Scala analysis: xen12-wilson-31-pentadic-diamond

1-5-7-11-15 Pentadic Diamond, Figure 31

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

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:         16/15            111.731285 minor diatonic semitone
  2:         15/14            119.442808 major diatonic semitone
  3:         11/10            165.004228 Ptolemy's second, 4/5-tone
  4:          8/7             231.174094 septimal whole tone
  5:          5/4             386.313714 major third
  6:         14/11            417.507964 undecimal diminished fourth or major third
  7:          4/3             498.044999 perfect fourth
  8:         15/11            536.950772 undecimal augmented fourth
  9:         11/8             551.317942 undecimal semi-augmented fourth
 10:          7/5             582.512193 septimal or Huygens' tritone, BP fourth
 11:         10/7             617.487807 Euler's tritone
 12:         16/11            648.682058 undecimal semi-diminished fifth
 13:         22/15            663.049228 undecimal diminished fifth
 14:          3/2             701.955001 perfect fifth
 15:         11/7             782.492036 undecimal augmented fifth
 16:          8/5             813.686286 minor sixth
 17:          7/4             968.825906 harmonic seventh
 18:         20/11           1034.995772 large minor seventh
 19:         28/15           1080.557192 grave major seventh
 20:         15/8            1088.268715 classic major seventh
 21:          2/1            1200.000000 octave
SHOW/INTERVAL
  0:         16/15            111.7313 minor diatonic semitone
  1:         16/15            111.7313 minor diatonic semitone
  2:        225/224             7.7115 septimal kleisma
  3:         77/75             45.5614 
  4:         80/77             66.1699 
  5:         35/32            155.1396 septimal neutral second
  6:         56/55             31.1943 undecimal diesis, konbini comma
  7:         22/21             80.5370 undecimal minor semitone
  8:         45/44             38.9058 1/5-tone
  9:        121/120            14.3672 undecimal seconds comma, biyatisma
 10:         56/55             31.1943 undecimal diesis, konbini comma
 11:         50/49             34.9756 Erlich's decatonic comma, tritonic diesis
 12:         56/55             31.1943 undecimal diesis, konbini comma
 13:        121/120            14.3672 undecimal seconds comma, biyatisma
 14:         45/44             38.9058 1/5-tone
 15:         22/21             80.5370 undecimal minor semitone
 16:         56/55             31.1943 undecimal diesis, konbini comma
 17:         35/32            155.1396 septimal neutral second
 18:         80/77             66.1699 
 19:         77/75             45.5614 
 20:        225/224             7.7115 septimal kleisma
 21:         16/15            111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   2 225/224             7.712 cents    septimal kleisma
  1:   2 121/120             14.367 cents   undecimal seconds comma, biyatisma
  1:   4 56/55               31.194 cents   undecimal diesis, konbini comma
  1:   1 50/49               34.976 cents   Erlich's decatonic comma, tritonic diesis
  1:   2 45/44               38.906 cents   1/5-tone
  1:   2 77/75               45.561 cents   
  1:   2 80/77               66.170 cents   
  1:   2 22/21               80.537 cents   undecimal minor semitone
  1:   2 16/15               111.731 cents  minor diatonic semitone
  1:   2 35/32               155.140 cents  septimal neutral second
  2:   2 77/75               45.561 cents   
  2:   4 33/32               53.273 cents   undecimal comma, al-Farabi's 1/4-tone
  2:   2 80/77               66.170 cents   
  2:   4 16/15               111.731 cents  minor diatonic semitone
  2:   4 15/14               119.443 cents  major diatonic semitone
  2:   2 49/44               186.334 cents  undecimal minor whole tone
  2:   2 25/22               221.309 cents  undecimal acute whole tone
  2:   1 256/225             223.463 cents  Neapolitan diminished third
  3:   2 22/21               80.537 cents   undecimal minor semitone
  3:   2 21/20               84.467 cents   minor semitone
  3:   1 128/121             97.364 cents   undecimal semitone
  3:   2 15/14               119.443 cents  major diatonic semitone
  3:   2 121/112             133.810 cents  
  3:   2 12/11               150.637 cents  undecimal neutral second, 3/4-tone
  3:   2 11/10               165.004 cents  Ptolemy's second, 4/5-tone
  3:   2 8/7                 231.174 cents  septimal whole tone
  3:   2 140/121             252.504 cents  
  3:   4 7/6                 266.871 cents  septimal minor third
