Scala analysis: geo

George Secor style circulating temperament

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

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:      55881/52796          98.315049
  2:          9/8             203.910002 major whole tone
  3:      15660/13199         295.986699
  4:     332913/263980        401.659893
  5:      35235/26398         499.896700
  6:      18660/13199         599.424427
  7:          3/2             701.955001 perfect fifth
  8:      83673/52796         797.200238
  9:      88935/52796         902.787201
 10:      23490/13199         997.941700
 11:        372/197          1100.528390
 12:          2/1            1200.000000 octave
SHOW/INTERVAL
  0:        197/186            99.4716 
  1:      55881/52796          98.3150 
  2:      13199/12418         105.5950 
  3:      13920/13199          92.0767 
  4:     110971/104400        105.6732 
  5:     117450/110971         98.2368 
  6:       2488/2349           99.5277 
  7:      13199/12440         102.5306 
  8:      27891/26398          95.2452 
  9:      29645/27891         105.5870 
 10:       6264/5929           95.1545 
 11:       4154/3915          102.5867 
 12:        197/186            99.4716 
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   1 13920/13199         92.077 cents   
  1:   1 6264/5929           95.154 cents   
  1:   1 27891/26398         95.245 cents   
  1:   1 117450/110971       98.237 cents   
  1:   1 55881/52796         98.315 cents   
  1:   1 197/186             99.472 cents   
  1:   1 2488/2349           99.528 cents   
  1:   1 13199/12440         102.531 cents  
  1:   1 4154/3915           102.587 cents  
  1:   1 29645/27891         105.587 cents  
  1:   1 13199/12418         105.595 cents  
  1:   1 110971/104400       105.673 cents  
  2:   1 6960/6209           197.672 cents  
  2:   1 33232/29645         197.741 cents  
  2:   1 221942/197985       197.750 cents  
  2:   1 124400/110971       197.765 cents  
  2:   1 27891/24880         197.776 cents  
  2:   1 18627/16616         197.787 cents  
  2:   1 1160/1033           200.741 cents  
  2:   1 29645/26398         200.832 cents  
  2:   2 13199/11745         202.058 cents  
  2:   2 9/8                 203.910 cents  major whole tone
  3:   3 15660/13199         295.987 cents  
  3:   1 105592/88935        297.213 cents  
  3:   1 1033/870            297.304 cents  
  3:   1 131990/110971       300.295 cents  
  3:   1 6209/5220           300.373 cents  
  3:   1 33232/27891         303.328 cents  
  3:   1 15853/13305         303.345 cents  
  3:   1 5929/4976           303.363 cents  
  3:   1 591/496             303.382 cents  
  3:   1 311/261             303.438 cents  
  4:   1 2610/2077           395.458 cents  
  4:   1 49760/39597         395.514 cents  
  4:   1 5322/4235           395.528 cents  
  4:   1 139455/110971       395.540 cents  
  4:   1 783/622             398.517 cents  
  4:   1 248/197             398.573 cents  
  4:   1 7830/6209           401.582 cents  
  4:   1 332913/263980       401.660 cents  
  4:   1 105592/83673        402.800 cents  
  4:   1 5929/4698           402.891 cents  
  4:   2 13199/10440         405.968 cents  
  5:   4 4/3                 498.045 cents  perfect fourth
  5:   1 35235/26398         499.897 cents  
  5:   1 2077/1555           501.104 cents  
  5:   1 24880/18627         501.109 cents  
  5:   1 12418/9297          501.115 cents  
  5:   1 39597/29645         501.123 cents  
  5:   1 21175/15853         501.127 cents  
  5:   1 110971/83080        501.132 cents  
  5:   1 3099/2320           501.214 cents  
  6:   1 8352/5929           593.199 cents  
  6:   1 18594/13199         593.290 cents  
  6:   1 156600/110971       596.282 cents  
  6:   1 18627/13199         596.360 cents  
  6:   1 11745/8308          599.368 cents  
  6:   1 18660/13199         599.424 cents  
  6:   1 13199/9330          600.576 cents  
  6:   1 16616/11745         600.632 cents  
  6:   1 26398/18627         603.640 cents  
  6:   1 110971/78300        603.718 cents  
  6:   1 13199/9297          606.710 cents  
  6:   1 5929/4176           606.801 cents  
  7:   1 4640/3099           698.786 cents  
  7:   1 166160/110971       698.868 cents  
  7:   1 31706/21175         698.873 cents  
  7:   1 59290/39597         698.877 cents  
  7:   1 9297/6209           698.885 cents  
  7:   1 18627/12440         698.891 cents  
  7:   1 3110/2077           698.896 cents  
  7:   1 52796/35235         700.103 cents  
  7:   4 3/2                 701.955 cents  perfect fifth
  8:   2 20880/13199         794.032 cents  
  8:   1 9396/5929           797.109 cents  
  8:   1 83673/52796         797.200 cents  
  8:   1 527960/332913       798.340 cents  
  8:   1 6209/3915           798.418 cents  
  8:   1 197/124             801.427 cents  
  8:   1 1244/783            801.483 cents  
  8:   1 221942/139455       804.460 cents  
  8:   1 4235/2661           804.472 cents  
  8:   1 39597/24880         804.486 cents  
  8:   1 2077/1305           804.542 cents  
  9:   1 522/311             896.562 cents  
  9:   1 992/591             896.618 cents  
  9:   1 9952/5929           896.637 cents  
  9:   1 26610/15853         896.655 cents  
  9:   1 27891/16616         896.672 cents  
  9:   1 10440/6209          899.627 cents  
  9:   1 110971/65995        899.705 cents  
  9:   1 1740/1033           902.696 cents  
  9:   1 88935/52796         902.787 cents  
  9:   3 13199/7830          904.013 cents  
