Scala analysis: 602_T9

Aristoxenian style tetrachord 3.5 + 3.5 + 23, Chapter 4

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

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:         58.333 cents      58.333330
  2:        116.667 cents     116.666670
  3:        500.000 cents     500.000000
SHOW/INTERVAL
  0:        383.3333 cents    383.3333
  1:         58.3333 cents     58.3333
  2:         58.3333 cents     58.3333
  3:        383.3333 cents    383.3333
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   2 58.33333 cents
  1:   1 383.33333 cents
  2:   1 116.66667 cents
  2:   2 441.66667 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  : 58.3  116.7 500.0
 58.3 : 58.3  441.7 500.0
 116.7: 383.3 441.7 500.0
 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  58.3333   .. 383.3333 cents      325.00000 cents                    58.33333 cents
  2:  116.6667  .. 441.6667 cents      325.00000 cents                   -266.66666 cents
SHOW DATA
Number of notes                     : 3
-- Interval properties --
Smallest interval                   : 58.33333 cents, class 1
Average step (divided formal octave): 166.6667 cents
Largest one step interval           : 383.33333 cents
Average / Smallest step             : 2.857143
Largest / Average step              : 2.300000
Largest / Smallest step             : 6.571429
Median interval of one step         : 58.33333 cents, amount: 2
Most common interval of one step    : 58.33333 cents, amount: 2
Least squares average step          : 127.97619 cents, oct.:  383.92857 cents
Scale is not proper
Scale has Myhill's property
  chromas: 325.00000 cents and 266.66667 cents, ratio: 1.218750
  generators: 1 of 58.33333 cents and 441.66667 cents
ET pair of linear temperament       : 34&86
Scale is distributional even
Scale is a mode of a 60-tone equal temperament with octave  500.000 cents
  degrees: 7 14 60
  generators: 7 and 53
Number of contiguous 1-step segments: 0
Step pattern alph. order: AAB
Step pattern size order : SSL
Interval vector is [ 0 0 0 0 0 0 2 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
Scale is sum-free (all different intervals)
Scale is a Constant Structure, by a margin of 58.33333 cents
Scale diversity                     : 0.555741
Lumma stability                     : 0.233333
Lumma impropriety factor            : 0.533333
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        : 58.33334 cents
Most common intervals               : 58.33333 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 1 2   N G T3   SD: 44.3576 c. M: 58.3333 c. 
  4:  0 1 3   N G T3   SD: 34.0207 c. M: 58.3333 c. 
  5:  0 1 4   N G T3   SD: 35.0264 c. M: 58.3333 c. 
  6:  1 0 5   N G T3   SD: 24.0563 c. M: 33.3333 c. 
  7:  1 1 5   N M DE S SD: 16.9059 c. M:-26.1905 c. 
  8:  1 1 6   N M DE S SD: 5.3791 c. M:-8.3333 c. 
  9:  1 1 7   N M DE S SD: 3.5861 c. M: 5.5556 c. 
 17:  2 2 13   N M DE S SD: 0.6328 c. M:-0.9804 c. 
 43:  5 5 33   N M DE S SD: 0.2502 c. M: 0.3876 c. 
 60:  7 7 46   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: 75.1085 cents
 7 x 8:9  S SD: 65.8142 cents
 8 x 9:11    SD: 50.6086 cents
 9 x 10:12  S SD: 32.8831 cents
 10 x 11:13    SD: 33.2899 cents
 11 x 12:15  S SD: 25.0965 cents
 12 x 13:16    SD: 10.9965 cents
 13 x 14:17    SD: 18.7128 cents
 14 x 15:19    SD: 14.4106 cents
 15 x 16:20  S SD: 2.6542 cents
 16 x 17:21    SD: 15.7394 cents
 17 x 18:23    SD: 14.6415 cents
 18 x 19:24    SD: 11.5732 cents
 19 x 20:25  S SD: 18.6802 cents
 20:21 x 27    SD: 16.3189 cents
 21:22 x 28    SD: 11.1448 cents
 24:25:26:32    SD: 8.4060 cents
 26:27:28:35  S SD: 6.6488 cents
 27:28:29:36    SD: 2.8844 cents
 30:31:32:40  S SD: 1.8449 cents
 57:59:61:76    SD: 0.8342 cents
 87:90:93:116    SD: 0.7753 cents
 116:120:124:155  S SD: 0.7248 cents
 143:148:153:191    SD: 0.5401 cents
 173:179:185:231    SD: 0.3484 cents
 230:238:246:307    SD: 0.2984 cents
 403:417:431:538    SD: 0.2980 cents
 442:457:473:590    SD: 0.2943 cents
 472:488:505:630    SD: 0.2376 cents
 529:547:566:706    SD: 0.2126 cents
 558:577:597:745    SD: 0.1990 cents
 588:608:629:785    SD: 0.1655 cents