  4:   2 16/15               111.731 cents  minor diatonic semitone
  4:   2 15/14               119.443 cents  major diatonic semitone
  4:   4 11/10               165.004 cents  Ptolemy's second, 4/5-tone
  4:   2 8/7                 231.174 cents  septimal whole tone
  4:   1 225/196             238.886 cents  two (major diatonic semitone)
  4:   2 75/64               274.582 cents  classic augmented second
  4:   2 88/75               276.736 cents  
  4:   2 196/165             298.065 cents  
  4:   2 105/88              305.777 cents  
  4:   2 40/33               333.041 cents  
  5:   1 242/225             126.098 cents  
  5:   2 12/11               150.637 cents  undecimal neutral second, 3/4-tone
  5:   2 28/25               196.198 cents  middle second
  5:   2 55/49               199.980 cents  quasi-equal major second
  5:   2 33/28               284.447 cents  undecimal minor third
  5:   2 105/88              305.777 cents  
  5:   2 77/64               320.144 cents  Keemun minor third
  5:   2 128/105             342.905 cents  septimal neutral third
  5:   2 150/121             371.947 cents  
  5:   2 56/45               378.602 cents  septimal narrow major third
  5:   2 5/4                 386.314 cents  major third
  6:   2 11/10               165.004 cents  Ptolemy's second, 4/5-tone
  6:   4 8/7                 231.174 cents  septimal whole tone
  6:   1 121/100             330.008 cents  two (Ptolemy's second, 4/5-tone)
  6:   2 60/49               350.617 cents  smaller approximation to neutral third
  6:   2 49/40               351.338 cents  larger approximation to neutral third
  6:   4 5/4                 386.314 cents  major third
  6:   4 14/11               417.508 cents  undecimal diminished fourth or major third
  6:   2 4/3                 498.045 cents  perfect fourth
  7:   1 9/8                 203.910 cents  major whole tone
  7:   2 121/105             245.541 cents  
  7:   2 64/55               262.368 cents  
  7:   2 5/4                 386.314 cents  major third
  7:   2 44/35               396.178 cents  
  7:   2 14/11               417.508 cents  undecimal diminished fourth or major third
  7:   2 225/176             425.219 cents  
  7:   2 77/60               431.875 cents  
  7:   2 4/3                 498.045 cents  perfect fourth
  7:   2 75/56               505.757 cents  marvelous fourth
  7:   2 224/165             529.239 cents  
  8:   2 88/75               276.736 cents  
  8:   2 33/28               284.447 cents  undecimal minor third
  8:   2 14/11               417.508 cents  undecimal diminished fourth or major third
  8:   2 165/128             439.587 cents  
  8:   2 100/77              452.484 cents  
  8:   1 64/49               462.348 cents  2 septatones or septatonic major third
  8:   2 98/75               463.069 cents  
  8:   4 15/11               536.951 cents  undecimal augmented fourth
  8:   2 11/8                551.318 cents  undecimal semi-augmented fourth
  8:   2 64/45               609.776 cents  2nd tritone
  9:   2 6/5                 315.641 cents  minor third
  9:   1 121/98              364.984 cents  
  9:   2 77/60               431.875 cents  
  9:   2 21/16               470.781 cents  narrow fourth
  9:   2 160/121             483.678 cents  
  9:   2 4/3                 498.045 cents  perfect fourth
  9:   2 11/8                551.318 cents  undecimal semi-augmented fourth
  9:   2 7/5                 582.512 cents  septimal or Huygens' tritone, BP fourth
  9:   4 10/7                617.488 cents  Euler's tritone
  9:   2 16/11               648.682 cents  undecimal semi-diminished fifth
 10:   2 44/35               396.178 cents  
 10:   2 21/16               470.781 cents  narrow fourth
 10:   2 4/3                 498.045 cents  perfect fourth
 10:   2 75/56               505.757 cents  marvelous fourth
 10:   2 224/165             529.239 cents  
 10:   2 7/5                 582.512 cents  septimal or Huygens' tritone, BP fourth
 10:   2 16/11               648.682 cents  undecimal semi-diminished fifth
 10:   2 225/154             656.394 cents  
 10:   4 22/15               663.049 cents  undecimal diminished fifth
 10:   1 25/16               772.627 cents  classic augmented fifth
 11:   1 32/25               427.373 cents  classic diminished fourth
 11:   4 15/11               536.951 cents  undecimal augmented fourth
 11:   2 308/225             543.606 cents  
 11:   2 11/8                551.318 cents  undecimal semi-augmented fourth
 11:   2 10/7                617.488 cents  Euler's tritone
 11:   2 165/112             670.761 cents  
 11:   2 112/75              694.243 cents  marvelous fifth
 11:   2 3/2                 701.955 cents  perfect fifth