 10:   2 16/9                996.090 cents  Pythagorean minor seventh
 10:   2 23490/13199         997.942 cents  
 10:   1 52796/29645         999.168 cents  
 10:   1 1033/580            999.259 cents  
 10:   1 33232/18627         1002.213 cents 
 10:   1 49760/27891         1002.224 cents 
 10:   1 110971/62200        1002.235 cents 
 10:   1 197985/110971       1002.250 cents 
 10:   1 29645/16616         1002.259 cents 
 10:   1 6209/3480           1002.328 cents 
 11:   1 208800/110971       1094.327 cents 
 11:   1 24836/13199         1094.405 cents 
 11:   1 55782/29645         1094.413 cents 
 11:   1 3915/2077           1097.413 cents 
 11:   1 24880/13199         1097.469 cents 
 11:   1 2349/1244           1100.472 cents 
 11:   1 372/197             1100.528 cents 
 11:   1 105592/55881        1101.685 cents 
 11:   1 110971/58725        1101.763 cents 
 11:   1 52796/27891         1104.755 cents 
 11:   1 5929/3132           1104.846 cents 
 11:   1 13199/6960          1107.923 cents 
Highest number of different intervals for one interval class: 12
Average number of different intervals per interval class: 10.54545 = 116/11
SHOW/LINE/CENTS INTERVALS
         1     2     3     4     5     6     7     8     9     10     11     12    
 0.0   : 98.3  203.9 296.0 401.7 499.9 599.4 702.0 797.2 902.8 997.9  1100.5 1200.0
 98.3  : 105.6 197.7 303.3 401.6 501.1 603.6 698.9 804.5 899.6 1002.2 1101.7 1200.0
 203.9 : 92.1  197.7 296.0 395.5 498.0 593.3 698.9 794.0 896.6 996.1  1094.4 1200.0
 296.0 : 105.7 203.9 303.4 406.0 501.2 606.8 702.0 804.5 904.0 1002.3 1107.9 1200.0
 401.7 : 98.2  197.8 300.3 395.5 501.1 596.3 698.9 798.3 896.7 1002.3 1094.3 1200.0
 499.9 : 99.5  202.1 297.3 402.9 498.0 600.6 700.1 798.4 904.0 996.1  1101.8 1200.0
 599.4 : 102.5 197.8 303.4 398.5 501.1 600.6 698.9 804.5 896.6 1002.2 1100.5 1200.0
 702.0 : 95.2  200.8 296.0 398.6 498.0 596.4 702.0 794.0 899.7 997.9  1097.5 1200.0
 797.2 : 105.6 200.7 303.3 402.8 501.1 606.7 698.8 804.5 902.7 1002.2 1104.8 1200.0
 902.8 : 95.2  197.7 297.2 395.5 501.1 593.2 698.9 797.1 896.6 999.2  1094.4 1200.0
 997.9 : 102.6 202.1 300.4 406.0 498.0 603.7 702.0 801.5 904.0 999.3  1104.8 1200.0
 1100.5: 99.5  197.8 303.4 395.5 501.1 599.4 698.9 801.4 896.7 1002.3 1097.4 1200.0
 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  92.0767   .. 105.6732 cents      1464706229/1453248000, 13.5965 cen 13920/13199, 92.0767 cents
  2:  197.6716  .. 203.9100 cents      18627/18560, 6.2384 cents          726624000/689018939, 91.9985 cents
  3:  295.9867  .. 303.4377 cents      4104889/4087260, 7.4510 cents      13920/13199, 92.0767 cents
  4:  395.4583  .. 405.9683 cents      27414323/27248400, 10.5100 cents   681210/645947, 92.0206 cents
  5:  498.0450  .. 501.2135 cents      9297/9280, 3.1685 cents            13920/13199, 92.0767 cents
  6:  593.1995  .. 606.8005 cents      35153041/34877952, 13.6010 cents   6458880/6124657, 91.9860 cents
  7:  698.7865  .. 701.9550 cents      9297/9280, 3.1685 cents            6458880/6124657, 91.9860 cents
  8:  794.0317  .. 804.5417 cents      27414323/27248400, 10.5100 cents   13920/13199, 92.0767 cents
  9:  896.5623  .. 904.0133 cents      4104889/4087260, 7.4510 cents      681210/645947, 92.0206 cents
 10:  996.0900  .. 1002.3284 cents     18627/18560, 6.2384 cents          13920/13199, 92.0767 cents
 11:  1094.3268 .. 1107.9233 cents     1464706229/1453248000, 13.5965 cen 726624000/689018939, 91.9985 cents
SHOW DATA
Number of notes                     : 12
-- Interval properties --
Smallest interval                   : 13920/13199, 92.0767 cents, class 1
Average step (divided formal octave): 100.0000 cents
Largest one step interval           : 110971/104400, 105.6732 cents
Average / Smallest step             : 1.086051
Largest / Average step              : 1.056732
Largest / Smallest step             : 1.147665
Median interval of one step         : 99.49967 cents, amount: 0
Least squares average step          : 99.99749 cents, oct.:  1199.96983 cents
Scale is strictly proper
Step pattern alph. order: ABCDEFGHIJKL
Step pattern size order : EKALDGHCJBIF
Scale is a Constant Structure, by a margin of 91.98596 cents
Scale diversity                     : 1.065795
Rothenberg stability                : 1.000000 = 1
Lumma stability                     : 0.920392
Rothenberg efficiency               : 0.187205   redundancy: 0.812795
Efficiency x scale size             : 2.246465
Number of different interval sizes  : 116 = 10.54545 / class
Number of one step interval sizes   : 12
Highest interval variety            : 12
Mean interval variety               : 10.54545 = 116/11
Median interval variety             : 9
Lowest interval variety             : 9
Smallest interval difference        : 251317609/251317000, 0.0042 cents
Most common intervals               : 4/3, 498.0450 cents & inv., amount: 4
Most common triad is 0.0 498.045 701.955 cents, amount: 2
Number of recognisable fifths       : 12, average 700.0000 cents
Scale is a well-temperament. It has 9 different sizes of fifth
Best fifths form a closed circle
Formal octave complements present   : 1 = 8.3333%
Limited transpositions with margin 7.4510 cents:
 1 2 3 4 5 6 7 8 9 10 11
Limited inverse transpositions      :
 5
Inversional symmetry on intervals   :
 2-3 8-9
-- Rational properties --
Prime limit                         : 1033
Odd number limit                    : 332913 (O: 332913 U: 332913)
Highest odd numerator or denominator: 332913
Scale harmonicity                   : 0.007035
Fundamental                         : 1/527960, -19.0101 octaves, 0.0005 Hz.
