Scala analysis: 621_T28

Aristoxenian style tetrachord 3 + 9 + 18, Chapter 4

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

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:         50.000 cents      50.000000
  2:        200.000 cents     200.000000
  3:        500.000 cents     500.000000
SHOW/INTERVAL
  0:        300.0000 cents    300.0000
  1:         50.0000 cents     50.0000
  2:        150.0000 cents    150.0000
  3:        300.0000 cents    300.0000
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   1 50.00000 cents
  1:   1 150.00000 cents
  1:   1 300.00000 cents
  2:   1 200.00000 cents
  2:   1 350.00000 cents
  2:   1 450.00000 cents
Highest number of different intervals for one interval class: 3
Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
        1     2     3    
 0.0  : 50.0  200.0 500.0
 50.0 : 150.0 450.0 500.0
 200.0: 300.0 350.0 500.0
 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  50.0000   .. 300.0000 cents      250.00000 cents                    50.00000 cents
  2:  200.0000  .. 450.0000 cents      250.00000 cents                   -100.00000 cents
SHOW DATA
Number of notes                     : 3
-- Interval properties --
Smallest interval                   : 50.00000 cents, class 1
Average step (divided formal octave): 166.6667 cents
Largest one step interval           : 300.00000 cents
Average / Smallest step             : 3.333333
Largest / Average step              : 1.800000
Largest / Smallest step             : 6.000000
Median interval of one step         : 150.00000 cents, amount: 1
Least squares average step          : 139.28571 cents, oct.:  417.85714 cents
Scale is not proper
Scale has trivalence property
Scale is a mode of a 10-tone equal temperament with octave  500.000 cents
  degrees: 1 4 10
Least number of segments generator  : 9 of 450.000 cents and inv.
  number of contiguous generator circle segments: 1
Shortest superset generator         : 7 of 350.000 cents and inv.
  generated superset size: 4 = 1 more = 133.333%
Number of contiguous 1-step segments: 1
Step pattern alph. order: ABC
Step pattern size order : SML
Interval vector is [ 1 0 1 1 0 ]
Scale is sum-free (all different intervals)
Scale is a Constant Structure, by a margin of 50.00000 cents
Scale diversity                     : 0.872124
Lumma stability                     : 0.200000
Lumma impropriety factor            : 0.200000
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        : 50.00000 cents
Number of recognisable fifths       : 0
Number of recognisable fourths      : 0
Steps are strictly increasing
Formal octave complements present   : 1 = 33.3333%
2/1 octave complements present      : 0 = 0.0000%
-- Rational properties --
FIT/MODE
  3:  0 1 2   N G T3   SD: 34.6944 c. M: 50.0000 c. 
  5:  0 2 3   N G T3   SD: 28.8675 c. M: 50.0000 c. 
  6:  1 1 4   N M DE S SD: 27.2166 c. M: 33.3333 c. 
  7:  1 2 4   N   T3   SD: 14.8690 c. M:-21.4286 c. 
  8:  1 2 5   N   T3   SD: 10.2062 c. M: 12.5000 c. 
 10:  1 3 6   N   T3   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: 71.0302 cents
 6 x 7:8  S SD: 33.4497 cents
 7 x 8:9  S SD: 36.0066 cents
 8 x 9:11    SD: 25.7333 cents
 9 x 10:12  S SD: 8.8523 cents
 10 x 11:13    SD: 28.8143 cents
 11 x 12:15  S SD: 30.8304 cents
 12 x 13:16    SD: 30.7292 cents
 13 x 15:17    SD: 29.7682 cents
 14:15:16:19    SD: 27.1151 cents
 15:16:17:20    SD: 21.3256 cents
 16:17:18:21  S SD: 20.7877 cents
 17:18:19:23    SD: 18.2444 cents
 18:19:20:24  S SD: 15.6868 cents
 21:22:24:28  S SD: 14.5608 cents
 22:23:25:29    SD: 13.5540 cents
 23:24:26:31    SD: 10.4979 cents
 24:25:27:32    SD: 7.0432 cents
 30:31:34:40    SD: 6.0375 cents
 32:33:36:43    SD: 4.1986 cents
 33:34:37:44    SD: 1.0736 cents
 105:108:118:140    SD: 1.0354 cents
 131:135:147:175    SD: 0.8401 cents
 138:142:155:184    SD: 0.7717 cents
 140:144:157:187    SD: 0.7703 cents
 164:169:184:219    SD: 0.7497 cents
 170:175:191:227    SD: 0.5858 cents
 203:209:228:271    SD: 0.3870 cents
 236:243:265:315    SD: 0.2976 cents
 269:277:302:359    SD: 0.2927 cents
 343:353:385:458    SD: 0.2064 cents
 376:387:422:502    SD: 0.1337 cents
 409:421:459:546    SD: 0.1235 cents