Scala analysis: 595_T2

Aristoxenian style tetrachord 2.5 + 2.5 + 25, Chapter 4

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

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:         41.667 cents      41.666670
  2:         83.333 cents      83.333330
  3:        500.000 cents     500.000000
SHOW/INTERVAL
  0:        416.6667 cents    416.6667
  1:         41.6667 cents     41.6667
  2:         41.6667 cents     41.6667
  3:        416.6667 cents    416.6667
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   2 41.66667 cents
  1:   1 416.66667 cents
  2:   1 83.33333 cents
  2:   2 458.33333 cents
Highest number of different intervals for one interval class: 2
Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
        1     2     3    
 0.0  : 41.7  83.3  500.0
 41.7 : 41.7  458.3 500.0
 83.3 : 416.7 458.3 500.0
 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  41.6667   .. 416.6667 cents      375.00000 cents                    41.66667 cents
  2:  83.3333   .. 458.3333 cents      375.00000 cents                   -333.33334 cents
SHOW DATA
Number of notes                     : 3
-- Interval properties --
Smallest interval                   : 41.66666 cents, class 1
Average step (divided formal octave): 166.6667 cents
Largest one step interval           : 416.66667 cents
Average / Smallest step             : 4.000001
Largest / Average step              : 2.500000
Largest / Smallest step             : 10.000002
Median interval of one step         : 41.66667 cents, amount: 2
Most common interval of one step    : 41.66667 cents, amount: 2
Least squares average step          : 122.02381 cents, oct.:  366.07143 cents
Scale is not proper
Scale has Myhill's property
  chromas: 375.00000 cents and 333.33333 cents, ratio: 1.125000
  generators: 1 of 41.66667 cents and 458.33333 cents
ET pair of linear temperament       : 22&24
Scale is distributional even
Scale is a mode of a 12-tone equal temperament with octave  500.000 cents
  degrees: 1 2 12
  generators: 1 and 11
Number of contiguous 1-step segments: 1
Step pattern alph. order: AAB
Step pattern size order : SSL
Interval vector is [ 2 1 0 0 0 0 ]
Scale is sum-free (all different intervals)
Scale is a Constant Structure, by a margin of 41.66666 cents
Scale diversity                     : 0.305007
Lumma stability                     : 0.166667
Lumma impropriety factor            : 0.666667
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        : 41.66666 cents
Most common intervals               : 41.66667 cents & inv., amount: 2
Number of recognisable fifths       : 0
Number of recognisable fourths      : 0
Steps are increasing
Formal octave complements present   : 1 = 33.3333%
2/1 octave complements present      : 0 = 0.0000%
Limited inverse transpositions      :
 2
Inversional symmetry on degrees     :
 1
Inversional symmetry on intervals   :
 2-3
-- Rational properties --
FIT/MODE
  3:  0 0 3   N M DE S SD: 53.7914 c. M: 83.3333 c. 
  5:  0 1 4   N G T3   SD: 25.9094 c. M: 41.6667 c. 
  6:  0 1 5   N G T3   SD: 24.0563 c. M: 41.6667 c. 
  7:  0 1 6   N G T3   SD: 25.0189 c. M: 41.6667 c. 
  8:  1 0 7   N G T3   SD: 17.0103 c. M:-20.8333 c. 
  9:  1 1 7   N M DE S SD: 17.9305 c. M:-27.7778 c. 
 10:  1 1 8   N M DE S SD: 10.7583 c. M:-16.6667 c. 
 11:  1 1 9   N M DE S SD: 4.8901 c. M:-7.5758 c. 
 12:  1 1 10   N M DE S SD: 0.0000 c. M:-0.0000 c. 
FIT/HARMONIC
 1 x x 2  S SD: 700.0000 cents
 2 x x 3  S SD: 201.9550 cents
 3 x x 4  S SD: 1.9550 cents
 4 x x 5  S SD: 113.6863 cents
 5 x x 7    SD: 82.5122 cents
 6 x 7:8  S SD: 91.7740 cents
 7 x 8:9  S SD: 80.7325 cents
 8 x 9:11    SD: 65.5215 cents
 9 x 10:12  S SD: 49.5448 cents
 10 x 11:13    SD: 46.8148 cents
 11 x 12:15  S SD: 38.3899 cents
 12 x 13:16    SD: 27.6370 cents
 13 x 14:17    SD: 28.6672 cents
 14 x 15:19    SD: 23.0589 cents
 15 x 16:20  S SD: 14.2326 cents
 16 x 17:21    SD: 18.1746 cents
 17 x 18:23    SD: 14.0339 cents
 18 x 19:24    SD: 5.2271 cents
 19 x 20:25  S SD: 12.7396 cents
 20 x 21:27    SD: 9.7921 cents
 21 x 22:28    SD: 1.7060 cents
 22 x 23:29    SD: 11.3283 cents
 23 x 24:31    SD: 9.6710 cents
 24 x 25:32    SD: 6.4055 cents
 25 x 26:33    SD: 12.3772 cents
 26 x 27:35    SD: 11.5906 cents
 27 x 28:36    SD: 10.2330 cents
 28:29 x 37    SD: 12.9406 cents
 29:30 x 39    SD: 10.6817 cents
 30:31 x 40    SD: 7.6131 cents
 33:34:35:44    SD: 7.0524 cents
 35:36:37:47    SD: 5.9963 cents
 36:37:38:48    SD: 3.9798 cents
 38:39:40:51    SD: 3.7876 cents
 39:40:41:52    SD: 1.4547 cents
 42:43:44:56    SD: 1.1788 cents
 81:83:85:108    SD: 0.6790 cents
 122:125:128:163    SD: 0.5502 cents
 161:165:169:215    SD: 0.4207 cents
 164:168:172:219    SD: 0.3710 cents
 203:208:213:271    SD: 0.1659 cents
 448:459:470:598    SD: 0.1574 cents