 11:   2 32/21               729.219 cents  wide fifth
 11:   2 35/22               803.822 cents  
 12:   2 11/8                551.318 cents  undecimal semi-augmented fourth
 12:   4 7/5                 582.512 cents  septimal or Huygens' tritone, BP fourth
 12:   2 10/7                617.488 cents  Euler's tritone
 12:   2 16/11               648.682 cents  undecimal semi-diminished fifth
 12:   2 3/2                 701.955 cents  perfect fifth
 12:   2 121/80              716.322 cents  
 12:   2 32/21               729.219 cents  wide fifth
 12:   2 120/77              768.125 cents  
 12:   1 196/121             835.016 cents  two (undecimal diminished fourth or major third)
 12:   2 5/3                 884.359 cents  major sixth, BP sixth
 13:   2 45/32               590.224 cents  diatonic tritone
 13:   2 16/11               648.682 cents  undecimal semi-diminished fifth
 13:   4 22/15               663.049 cents  undecimal diminished fifth
 13:   2 75/49               736.931 cents  BP fifth
 13:   1 49/32               737.652 cents  
 13:   2 77/50               747.516 cents  
 13:   2 256/165             760.413 cents  
 13:   2 11/7                782.492 cents  undecimal augmented fifth
 13:   2 56/33               915.553 cents  
 13:   2 75/44               923.264 cents  
 14:   2 165/112             670.761 cents  
 14:   2 112/75              694.243 cents  marvelous fifth
 14:   2 3/2                 701.955 cents  perfect fifth
 14:   2 120/77              768.125 cents  
 14:   2 352/225             774.781 cents  
 14:   2 11/7                782.492 cents  undecimal augmented fifth
 14:   2 35/22               803.822 cents  
 14:   2 8/5                 813.686 cents  minor sixth
 14:   2 55/32               937.632 cents  
 14:   2 210/121             954.459 cents  
 14:   1 16/9                996.090 cents  Pythagorean minor seventh
 15:   2 3/2                 701.955 cents  perfect fifth
 15:   4 11/7                782.492 cents  undecimal augmented fifth
 15:   4 8/5                 813.686 cents  minor sixth
 15:   2 80/49               848.662 cents  smaller approximation to neutral sixth
 15:   2 49/30               849.383 cents  larger approximation to neutral sixth
 15:   1 200/121             869.992 cents  
 15:   4 7/4                 968.826 cents  harmonic seventh
 15:   2 20/11               1034.996 cents large minor seventh
 16:   2 8/5                 813.686 cents  minor sixth
 16:   2 45/28               821.398 cents  septimale wide minor sixth
 16:   2 121/75              828.053 cents  
 16:   2 105/64              857.095 cents  septimal neutral sixth
 16:   2 128/77              879.856 cents  
 16:   2 176/105             894.223 cents  
 16:   2 56/33               915.553 cents  
 16:   2 98/55               1000.020 cents quasi-equal minor seventh
 16:   2 25/14               1003.802 cents middle minor seventh
 16:   2 11/6                1049.363 cents undecimal neutral seventh, 21/4-tone
 16:   1 225/121             1073.902 cents two (undecimal augmented fourth)
 17:   2 33/20               866.959 cents  
 17:   2 176/105             894.223 cents  
 17:   2 165/98              901.935 cents  
 17:   2 75/44               923.264 cents  
 17:   2 128/75              925.418 cents  diminished seventh
 17:   1 392/225             961.114 cents  
 17:   2 7/4                 968.826 cents  harmonic seventh
 17:   4 20/11               1034.996 cents large minor seventh
 17:   2 28/15               1080.557 cents grave major seventh
 17:   2 15/8                1088.269 cents classic major seventh
 18:   4 12/7                933.129 cents  septimal major sixth
 18:   2 121/70              947.496 cents  
 18:   2 7/4                 968.826 cents  harmonic seventh
 18:   2 20/11               1034.996 cents large minor seventh
 18:   2 11/6                1049.363 cents undecimal neutral seventh, 21/4-tone
 18:   2 224/121             1066.190 cents 
 18:   2 28/15               1080.557 cents grave major seventh
 18:   1 121/64              1102.636 cents two (undecimal semi-augmented fourth)
 18:   2 40/21               1115.533 cents acute major seventh
 18:   2 21/11               1119.463 cents undecimal major seventh
 19:   1 225/128             976.537 cents  augmented sixth
 19:   2 44/25               978.691 cents  undecimal grave minor seventh
 19:   2 88/49               1013.666 cents undecimal minor seventh
 19:   4 28/15               1080.557 cents grave major seventh
 19:   4 15/8                1088.269 cents classic major seventh
 19:   2 77/40               1133.830 cents 
 19:   4 64/33               1146.727 cents 33rd subharmonic
