Scala analysis: 635_T42

Aristoxenian style tetrachord 3 + 12 + 15, 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:        250.000 cents     250.000000
  3:        500.000 cents     500.000000
SHOW/INTERVAL
  0:        250.0000 cents    250.0000
  1:         50.0000 cents     50.0000
  2:        200.0000 cents    200.0000
  3:        250.0000 cents    250.0000
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   1 50.00000 cents
  1:   1 200.00000 cents
  1:   1 250.00000 cents
  2:   1 250.00000 cents
  2:   1 300.00000 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  250.0 500.0
 50.0 : 200.0 450.0 500.0
 250.0: 250.0 300.0 500.0
 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  50.0000   .. 250.0000 cents      200.00000 cents                    50.00000 cents
  2:  250.0000  .. 450.0000 cents      200.00000 cents                    1/1, 0.0000 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           : 250.00000 cents
Average / Smallest step             : 3.333333
Largest / Average step              : 1.500000
Largest / Smallest step             : 5.000000
Median interval of one step         : 200.00000 cents, amount: 1
Least squares average step          : 146.42857 cents, oct.:  439.28571 cents
Scale is proper
Scale has trivalence property
Scale is a mode of a 10-tone equal temperament with octave  500.000 cents
  degrees: 1 5 10
Least number of segments generator  : 7 of 350.000 cents and inv.
  number of contiguous generator circle segments: 1
Shortest superset generator         : 7 of 350.000 cents and inv.
  generated superset size: 6 = 3 more = 200.000%
Number of contiguous 1-step segments: 1
Step pattern alph. order: ABC
Step pattern size order : SML
Interval vector is [ 1 0 0 1 1 ]
Scale is sum-free (all different intervals)
Scale is not a Constant Structure
Scale diversity                     : 0.739849
Rothenberg stability                : 0.666667 = 2/3
Lumma stability                     : 0.200000
Rothenberg efficiency               : 0.777778   redundancy: 0.222222
Efficiency x scale size             : 2.333333
Number of different interval sizes  : 5 = 2.50000 / 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
Most common intervals               : 250.00000 cents & inv., amount: 2
Number of recognisable fifths       : 0
Number of recognisable fourths      : 0
Steps are strictly increasing
Formal octave complements present   : 2 = 66.6667%
2/1 octave complements present      : 0 = 0.0000%
-- Rational properties --
FIT/MODE
  3:  0 1 2   N G T3   SD: 56.1084 c. M: 83.3333 c. 
  4:  0 2 2   P M DE S SD: 28.8675 c. M: 50.0000 c. 
  6:  1 2 3   P   T3   SD: 19.2450 c. M:-33.3333 c. 
  8:  1 3 4   P   T3   SD: 7.2169 c. M:-12.5000 c. 
 10:  1 4 5   P   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: 52.7187 cents
 6 x 7:8  S SD: 8.4919 cents
 7 x 8:9  S SD: 33.7953 cents
 8 x 9:11    SD: 34.4885 cents
 9 x 10:12  S SD: 33.8123 cents
 10 x 12:13  S SD: 40.0161 cents
 11 x 13:15    SD: 26.9386 cents
 14:15:16:19    SD: 25.8192 cents
 15:16:17:20    SD: 23.3912 cents
 17:18:20:23    SD: 20.8797 cents
 18:19:21:24    SD: 15.5980 cents
 19:20:22:25    SD: 15.4174 cents
 20:21:23:27    SD: 13.4778 cents
 21:22:24:28  S SD: 11.9757 cents
 24:25:28:32    SD: 8.9181 cents
 26:27:30:35  S SD: 7.1012 cents
 27:28:31:36    SD: 5.6675 cents
 32:33:37:43    SD: 4.0163 cents
 33:34:38:44    SD: 2.1037 cents
 65:67:75:87    SD: 1.9202 cents
 71:73:82:95    SD: 1.5311 cents
 96:99:111:128    SD: 1.3475 cents
 102:105:118:136    SD: 0.9983 cents
 134:138:155:179    SD: 0.8589 cents
 135:139:156:180    SD: 0.6846 cents
 167:172:193:223    SD: 0.4480 cents
 200:206:231:267    SD: 0.4345 cents
 206:212:238:275    SD: 0.1100 cents
 579:596:669:773    SD: 0.1100 cents