Guide tone                          : too high to compute
Exponens Consonantiae               : 6.178374E+28, 95.64121 octaves
Euler's gradus suavitatis           : 2876
Sum of Mann's harmonic distance     : 571702.0, average 47641.83333
Mersenne's string divisions         : too high to compute
Sum of van Prooijen's expressibility: 40.77568, average 3.39797
Sum of Tenney's harmonic distance   : 81.69890, average 6.80824
Vogel's harmonic complexity         : 309.83333
Wille's k value                     : 296977
Wilson's harmonic complexity        : 2890
Rectangular lattice diameter        : 20
Triangular lattice diameter         : 7
Lattice compactness                 : 277.59920, average 3.55896
Lattice compactness (without 2's)   : 194.97874, average 2.49973
Number of different primes          : 14
Prime exponents' range, average, count, tones@limit:
  2:  -3 .. 2        -0.41667   21    1
  3:   0 .. 5         2.08333   25    2
  5:  -1 .. 1         0.33333   6
  7:   0 .. 2         0.33333   4
 11:   0 .. 2         0.16667   2
 29:   0 .. 1         0.25000   3
 31:   0 .. 1         0.08333   1
 67:  -1 .. 0        -0.66667   8
 83:   0 .. 1         0.08333   1
 191:  0 .. 1         0.08333   1
 197: -1 .. 0        -0.75000   9     6
 311:  0 .. 1         0.08333   1     1
 887:  0 .. 1         0.08333   1     1
 1033:  0 .. 1        0.08333   1     1
Average exponent except 2's         : 27 / 12 = 2.25000
Average absolute exponent except 2's: 63 / 12 = 5.25000
Scale is JI-epimorphic with val: <12 19 27 33 42 58 59 72 76 90 91 99 117 119|
Scale is weakly epimorphic with val: <12 19 27 33 42 59 59 73 76 91 91 100 118 121|
Scale is weakly epimorphic with val: <12 19 27 33 42 59 59 73 77 90 91 100 118 121|
Scale is weakly epimorphic with val: <12 19 27 33 42 59 59 73 78 91 91 98 118 121|
Scale is weakly epimorphic with val: <12 19 27 33 42 59 60 72 76 91 92 100 118 121|
Scale is weakly epimorphic with val: <12 19 27 33 42 59 60 72 77 90 92 100 118 121|
Scale is weakly epimorphic with val: <12 19 27 33 42 59 60 72 77 92 92 98 118 121|
Scale is weakly epimorphic with val: <12 19 27 33 42 59 60 72 78 91 92 98 118 121|
Scale is weakly epimorphic with val: <12 19 27 33 43 57 58 74 76 92 92 100 117 119|
Scale is weakly epimorphic with val: <12 19 27 33 43 57 58 74 77 91 92 100 117 119|
Scale is weakly epimorphic with val: <12 19 27 33 43 57 58 74 77 92 92 99 117 119|
Scale is weakly epimorphic with val: <12 19 27 33 43 57 58 74 78 90 92 100 117 119|
Scale is weakly epimorphic with val: <12 19 27 33 43 57 58 74 78 91 92 99 117 119|
Scale is weakly epimorphic with val: <12 19 27 33 43 58 58 74 77 91 91 100 117 119|
Scale is weakly epimorphic with val: <12 19 27 33 43 58 58 74 78 90 91 100 117 119|
Scale is weakly epimorphic with val: <12 19 27 33 43 58 58 74 78 91 91 99 117 119|
Scale is weakly epimorphic with val: <12 19 27 33 43 58 59 73 76 92 92 100 117 119|
Scale is weakly epimorphic with val: <12 19 27 33 43 58 59 73 77 91 92 100 117 119|
Scale is weakly epimorphic with val: <12 19 27 33 43 58 59 73 77 92 92 99 117 119|
Scale is weakly epimorphic with val: <12 19 27 33 43 58 59 73 78 90 92 100 117 119|
Scale is weakly epimorphic with val: <12 19 27 33 43 58 59 73 78 91 92 99 117 119|
Scale is weakly epimorphic with val: <12 19 27 34 41 59 59 73 76 90 91 100 117 121|
Scale is weakly epimorphic with val: <12 19 27 34 41 59 59 73 77 91 91 98 117 121|
Scale is weakly epimorphic with val: <12 19 27 34 41 59 59 73 78 90 91 98 117 121|
Scale is weakly epimorphic with val: <12 19 27 34 41 59 60 72 76 90 92 100 117 121|
Scale is weakly epimorphic with val: <12 19 27 34 41 59 60 72 76 92 92 98 117 121|
Scale is weakly epimorphic with val: <12 19 27 34 41 59 60 72 77 91 92 98 117 121|
Scale is weakly epimorphic with val: <12 19 27 34 41 59 60 72 78 90 92 98 117 121|
Scale is weakly epimorphic with val: <12 19 27 34 43 58 59 72 78 91 91 99 119 120|
