Scala analysis: 396_D6

  0:          1/1               0.000000 unison, perfect prime
  1:         77/72            116.233847 undecimal secor
  2:          7/6             266.870906 septimal minor third
  3:          4/3             498.044999 perfect fourth

  0:          8/7             231.1741 septimal whole tone
  1:         77/72            116.2338 undecimal secor
  2:         12/11            150.6371 undecimal neutral second, 3/4-tone
  3:          8/7             231.1741 septimal whole tone

Interval class, Number of incidences, Size:
  1:   1 77/72               116.234 cents  undecimal secor
  1:   1 12/11               150.637 cents  undecimal neutral second, 3/4-tone
  1:   1 8/7                 231.174 cents  septimal whole tone
  2:   1 7/6                 266.871 cents  septimal minor third
  2:   1 11/9                347.408 cents  undecimal neutral third
  2:   1 96/77               381.811 cents  
Highest number of different intervals for one interval class: 3
Average number of different intervals per interval class: 3.00000 = 3

        1     2     3    
 0.0  : 116.2 266.9 498.0
 116.2: 150.6 381.8 498.0
 266.9: 231.2 347.4 498.0
 498.0

Interval class, Interval span, Span size, Gap to prev. class:
  1:  116.2338  .. 231.1741 cents      576/539, 114.9402 cents            77/72, 116.2338 cents
  2:  266.8709  .. 381.8112 cents      576/539, 114.9402 cents            49/48, 35.6968 cents

Number of notes                     : 3
-- Interval properties --
Smallest interval                   : 77/72, 116.2338 cents, class 1
Average step (divided formal octave): 166.0150 cents
Largest one step interval           : 8/7, 231.1741 cents
Average / Smallest step             : 1.428284
Largest / Average step              : 1.392489
Largest / Smallest step             : 1.988871
Median interval of one step         : 12/11, 150.6371 cents, amount: 1
Least squares average step          : 153.15076 cents, oct.:  459.45228 cents
Scale is strictly proper
Scale has trivalence property
Scale is a mode of a 1144-tone equal temperament with octave  4/3
  degrees: 267 613 1144
Least number of segments generator  : 573 of 249.458 cents and inv.
  number of contiguous generator circle segments: 1
Shortest superset generator         : 1011 of 440.143 cents and inv.
  generated superset size: 48 = 45 more = 1600.000%
Number of contiguous 1-step segments: 0
Step pattern alph. order: ABC
Step pattern size order : SML
Scale is sum-free (all different intervals)
Scale is a Constant Structure, by a margin of 35.69681 cents
Scale diversity                     : 1.280046
Rothenberg stability                : 1.000000 = 1
Lumma stability                     : 0.538434
Rothenberg efficiency               : 0.666667   redundancy: 0.333333
Efficiency x scale size             : 2.000000
Number of different interval sizes  : 6 = 3.00000 / class
Number of one step interval sizes   : 3
Highest interval variety            : 3
Mean interval variety               : 3.00000 = 3
Median interval variety             : 3
Lowest interval variety             : 3
Smallest interval difference        : 864/847, 34.4032 cents
Number of recognisable fifths       : 0
Number of recognisable fourths      : 0
Best minor thirds form a closed circle
Steps are strictly increasing
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
-- Rational properties --
Prime limit                         : 11
Odd number limit                    : 77 (O: 77 U: 77)
Highest odd numerator or denominator: 77
Scale harmonicity                   : 0.025773
Average absolute harmonicity        : 0.104377
Specific harmonicity                : 0.125305
Fundamental                         : 1/72, -6.1699 octaves, 3.6337 Hz.
Guide tone                          : 308,  8.2668 octaves, 80580.674 Hz.
Exponens Consonantiae               : 2.217600E+04, 14.43671 octaves
Euler's gradus suavitatis           : 26
Sum of Mann's harmonic distance     : 84.5, average 28.16667
Mersenne's string divisions         : 13559
Sum of van Prooijen's expressibility: 3.20871, average 1.06957
Sum of Tenney's harmonic distance   : 6.44625, average 2.14875
Vogel's harmonic complexity         : 12.66667
Wille's k value                     : 38
Wilson's harmonic complexity        : 24
Rectangular lattice diameter        : 4
Triangular lattice diameter         : 2
Lattice compactness                 : 18.74437, average 3.12406
Lattice compactness (without 2's)   : 9.00997, average 1.50166
Number of different primes          : 4
Prime exponents' range, average, count, tones@limit:
  2:  -3 .. 2        -0.66667   6
  3:  -2 ..-1        -1.33333   4     1
  7:   0 .. 1         0.66667   2     1
 11:   0 .. 1         0.33333   1     1
Average exponent except 2's         :-1 / 3 =-0.33333
Average absolute exponent except 2's: 7 / 3 = 2.33333
Scale is weakly epimorphic with val: <6 10 19 23|
Scale is weakly epimorphic with val: <6 10 19 26|
Scale is weakly epimorphic with val: <6 11 19 24|
Scale is weakly epimorphic with val: <6 11 20 25|
Scale is weakly epimorphic with val: <7 10 19 25|
Scale is weakly epimorphic with val: <7 10 20 23|
Scale is weakly epimorphic with val: <7 10 20 26|
Scale is weakly epimorphic with val: <7 11 19 23|
Scale is weakly epimorphic with val: <7 11 19 26|
Scale is JI-epimorphic with val: <7 11 20 24|
Scale is weakly epimorphic with val: <7 11 20 27|
Scale is weakly epimorphic with val: <7 11 22 23|
Scale is weakly epimorphic with val: <7 11 22 26|
Scale is weakly epimorphic with val: <7 12 22 24|
Scale is weakly epimorphic with val: <7 12 22 27|
Scale is weakly epimorphic with val: <8 11 22 25|

