Scala analysis: 484_R8

  0:          1/1               0.000000 unison, perfect prime
  1:         18/17             98.954592 Arabic lute index finger
  2:        324/289           197.909184 two (Arabic lute index finger)
  3:          4/3             498.044999 perfect fourth

  0:        289/243           300.1358 
  1:         18/17             98.9546 Arabic lute index finger
  2:         18/17             98.9546 Arabic lute index finger
  3:        289/243           300.1358 

Interval class, Number of incidences, Size:
  1:   2 18/17               98.955 cents   Arabic lute index finger
  1:   1 289/243             300.136 cents  
  2:   1 324/289             197.909 cents  two (Arabic lute index finger)
  2:   2 34/27               399.090 cents  septendecimal major third
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  : 99.0  197.9 498.0
 99.0 : 99.0  399.1 498.0
 197.9: 300.1 399.1 498.0
 498.0

Interval class, Interval span, Span size, Gap to prev. class:
  1:  98.9546   .. 300.1358 cents      4913/4374, 201.1812 cents          18/17, 98.9546 cents
  2:  197.9092  .. 399.0904 cents      4913/4374, 201.1812 cents          78732/83521,-102.2266 cents

Number of notes                     : 3
-- Interval properties --
Smallest interval                   : 18/17, 98.9546 cents, class 1
Average step (divided formal octave): 166.0150 cents
Largest one step interval           : 289/243, 300.1358 cents
Average / Smallest step             : 1.677689
Largest / Average step              : 1.807884
Largest / Smallest step             : 3.033066
Median interval of one step         : 18/17, 98.9546 cents, amount: 2
Most common interval of one step    : 18/17, 98.9546 cents, amount: 2
Least squares average step          : 142.06485 cents, oct.:  426.19456 cents
Scale is not proper
Scale has Myhill's property
  chromas: 4913/4374, 201.1812 cents and 83521/78732, 102.2266 cents, ratio: 1.967992
  generators: 1 of 98.95459 cents and 399.09041 cents
ET pair of linear temperament       : 302&1218
Scale is distributional even
Scale is a mode of a 458-tone equal temperament with octave  4/3
  degrees: 91 182 458
  generators: 91 and 367
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 98.95459 cents
Scale diversity                     : 1.066739
Lumma stability                     : 0.397372
Lumma impropriety factor            : 0.205256
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        : 18/17, 98.9546 cents
Most common intervals               : 18/17, 98.9546 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                         : 17
Odd number limit                    : 289 (O: 289 U: 289)
Highest odd numerator or denominator: 289
Scale harmonicity                   : 0.013233
Average absolute harmonicity        : 0.085145
Specific harmonicity                : 0.060800
Fundamental                         : 1/867, -9.7599 octaves, 0.3018 Hz.
Guide tone                          : 324,  8.3399 octaves, 84766.683 Hz.
Exponens Consonantiae               : 2.809080E+05, 18.09974 octaves
Euler's gradus suavitatis           : 45
Sum of Mann's harmonic distance     : 327.5, average 109.16667
Mersenne's string divisions         : 21455
Sum of van Prooijen's expressibility: 4.16847, average 1.38949
Sum of Tenney's harmonic distance   : 8.53635, average 2.84545
Vogel's harmonic complexity         : 26.66667
Wille's k value                     : 229
Wilson's harmonic complexity        : 49
Rectangular lattice diameter        : 7
Triangular lattice diameter         : 5
Lattice compactness                 : 20.73582, average 3.45597
Lattice compactness (without 2's)   : 18.49171, average 3.08195
Number of different primes          : 3
Prime exponents' range, average, count, tones@limit:
  2:   1 .. 2         1.66667   5
  3:  -1 .. 4         1.66667   7     1
 17:  -2 .. 0        -1.00000   3     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 27|
Scale is JI-epimorphic with val: <7 11 28|
Scale is weakly epimorphic with val: <7 11 30| = patent
Scale is weakly epimorphic with val: <7 11 31|
Scale is weakly epimorphic with val: <7 11 33|

  3:  0 1 2   N G T3   SD: 60.0257 c. M: 98.9546 c. 
  4:  1 1 2   P M ME S SD: 32.9935 c. M:-51.1133 c. 
  5:  1 1 3   N M DE S SD: 0.8448 c. M:-1.3088 c. 
 81:  16 16 49   N M DE S SD: 0.7428 c. M: 1.1507 c. 
 86:  17 17 52   N M DE S SD: 0.6505 c. M: 1.0077 c. 
 91:  18 18 55   N M DE S SD: 0.5683 c. M: 0.8804 c. 
 96:  19 19 58   N M DE S SD: 0.4947 c. M: 0.7664 c. 
 101: 20 20 61   N M DE S SD: 0.4284 c. M: 0.6636 c. 
 106: 21 21 64   N M DE S SD: 0.3683 c. M: 0.5706 c. 
 111: 22 22 67   N M DE S SD: 0.3137 c. M: 0.4859 c. 
 116: 23 23 70   N M DE S SD: 0.2637 c. M: 0.4086 c. 
 121: 24 24 73   N M DE S SD: 0.2179 c. M: 0.3376 c. 
 126: 25 25 76   N M DE S SD: 0.1758 c. M: 0.2723 c. 
 131: 26 26 79   N M DE S SD: 0.1368 c. M: 0.2119 c. 
 136: 27 27 82   N M DE S SD: 0.1007 c. M: 0.1560 c. 
 141: 28 28 85   N M DE S SD: 0.0672 c. M: 0.1041 c. 
 146: 29 29 88   N M DE S SD: 0.0359 c. M: 0.0557 c. 
 151: 30 30 91   N M DE S SD: 0.0068 c. M: 0.0105 c. 
 458: 91 91 276   N M DE S SD: 0.0025 c. M:-0.0039 c. 
 609: 121 121 367   N M DE S SD: 0.0002 c. M:-0.0003 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: 72.4492 cents
 6 x 7:8  S SD: 34.4809 cents
 7 x 8:9  S SD: 35.6042 cents
 8 x 9:11    SD: 26.8049 cents
 9 x 10:12  S SD: 7.7527 cents
 10 x 11:13    SD: 27.4039 cents
 11 x 12:15  S SD: 30.6117 cents
 12:13 x 16    SD: 19.8090 cents
 14:15:16:19    SD: 16.5505 cents
 15:16:17:20    SD: 7.5707 cents
 18:19:20:24  S SD: 5.4677 cents
 32:34:36:43    SD: 5.3076 cents
 33:35:37:44    SD: 0.9722 cents
 117:124:131:156    SD: 0.9258 cents
 150:159:168:200    SD: 0.8578 cents
 156:165:175:208    SD: 0.7111 cents
 189:200:212:252    SD: 0.4539 cents
 222:235:249:296    SD: 0.3015 cents
 255:270:286:340    SD: 0.2374 cents
 273:289:306:364    SD: 0.1661 cents
 306:324:343:408    SD: 0.0990 cents
 528:559:592:704    SD: 0.0812 cents
 561:594:629:748    SD: 0.0540 cents