.5 1151.2 1178.5
 1200.0
 347.4 : 38.9 70.1 87.7  123.4 150.6 172.1 203.9 235.1 270.1 301.3 333.0 354.5 381.8 417.5 435.1 466.3 505.2 537.0 558.5 585.7
 621.4 648.7 670.2 702.0 740.9 768.1 799.3 831.1 852.6 874.1 905.9 937.1 964.3 1003.2 1017.6 1056.5 1083.8 1119.5 1146.7 1168.2
 1200.0
 386.3 : 31.2 48.8 84.5  111.7 133.2 165.0 196.2 231.2 262.4 294.1 315.6 342.9 378.6 396.2 427.4 466.3 498.0 519.6 546.8 582.5
 609.8 631.3 663.0 702.0 729.2 760.4 792.2 813.7 835.2 867.0 898.2 925.4 964.3 978.7  1017.6 1044.9 1080.6 1107.8 1129.3 1161.1
 1200.0
 417.5 : 17.6 53.3 80.5  102.0 133.8 165.0 200.0 231.2 262.9 284.4 311.7 347.4 365.0 396.2 435.1 466.9 488.4 515.6 551.3 578.6
 600.1 631.9 670.8 698.0 729.2 761.0 782.5 804.0 835.8 867.0 894.2 933.1 947.5 986.4  1013.7 1049.4 1076.6 1098.1 1129.9 1168.8
 1200.0
 435.1 : 35.7 63.0 84.5  116.2 147.4 182.4 213.6 245.4 266.9 294.1 329.8 347.4 378.6 417.5 449.3 470.8 498.0 533.7 561.0 582.5
 614.3 653.2 680.4 711.6 743.4 764.9 786.4 818.2 849.4 876.6 915.6 929.9 968.8 996.1  1031.8 1059.1 1080.6 1112.3 1151.2 1182.4
 1200.0
 470.8 : 27.3 48.8 80.5  111.7 146.7 177.9 209.7 231.2 258.4 294.1 311.7 342.9 381.8 413.6 435.1 462.3 498.0 525.3 546.8 578.6
 617.5 644.8 675.9 707.7 729.2 750.7 782.5 813.7 841.0 879.9 894.2 933.1 960.4 996.1  1023.4 1044.9 1076.6 1115.5 1146.7 1164.3
 1200.0
 498.0 : 21.5 53.3 84.5  119.4 150.6 182.4 203.9 231.2 266.9 284.4 315.6 354.5 386.3 407.8 435.1 470.8 498.0 519.6 551.3 590.2
 617.5 648.7 680.4 702.0 723.5 755.2 786.4 813.7 852.6 867.0 905.9 933.1 968.8 996.1  1017.6 1049.4 1088.3 1119.5 1137.0 1172.7
 1200.0
 519.6 : 31.8 63.0 97.9  129.1 160.9 182.4 209.7 245.4 262.9 294.1 333.0 364.8 386.3 413.6 449.3 476.5 498.0 529.8 568.7 596.0
 627.2 658.9 680.4 702.0 733.7 764.9 792.2 831.1 845.5 884.4 911.6 947.3 974.6 996.1  1027.9 1066.8 1098.0 1115.5 1151.2 1178.5
 1200.0
 551.3 : 31.2 66.2 97.4  129.1 150.6 177.9 213.6 231.2 262.4 301.3 333.0 354.5 381.8 417.5 444.8 466.3 498.0 537.0 564.2 595.4
 627.2 648.7 670.2 702.0 733.1 760.4 799.3 813.7 852.6 879.9 915.6 942.8 964.3 996.1  1035.0 1066.2 1083.8 1119.5 1146.7 1168.2
 1200.0
 582.5 : 35.0 66.2 97.9  119.4 146.7 182.4 200.0 231.2 270.1 301.8 323.4 350.6 386.3 413.6 435.1 466.9 505.8 533.0 564.2 596.0
 617.5 639.0 670.8 702.0 729.2 768.1 782.5 821.4 848.7 884.4 911.6 933.1 964.9 1003.8 1035.0 1052.6 1088.3 1115.5 1137.0 1168.8
 1200.0
 617.5 : 31.2 63.0 84.5  111.7 147.4 165.0 196.2 235.1 266.9 288.4 315.6 351.3 378.6 400.1 431.9 470.8 498.0 529.2 561.0 582.5
 604.0 635.8 667.0 694.2 733.1 747.5 786.4 813.7 849.4 876.6 898.2 929.9 968.8 1000.0 1017.6 1053.3 1080.6 1102.1 1133.8 1165.0
 1200.0
 648.7 : 31.8 53.3 80.5  116.2 133.8 165.0 203.9 235.7 257.2 284.4 320.1 347.4 368.9 400.7 439.6 466.9 498.0 529.8 551.3 572.8
 604.6 635.8 663.0 702.0 716.3 755.2 782.5 818.2 845.5 867.0 898.7 937.6 968.8 986.4  1022.1 1049.4 1070.9 1102.6 1133.8 1168.8
 1200.0
 680.4 : 21.5 48.8 84.5  102.0 133.2 172.1 203.9 225.4 252.7 288.4 315.6 337.1 368.9 407.8 435.1 466.3 498.0 519.6 541.1 572.8
 604.0 631.3 670.2 684.6 723.5 750.7 786.4 813.7 835.2 867.0 905.9 937.1 954.6 990.3  1017.6 1039.1 1070.9 1102.1 1137.0 1168.2