 19:   2 150/77              1154.439 cents 
 20:   2 64/35               1044.860 cents septimal neutral seventh
 20:   2 15/8                1088.269 cents classic major seventh
 20:   2 21/11               1119.463 cents undecimal major seventh
 20:   2 77/40               1133.830 cents 
 20:   2 150/77              1154.439 cents 
 20:   2 88/45               1161.094 cents 
 20:   1 49/25               1165.024 cents BP eighth
 20:   4 55/28               1168.806 cents 
 20:   2 240/121             1185.633 cents 
 20:   2 448/225             1192.288 cents 
Highest number of different intervals for one interval class: 11
Average number of different intervals per interval class: 9.80000 = 49/5
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    
 0.0   : 111.7 119.4 165.0 231.2 386.3 417.5 498.0 537.0 551.3 582.5 617.5 648.7 663.0 702.0 782.5  813.7  968.8  1035.0 1080.6
 1088.3 1200.0
 111.7 : 7.7   53.3  119.4 274.6 305.8 386.3 425.2 439.6 470.8 505.8 537.0 551.3 590.2 670.8 702.0  857.1  923.3  968.8  976.5 
 1088.3 1200.0
 119.4 : 45.6  111.7 266.9 298.1 378.6 417.5 431.9 463.1 498.0 529.2 543.6 582.5 663.0 694.2 849.4  915.6  961.1  968.8  1080.6
 1192.3 1200.0
 165.0 : 66.2  221.3 252.5 333.0 371.9 386.3 417.5 452.5 483.7 498.0 537.0 617.5 648.7 803.8 870.0  915.6  923.3  1035.0 1146.7
 1154.4 1200.0
 231.2 : 155.1 186.3 266.9 305.8 320.1 351.3 386.3 417.5 431.9 470.8 551.3 582.5 737.7 803.8 849.4  857.1  968.8  1080.6 1088.3
 1133.8 1200.0
 386.3 : 31.2  111.7 150.6 165.0 196.2 231.2 262.4 276.7 315.6 396.2 427.4 582.5 648.7 694.2 702.0  813.7  925.4  933.1  978.7 
 1044.9 1200.0
 417.5 : 80.5  119.4 133.8 165.0 200.0 231.2 245.5 284.4 365.0 396.2 551.3 617.5 663.0 670.8 782.5  894.2  901.9  947.5  1013.7
 1168.8 1200.0
 498.0 : 38.9  53.3  84.5  119.4 150.6 165.0 203.9 284.4 315.6 470.8 537.0 582.5 590.2 702.0 813.7  821.4  867.0  933.1  1088.3
 1119.5 1200.0
 537.0 : 14.4  45.6  80.5  111.7 126.1 165.0 245.5 276.7 431.9 498.0 543.6 551.3 663.0 774.8 782.5  828.1  894.2  1049.4 1080.6
 1161.1 1200.0
 551.3 : 31.2  66.2  97.4  111.7 150.6 231.2 262.4 417.5 483.7 529.2 537.0 648.7 760.4 768.1 813.7  879.9  1035.0 1066.2 1146.7
 1185.6 1200.0
 582.5 : 35.0  66.2  80.5  119.4 200.0 231.2 386.3 452.5 498.0 505.8 617.5 729.2 736.9 782.5 848.7  1003.8 1035.0 1115.5 1154.4
 1168.8 1200.0
 617.5 : 31.2  45.6  84.5  165.0 196.2 351.3 417.5 463.1 470.8 582.5 694.2 702.0 747.5 813.7 968.8  1000.0 1080.6 1119.5 1133.8
 1165.0 1200.0
 648.7 : 14.4  53.3  133.8 165.0 320.1 386.3 431.9 439.6 551.3 663.0 670.8 716.3 782.5 937.6 968.8  1049.4 1088.3 1102.6 1133.8
 1168.8 1200.0
 663.0 : 38.9  119.4 150.6 305.8 371.9 417.5 425.2 537.0 648.7 656.4 702.0 768.1 923.3 954.5 1035.0 1073.9 1088.3 1119.5 1154.4
 1185.6 1200.0
 702.0 : 80.5  111.7 266.9 333.0 378.6 386.3 498.0 609.8 617.5 663.0 729.2 884.4 915.6 996.1 1035.0 1049.4 1080.6 1115.5 1146.7
 1161.1 1200.0
 782.5 : 31.2  186.3 252.5 298.1 305.8 417.5 529.2 537.0 582.5 648.7 803.8 835.0 915.6 954.5 968.8  1000.0 1035.0 1066.2 1080.6
 1119.5 1200.0
 813.7 : 155.1 221.3 266.9 274.6 386.3 498.0 505.8 551.3 617.5 772.6 803.8 884.4 923.3 937.6 968.8  1003.8 1035.0 1049.4 1088.3
 1168.8 1200.0
 968.8 : 66.2  111.7 119.4 231.2 342.9 350.6 396.2 462.3 617.5 648.7 729.2 768.1 782.5 813.7 848.7  879.9  894.2  933.1  1013.7
 1044.9 1200.0
 1035.0: 45.6  53.3  165.0 276.7 284.4 330.0 396.2 551.3 582.5 663.0 702.0 716.3 747.5 782.5 813.7  828.1  867.0  947.5  978.7 
 1133.8 1200.0
 1080.6: 7.7   119.4 231.2 238.9 284.4 350.6 505.8 537.0 617.5 656.4 670.8 702.0 736.9 768.1 782.5  821.4  901.9  933.1  1088.3
 1154.4 1200.0
 1088.3: 111.7 223.5 231.2 276.7 342.9 498.0 529.2 609.8 648.7 663.0 694.2 729.2 760.4 774.8 813.7  894.2  925.4  1080.6 1146.7
 1192.3 1200.0
 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  7.7115    .. 155.1396 cents      49/45, 147.4281 cents              225/224, 7.7115 cents
  2:  45.5614   .. 223.4626 cents      256/231, 177.9012 cents            352/375,-109.5782 cents
  3:  80.5370   .. 266.8709 cents      49/44, 186.3339 cents              825/896,-142.9255 cents
  4:  111.7313  .. 333.0408 cents      25/22, 221.3095 cents              32/35,-155.1396 cents
  5:  126.0985  .. 386.3137 cents      1125/968, 260.2153 cents           1331/1500,-206.9423 cents
  6:  165.0042  .. 498.0450 cents      40/33, 333.0408 cents              22/25,-221.3095 cents
  7:  203.9100  .. 529.2392 cents      1792/1485, 325.3292 cents          27/32,-294.1350 cents
  8:  276.7355  .. 609.7763 cents      40/33, 333.0408 cents              121/140,-252.5037 cents
  9:  315.6413  .. 648.6821 cents      40/33, 333.0408 cents              27/32,-294.1350 cents
