Scala analysis: xen15-chalmers-triadic-diamond-8-7-tetrachord

  0:          1/1               0.000000 unison, perfect prime
  1:         64/63             27.264092 septimal comma, Archytas' comma
  2:          7/6             266.870906 septimal minor third
  3:          4/3             498.044999 perfect fourth

  0:          8/7             231.1741 septimal whole tone
  1:         64/63             27.2641 septimal comma, Archytas' comma
  2:        147/128           239.6068 
  3:          8/7             231.1741 septimal whole tone

Interval class, Number of incidences, Size:
  1:   1 64/63               27.264 cents   septimal comma, Archytas' comma
  1:   1 8/7                 231.174 cents  septimal whole tone
  1:   1 147/128             239.607 cents  
  2:   1 512/441             258.438 cents  
  2:   1 7/6                 266.871 cents  septimal minor third
  2:   1 21/16               470.781 cents  narrow fourth
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  : 27.3  266.9 498.0
 27.3 : 239.6 470.8 498.0
 266.9: 231.2 258.4 498.0
 498.0

Interval class, Interval span, Span size, Gap to prev. class:
  1:  27.2641   .. 239.6068 cents      9261/8192, 212.3427 cents          64/63, 27.2641 cents
  2:  258.4382  .. 470.7809 cents      9261/8192, 212.3427 cents          65536/64827, 18.8314 cents

Number of notes                     : 3
-- Interval properties --
Smallest interval                   : 64/63, 27.2641 cents, class 1
Average step (divided formal octave): 166.0150 cents
Largest one step interval           : 147/128, 239.6068 cents
Average / Smallest step             : 6.089145
Largest / Average step              : 1.443284
Largest / Smallest step             : 8.788366
Median interval of one step         : 8/7, 231.1741 cents, amount: 1
Least squares average step          : 146.79578 cents, oct.:  440.38734 cents
Scale is strictly proper
Scale has trivalence property
Scale is a mode of a 2247-tone equal temperament with octave  4/3
  degrees: 123 1204 2247
Least number of segments generator  : 1124 of 249.133 cents and inv.
  number of contiguous generator circle segments: 1
Shortest superset generator         : 2039 of 451.942 cents and inv.
  generated superset size: 50 = 47 more = 1666.667%
Number of contiguous 1-step segments: 0
Step pattern alph. order: ABC
Step pattern size order : SLM
Scale is sum-free (all different intervals)
Scale is a Constant Structure, by a margin of 18.83137 cents
Scale diversity                     : 0.433097
Rothenberg stability                : 1.000000 = 1
Lumma stability                     : 0.147295
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        : 1029/1024, 8.4327 cents
Number of recognisable fifths       : 0
Number of recognisable fourths      : 0
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 with margin 212.3427 cents:
 1
-- Rational properties --
Prime limit                         : 7
Odd number limit                    : 441 (O: 147 U: 441)
Highest odd numerator or denominator: 63
Scale harmonicity                   : 0.030391
Average absolute harmonicity        : 0.110737
Specific harmonicity                : 0.158865
Fundamental                         : 1/126, -6.9773 octaves, 2.0764 Hz.
Guide tone                          : 448,  8.8074 octaves, 117208.253 Hz.
Exponens Consonantiae               : 5.644800E+04, 15.78463 octaves
Euler's gradus suavitatis           : 24
Sum of Mann's harmonic distance     : 73.5, average 24.50000
Mersenne's string divisions         : 11557
Sum of van Prooijen's expressibility: 3.12156, average 1.04052
Sum of Tenney's harmonic distance   : 6.30795, average 2.10265
Vogel's harmonic complexity         : 12.33333
Wille's k value                     : 73
Wilson's harmonic complexity        : 20
Rectangular lattice diameter        : 4
Triangular lattice diameter         : 3
Lattice compactness                 : 25.12463, average 4.18744
Lattice compactness (without 2's)   : 9.30056, average 1.55009
Number of different primes          : 3
Prime exponents' range, average, count, tones@limit:
  2:  -1 .. 6         2.33333   9
  3:  -2 ..-1        -1.33333   4     1
  7:  -1 .. 1         0.00000   2     2
Average exponent except 2's         :-4 / 3 =-1.33333
Average absolute exponent except 2's: 6 / 3 = 2.00000
Scale is weakly epimorphic with val: <7 10 19|
Scale is weakly epimorphic with val: <7 10 20|
Scale is weakly epimorphic with val: <8 11 22|