Scale is weakly epimorphic with val: <12 19 27 35 41 57 59 73 76 90 91 100 119 121|
Scale is weakly epimorphic with val: <12 19 27 35 41 57 59 73 76 91 91 99 119 121|
Scale is weakly epimorphic with val: <12 19 27 35 41 57 59 73 77 90 91 99 119 121|
Scale is weakly epimorphic with val: <12 19 27 35 41 57 60 72 76 90 92 100 119 121|
Scale is weakly epimorphic with val: <12 19 27 35 41 57 60 72 76 91 92 99 119 121|
Scale is weakly epimorphic with val: <12 19 27 35 41 57 60 72 77 90 92 99 119 121|
Scale is weakly epimorphic with val: <12 19 27 35 42 58 59 72 77 91 91 99 118 120|
Scale is weakly epimorphic with val: <12 19 27 35 42 58 59 72 78 90 91 99 118 120|
Scale is weakly epimorphic with val: <12 19 27 35 42 58 59 72 78 91 91 99 118 119|
Scale is weakly epimorphic with val: <12 19 28 33 41 57 59 72 76 91 91 98 117 120|
Scale is weakly epimorphic with val: <12 19 28 33 41 57 59 72 77 90 91 98 117 120|
Scale is JI-epimorphic with val: <12 19 28 33 42 58 59 73 77 91 91 99 118 120|
Scale is JI-epimorphic with val: <12 19 28 33 42 58 59 73 78 90 91 99 118 120|
Scale is JI-epimorphic with val: <12 19 28 33 42 58 60 72 76 92 92 99 118 120|
Scale is JI-epimorphic with val: <12 19 28 33 42 58 60 72 77 91 92 99 118 120|
Scale is JI-epimorphic with val: <12 19 28 33 42 58 60 72 78 90 92 99 118 120|
Scale is weakly epimorphic with val: <12 19 28 33 42 59 59 72 76 91 92 98 118 120|
Scale is weakly epimorphic with val: <12 19 28 33 42 59 59 72 77 90 92 98 118 120|
Scale is weakly epimorphic with val: <12 19 28 33 43 57 58 73 77 92 92 99 117 119|
Scale is weakly epimorphic with val: <12 19 28 33 43 57 58 73 78 91 92 99 117 119|
Scale is weakly epimorphic with val: <12 19 28 33 43 57 58 73 78 92 92 98 117 119|
Scale is weakly epimorphic with val: <12 19 28 33 43 58 58 72 76 92 92 99 118 120|
Scale is weakly epimorphic with val: <12 19 28 33 43 58 58 72 77 91 92 99 118 120|
Scale is weakly epimorphic with val: <12 19 28 33 43 58 58 72 78 90 92 99 118 120|
Scale is weakly epimorphic with val: <12 19 28 33 43 58 59 74 78 92 92 100 118 120|
Scale is weakly epimorphic with val: <12 19 28 33 43 58 60 74 78 92 92 100 117 120|
Scale is JI-epimorphic with val: <12 19 28 34 41 58 59 73 76 91 91 99 117 120|
Scale is JI-epimorphic with val: <12 19 28 34 41 58 59 73 77 90 91 99 117 120|
Scale is JI-epimorphic with val: <12 19 28 34 41 58 60 72 76 91 92 99 117 120|
Scale is JI-epimorphic with val: <12 19 28 34 41 58 60 72 77 90 92 99 117 120|
Scale is weakly epimorphic with val: <12 19 28 34 41 59 59 72 76 90 92 98 117 120|
Scale is weakly epimorphic with val: <12 19 28 34 42 58 58 72 76 91 92 99 117 120|
Scale is weakly epimorphic with val: <12 19 28 34 42 58 58 72 77 90 92 99 117 120|
Scale is weakly epimorphic with val: <12 19 28 34 42 58 59 74 77 92 92 100 117 120|
Scale is weakly epimorphic with val: <12 19 28 34 42 58 59 74 78 91 92 100 117 120|
Scale is weakly epimorphic with val: <12 19 28 34 42 58 59 74 78 92 92 99 117 120|
Scale is weakly epimorphic with val: <12 19 28 35 42 58 60 72 78 92 92 99 119 121|
Scale is weakly epimorphic with val: <12 19 28 35 42 59 59 72 78 92 92 98 118 121|
Scale is weakly epimorphic with val: <12 19 29 33 41 57 58 74 76 90 92 98 117 119|
Scale is weakly epimorphic with val: <12 19 29 33 41 57 59 73 78 91 91 98 118 121|
Scale is weakly epimorphic with val: <12 19 29 33 41 57 60 72 77 92 92 98 118 121|
Scale is weakly epimorphic with val: <12 19 29 33 41 57 60 72 78 91 92 98 118 121|
Scale is JI-epimorphic with val: <12 19 29 33 42 58 60 73 78 92 92 99 119 121|
Scale is weakly epimorphic with val: <12 19 29 33 42 59 59 73 77 92 92 98 119 121|
Scale is weakly epimorphic with val: <12 19 29 33 42 59 59 73 78 91 92 98 119 121|
Scale is weakly epimorphic with val: <12 19 29 33 43 57 58 72 78 91 91 99 119 120|
Scale is weakly epimorphic with val: <12 19 29 33 43 57 58 72 78 91 91 100 119 119|
Scale is weakly epimorphic with val: <12 19 29 33 43 58 58 73 78 92 92 99 119 121|