 10:  396.1783  .. 772.6274 cents      875/704, 376.4491 cents            121/140,-252.5037 cents
 11:  427.3726  .. 803.8217 cents      875/704, 376.4491 cents            512/625,-345.2549 cents
 12:  551.3179  .. 884.3587 cents      40/33, 333.0408 cents              121/140,-252.5037 cents
 13:  590.2237  .. 923.2645 cents      40/33, 333.0408 cents              27/32,-294.1350 cents
 14:  670.7608  .. 996.0900 cents      1792/1485, 325.3292 cents          121/140,-252.5037 cents
 15:  701.9550  .. 1034.9958 cents     40/33, 333.0408 cents              27/32,-294.1350 cents
 16:  813.6863  .. 1073.9015 cents     1125/968, 260.2153 cents           22/25,-221.3095 cents
 17:  866.9592  .. 1088.2687 cents     25/22, 221.3095 cents              1331/1500,-206.9423 cents
 18:  933.1291  .. 1119.4630 cents     49/44, 186.3339 cents              32/35,-155.1396 cents
 19:  976.5374  .. 1154.4386 cents     256/231, 177.9012 cents            825/896,-142.9255 cents
 20:  1044.8604 .. 1192.2885 cents     49/45, 147.4281 cents              352/375,-109.5782 cents
SHOW DATA
Number of notes                     : 21
-- Interval properties --
Smallest interval                   : 225/224, 7.7115 cents, class 1
Average step (divided formal octave): 57.1429 cents
Largest one step interval           : 35/32, 155.1396 cents
Average / Smallest step             : 7.410061
Largest / Average step              : 2.714943
Largest / Smallest step             : 20.117896
Median interval of one step         : 45/44, 38.9058 cents, amount: 2
Most common interval of one step    : 56/55, 31.1943 cents, amount: 4
Least squares average step          : 55.92017 cents, oct.:  1174.32364 cents
Scale is not proper
Step pattern alph. order: ABCDEFGHIFJFIHGFEDCBA
Step pattern size order : IAFGJCHEBCDCBEHCJGFAI
Scale is not a Constant Structure
Scale diversity                     : 1.497337
Lumma stability                     : 0.012853
Lumma impropriety factor            : 0.924064
Number of different interval sizes  : 130 = 6.50000 / class
Number of one step interval sizes   : 10
Highest interval variety            : 11
Mean interval variety               : 9.80000 = 49/5
Median interval variety             : 8
Lowest interval variety             : 8
Smallest interval difference        : 2401/2400, 0.7212 cents
Number of recognisable fifths       : 14, average 701.8042 cents
Number of appreciable fifths        : 12, average 699.3845 cents
Scale is a complete diamond         : 1 5 7 11 15
Length of longest harmonic part     : 1 at degree 0
Length of longest subharmonic part  : 1 at degree 0
Formal octave complements present   : 21 = 100.0000%
Scale is n-1 differentially coherent in interval classes 2 and 3 combined
Scale is n-1 differentially coherent in interval classes 3 and 4 combined
Inversional symmetry on degrees     :
 0
Inversional symmetry on intervals   :
 10-11
-- Rational properties --
Prime limit                         : 11
Odd number limit                    : 225 (O: 225 U: 225)
Highest odd numerator or denominator: 15
Scale harmonicity                   : 0.012185
Average absolute harmonicity        : 0.121481
Specific harmonicity                : 0.077228
Fundamental                         : 1/9240, -13.1737 octaves, 0.0283 Hz.
Guide tone                          : 18480,  14.1737 octaves, 4834840.447 Hz.
Exponens Consonantiae               : 1.707552E+08, 27.34735 octaves
Euler's gradus suavitatis           : 52
Sum of Mann's harmonic distance     : 211.0, average 10.04762
Mersenne's string divisions         : too high to compute
Sum of van Prooijen's expressibility: 19.03748, average 0.90655
Sum of Tenney's harmonic distance   : 38.43465, average 1.83022
Vogel's harmonic complexity         : 29.52381
Wille's k value                     : 8662
Wilson's harmonic complexity        : 52
Rectangular lattice diameter        : 8
Triangular lattice diameter         : 4
Lattice compactness                 : 733.09845, average 3.17359
Lattice compactness (without 2's)   : 405.04645, average 1.75345
Number of different primes          : 5
Prime exponents' range, average, count, tones@limit:
  2:  -3 .. 4         0.52381   37    1
  3:  -1 .. 1         0.00000   8     2
  5:  -1 .. 1         0.00000   12    4
  7:  -1 .. 1         0.00000   8     6
 11:  -1 .. 1         0.00000   8     8
Average exponent except 2's         : 0 / 21 = 0.00000
Average absolute exponent except 2's: 36 / 21 = 1.71429
Scale is weakly epimorphic with val: <21 30 52 56 76|
Scale is weakly epimorphic with val: <21 33 47 62 70|
Scale is weakly epimorphic with val: <21 36 47 59 70|
FIT/MODE
 21:  2 0 1 1 3 0 2 0 1 0 1 0 1 0 2 0 3 1 1 0 2   N      I SD: 13.3800 c. M:-22.6651 c. 
