Scala analysis: 628_T35

Aristoxenian style tetrachord 6.5 + 6.5 + 17, Chapter 4

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

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:        108.333 cents     108.333330
  2:        216.667 cents     216.666670
  3:        500.000 cents     500.000000
SHOW/INTERVAL
  0:        283.3333 cents    283.3333
  1:        108.3333 cents    108.3333
  2:        108.3333 cents    108.3333
  3:        283.3333 cents    283.3333
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   2 108.33333 cents
  1:   1 283.33333 cents
  2:   1 216.66667 cents
  2:   2 391.66667 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  : 108.3 216.7 500.0
 108.3: 108.3 391.7 500.0
 216.7: 283.3 391.7 500.0
 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  108.3333  .. 283.3333 cents      175.00000 cents                    108.33333 cents
  2:  216.6667  .. 391.6667 cents      175.00000 cents                   -66.66666 cents
SHOW DATA
Number of notes                     : 3
-- Interval properties --
Smallest interval                   : 108.33333 cents, class 1
Average step (divided formal octave): 166.6667 cents
Largest one step interval           : 283.33333 cents
Average / Smallest step             : 1.538462
Largest / Average step              : 1.700000
Largest / Smallest step             : 2.615385
Median interval of one step         : 108.33333 cents, amount: 2
Most common interval of one step    : 108.33333 cents, amount: 2
Least squares average step          : 145.83333 cents, oct.:  437.50000 cents
Scale is not proper
Scale has Myhill's property
  chromas: 175.00000 cents and 66.66667 cents, ratio: 2.625000
  generators: 1 of 108.33333 cents and 391.66667 cents
ET pair of linear temperament       : 28&46
Scale is distributional even
Scale is a mode of a 60-tone equal temperament with octave  500.000 cents
  degrees: 13 26 60
  generators: 13 and 47
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 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ]
Scale is sum-free (all different intervals)
Scale is a Constant Structure, by a margin of 66.66666 cents
Scale diversity                     : 1.117221
Lumma stability                     : 0.433333
Lumma impropriety factor            : 0.133333
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        : 66.66666 cents
Most common intervals               : 108.33333 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: 68.8866 c. M: 108.3333 c. 
  4:  1 1 2   P M ME S SD: 21.5166 c. M:-33.3333 c. 
  5:  1 1 3   N M DE S SD: 10.7583 c. M: 16.6667 c. 
  9:  2 2 5   N M DE S SD: 3.5861 c. M:-5.5556 c. 
 14:  3 3 8   N M DE S SD: 1.5369 c. M: 2.3810 c. 
 23:  5 5 13   N M DE S SD: 0.4678 c. M:-0.7246 c. 
 37:  8 8 21   N M DE S SD: 0.2908 c. M: 0.4505 c. 
 60:  13 13 34   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 6:7  S SD: 64.4287 cents
 6 x 7:8  S SD: 25.1211 cents
 7 x 8:9  S SD: 33.2586 cents
 8 x 9:11    SD: 26.4399 cents
 9 x 10:12  S SD: 17.1593 cents
 10 x 11:13    SD: 34.5158 cents
 11:12 x 15  S SD: 28.0845 cents
 12:13:14:16  S SD: 19.5468 cents
 13:14:15:17    SD: 17.0932 cents
 14:15:16:19    SD: 11.3374 cents
 15:16:17:20    SD: 1.3068 cents
 126:134:143:168    SD: 1.1970 cents
 141:150:160:188    SD: 1.0577 cents
 143:152:162:191    SD: 0.9848 cents
 156:166:177:208    SD: 0.9616 cents
 158:168:179:211    SD: 0.7722 cents
 173:184:196:231    SD: 0.5983 cents
 188:200:213:251    SD: 0.4548 cents
 203:216:230:271    SD: 0.3370 cents
 218:232:247:291    SD: 0.2436 cents
 233:248:264:311    SD: 0.1785 cents
 248:264:281:331    SD: 0.1514 cents