 1200.0
 702.0 : 27.3 63.0 80.5  111.7 150.6 182.4 203.9 231.2 266.9 294.1 315.6 347.4 386.3 413.6 444.8 476.5 498.0 519.6 551.3 582.5
 609.8 648.7 663.0 702.0 729.2 764.9 792.2 813.7 845.5 884.4 915.6 933.1 968.8 996.1  1017.6 1049.4 1080.6 1115.5 1146.7 1178.5
 1200.0
 729.2 : 35.7 53.3 84.5  123.4 155.1 176.6 203.9 239.6 266.9 288.4 320.1 359.0 386.3 417.5 449.3 470.8 492.3 524.1 555.2 582.5
 621.4 635.8 674.7 702.0 737.7 764.9 786.4 818.2 857.1 888.3 905.9 941.6 968.8 990.3  1022.1 1053.3 1088.3 1119.5 1151.2 1172.7
 1200.0
 764.9 : 17.6 48.8 87.7  119.4 140.9 168.2 203.9 231.2 252.7 284.4 323.4 350.6 381.8 413.6 435.1 456.6 488.4 519.6 546.8 585.7
 600.1 639.0 666.3 702.0 729.2 750.7 782.5 821.4 852.6 870.2 905.9 933.1 954.6 986.4  1017.6 1052.6 1083.8 1115.5 1137.0 1164.3
 1200.0
 782.5 : 31.2 70.1 101.9 123.4 150.6 186.3 213.6 235.1 266.9 305.8 333.0 364.2 396.0 417.5 439.0 470.8 502.0 529.2 568.1 582.5
 621.4 648.7 684.4 711.6 733.1 764.9 803.8 835.0 852.6 888.3 915.6 937.1 968.8 1000.0 1035.0 1066.2 1098.0 1119.5 1146.7 1182.4
 1200.0
 813.7 : 38.9 70.7 92.2  119.4 155.1 182.4 203.9 235.7 274.6 301.8 333.0 364.8 386.3 407.8 439.6 470.8 498.0 537.0 551.3 590.2
 617.5 653.2 680.4 702.0 733.7 772.6 803.8 821.4 857.1 884.4 905.9 937.6 968.8 1003.8 1035.0 1066.8 1088.3 1115.5 1151.2 1168.8
 1200.0
 852.6 : 31.8 53.3 80.5  116.2 143.5 165.0 196.8 235.7 262.9 294.1 325.9 347.4 368.9 400.7 431.9 459.1 498.0 512.4 551.3 578.6
 614.3 641.5 663.0 694.8 733.7 764.9 782.5 818.2 845.5 867.0 898.7 929.9 964.9 996.1  1027.9 1049.4 1076.6 1112.3 1129.9 1161.1
 1200.0
 884.4 : 21.5 48.8 84.5  111.7 133.2 165.0 203.9 231.2 262.4 294.1 315.6 337.1 368.9 400.1 427.4 466.3 480.6 519.6 546.8 582.5
 609.8 631.3 663.0 702.0 733.1 750.7 786.4 813.7 835.2 867.0 898.2 933.1 964.3 996.1  1017.6 1044.9 1080.6 1098.1 1129.3 1168.2
 1200.0
 905.9 : 27.3 63.0 90.2  111.7 143.5 182.4 209.7 240.9 272.6 294.1 315.6 347.4 378.6 405.9 444.8 459.1 498.0 525.3 561.0 588.3
 609.8 641.5 680.4 711.6 729.2 764.9 792.2 813.7 845.5 876.6 911.6 942.8 974.6 996.1  1023.4 1059.1 1076.6 1107.8 1146.7 1178.5
 1200.0
 933.1 : 35.7 63.0 84.5  116.2 155.1 182.4 213.6 245.4 266.9 288.4 320.1 351.3 378.6 417.5 431.9 470.8 498.0 533.7 561.0 582.5
 614.3 653.2 684.4 702.0 737.7 764.9 786.4 818.2 849.4 884.4 915.6 947.3 968.8 996.1  1031.8 1049.4 1080.6 1119.5 1151.2 1172.7
 1200.0
 968.8 : 27.3 48.8 80.5  119.4 146.7 177.9 209.7 231.2 252.7 284.4 315.6 342.9 381.8 396.2 435.1 462.3 498.0 525.3 546.8 578.6
 617.5 648.7 666.3 702.0 729.2 750.7 782.5 813.7 848.7 879.9 911.6 933.1 960.4 996.1  1013.7 1044.9 1083.8 1115.5 1137.0 1164.3
 1200.0
 996.1 : 21.5 53.3 92.2  119.4 150.6 182.4 203.9 225.4 257.2 288.4 315.6 354.5 368.9 407.8 435.1 470.8 498.0 519.6 551.3 590.2
 621.4 639.0 674.7 702.0 723.5 755.2 786.4 821.4 852.6 884.4 905.9 933.1 968.8 986.4  1017.6 1056.5 1088.3 1109.8 1137.0 1172.7
 1200.0
 1017.6: 31.8 70.7 97.9  129.1 160.9 182.4 203.9 235.7 266.9 294.1 333.0 347.4 386.3 413.6 449.3 476.5 498.0 529.8 568.7 599.9
 617.5 653.2 680.4 702.0 733.7 764.9 799.9 831.1 862.9 884.4 911.6 947.3 964.9 996.1  1035.0 1066.8 1088.3 1115.5 1151.2 1178.5
