Scala analysis: 625_T32

Aristoxenian style tetrachord 5 + 7 + 18, Chapter 4

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

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:         83.333 cents      83.333330
  2:        200.000 cents     200.000000
  3:        500.000 cents     500.000000
SHOW/INTERVAL
  0:        300.0000 cents    300.0000
  1:         83.3333 cents     83.3333
  2:        116.6667 cents    116.6667
  3:        300.0000 cents    300.0000
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   1 83.33333 cents
  1:   1 116.66667 cents
  1:   1 300.00000 cents
  2:   1 200.00000 cents
  2:   1 383.33333 cents
  2:   1 416.66667 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  : 83.3  200.0 500.0
 83.3 : 116.7 416.7 500.0
 200.0: 300.0 383.3 500.0
 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  83.3333   .. 300.0000 cents      216.66667 cents                    83.33333 cents
  2:  200.0000  .. 416.6667 cents      216.66667 cents                   -100.00000 cents
SHOW DATA
Number of notes                     : 3
-- Interval properties --
Smallest interval                   : 83.33333 cents, class 1
Average step (divided formal octave): 166.6667 cents
Largest one step interval           : 300.00000 cents
Average / Smallest step             : 2.000000
Largest / Average step              : 1.800000
Largest / Smallest step             : 3.600000
Median interval of one step         : 116.66667 cents, amount: 1
Least squares average step          : 141.66667 cents, oct.:  425.00000 cents
Scale is not proper
Scale has trivalence property
Scale is a mode of a 30-tone equal temperament with octave  500.000 cents
  degrees: 5 12 30
Least number of segments generator  : 17 of 283.333 cents and inv.
  number of contiguous generator circle segments: 1
Shortest superset generator         : 23 of 383.333 cents and inv.
  generated superset size: 7 = 4 more = 233.333%
Number of contiguous 1-step segments: 0
Step pattern alph. order: ABC
Step pattern size order : SML
Interval vector is [ 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 ]
Scale is sum-free (all different intervals)
Scale is a Constant Structure, by a margin of 83.33333 cents
Scale diversity                     : 1.078374
Lumma stability                     : 0.333333
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        : 33.33334 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: 51.8188 c. M: 83.3333 c. 
  5:  1 1 3   N M DE S SD: 9.6225 c. M:-16.6667 c. 
  7:  1 2 4   N   T3   SD: 10.7363 c. M:-14.2857 c. 
 12:  2 3 7   N   T3   SD: 4.8113 c. M:-8.3333 c. 
 13:  2 3 8   N   T3   SD: 5.7811 c. M: 7.6923 c. 
 17:  3 4 10   N   T3   SD: 4.4208 c. M:-5.8824 c. 
 18:  3 4 11   N   T3   SD: 3.2075 c. M: 5.5556 c. 
 23:  4 5 14   N   T3   SD: 3.2676 c. M: 4.3478 c. 
 25:  4 6 15   N   T3   SD: 1.9245 c. M: 3.3333 c. 
 30:  5 7 18   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
 12:13 x 16    SD: 27.6370 cents
 13:14:15:17    SD: 24.8695 cents
 14:15:16:19    SD: 18.5552 cents
 15:16:17:20    SD: 10.9985 cents
 17:18:19:23    SD: 9.6792 cents
 18:19:20:24  S SD: 6.8225 cents
 24:25:27:32    SD: 4.4648 cents
 39:41:44:52    SD: 3.2046 cents
 41:43:46:55    SD: 2.8834 cents
 42:44:47:56    SD: 2.0939 cents
 57:60:64:76    SD: 1.9436 cents
 80:84:90:107    SD: 1.7781 cents
 81:85:91:108    SD: 0.8291 cents
 122:128:137:163    SD: 0.5907 cents
 164:172:184:219    SD: 0.4543 cents
 203:213:228:271    SD: 0.3609 cents
 221:232:248:295    SD: 0.2942 cents
 245:257:275:327    SD: 0.1938 cents
 424:445:476:566    SD: 0.1530 cents
 466:489:523:622    SD: 0.0847 cents
 588:617:660:785    SD: 0.0843 cents