Scala analysis: 487_R11

  0:          1/1               0.000000 unison, perfect prime
  1:         25/24             70.672427 classic chromatic semitone, minor chroma
  2:        625/576           141.344854 two (classic chromatic semitone, minor chroma)
  3:          4/3             498.044999 perfect fourth

  0:        768/625           356.7001 
  1:         25/24             70.6724 classic chromatic semitone, minor chroma
  2:         25/24             70.6724 classic chromatic semitone, minor chroma
  3:        768/625           356.7001 

Interval class, Number of incidences, Size:
  1:   2 25/24               70.672 cents   classic chromatic semitone, minor chroma
  1:   1 768/625             356.700 cents  
  2:   1 625/576             141.345 cents  two (classic chromatic semitone, minor chroma)
  2:   2 32/25               427.373 cents  classic diminished fourth
Highest number of different intervals for one interval class: 2
Average number of different intervals per interval class: 2.00000 = 2

        1     2     3    
 0.0  : 70.7  141.3 498.0
 70.7 : 70.7  427.4 498.0
 141.3: 356.7 427.4 498.0
 498.0

Interval class, Interval span, Span size, Gap to prev. class:
  1:  70.6724   .. 356.7001 cents      18432/15625, 286.0277 cents        25/24, 70.6724 cents
  2:  141.3449  .. 427.3726 cents      18432/15625, 286.0277 cents        390625/442368,-215.3553 cents

Number of notes                     : 3
-- Interval properties --
Smallest interval                   : 25/24, 70.6724 cents, class 1
Average step (divided formal octave): 166.0150 cents
Largest one step interval           : 768/625, 356.7001 cents
Average / Smallest step             : 2.349077
Largest / Average step              : 2.148602
Largest / Smallest step             : 5.047232
Median interval of one step         : 25/24, 70.6724 cents, amount: 2
Most common interval of one step    : 25/24, 70.6724 cents, amount: 2
Least squares average step          : 131.96408 cents, oct.:  395.89224 cents
Scale is not proper
Scale has Myhill's property
  chromas: 18432/15625, 286.0277 cents and 442368/390625, 215.3553 cents, ratio: 1.328167
  generators: 1 of 70.67243 cents and 427.37257 cents
ET pair of linear temperament       : 296&1494
Scale is distributional even
Scale is a mode of a 599-tone equal temperament with octave  4/3
  degrees: 85 170 599
  generators: 85 and 514
Number of contiguous 1-step segments: 0
Step pattern alph. order: AAB
Step pattern size order : SSL
Scale is sum-free (all different intervals)
Scale is a Constant Structure, by a margin of 70.67243 cents
Scale diversity                     : 0.739703
Lumma stability                     : 0.283799
Lumma impropriety factor            : 0.432401
Rothenberg efficiency               : 0.888889   redundancy: 0.111111
Efficiency x scale size             : 2.666667
Number of different interval sizes  : 4 = 2.00000 / class
Number of one step interval sizes   : 2
Highest interval variety            : 2
Mean interval variety               : 2.00000 = 2
Median interval variety             : 2
Lowest interval variety             : 2
Smallest interval difference        : 25/24, 70.6724 cents
Most common intervals               : 25/24, 70.6724 cents & inv., amount: 2
Number of recognisable fifths       : 0
Number of recognisable fourths      : 0
Steps are increasing
Length of longest harmonic part     : 1 at degree 0
Length of longest subharmonic part  : 1 at degree 0
Formal octave complements present   : 1 = 33.3333%
2/1 octave complements present      : 0 = 0.0000%
Scale is n-1 differentially coherent in interval class 1
Limited inverse transpositions      :
 2
Inversional symmetry on degrees     :
 1
Inversional symmetry on intervals   :
 2-3
-- Rational properties --
Prime limit                         : 5
Odd number limit                    : 625 (O: 625 U: 625)
Highest odd numerator or denominator: 625
Scale harmonicity                   : 0.025685
Average absolute harmonicity        : 0.098504
Specific harmonicity                : 0.120663
Fundamental                         : 1/576, -9.1699 octaves, 0.4542 Hz.
Guide tone                          : 2500,  11.2877 octaves, 654063.913 Hz.
Exponens Consonantiae               : 1.440000E+06, 20.45764 octaves
Euler's gradus suavitatis           : 29
Sum of Mann's harmonic distance     : 628.5, average 209.50000
Mersenne's string divisions         : 58849
Sum of van Prooijen's expressibility: 4.67094, average 1.55698
Sum of Tenney's harmonic distance   : 9.41363, average 3.13788
Vogel's harmonic complexity         : 15.66667
Wille's k value                     : 312
Wilson's harmonic complexity        : 26
Rectangular lattice diameter        : 6
Triangular lattice diameter         : 4
Lattice compactness                 : 31.58786, average 5.26464
Lattice compactness (without 2's)   : 16.06738, average 2.67790
Number of different primes          : 3
Prime exponents' range, average, count, tones@limit:
  2:  -6 .. 2        -2.33333   11
  3:  -2 ..-1        -1.33333   4     1
  5:   0 .. 4         2.00000   6     2
Average exponent except 2's         : 2 / 3 = 0.66667
Average absolute exponent except 2's: 10 / 3 = 3.33333
Scale is weakly epimorphic with val: <7 11 15|
Scale is weakly epimorphic with val: <7 11 17| = patent
Scale is weakly epimorphic with val: <7 11 18|