 22:  2 0 1 1 3 1 1 1 0 1 0 1 0 1 1 1 3 1 1 0 2   N      I SD: 10.3463 c. M:-18.8557 c. 
 29:  3 0 1 2 3 1 2 1 0 1 1 1 0 1 2 1 3 2 1 0 3   N      I SD: 9.0940 c. M:-17.1018 c. 
 31:  3 0 1 2 4 1 2 1 0 1 1 1 0 1 2 1 4 2 1 0 3   N      I SD: 5.7530 c. M: 10.1655 c. 
 43:  4 0 2 2 6 1 3 1 1 1 1 1 1 1 3 1 6 2 2 0 4   N      I SD: 5.0956 c. M:-7.9183 c. 
 52:  5 0 2 3 7 1 4 1 1 1 2 1 1 1 4 1 7 3 2 0 5   N      I SD: 4.8926 c. M:-9.6473 c. 
 58:  5 1 2 3 8 1 4 2 1 1 2 1 1 2 4 1 8 3 2 1 5   N      I SD: 4.6850 c. M:-8.2830 c. 
 63:  6 0 3 3 8 2 4 2 1 2 1 2 1 2 4 2 8 3 3 0 6   N      I SD: 4.3403 c. M:-7.9640 c. 
 68:  6 1 2 4 9 2 4 2 1 2 2 2 1 2 4 2 9 4 2 1 6   N      I SD: 4.6043 c. M:-7.5390 c. 
 72:  7 0 3 4 9 2 5 2 1 2 2 2 1 2 5 2 9 4 3 0 7   N      I SD: 2.5523 c. M: 4.9354 c. 
 87:  8 1 3 5 11 2 6 3 1 2 3 2 1 3 6 2 11 5 3 1 8   N      I SD: 2.4416 c. M:-4.6951 c. 
 109: 10 1 4 6 14 3 7 4 1 3 3 3 1 4 7 3 14 6 4 1 10   N      I SD: 1.4477 c. M:-2.6322 c. 
 130: 12 1 5 7 17 3 9 4 2 3 4 3 2 4 9 3 17 7 5 1 12   N      I SD: 1.3486 c. M:-2.5282 c. 
 152: 14 1 6 8 20 4 10 5 2 4 4 4 2 5 10 4 20 8 6 1 14   N      I SD: 1.1655 c. M: 2.2267 c. 
 161: 15 1 6 9 21 4 11 5 2 4 5 4 2 5 11 4 21 9 6 1 15   N      I SD: 0.7537 c. M:-1.3339 c. 
 239: 22 2 9 13 31 6 16 8 3 6 7 6 3 8 16 6 31 13 9 2 22   N      I SD: 0.7523 c. M: 1.2710 c. 
 270: 25 2 10 15 35 7 18 9 3 7 8 7 3 9 18 7 35 15 10 2 25   N      I SD: 0.4464 c. M:-0.8270 c. 
 342: 32 2 13 19 44 9 23 11 4 9 10 9 4 11 23 9 44 19 13 2 32   N      I SD: 0.2874 c. M:-0.5494 c. 
 451: 42 3 17 25 58 12 30 15 5 12 13 12 5 15 30 12 58 25 17 3 42   N      I SD: 0.3557 c. M: 0.5419 c. 
 472: 44 3 18 26 61 12 32 15 6 12 14 12 6 15 32 12 61 26 18 3 44   N      I SD: 0.3100 c. M:-0.5588 c. 
 494: 46 3 19 27 64 13 33 16 6 13 14 13 6 16 33 13 64 27 19 3 46   N      I SD: 0.2632 c. M:-0.4838 c. 
 581: 54 4 22 32 75 15 39 19 7 15 17 15 7 19 39 15 75 32 22 4 54   N      I SD: 0.2049 c. M:-0.3507 c. 
 612: 57 4 23 34 79 16 41 20 7 16 18 16 7 20 41 16 79 34 23 4 57   N      I SD: 0.1975 c. M: 0.3376 c. 
 742: 69 5 28 41 96 19 50 24 9 19 22 19 9 24 50 19 96 41 28 5 69   N      I SD: 0.1742 c. M:-0.3020 c. 
 764: 71 5 29 42 99 20 51 25 9 20 22 20 9 25 51 20 99 42 29 5 71   N      I SD: 0.1805 c. M:-0.2931 c. 
 836: 78 5 32 46 108 22 56 27 10 22 24 22 10 27 56 22 108 46 32 5 78   N      I SD: 0.1765 c. M: 0.3041 c. 