Scale is JI-epimorphic with val: <12 19 29 34 41 58 59 74 78 91 91 99 118 121|
Scale is JI-epimorphic with val: <12 19 29 34 41 58 60 73 77 92 92 99 118 121|
Scale is JI-epimorphic with val: <12 19 29 34 41 58 60 73 78 91 92 99 118 121|
Scale is weakly epimorphic with val: <12 19 29 34 41 59 59 73 76 92 92 98 118 121|
Scale is weakly epimorphic with val: <12 19 29 34 41 59 59 73 77 91 92 98 118 121|
Scale is weakly epimorphic with val: <12 19 29 34 41 59 59 73 78 90 92 98 118 121|
Scale is weakly epimorphic with val: <12 19 29 34 42 57 58 72 77 91 91 99 118 120|
Scale is weakly epimorphic with val: <12 19 29 34 42 57 58 72 77 91 91 100 118 119|
Scale is weakly epimorphic with val: <12 19 29 34 42 57 58 72 78 90 91 99 118 120|
Scale is weakly epimorphic with val: <12 19 29 34 42 57 58 72 78 90 91 100 118 119|
Scale is weakly epimorphic with val: <12 19 29 34 42 57 58 74 78 92 92 99 117 120|
Scale is weakly epimorphic with val: <12 19 29 34 42 57 58 74 78 92 92 100 117 119|
Scale is weakly epimorphic with val: <12 19 29 34 42 58 58 73 77 92 92 99 118 121|
Scale is weakly epimorphic with val: <12 19 29 34 42 58 58 73 78 91 92 99 118 121|
Scale is weakly epimorphic with val: <12 19 29 34 43 59 59 72 77 91 91 100 119 121|
Scale is weakly epimorphic with val: <12 19 29 34 43 59 59 72 78 90 91 100 119 121|
Scale is weakly epimorphic with val: <12 19 29 35 41 57 58 72 76 91 91 99 117 120|
Scale is weakly epimorphic with val: <12 19 29 35 41 57 58 72 76 91 91 100 117 119|
Scale is weakly epimorphic with val: <12 19 29 35 41 57 58 72 77 90 91 99 117 120|
Scale is weakly epimorphic with val: <12 19 29 35 41 57 58 72 77 90 91 100 117 119|
Scale is weakly epimorphic with val: <12 19 29 35 41 58 58 73 76 92 92 99 117 121|
Scale is weakly epimorphic with val: <12 19 29 35 41 58 58 73 77 91 92 99 117 121|
Scale is weakly epimorphic with val: <12 19 29 35 41 58 58 73 78 90 92 99 117 121|
Scale is weakly epimorphic with val: <12 19 29 35 42 59 59 72 76 90 91 100 119 121|
Scale is weakly epimorphic with val: <12 19 29 35 42 59 59 72 76 91 91 100 118 121|
Scale is weakly epimorphic with val: <12 19 29 35 42 59 59 72 77 90 91 100 118 121|
Scale is weakly epimorphic with val: <12 19 29 35 43 59 59 72 76 90 91 100 117 121|
FIT/MODE
 12:  1 1 1 1 1 1 1 1 1 1 1 1  SP B ME I SD: 2.2597 c. M:-4.0133 c.  Twelve-tone Chromatic (1/11-comma)
 113: 9 10 9 10 9 9 10 9 10 9 10 9  SP M ME   SD: 2.1883 c. M: 4.7342 c. 
 122: 10 11 9 11 10 10 10 10 11 9 11 10  SP   D3 I SD: 2.1012 c. M: 4.4991 c. 
 125: 10 11 10 11 10 10 11 10 11 10 11 10  SP M ME   SD: 1.9981 c. M: 4.2244 c. 
 134: 11 12 10 12 11 11 11 11 12 10 12 11  SP   D3 I SD: 1.8289 c. M: 3.9118 c. 
 137: 11 12 11 12 11 11 12 11 12 11 12 11  SP M ME   SD: 1.8621 c. M: 3.8040 c. 
 143: 12 12 11 13 12 11 13 11 13 11 12 12  SP        SD: 2.3705 c. M: 3.6202 c. 
 146: 12 13 11 13 12 12 12 12 13 11 13 12  SP   D3 I SD: 1.6191 c. M: 3.4212 c. 
 155: 13 13 12 14 13 12 14 12 14 12 13 13  SP        SD: 2.1600 c. M:-3.3291 c. 
 158: 13 14 12 14 13 13 13 13 14 12 14 13  SP   D3 I SD: 1.4594 c. M: 3.2208 c. 
 159: 13 14 12 14 13 13 14 13 14 12 14 13  SP        SD: 1.8217 c. M: 3.1980 c. 
 161: 13 14 13 14 13 13 14 13 14 13 14 13  SP M ME   SD: 1.6999 c. M: 3.1511 c. 
 166: 14 14 13 15 13 14 14 13 15 13 14 14  SP   D3 I SD: 1.6005 c. M:-3.1594 c. 
 167: 14 14 13 15 14 13 15 13 15 13 14 14  SP        SD: 1.9927 c. M:-3.0973 c. 
 170: 14 15 13 15 14 14 14 14 15 13 15 14  SP   D3 I SD: 1.3405 c. M: 3.1315 c. 
 171: 14 15 13 15 14 14 15 14 15 13 15 14  SP        SD: 1.6691 c. M: 2.9332 c. 
 173: 14 15 14 15 14 14 15 14 15 14 15 14  SP M ME   SD: 1.6554 c. M: 2.8926 c. 
 176: 14 16 13 16 14 15 15 14 15 14 15 15  SP        SD: 1.9159 c. M: 2.8605 c. 
 178: 15 15 14 16 14 15 15 14 16 14 15 15  SP   D3 I SD: 1.5039 c. M:-2.8345 c. 
 180: 15 16 13 16 15 15 15 15 15 15 15 15  SP   T3   SD: 1.9262 c. M:-2.7998 c. 
 182: 15 16 14 16 15 15 15 15 16 14 16 15  SP   D3 I SD: 1.2548 c. M: 3.0539 c. 