  3:  0 1 2   N G T3   SD: 43.2173 c. M: 70.6724 c. 
  4:  0 1 3   N G T3   SD: 41.9443 c. M: 70.6724 c. 
  5:  1 0 4   N G T3   SD: 29.3212 c. M: 41.7359 c. 
  6:  1 1 4   N M DE S SD: 15.9245 c. M:-24.6701 c. 
  7:  1 1 5   N M DE S SD: 0.6156 c. M:-0.9537 c. 
 78:  11 11 56   N M DE S SD: 0.5620 c. M: 0.8706 c. 
 85:  12 12 61   N M DE S SD: 0.4650 c. M: 0.7204 c. 
 92:  13 13 66   N M DE S SD: 0.3828 c. M: 0.5930 c. 
 99:  14 14 71   N M DE S SD: 0.3122 c. M: 0.4836 c. 
 106: 15 15 76   N M DE S SD: 0.2509 c. M: 0.3887 c. 
 113: 16 16 81   N M DE S SD: 0.1972 c. M: 0.3056 c. 
 120: 17 17 86   N M DE S SD: 0.1498 c. M: 0.2321 c. 
 127: 18 18 91   N M DE S SD: 0.1076 c. M: 0.1667 c. 
 134: 19 19 96   N M DE S SD: 0.0699 c. M: 0.1082 c. 
 141: 20 20 101   N M DE S SD: 0.0358 c. M: 0.0555 c. 
 148: 21 21 106   N M DE S SD: 0.0050 c. M: 0.0078 c. 
 451: 64 64 323   N M DE S SD: 0.0046 c. M:-0.0072 c. 
 599: 85 85 429   N M DE S SD: 0.0022 c. M:-0.0035 c. 
 747: 106 106 535   N M DE S SD: 0.0008 c. M:-0.0013 c. 
 895: 127 127 641   N M DE S SD: 0.0002 c. M: 0.0002 c. 

 1 x x 2  S SD: 701.9550 cents
 2 x x 3  S SD: 203.9100 cents
 3 x x 4  S SD: 0.0000 cents
 4 x x 5  S SD: 111.7313 cents
 5 x 6:7  S SD: 96.8426 cents
 6 x 7:8  S SD: 62.7630 cents
 7 x 8:9  S SD: 54.8484 cents
 8 x 9:11    SD: 41.0865 cents
 9 x 10:12  S SD: 20.5294 cents
 10 x 11:13    SD: 24.9045 cents
 11 x 12:15  S SD: 20.0000 cents
 12 x 13:16    SD: 1.3861 cents
 13 x 14:17    SD: 18.0301 cents
 14 x 15:19    SD: 18.8324 cents
 15 x 16:20  S SD: 14.8068 cents
 16:17 x 21    SD: 21.9012 cents
 17:18 x 23    SD: 18.9648 cents
 18:19:20:24  S SD: 15.6760 cents
 19:20:21:25    SD: 14.4281 cents
 20:21:22:27    SD: 11.6074 cents
 21:22:23:28    SD: 6.3077 cents
 24:25:26:32    SD: 0.9241 cents
 93:97:101:124    SD: 0.8999 cents
 117:122:127:156    SD: 0.6288 cents
 141:147:153:188    SD: 0.4913 cents
 165:172:179:220    SD: 0.4357 cents
 189:197:205:252    SD: 0.4272 cents
 315:328:342:420    SD: 0.4073 cents
 339:353:368:452    SD: 0.3254 cents
 363:378:394:484    SD: 0.2592 cents
 387:403:420:516    SD: 0.2087 cents
 411:428:446:548    SD: 0.1750 cents
 435:453:472:580    SD: 0.1593 cents
 504:525:547:672    SD: 0.1319 cents
 528:550:573:704    SD: 0.0839 cents
 552:575:599:736    SD: 0.0401 cents
 576:600:625:768    SD: 0.0000 cents