 923: 86 6 35 51 119 24 62 30 11 24 27 24 11 30 62 24 119 51 35 6 86   N      I SD: 0.1342 c. M:-0.2452 c. 
 1075: 100 7 41 59 139 28 72 35 13 28 31 28 13 35 72 28 139 59 41 7 100   N      I SD: 0.1214 c. M: 0.2051 c. 
 1084: 101 7 41 60 140 28 73 35 13 28 32 28 13 35 73 28 140 60 41 7 101   N      I SD: 0.1207 c. M:-0.2244 c. 
 1106: 103 7 42 61 143 29 74 36 13 29 32 29 13 36 74 29 143 61 42 7 103   N      I SD: 0.1081 c. M:-0.2136 c. 
 1236: 115 8 47 68 160 32 83 40 15 32 36 32 15 40 83 32 160 68 47 8 115   N      I SD: 0.0711 c. M:-0.1384 c. 
 1578: 147 10 60 87 204 41 106 51 19 41 46 41 19 51 106 41 204 87 60 10 147   N      I SD: 0.0366 c. M:-0.0686 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: 23.5575 cents
 4 .. 8  match: 4  H SD: 0.0000 cents
 5 .. 10  match: 5  H SD: 14.5566 cents
 6 .. 12  match: 6  H SD: 13.4115 cents
 7 .. 14  match: 7  H SD: 5.8232 cents
 8 .. 16  match: 8  H SD: 4.7824 cents
 9 .. 18  match: 8  S SD: 7.0461 cents
 10 .. 20  match: 8    SD: 5.8308 cents
 11 .. 22  match: 11  H SD: 7.8235 cents
 12 .. 24  match: 11    SD: 5.5111 cents
 13 .. 26  match: 11    SD: 6.2533 cents
 14 .. 28  match: 10    SD: 3.7798 cents
 15 .. 30  match: 12    SD: 3.9993 cents
 16 .. 32  match: 13  S SD: 3.8431 cents
 17 .. 34  match: 13    SD: 4.9655 cents
 18 .. 36  match: 14    SD: 4.4343 cents
 19 .. 38  match: 14    SD: 4.5049 cents
 20 .. 40  match: 15    SD: 3.5443 cents
 21 .. 42  match: 16    SD: 3.5586 cents
 22 .. 44  match: 14    SD: 3.6661 cents
 23 .. 46  match: 14    SD: 3.6795 cents
 24 .. 48  match: 14    SD: 3.4777 cents
 25 .. 50  match: 17    SD: 3.7134 cents
 26 .. 52  match: 15    SD: 3.1991 cents
 27 .. 54  match: 17    SD: 2.8739 cents
 28 .. 56  match: 18    SD: 1.9617 cents
 29 .. 58  match: 16    SD: 2.7940 cents
 30 .. 60  match: 16    SD: 1.8000 cents
 31 .. 62  match: 16    SD: 2.8898 cents
 32 .. 64  match: 17    SD: 2.0542 cents
 33 .. 66  match: 17    SD: 1.9559 cents
 34 .. 68  match: 18    SD: 2.7042 cents
 35 .. 70  match: 18    SD: 2.4346 cents
 36 .. 72  match: 20    SD: 2.4131 cents
 37 .. 74  match: 19    SD: 2.3276 cents
 38 .. 76  match: 17    SD: 2.1933 cents
 39 .. 78  match: 18    SD: 2.1683 cents
 40 .. 80  match: 18    SD: 1.2155 cents
 41 .. 82  match: 17    SD: 2.0323 cents
 42 .. 84  match: 19    SD: 1.5852 cents
 43 .. 86  match: 18    SD: 1.8107 cents
 44 .. 88  match: 20    SD: 1.6831 cents
 45 .. 90  match: 19    SD: 1.8386 cents
 46 .. 92  match: 17    SD: 2.2173 cents
 47 .. 94  match: 19    SD: 1.5866 cents
 48 .. 96  match: 18    SD: 1.3280 cents
 49 .. 98  match: 20    SD: 1.6549 cents
 50 .. 100  match: 20    SD: 1.6949 cents
 51 .. 102  match: 20    SD: 1.4968 cents
 52 .. 104  match: 20    SD: 1.6089 cents
 53 .. 106  match: 19    SD: 1.5865 cents
 54 .. 108  match: 17    SD: 1.6161 cents
 55 .. 110  match: 19    SD: 1.4373 cents
 56 .. 112  match: 19    SD: 1.2305 cents
 57 .. 114  match: 19    SD: 1.4303 cents
 58 .. 116  match: 20    SD: 1.2416 cents
 59 .. 118  match: 20    SD: 1.4017 cents
 60 .. 120  match: 20    SD: 1.0724 cents
 61 .. 122  match: 18    SD: 1.2422 cents
 62 .. 124  match: 18    SD: 1.2635 cents
 63 .. 126  match: 19    SD: 1.2617 cents
 65 .. 130  match: 19    SD: 1.3613 cents
 66 .. 132  match: 21    SD: 1.2637 cents
 68 .. 136  match: 20    SD: 1.0472 cents
 69 .. 138  match: 19    SD: 1.1019 cents