 1200.0
 1049.4: 38.9 66.2 97.4  129.1 150.6 172.1 203.9 235.1 262.4 301.3 315.6 354.5 381.8 417.5 444.8 466.3 498.0 537.0 568.1 585.7
 621.4 648.7 670.2 702.0 733.1 768.1 799.3 831.1 852.6 879.9 915.6 933.1 964.3 1003.2 1035.0 1056.5 1083.8 1119.5 1146.7 1168.2
 1200.0
 1088.3: 27.3 58.5 90.2  111.7 133.2 165.0 196.2 223.5 262.4 276.7 315.6 342.9 378.6 405.9 427.4 459.1 498.0 529.2 546.8 582.5
 609.8 631.3 663.0 694.2 729.2 760.4 792.2 813.7 841.0 876.6 894.2 925.4 964.3 996.1  1017.6 1044.9 1080.6 1107.8 1129.3 1161.1
 1200.0
 1115.5: 31.2 63.0 84.5  106.0 137.7 168.9 196.2 235.1 249.5 288.4 315.6 351.3 378.6 400.1 431.9 470.8 502.0 519.6 555.2 582.5
 604.0 635.8 667.0 702.0 733.1 764.9 786.4 813.7 849.4 867.0 898.2 937.1 968.8 990.3  1017.6 1053.3 1080.6 1102.1 1133.8 1172.7
 1200.0
 1146.7: 31.8 53.3 74.8  106.5 137.7 165.0 203.9 218.3 257.2 284.4 320.1 347.4 368.9 400.7 439.6 470.8 488.4 524.1 551.3 572.8
 604.6 635.8 670.8 702.0 733.7 755.2 782.5 818.2 835.8 867.0 905.9 937.6 959.1 986.4  1022.1 1049.4 1070.9 1102.6 1141.5 1168.8
 1200.0
 1178.5: 21.5 43.0 74.8  106.0 133.2 172.1 186.5 225.4 252.7 288.4 315.6 337.1 368.9 407.8 439.0 456.6 492.3 519.6 541.1 572.8
 604.0 639.0 670.2 702.0 723.5 750.7 786.4 804.0 835.2 874.1 905.9 927.4 954.6 990.3  1017.6 1039.1 1070.9 1109.8 1137.0 1168.2
 1200.0
 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  14.3672   .. 38.9058 cents       1350/1331, 24.5386 cents           121/120, 14.3672 cents
  2:  43.0126   .. 70.6724 cents       20000/19683, 27.6598 cents         8019/8000, 4.1068 cents
  3:  74.7792   .. 101.8667 cents      89600/88209, 27.0874 cents         8019/8000, 4.1068 cents
  4:  102.0433  .. 129.1308 cents      89600/88209, 27.0874 cents         9801/9800, 0.1766 cents
  5:  133.2376  .. 160.8974 cents      20000/19683, 27.6598 cents         8019/8000, 4.1068 cents
  6:  165.0042  .. 186.3339 cents      245/242, 21.3296 cents             8019/8000, 4.1068 cents
  7:  186.5105  .. 221.3095 cents      10000/9801, 34.7990 cents          9801/9800, 0.1766 cents
  8:  218.2772  .. 252.5037 cents      44800/43923, 34.2266 cents         3993/4000,-3.0323 cents
  9:  249.4714  .. 274.5824 cents      625/616, 25.1110 cents             3993/4000,-3.0323 cents
 10:  276.7355  .. 305.7767 cents      7875/7744, 29.0412 cents           5632/5625, 2.1531 cents
 11:  311.7111  .. 333.0408 cents      245/242, 21.3296 cents             15488/15435, 5.9344 cents
 12:  337.1476  .. 364.8074 cents      20000/19683, 27.6598 cents         8019/8000, 4.1068 cents
 13:  364.9841  .. 396.0017 cents      109760/107811, 31.0176 cents       9801/9800, 0.1766 cents
 14:  396.1783  .. 417.5080 cents      245/242, 21.3296 cents             9801/9800, 0.1766 cents
 15:  427.3726  .. 452.4836 cents      625/616, 25.1110 cents             176/175, 9.8646 cents
 16:  456.5904  .. 483.6778 cents      89600/88209, 27.0874 cents         8019/8000, 4.1068 cents
 17:  480.6455  .. 515.4445 cents      10000/9801, 34.7990 cents          3993/4000,-3.0323 cents
 18:  512.4122  .. 536.9508 cents      1350/1331, 24.5386 cents           3993/4000,-3.0323 cents