 184: 15 16 14 17 15 15 16 14 16 15 16 15  SP        SD: 1.8461 c. M: 2.7872 c. 
 185: 15 16 15 16 15 15 16 15 16 15 16 15  SP M ME   SD: 1.6270 c. M: 2.8289 c. 
 190: 16 16 15 17 15 16 16 15 17 15 16 16  SP   D3 I SD: 1.4337 c. M:-2.7376 c. 
 194: 16 17 15 17 16 16 16 16 17 15 17 16  SP   D3 I SD: 1.1963 c. M: 2.9859 c. 
 202: 17 17 16 18 16 17 17 16 18 16 17 17  SP   D3 I SD: 1.3845 c. M:-2.6750 c. 
 206: 17 18 16 18 17 17 18 16 18 16 18 17  SP   D3   SD: 1.1537 c. M:-2.8994 c. 
 214: 18 18 17 19 17 18 18 17 19 17 18 18  SP   D3 I SD: 1.3519 c. M:-2.6195 c. 
 218: 18 19 17 19 18 18 19 17 19 17 19 18  SP   D3   SD: 1.0897 c. M:-2.6322 c. 
 226: 19 19 18 20 18 19 19 18 20 18 19 19  SP   D3 I SD: 1.3322 c. M:-2.5699 c. 
 230: 19 20 18 20 19 19 20 18 20 18 20 19  SP   D3   SD: 1.0458 c. M:-2.3928 c. 
 242: 20 21 19 21 20 20 21 19 21 19 21 20  SP   D3   SD: 1.0184 c. M:-2.1772 c. 
 243: 20 21 19 21 20 20 21 19 22 19 21 20  SP        SD: 1.1760 c. M: 2.1385 c. 
 245: 20 22 18 22 20 20 21 20 21 20 21 20  SP        SD: 1.3373 c. M: 2.1091 c. 
 248: 20 22 19 22 20 21 21 20 21 20 21 21  SP        SD: 1.3347 c. M: 2.7872 c. 
 250: 20 22 20 22 20 21 21 20 22 20 21 21  SP   D3   SD: 1.2944 c. M: 2.3150 c. 
 252: 21 22 19 22 21 21 21 20 23 20 21 21  SP        SD: 1.3937 c. M:-2.0583 c. 
 254: 21 22 20 22 21 21 22 20 22 20 22 21  SP   D3   SD: 1.0045 c. M:-1.9820 c. 
 255: 21 22 20 22 21 21 22 20 23 20 22 21  SP        SD: 1.1284 c. M: 1.9061 c. 
 256: 21 23 19 23 21 21 22 20 23 20 22 21  SP        SD: 1.2110 c. M:-2.3400 c. 
 257: 21 23 19 23 21 21 22 21 22 21 22 21  SP        SD: 1.2653 c. M: 1.8233 c. 
 260: 21 23 20 23 21 22 22 21 23 20 22 22  SP        SD: 1.1480 c. M: 2.0669 c. 
 266: 22 23 21 23 22 22 23 21 23 21 23 22  SP   D3   SD: 1.0013 c. M:-1.8044 c. 
 267: 22 23 21 23 22 22 23 21 24 21 23 22  SP        SD: 1.0946 c. M: 1.6946 c. 
 268: 22 24 20 24 22 22 23 21 24 21 23 22  SP        SD: 1.0929 c. M:-2.0601 c. 
 269: 22 24 20 24 22 22 23 22 23 22 23 22  SP        SD: 1.2081 c. M: 1.6720 c. 
 272: 22 24 21 24 22 23 23 22 24 21 23 23  SP        SD: 1.0927 c. M: 1.9990 c. 
 278: 23 24 22 24 23 23 24 22 24 22 24 23  SP   D3   SD: 1.0062 c. M:-1.8550 c. 
 280: 23 25 21 25 23 23 24 22 25 22 24 23  SP        SD: 0.9906 c. M:-1.8043 c. 
 292: 24 26 22 26 24 24 25 23 26 23 25 24  SP        SD: 0.9032 c. M:-1.5695 c. 
 304: 25 27 23 27 25 25 26 24 27 24 26 25  SP        SD: 0.8299 c. M:-1.4191 c. 
 316: 26 28 24 28 26 26 27 25 28 25 27 26  SP        SD: 0.7700 c. M:-1.3691 c. 
 328: 27 29 25 29 27 27 28 26 29 26 28 27  SP        SD: 0.7230 c. M:-1.3228 c. 
 340: 28 30 26 30 28 28 29 27 30 27 29 28  SP        SD: 0.6881 c. M:-1.2798 c. 
 352: 29 31 27 31 29 29 30 28 31 28 30 29  SP        SD: 0.6645 c. M:-1.2397 c. 
 364: 30 32 28 32 30 30 31 29 32 29 31 30  SP        SD: 0.6510 c. M:-1.2022 c. 
 376: 31 33 29 33 31 31 32 30 33 30 32 31  SP        SD: 0.6464 c. M:-1.1671 c. 
 388: 32 34 30 34 32 32 33 31 34 31 33 32  SP        SD: 0.6492 c. M:-1.1342 c. 
 400: 33 35 31 35 33 33 34 32 35 32 34 33  SP        SD: 0.6581 c. M:-1.1033 c. 
 412: 34 36 32 36 34 34 35 33 36 33 35 34  SP        SD: 0.6719 c. M:-1.1007 c. 
 441: 36 39 34 39 36 36 38 35 39 35 37 37  SP        SD: 0.6599 c. M: 1.2087 c. 
 449: 37 39 35 39 37 37 39 35 40 35 39 37  SP        SD: 0.6970 c. M: 1.0597 c. 
 451: 37 40 34 40 37 37 39 36 39 36 39 37  SP        SD: 0.6483 c. M:-1.0259 c. 