 70 .. 140  match: 19    SD: 0.9745 cents
 71 .. 142  match: 19    SD: 1.1440 cents
 72 .. 144  match: 20    SD: 0.7836 cents
 73 .. 146  match: 19    SD: 1.0586 cents
 74 .. 148  match: 20    SD: 1.2283 cents
 75 .. 150  match: 20    SD: 0.9775 cents
 76 .. 152  match: 19    SD: 1.1709 cents
 77 .. 154  match: 20    SD: 0.8754 cents
 78 .. 156  match: 20    SD: 1.1291 cents
 79 .. 158  match: 21    SD: 1.0438 cents
 80 .. 160  match: 21    SD: 0.8495 cents
 83 .. 166  match: 20    SD: 0.9017 cents
 84 .. 168  match: 20    SD: 0.8393 cents
 85 .. 170  match: 19    SD: 0.9970 cents
 86 .. 172  match: 19    SD: 1.0321 cents
 87 .. 174  match: 20    SD: 0.9715 cents
 88 .. 176  match: 20    SD: 0.6087 cents
 89 .. 178  match: 20    SD: 0.9127 cents
 90 .. 180  match: 20    SD: 0.7943 cents
 93 .. 186  match: 20    SD: 0.8162 cents
 96 .. 192  match: 21    SD: 0.7160 cents
 98 .. 196  match: 20    SD: 0.7290 cents
 99 .. 198  match: 20    SD: 0.6695 cents
 100 .. 200  match: 20    SD: 0.7100 cents
 101 .. 202  match: 19    SD: 0.8596 cents
 102 .. 204  match: 20    SD: 0.7958 cents
 103 .. 206  match: 20    SD: 0.7014 cents
 104 .. 208  match: 20    SD: 0.7286 cents
 105 .. 210  match: 21    SD: 0.7064 cents
 107 .. 214  match: 21    SD: 0.6766 cents
 110 .. 220  match: 21    SD: 0.5968 cents
 112 .. 224  match: 21    SD: 0.5553 cents
 113 .. 226  match: 20    SD: 0.6818 cents
 114 .. 228  match: 20    SD: 0.7008 cents
 115 .. 230  match: 20    SD: 0.7385 cents
 116 .. 232  match: 20    SD: 0.7552 cents
 117 .. 234  match: 20    SD: 0.6277 cents
 118 .. 236  match: 20    SD: 0.6525 cents
 120 .. 240  match: 21    SD: 0.5158 cents
 128 .. 256  match: 20    SD: 0.4375 cents
 129 .. 258  match: 20    SD: 0.6137 cents
 130 .. 260  match: 20    SD: 0.6436 cents
 131 .. 262  match: 20    SD: 0.6171 cents
 132 .. 264  match: 20    SD: 0.5110 cents
 140 .. 280  match: 21    SD: 0.4548 cents
 143 .. 286  match: 20    SD: 0.5105 cents
 144 .. 288  match: 20    SD: 0.5431 cents
 145 .. 290  match: 20    SD: 0.5944 cents
 146 .. 292  match: 20    SD: 0.6199 cents
 147 .. 294  match: 21    SD: 0.5191 cents
 148 .. 296  match: 21    SD: 0.5134 cents
 150 .. 300  match: 21    SD: 0.4699 cents
 152 .. 304  match: 21    SD: 0.3757 cents
 158 .. 316  match: 20    SD: 0.5188 cents
 159 .. 318  match: 20    SD: 0.4751 cents
 160 .. 320  match: 20    SD: 0.4050 cents
 168 .. 336  match: 21    SD: 0.3004 cents
 173 .. 346  match: 20    SD: 0.4387 cents
 174 .. 348  match: 20    SD: 0.5290 cents
 175 .. 350  match: 21    SD: 0.5032 cents
 176 .. 352  match: 21    SD: 0.4219 cents
 180 .. 360  match: 21    SD: 0.3093 cents
 188 .. 376  match: 20    SD: 0.4450 cents
 189 .. 378  match: 21    SD: 0.4298 cents
 191 .. 382  match: 21    SD: 0.4194 cents
 192 .. 384  match: 21    SD: 0.3453 cents
 198 .. 396  match: 21    SD: 0.3266 cents
 208 .. 416  match: 21    SD: 0.2782 cents
 238 .. 476  match: 21    SD: 0.2719 cents
 240 .. 480  match: 21    SD: 0.1914 cents
 280 .. 560  match: 21    SD: 0.1817 cents
 352 .. 704  match: 21    SD: 0.1582 cents
 360 .. 720  match: 21    SD: 0.1510 cents
 392 .. 784  match: 21    SD: 0.1197 cents
 448 .. 896  match: 21    SD: 0.1040 cents
 560 .. 1120  match: 21    SD: 0.1007 cents
 572 .. 1144  match: 21    SD: 0.0990 cents
 600 .. 1200  match: 21    SD: 0.0667 cents