 19:  541.0576  .. 568.7174 cents      20000/19683, 27.6598 cents         8019/8000, 4.1068 cents
 20:  572.8242  .. 599.9117 cents      89600/88209, 27.0874 cents         8019/8000, 4.1068 cents
 21:  600.0883  .. 627.1758 cents      89600/88209, 27.0874 cents         9801/9800, 0.1766 cents
 22:  631.2826  .. 658.9424 cents      20000/19683, 27.6598 cents         8019/8000, 4.1068 cents
 23:  663.0492  .. 687.5878 cents      1350/1331, 24.5386 cents           8019/8000, 4.1068 cents
 24:  684.5555  .. 719.3545 cents      10000/9801, 34.7990 cents          3993/4000,-3.0323 cents
 25:  716.3222  .. 743.4096 cents      89600/88209, 27.0874 cents         3993/4000,-3.0323 cents
 26:  747.5164  .. 772.6274 cents      625/616, 25.1110 cents             8019/8000, 4.1068 cents
 27:  782.4920  .. 803.8217 cents      245/242, 21.3296 cents             176/175, 9.8646 cents
 28:  803.9983  .. 835.0159 cents      109760/107811, 31.0176 cents       9801/9800, 0.1766 cents
 29:  835.1926  .. 862.8524 cents      20000/19683, 27.6598 cents         9801/9800, 0.1766 cents
 30:  866.9592  .. 888.2889 cents      245/242, 21.3296 cents             8019/8000, 4.1068 cents
 31:  894.2233  .. 923.2645 cents      7875/7744, 29.0412 cents           15488/15435, 5.9344 cents
 32:  925.4176  .. 950.5286 cents      625/616, 25.1110 cents             5632/5625, 2.1531 cents
 33:  947.4963  .. 981.7228 cents      44800/43923, 34.2266 cents         3993/4000,-3.0323 cents
 34:  978.6905  .. 1013.4895 cents     10000/9801, 34.7990 cents          3993/4000,-3.0323 cents
 35:  1013.6661 .. 1034.9958 cents     245/242, 21.3296 cents             9801/9800, 0.1766 cents
 36:  1039.1026 .. 1066.7624 cents     20000/19683, 27.6598 cents         8019/8000, 4.1068 cents
 37:  1070.8692 .. 1097.9567 cents     89600/88209, 27.0874 cents         8019/8000, 4.1068 cents
 38:  1098.1333 .. 1125.2208 cents     89600/88209, 27.0874 cents         9801/9800, 0.1766 cents
 39:  1129.3276 .. 1156.9874 cents     20000/19683, 27.6598 cents         8019/8000, 4.1068 cents
 40:  1161.0942 .. 1185.6328 cents     1350/1331, 24.5386 cents           8019/8000, 4.1068 cents
SHOW DATA
Number of notes                     : 41
-- Interval properties --
Smallest interval                   : 121/120, 14.3672 cents, class 1
Average step (divided formal octave): 29.2683 cents
Largest one step interval           : 45/44, 38.9058 cents
Average / Smallest step             : 2.037165
Largest / Average step              : 1.329281
Largest / Smallest step             : 2.707964
Median interval of one step         : 56/55, 31.1943 cents, amount: 6
Most common interval of one step    : 64/63, 27.2641 cents, amount: 8
Least squares average step          : 29.28568 cents, oct.:  1200.71276 cents
Scale is not proper
Step pattern alph. order: ABCDEFEDGDABECHGDABCICBADGHCEBADGDABEDCBA
Step pattern size order : CFEDIAIDHDCFIEBHDCFEGEFCDHBEIFCDHDCFIDEFC
Scale is a Constant Structure, by a margin of 0.17665 cents
Scale diversity                     : 1.487071
Lumma stability                     : 0.109948
Lumma impropriety factor            : 0.020215