 458: 38 40 35 40 38 38 39 36 41 36 39 38  SP        SD: 0.6429 c. M:-1.2483 c. 
 461: 38 40 36 40 38 38 40 36 41 36 40 38  SP        SD: 0.6801 c. M: 0.9786 c. 
 463: 38 41 35 41 38 38 40 37 40 37 40 38  SP        SD: 0.6226 c. M:-1.0719 c. 
 470: 39 41 36 41 39 39 40 37 42 37 40 39  SP        SD: 0.6207 c. M:-1.2594 c. 
 473: 39 41 37 41 39 39 41 37 42 37 41 39  SP        SD: 0.6690 c. M: 0.9502 c. 
 475: 39 42 36 42 39 39 41 38 41 38 41 39  SP        SD: 0.6035 c. M:-1.1156 c. 
 487: 40 43 37 43 40 40 42 39 42 39 42 40  SP        SD: 0.5906 c. M:-1.1571 c. 
 492: 40 44 37 44 40 41 42 39 43 39 42 41  SP        SD: 0.5854 c. M:-0.9680 c. 
 494: 40 44 38 43 41 41 42 39 44 39 42 41  SP        SD: 0.5721 c. M: 1.1491 c. 
 504: 41 45 38 45 41 42 43 40 44 40 43 42  SP        SD: 0.5430 c. M:-0.8519 c. 
 516: 42 46 39 46 42 43 44 41 45 41 44 43  SP        SD: 0.5064 c. M:-0.7412 c. 
 528: 43 47 40 47 43 44 45 42 46 42 45 44  SP        SD: 0.4760 c. M:-0.6355 c. 
 540: 44 48 41 48 44 45 46 43 47 43 46 45  SP        SD: 0.4517 c. M:-0.5775 c. 
 552: 45 49 42 49 45 46 47 44 48 44 47 46  SP        SD: 0.4337 c. M:-0.6258 c. 
 564: 46 50 43 50 46 47 48 45 49 45 48 47  SP        SD: 0.4218 c. M:-0.6721 c. 
 576: 47 51 44 51 47 48 49 46 50 46 49 48  SP        SD: 0.4158 c. M:-0.7164 c. 
 588: 48 52 45 52 48 49 50 47 51 47 50 49  SP        SD: 0.4151 c. M:-0.7589 c. 
 653: 53 58 50 58 53 54 56 52 57 52 56 54  SP        SD: 0.4119 c. M: 0.9184 c. 
 658: 54 58 50 58 54 55 56 52 58 52 56 55  SP        SD: 0.4016 c. M: 0.8323 c. 
 665: 54 59 51 59 54 55 57 53 58 53 57 55  SP        SD: 0.3997 c. M: 0.8714 c. 
 670: 55 59 51 59 55 56 57 53 59 53 57 56  SP        SD: 0.3837 c. M: 0.8269 c. 
 682: 56 60 52 60 56 57 58 54 60 54 58 57  SP        SD: 0.3704 c. M: 0.8216 c. 
 694: 57 61 53 61 57 58 59 55 61 55 59 58  SP        SD: 0.3616 c. M: 0.8166 c. 
 706: 58 62 54 62 58 59 60 56 62 56 60 59  SP        SD: 0.3574 c. M: 0.8117 c. 
 711: 58 63 54 63 58 59 61 56 63 56 61 59  SP        SD: 0.3492 c. M: 0.6280 c. 
 723: 59 64 55 64 59 60 62 57 64 57 62 60  SP        SD: 0.3125 c. M: 0.5510 c. 
 735: 60 65 56 65 60 61 63 58 65 58 63 61  SP        SD: 0.2785 c. M: 0.4765 c. 
 747: 61 66 57 66 61 62 64 59 66 59 64 62  SP        SD: 0.2477 c. M: 0.4131 c. 
 759: 62 67 58 67 62 63 65 60 67 60 65 63  SP        SD: 0.2206 c. M: 0.3623 c. 
 771: 63 68 59 68 63 64 66 61 68 61 66 64  SP        SD: 0.1981 c. M: 0.3131 c. 
 783: 64 69 60 69 64 65 67 62 69 62 67 65  SP        SD: 0.1809 c. M: 0.2798 c. 
 795: 65 70 61 70 65 66 68 63 70 63 68 66  SP        SD: 0.1701 c. M: 0.2741 c. 
 807: 66 71 62 71 66 67 69 64 71 64 69 67  SP        SD: 0.1661 c. M: 0.2684 c. 
 819: 67 72 63 72 67 68 70 65 72 65 70 68  SP        SD: 0.1689 c. M: 0.2630 c. 
 1087: 89 96 83 96 89 90 93 86 96 86 93 90  SP        SD: 0.1627 c. M:-0.3218 c. 
 1099: 90 97 84 97 90 91 94 87 97 87 94 91  SP        SD: 0.1419 c. M:-0.2756 c. 
 1111: 91 98 85 98 91 92 95 88 98 88 95 92  SP        SD: 0.1235 c. M:-0.2304 c. 
 1123: 92 99 86 99 92 93 96 89 99 89 96 93  SP        SD: 0.1084 c. M:-0.1923 c. 
 1135: 93 100 87 100 93 94 97 90 100 90 97 94  SP        SD: 0.0976 c. M:-0.1914 c. 
 1147: 94 101 88 101 94 95 98 91 101 91 98 95  SP        SD: 0.0923 c. M:-0.1905 c. 
 1159: 95 102 89 102 95 96 99 92 102 92 99 96  SP        SD: 0.0929 c. M:-0.1896 c. 
 1171: 96 103 90 103 96 97 100 93 103 93 100 97  SP        SD: 0.0991 c. M:-0.1887 c. 
 1882: 154 166 144 166 154 156 161 149 166 149 161 156  SP        SD: 0.0914 c. M: 0.1758 c. 