  3:  0 2 1   N G T3   SD: 40.7801 c. M:-65.1591 c. 
  4:  0 2 2   P M DE S SD: 18.8140 c. M: 27.2641 c. 
  6:  0 3 3   P M DE S SD: 18.8140 c. M: 27.2641 c. 
  7:  0 4 3   N G T3   SD: 18.7754 c. M: 27.2641 c. 
  9:  1 4 4  SP M DE S SD: 17.1718 c. M:-28.0742 c. 
 11:  1 5 5  SP M DE S SD: 10.7611 c. M:-18.0127 c. 
 12:  1 5 6   P   T3   SD: 13.1825 c. M: 17.8484 c. 
 13:  1 6 6  SP M DE S SD: 6.4225 c. M:-11.0471 c. 
 15:  1 7 7  SP M DE S SD: 3.5036 c. M:-5.9389 c. 
 17:  1 8 8  SP M DE S SD: 2.1888 c. M: 3.2000 c. 
 35:  2 17 16  SP   T3   SD: 2.1334 c. M:-3.4964 c. 
 37:  2 18 17  SP   T3   SD: 1.3669 c. M:-2.3426 c. 
 39:  2 19 18  SP   T3   SD: 1.2488 c. M: 1.7233 c. 
 52:  3 25 24  SP   T3   SD: 1.1354 c. M:-1.4693 c. 
 54:  3 26 25  SP   T3   SD: 0.4169 c. M:-0.5977 c. 
 56:  3 27 26  SP   T3   SD: 0.3385 c. M: 0.5831 c. 
 110: 6 53 51  SP   T3   SD: 0.1617 c. M:-0.2623 c. 
 127: 7 61 59  SP   T3   SD: 0.1586 c. M: 0.2011 c. 
 181: 10 87 84  SP   T3   SD: 0.1472 c. M:-0.2522 c. 
 183: 10 88 85  SP   T3   SD: 0.0956 c. M: 0.1583 c. 
 237: 13 114 110  SP   T3   SD: 0.0327 c. M:-0.0548 c. 
 530: 29 255 246  SP   T3   SD: 0.0081 c. M: 0.0126 c. 
 767: 42 369 356  SP   T3   SD: 0.0068 c. M:-0.0085 c. 
 1297: 71 624 602  SP   T3   SD: 0.0043 c. M:-0.0075 c. 
 1827: 100 879 848  SP   T3   SD: 0.0046 c. M:-0.0071 c. 
 2064: 113 993 958  SP   T3   SD: 0.0048 c. M:-0.0079 c. 
 2247: 123 1081 1043  SP   T3   SD: 0.0034 c. M: 0.0057 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 x 11:12    SD: 40.2685 cents
 10 x 12:13  S SD: 32.7861 cents
 11 x 13:15    SD: 22.4315 cents
 18:19:21:24    SD: 22.1130 cents
 20:21:23:27    SD: 21.9981 cents
 21:22:25:28    SD: 21.2428 cents
 22:23:26:29    SD: 19.3213 cents
 23:24:27:31    SD: 17.0610 cents
 24:25:28:32    SD: 14.4694 cents
 28:29:33:37    SD: 13.6276 cents
 29:30:34:39    SD: 11.9298 cents
 30:31:35:40    SD: 9.8343 cents
 35:36:41:47    SD: 8.5899 cents
 36:37:42:48    SD: 6.7233 cents
 41:42:48:55    SD: 6.2889 cents
 42:43:49:56    SD: 4.4909 cents
 48:49:56:64  S SD: 2.8109 cents
 54:55:63:72    SD: 1.5009 cents
 60:61:70:80    SD: 0.4507 cents
 66:67:77:88    SD: 0.4100 cents
 126:128:147:168    SD: 0.0000 cents