Number of different interval sizes  : 336 = 8.40000 / class
Number of one step interval sizes   : 9
Highest interval variety            : 10
Mean interval variety               : 8.40000 = 42/5
Median interval variety             : 6.5
Lowest interval variety             : 6
Smallest interval difference        : 9801/9800, 0.1766 cents
Most common intervals               : 4/3, 498.0450 cents & inv., amount: 28
Most common triad is 0.0 498.045 701.955 cents, amount: 18
Number of recognisable fifths       : 42, average 702.8418 cents
Number of appreciable fifths        : 39, average 702.4638 cents
Scale contains a complete diamond   : 1 3 5 7 21
All steps are superparticular (epimoric)
Length of longest harmonic part     : 2 at degree 1
Length of longest subharmonic part  : 2 at degree 21
Formal octave complements present   : 39 = 95.1220%
Scale is differentially coherent in interval class 1
-- Rational properties --
Prime limit                         : 11
Odd number limit                    : 6561 (O: 6561 U: 6561)
Highest odd numerator or denominator: 81
Scale harmonicity                   : 0.009797
Average absolute harmonicity        : 0.096505
Specific harmonicity                : 0.077395
Fundamental                         : 1/997920, -19.9286 octaves, 0.0003 Hz.
Guide tone                          : 1995840,  20.9286 octaves, 522162768.250 Hz.
Exponens Consonantiae               : 1.991689E+12, 40.85713 octaves
Euler's gradus suavitatis           : 68
Sum of Mann's harmonic distance     : 731.5, average 17.84146
Mersenne's string divisions         : too high to compute
Sum of van Prooijen's expressibility: 43.18497, average 1.05329
Sum of Tenney's harmonic distance   : 86.92412, average 2.12010
Vogel's harmonic complexity         : 40.63415
Wille's k value                     : 514552
Wilson's harmonic complexity        : 70
Rectangular lattice diameter        : 14
Triangular lattice diameter         : 8
Lattice compactness                 : 3717.24586, average 4.31736
Lattice compactness (without 2's)   : 2119.16247, average 2.46128
Number of different primes          : 5
Prime exponents' range, average, count, tones@limit:
  2:  -5 .. 6         0.46341   95    1
  3:  -4 .. 4         0.04878   50    6
  5:  -1 .. 1        -0.04878   16    11
  7:  -1 .. 1         0.00000   14    12
 11:  -1 .. 1         0.02439   11    11
Average exponent except 2's         : 1 / 41 = 0.02439
Average absolute exponent except 2's: 91 / 41 = 2.21951
Scale is JI-epimorphic with val: <41 65 95 115 142| = patent
FIT/MODE
 41:  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1  SP B ME I SD: 4.9560 c. M:-10.6055 c. 
 46:  1 1 1 1 2 0 2 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1   N   D3   SD: 5.3104 c. M:-8.5991 c. 
 53:  1 1 2 1 2 0 2 1 2 1 1 1 2 1 1 2 1 1 1 2 1 2 1 1 1 2 1 1 2 1 1 1 2 1 1 1 2 1 2 1 1   N   D3   SD: 5.1610 c. M: 9.9608 c. 
 58:  1 2 1 1 2 1 2 1 2 1 1 2 2 1 1 2 1 1 2 1 2 1 2 1 1 2 1 1 2 2 1 1 2 1 1 2 2 1 1 2 1   N   D3   SD: 4.6373 c. M: 8.7960 c. 
 63:  1 2 1 2 2 1 2 1 2 1 2 1 2 2 1 2 1 1 2 2 1 2 2 1 1 2 1 2 2 1 2 1 2 1 1 2 2 2 1 2 1   N   D3   SD: 5.0296 c. M: 8.4207 c. 
