Scala analysis: 594_T1

Aristoxenian style tetrachord 2 + 2 + 26, Chapter 4

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

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:         33.333 cents      33.333330
  2:         66.667 cents      66.666670
  3:        500.000 cents     500.000000
SHOW/INTERVAL
  0:        433.3333 cents    433.3333
  1:         33.3333 cents     33.3333
  2:         33.3333 cents     33.3333
  3:        433.3333 cents    433.3333
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   2 33.33333 cents
  1:   1 433.33333 cents
  2:   1 66.66667 cents
  2:   2 466.66667 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  : 33.3  66.7  500.0
 33.3 : 33.3  466.7 500.0
 66.7 : 433.3 466.7 500.0
 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  33.3333   .. 433.3333 cents      400.00000 cents                    33.33333 cents
  2:  66.6667   .. 466.6667 cents      400.00000 cents                   -366.66666 cents
SHOW DATA
Number of notes                     : 3
-- Interval properties --
Smallest interval                   : 33.33333 cents, class 1
Average step (divided formal octave): 166.6667 cents
Largest one step interval           : 433.33333 cents
Average / Smallest step             : 5.000001
Largest / Average step              : 2.600000
Largest / Smallest step             : 13.000001
Median interval of one step         : 33.33333 cents, amount: 2
Most common interval of one step    : 33.33333 cents, amount: 2
Least squares average step          : 119.04762 cents, oct.:  357.14286 cents
Scale is not proper
Scale has Myhill's property
  chromas: 400.00000 cents and 366.66667 cents, ratio: 1.090909
  generators: 1 of 33.33333 cents and 466.66667 cents
ET pair of linear temperament       : 30&19999982
Scale is distributional even
Scale is a mode of a 15-tone equal temperament with octave  500.000 cents
  degrees: 1 2 15
  generators: 1 and 14
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 0 ]
Scale is sum-free (all different intervals)
Scale is a Constant Structure, by a margin of 33.33333 cents
Scale diversity                     : 0.182799
Lumma stability                     : 0.133333
Lumma impropriety factor            : 0.733333
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        : 33.33334 cents
Most common intervals               : 33.33333 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 0 3   N M DE S SD: 43.0331 c. M: 66.6667 c. 
  5:  0 1 4   N G T3   SD: 27.2165 c. M:-33.3333 c. 
  6:  0 1 5   N G T3   SD: 21.5166 c. M: 33.3333 c. 
  7:  0 1 6   N G T3   SD: 19.4404 c. M: 33.3333 c. 
  8:  0 1 7   N G T3   SD: 19.3948 c. M: 33.3333 c. 
  9:  0 1 8   N G T3   SD: 20.2860 c. M: 33.3333 c. 
 10:  0 1 9   N G T3   SD: 21.5166 c. M: 33.3333 c. 
 11:  1 1 9   N M DE S SD: 15.6484 c. M:-24.2424 c. 
 12:  1 1 10   N M DE S SD: 10.7583 c. M:-16.6667 c. 
 13:  1 1 11   N M DE S SD: 6.6205 c. M:-10.2564 c. 
 14:  1 1 12   N M DE S SD: 3.0738 c. M:-4.7619 c. 
 15:  1 1 13   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: 100.1069 cents
 7 x 8:9  S SD: 88.4262 cents
 8 x 9:11    SD: 73.2620 cents
 9 x 10:12  S SD: 57.8768 cents
 10 x 11:13    SD: 54.2371 cents
 11 x 12:15  S SD: 45.8704 cents
 12 x 13:16    SD: 35.9663 cents
 13 x 14:17    SD: 35.5803 cents
 14 x 15:19    SD: 30.0344 cents
 15 x 16:20  S SD: 22.5535 cents
 16 x 17:21    SD: 24.0821 cents
 17 x 18:23    SD: 19.9141 cents
 18 x 19:24    SD: 13.5036 cents
 19 x 20:25  S SD: 16.6524 cents
 20 x 21:27    SD: 13.2204 cents
 21 x 22:28    SD: 7.0037 cents
 22 x 23:29    SD: 12.0264 cents
 23 x 24:31    SD: 9.0848 cents
 24 x 25:32    SD: 2.2287 cents
 25 x 26:33    SD: 9.6969 cents
 26 x 27:35    SD: 7.3362 cents
 27 x 28:36    SD: 2.0949 cents
 28 x 29:37    SD: 9.2278 cents
 29 x 30:39    SD: 7.5854 cents
 30 x 31:40    SD: 5.0455 cents
 31 x 32:41    SD: 9.9006 cents
 32 x 33:43    SD: 8.8325 cents
 33 x 34:44    SD: 7.5556 cents
 34 x 35:45    SD: 11.0532 cents
 35:36 x 47    SD: 9.2975 cents
 36:37 x 48    SD: 7.1178 cents
 37:38 x 49    SD: 9.3839 cents
 38:39 x 51    SD: 7.4786 cents
 41:42:43:55    SD: 6.6083 cents
 42:43:44:56    SD: 5.2812 cents
 44:45:46:59    SD: 4.6977 cents
 45:46:47:60    SD: 3.3386 cents
 47:48:49:63    SD: 3.1969 cents
 48:49:50:64    SD: 1.6817 cents
 51:52:53:68    SD: 0.6589 cents
 152:155:158:203    SD: 0.3610 cents
 203:207:211:271    SD: 0.1806 cents
 254:259:264:339    SD: 0.1731 cents
 409:417:425:546    SD: 0.1158 cents
 460:469:478:614    SD: 0.1034 cents