  3:  1 1 1  SP B ME I SD: 47.3423 c. M:-65.1591 c. 
  4:  1 1 2   P M ME S SD: 11.3590 c. M: 17.8484 c. 
  9:  2 3 4  SP   T3   SD: 6.5148 c. M:-9.8208 c. 
 13:  3 4 6  SP   T3   SD: 1.0645 c. M:-1.3072 c. 
 30:  7 9 14  SP   T3   SD: 0.7200 c. M: 1.2469 c. 
 43:  10 13 20  SP   T3   SD: 0.3619 c. M: 0.4747 c. 
 56:  13 17 26  SP   T3   SD: 0.3575 c. M: 0.6163 c. 
 99:  23 30 46  SP   T3   SD: 0.3342 c. M: 0.5264 c. 
 142: 33 43 66  SP   T3   SD: 0.3357 c. M: 0.4910 c. 
 185: 43 56 86  SP   T3   SD: 0.3391 c. M: 0.4720 c. 
 192: 45 58 89  SP   T3   SD: 0.3373 c. M:-0.4954 c. 
 205: 48 62 95  SP   T3   SD: 0.3080 c. M:-0.3816 c. 
 209: 49 63 97  SP   T3   SD: 0.3079 c. M:-0.5327 c. 
 218: 51 66 101  SP   T3   SD: 0.2959 c. M:-0.4285 c. 
 222: 52 67 103  SP   T3   SD: 0.2522 c. M:-0.4253 c. 
 235: 55 71 109  SP   T3   SD: 0.2132 c. M:-0.3299 c. 
 248: 58 75 115  SP   T3   SD: 0.1921 c. M:-0.2444 c. 
 261: 61 79 121  SP   T3   SD: 0.1882 c. M:-0.2797 c. 
 265: 62 80 123  SP   T3   SD: 0.1674 c. M:-0.2899 c. 
 278: 65 84 129  SP   T3   SD: 0.1303 c. M:-0.2155 c. 
 291: 68 88 135  SP   T3   SD: 0.1108 c. M:-0.1478 c. 
 321: 75 97 149  SP   T3   SD: 0.0762 c. M:-0.1318 c. 
 334: 78 101 155  SP   T3   SD: 0.0512 c. M:-0.0761 c. 
 364: 85 110 169  SP   T3   SD: 0.0527 c. M:-0.0679 c. 
 377: 88 114 175  SP   T3   SD: 0.0144 c. M:-0.0207 c. 
 767: 179 232 356  SP   T3   SD: 0.0050 c. M:-0.0085 c. 
 1144: 267 346 531  SP   T3   SD: 0.0033 c. M:-0.0057 c. 
 1911: 446 578 887  SP   T3   SD: 0.0028 c. M:-0.0041 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: 48.7680 cents
 6 x 7:8  S SD: 0.0000 cents
 7 x 8:9  S SD: 36.1882 cents
 8 x 9:11    SD: 41.2374 cents
 9:10:11:12  H SD: 34.7446 cents
 10:11:12:13  H SD: 27.2402 cents
 11:12:13:15    SD: 18.8452 cents
 12:13:14:16  S SD: 7.4463 cents
 29:31:34:39    SD: 5.7136 cents
 30:32:35:40    SD: 1.5009 cents
 42:45:49:56    SD: 1.0697 cents
 72:77:84:96    SD: 0.0000 cents