 66:  1 2 2 1 2 1 2 2 2 1 1 2 2 2 1 2 1 2 1 2 2 2 1 2 1 2 1 2 2 2 1 1 2 2 1 2 2 1 2 2 1   N   D3   SD: 4.3854 c. M:-7.7214 c. 
 72:  1 2 2 2 2 1 2 2 2 2 1 2 2 2 1 2 2 1 2 2 2 2 2 1 2 2 1 2 2 2 1 2 2 2 1 2 2 2 2 2 1   P   D3   SD: 2.8652 c. M:-5.8650 c. 
 94:  2 2 3 2 3 1 3 2 3 2 2 2 3 3 1 3 2 2 2 3 2 3 2 2 2 3 1 3 3 2 2 2 3 2 2 2 3 2 3 2 2   N        SD: 2.8285 c. M:-4.8945 c. 
 111: 2 3 3 2 4 1 4 2 4 2 2 3 4 3 1 4 2 2 3 3 3 3 3 2 2 4 1 3 4 3 2 2 4 2 2 3 4 2 3 3 2   N        SD: 2.4671 c. M:-4.8948 c. 
 114: 2 3 3 3 3 2 3 3 3 3 2 3 4 3 1 4 2 2 3 3 4 3 3 2 2 4 1 3 4 3 2 3 3 3 2 3 3 3 3 3 2   N        SD: 2.8451 c. M: 4.0582 c. 
 115: 2 3 3 3 3 2 4 2 4 2 2 3 4 3 2 3 3 2 3 3 3 3 3 2 3 3 2 3 4 3 2 2 4 2 3 3 3 3 3 3 2   P        SD: 2.6404 c. M:-5.0124 c. 
 118: 2 3 3 3 4 1 4 3 3 3 2 3 4 3 2 3 3 2 3 3 4 3 3 2 3 3 2 3 4 3 2 3 3 3 2 3 4 3 3 3 2   N        SD: 1.8272 c. M:-3.1113 c. 
 130: 2 4 3 3 4 2 4 3 4 3 2 4 4 3 2 4 3 2 4 3 4 3 4 2 3 4 2 3 4 4 2 3 4 3 2 4 4 3 3 4 2   P        SD: 1.8259 c. M: 3.3613 c. 
 152: 3 4 4 3 5 2 5 3 5 3 3 4 5 4 2 5 3 3 4 4 4 4 4 3 3 5 2 4 5 4 3 3 5 3 3 4 5 3 4 4 3   P        SD: 1.5272 c. M:-2.9033 c. 
 159: 3 4 4 4 5 2 5 4 4 4 3 4 5 4 3 4 4 3 4 4 5 4 4 3 4 4 3 4 5 4 3 4 4 4 3 4 5 4 4 4 3   P        SD: 1.5739 c. M:-2.8564 c. 
 176: 3 5 4 4 6 2 6 4 5 4 3 5 6 4 3 5 4 3 5 4 6 4 5 3 4 5 3 4 6 5 3 4 5 4 3 5 6 4 4 5 3   N        SD: 1.5244 c. M:-2.9667 c. 
 180: 3 5 5 4 6 2 6 4 5 4 3 5 6 5 2 6 4 3 5 4 6 4 5 3 4 6 2 5 6 5 3 4 5 4 4 4 6 4 5 5 3   N        SD: 1.8525 c. M:-2.7567 c. 
 181: 3 5 5 4 6 2 6 4 5 4 4 4 6 5 3 5 4 3 5 5 5 5 5 3 4 5 3 5 6 4 4 4 5 4 3 5 6 4 5 5 3   N        SD: 1.6986 c. M: 3.2316 c. 
 183: 3 5 5 4 6 2 6 4 6 4 3 5 6 5 2 6 4 3 5 5 5 5 5 3 4 6 2 5 6 5 3 4 6 4 3 5 6 4 5 5 3   N        SD: 1.2256 c. M: 2.2972 c. 
 224: 4 6 6 5 7 3 7 5 7 5 4 6 7 6 3 7 5 4 6 6 6 6 6 4 5 7 3 6 7 6 4 5 7 5 4 6 7 5 6 6 4   P        SD: 0.7190 c. M:-1.4164 c. 
 270: 5 7 7 6 9 3 9 6 8 6 5 7 9 7 4 8 6 5 7 7 8 7 7 5 6 8 4 7 9 7 5 6 8 6 5 7 9 6 7 7 5   N        SD: 0.4282 c. M:-0.8017 c. 