 1894: 155 167 145 167 155 157 162 150 167 150 162 157  SP        SD: 0.0776 c. M: 0.1569 c. 
 1906: 156 168 146 168 156 158 163 151 168 151 163 158  SP        SD: 0.0643 c. M: 0.1383 c. 
 1918: 157 169 147 169 157 159 164 152 169 152 164 159  SP        SD: 0.0521 c. M: 0.1199 c. 
 1930: 158 170 148 170 158 160 165 153 170 153 165 160  SP        SD: 0.0414 c. M: 0.1018 c. 
 1942: 159 171 149 171 159 161 166 154 171 154 166 161  SP        SD: 0.0336 c. M: 0.0839 c. 
 1954: 160 172 150 172 160 162 167 155 172 155 167 162  SP        SD: 0.0307 c. M: 0.0662 c. 
 1966: 161 173 151 173 161 163 168 156 173 156 168 163  SP        SD: 0.0338 c. M: 0.0487 c. 
FIT/HARMONIC
 1 x x x x x x x x x x x 2  S SD: 0.0000 cents
 2 x x x x x x 3 x x x x 4  S SD: 0.0000 cents
 3 x x x x 4 x x x 5 x x 6  S SD: 6.1738 cents
 4 x x x 5 x x 6 x x 7 x 8  S SD: 8.2281 cents
 5 x x 6 x x 7 x 8 x 9 x 10  S SD: 7.2950 cents
 6 x x 7 x 8 x 9 x 10 x 11:12  S SD: 10.2857 cents
 7 x 8 x 9 x 10 x 11:12 x 13:14  S SD: 9.2082 cents
 8 x 9 x 10 x 11:12:13 x 14:15:16  S SD: 9.2069 cents
 9 x 10:11 x 12:13 x 14:15:16:17:18  S SD: 8.5194 cents
 10 x 11:12 x 13:14:15:16:17:18:19:20  S SD: 7.2775 cents
 11:12 x 13:14:15:16 x 17:19:20:21:22    SD: 11.1119 cents
 12:13 x 14:15:16:17:18:19:20:21:23:24    SD: 6.1492 cents
 13:14:15 x 16:17:18:20:21:22:23:25:26    SD: 9.6789 cents
 14:15:16:17:18:19:20:21:22:24:25:26:28  S SD: 7.0098 cents
 15:16:17:18:19:20:21:23:24:25:27:28:30    SD: 5.2181 cents
 16:17:18:19:20:21:23:24:25:27:28:30:32    SD: 4.9814 cents
 22:23:25:26:28:29:31:33:35:37:39:42:44    SD: 3.7386 cents
 26:28:29:31:33:35:37:39:41:44:46:49:52    SD: 3.6480 cents
 30:32:34:36:38:40:42:45:48:51:53:57:60    SD: 3.6084 cents
 31:33:35:37:39:41:44:47:49:52:55:59:62    SD: 2.8757 cents
 32:34:36:38:40:43:45:48:51:54:57:60:64    SD: 2.2943 cents
 38:40:43:45:48:51:54:57:60:64:68:72:76    SD: 1.9493 cents
 48:51:54:57:61:64:68:72:76:81:85:91:96    SD: 1.6084 cents
 50:53:56:59:63:67:71:75:79:84:89:94:100    SD: 1.6032 cents
 54:57:61:64:68:72:76:81:86:91:96:102:108    SD: 1.2425 cents
 70:74:79:83:88:93:99:105:111:118:125:132:140    SD: 1.0976 cents
 72:76:81:85:91:96:102:108:114:121:128:136:144    SD: 1.0208 cents
 80:85:90:95:101:107:113:120:127:135:142:151:160    SD: 0.8505 cents
 96:102:108:114:121:128:136:144:152:162:171:181:192    SD: 0.7693 cents
 104:110:117:123:131:139:147:156:165:175:185:196:208    SD: 0.6488 cents
 118:125:133:140:149:158:167:177:187:199:210:223:236    SD: 0.6272 cents
 134:142:151:159:169:179:189:201:212:226:238:253:268    SD: 0.6257 cents
 135:143:152:160:170:180:191:203:214:227:240:255:270    SD: 0.5937 cents
 150:159:169:178:189:200:212:225:238:253:267:283:300    SD: 0.4614 cents
 176:186:198:209:222:235:249:264:279:296:313:332:352    SD: 0.4078 cents
 200:212:225:237:252:267:283:300:317:337:356:378:400    SD: 0.3602 cents
 222:235:250:263:280:296:314:333:352:374:395:419:444    SD: 0.3275 cents
 241:255:271:286:304:322:341:362:382:406:429:455:482    SD: 0.2943 cents
 256:271:288:304:323:342:362:384:406:431:456:483:512    SD: 0.2929 cents
 272:288:306:323:343:363:385:408:431:458:484:514:544    SD: 0.2554 cents
 310:328:349:368:391:414:438:465:491:522:552:585:620    SD: 0.2423 cents
 322:341:362:382:406:430:455:483:510:542:573:608:644    SD: 0.2175 cents
 326:345:367:387:411:435:461:489:517:549:580:616:652    SD: 0.2088 cents
 376:398:423:446:474:502:532:564:596:633:669:710:752    SD: 0.1692 cents
 440:466:495:522:555:587:622:660:697:741:783:831:880    SD: 0.1441 cents
 498:527:560:591:628:665:704:747:789:839:886:940:996    SD: 0.1354 cents
 510:540:574:605:643:681:721:765:808:859:908:963:1020    SD: 0.1344 cents
 568:601:639:674:716:758:803:852:900:957:1011:1073:1136    SD: 0.1142 cents
 600:635:675:712:757:801:848:900:951:1011:1068:1133:1200    SD: 0.0988 cents