 342: 6 9 9 8 11 4 11 8 10 8 6 9 11 9 5 10 8 6 9 9 10 9 9 6 8 10 5 9 11 9 6 8 10 8 6 9 11 8 9 9 6   N        SD: 0.3556 c. M: 0.6414 c. 
 494: 9 13 13 11 16 6 16 11 15 11 9 13 16 13 7 15 11 9 13 13 14 13 13 9 11 15 7 13 16 13 9 11 15 11 9 13 16 11 13 13 9   N        SD: 0.2785 c. M:-0.5530 c. 
 612: 11 16 16 14 20 7 20 14 18 14 11 16 20 16 9 18 14 11 16 16 18 16 16 11 14 18 9 16 20 16 11 14 18 14 11 16 20 14 16 16 11   N        SD: 0.1916 c. M: 0.3491 c. 
 836: 15 22 22 19 27 10 27 19 25 19 15 22 27 22 12 25 19 15 22 22 24 22 22 15 19 25 12 22 27 22 15 19 25 19 15 22 27 19 22 22 15   N        SD: 0.1392 c. M:-0.2629 c. 
 1106: 20 29 29 25 36 13 36 25 33 25 20 29 36 29 16 33 25 20 29 29 32 29 29 20 25 33 16 29 36 29 20 25 33 25 20 29 36 25 29 29 20   N        SD: 0.1242 c. M:-0.2136 c. 
 1236: 22 33 32 28 40 15 40 28 37 28 22 33 40 32 18 37 28 22 33 32 36 32 33 22 28 37 18 32 40 33 22 28 37 28 22 33 40 28 32 33 22   N        SD: 0.1024 c. M: 0.1649 c. 
 1506: 27 40 39 34 49 18 49 34 45 34 27 40 49 39 22 45 34 27 40 39 44 39 40 27 34 45 22 39 49 40 27 34 45 34 27 40 49 34 39 40 27   N        SD: 0.0830 c. M:-0.1775 c. 
 1848: 33 49 48 42 60 22 60 42 55 42 33 49 60 48 27 55 42 33 49 48 54 48 49 33 42 55 27 48 60 49 33 42 55 42 33 49 60 42 48 49 33   N        SD: 0.0387 c. M:-0.0777 c. 
FIT/HARMONIC
 1 .. 2  match: 1  H SD: 0.0000 cents
 2 .. 4  match: 2  H SD: 0.0000 cents
 3 .. 6  match: 3  H SD: 0.0000 cents
 4 .. 8  match: 4  H SD: 0.0000 cents
 5 .. 10  match: 5  H SD: 0.0000 cents
 6 .. 12  match: 6  H SD: 0.0000 cents
 7 .. 14  match: 7  H SD: 2.3667 cents
 8 .. 16  match: 8  H SD: 1.5080 cents
 9 .. 18  match: 9  H SD: 2.7477 cents
 10 .. 20  match: 10  H SD: 2.1366 cents
 11 .. 22  match: 11  H SD: 2.4904 cents
 12 .. 24  match: 12  H SD: 2.1123 cents
 13 .. 26  match: 13  H SD: 3.3983 cents
 14 .. 28  match: 14  H SD: 1.9495 cents
 15 .. 30  match: 15  H SD: 2.0194 cents
 16 .. 32  match: 16  H SD: 1.4322 cents
 17 .. 34  match: 17  H SD: 2.6373 cents
 18 .. 36  match: 18  H SD: 1.8922 cents
 19 .. 38  match: 19  H SD: 2.0393 cents
 20 .. 40  match: 20  H SD: 1.7187 cents
 21 .. 42  match: 21  H SD: 1.8189 cents
 22 .. 44  match: 22  H SD: 1.8094 cents
 23 .. 46  match: 23  H SD: 1.8755 cents
 24 .. 48  match: 24  H SD: 1.7536 cents
 25 .. 50  match: 25  H SD: 1.8162 cents
 26 .. 52  match: 26  H SD: 2.2049 cents
 27 .. 54  match: 27  H SD: 1.8569 cents
 28 .. 56  match: 27    SD: 1.5537 cents
 29 .. 58  match: 29  H SD: 1.6129 cents
 30 .. 60  match: 29    SD: 1.4278 cents
 31 .. 62  match: 31  H SD: 1.3957 cents
 32 .. 64  match: 32  H SD: 1.2469 cents
 33 .. 66  match: 32    SD: 1.4221 cents
 34 .. 68  match: 31  S SD: 1.7536 cents
 35 .. 70  match: 34  S SD: 1.1996 cents
 36 .. 72  match: 35  S SD: 1.4156 cents
 37 .. 74  match: 33    SD: 1.5079 cents
 38 .. 76  match: 34    SD: 1.4589 cents
 39 .. 78  match: 35    SD: 1.4387 cents
 40 .. 80  match: 36    SD: 1.0907 cents
 41 .. 82  match: 35    SD: 1.2891 cents
 42 .. 84  match: 37    SD: 1.0708 cents
 43 .. 86  match: 38    SD: 1.4116 cents
 44 .. 88  match: 37    SD: 1.2096 cents
 45 .. 90  match: 38    SD: 1.2006 cents
 46 .. 92  match: 37    SD: 1.3187 cents
 47 .. 94  match: 37    SD: 1.2934 cents
 48 .. 96  match: 39    SD: 1.0209 cents
 49 .. 98  match: 40    SD: 1.1136 cents
 50 .. 100  match: 38    SD: 1.1778 cents
 51 .. 102  match: 38    SD: 1.2104 cents
 52 .. 104  match: 37    SD: 1.1664 cents
 53 .. 106  match: 40    SD: 1.2132 cents
 54 .. 108  match: 39    SD: 0.9692 cents
 55 .. 110  match: 40    SD: 0.9692 cents
 57 .. 114  match: 39    SD: 1.0223 cents
 58 .. 116  match: 41    SD: 0.9502 cents
 59 .. 118  match: 41    SD: 0.9322 cents
 60 .. 120  match: 41    SD: 0.8431 cents
 61 .. 122  match: 39    SD: 0.8879 cents
 62 .. 124  match: 40    SD: 0.9573 cents
 63 .. 126  match: 40    SD: 0.7663 cents
 64 .. 128  match: 40    SD: 0.7951 cents
 68 .. 136  match: 40    SD: 0.8883 cents
 69 .. 138  match: 41    SD: 0.8753 cents
 70 .. 140  match: 41    SD: 0.7729 cents
 72 .. 144  match: 40    SD: 0.6941 cents
 73 .. 146  match: 40    SD: 0.7810 cents
 74 .. 148  match: 40    SD: 0.7727 cents
 76 .. 152  match: 41    SD: 0.7654 cents
 77 .. 154  match: 41    SD: 0.5814 cents
 83 .. 166  match: 40    SD: 0.7170 cents
 84 .. 168  match: 40    SD: 0.6594 cents
 85 .. 170  match: 41    SD: 0.6562 cents
 86 .. 172  match: 41    SD: 0.6432 cents
 88 .. 176  match: 41    SD: 0.6009 cents
 90 .. 180  match: 41    SD: 0.5681 cents
 94 .. 188  match: 40    SD: 0.6193 cents
 95 .. 190  match: 41    SD: 0.5635 cents
 96 .. 192  match: 41    SD: 0.5055 cents
 103 .. 206  match: 41    SD: 0.5048 cents
 112 .. 224  match: 41    SD: 0.4725 cents
 119 .. 238  match: 41    SD: 0.4373 cents
 120 .. 240  match: 41    SD: 0.3986 cents
 135 .. 270  match: 41    SD: 0.3793 cents
 140 .. 280  match: 41    SD: 0.3596 cents
 150 .. 300  match: 41    SD: 0.3569 cents
 151 .. 302  match: 41    SD: 0.3532 cents
 154 .. 308  match: 41    SD: 0.3359 cents
 157 .. 314  match: 41    SD: 0.3343 cents
 160 .. 320  match: 41    SD: 0.2924 cents
 168 .. 336  match: 41    SD: 0.2595 cents
 198 .. 396  match: 41    SD: 0.2488 cents
 216 .. 432  match: 41    SD: 0.2407 cents
 220 .. 440  match: 41    SD: 0.2161 cents
 231 .. 462  match: 41    SD: 0.2143 cents
 240 .. 480  match: 41    SD: 0.1895 cents
 280 .. 560  match: 41    SD: 0.1781 cents
 288 .. 576  match: 41    SD: 0.1658 cents
 301 .. 602  match: 41    SD: 0.1645 cents
 315 .. 630  match: 41    SD: 0.1611 cents
 319 .. 638  match: 41    SD: 0.1469 cents
 320 .. 640  match: 41    SD: 0.1333 cents
 360 .. 720  match: 41    SD: 0.1263 cents
 378 .. 756  match: 41    SD: 0.1131 cents
 420 .. 840  match: 41    SD: 0.1018 cents
 480 .. 960  match: 41    SD: 0.0747 cents