Scala analysis: 601_T8

Aristoxenian style tetrachord 4 + 3 + 23, Chapter 3

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

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:         66.667 cents      66.666670
  2:        116.667 cents     116.666670
  3:        500.000 cents     500.000000
SHOW/INTERVAL
  0:        383.3333 cents    383.3333
  1:         66.6667 cents     66.6667
  2:         50.0000 cents     50.0000
  3:        383.3333 cents    383.3333
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   1 50.00000 cents
  1:   1 66.66667 cents
  1:   1 383.33333 cents
  2:   1 116.66667 cents
  2:   1 433.33333 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  : 66.7  116.7 500.0
 66.7 : 50.0  433.3 500.0
 116.7: 383.3 450.0 500.0
 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  50.0000   .. 383.3333 cents      333.33333 cents                    50.00000 cents
  2:  116.6667  .. 450.0000 cents      333.33333 cents                   -266.66666 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           : 383.33333 cents
Average / Smallest step             : 3.333333
Largest / Average step              : 2.300000
Largest / Smallest step             : 7.666667
Median interval of one step         : 66.66667 cents, amount: 1
Least squares average step          : 128.57143 cents, oct.:  385.71429 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: 4 7 30
Least number of segments generator  : 19 of 316.667 cents and inv.
  number of contiguous generator circle segments: 1
Shortest superset generator         : 29 of 483.333 cents and inv.
  generated superset size: 8 = 5 more = 266.667%
Number of contiguous 1-step segments: 0
Step pattern alph. order: ABC
Step pattern size order : MSL
Interval vector is [ 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 ]
Scale is sum-free (all different intervals)
Scale is a Constant Structure, by a margin of 50.00000 cents
Scale diversity                     : 0.543715
Lumma stability                     : 0.200000
Lumma impropriety factor            : 0.533333
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        : 16.66667 cents
Number of recognisable fifths       : 0
Number of recognisable fourths      : 0
Formal octave complements present   : 1 = 33.3333%
2/1 octave complements present      : 0 = 0.0000%
Limited inverse transpositions with margin 333.3333 cents:
 2
-- Rational properties --
FIT/MODE
  3:  0 1 2   N G T3   SD: 48.1125 c. M: 66.6667 c. 
  4:  1 0 3   N G T3   SD: 34.0207 c. M:-58.3333 c. 
  5:  1 0 4   N G T3   SD: 21.5166 c. M:-33.3333 c. 
  7:  1 1 5   N M DE S SD: 15.3690 c. M:-26.1905 c. 
  8:  1 1 6   N M DE S SD: 5.3791 c. M:-8.3333 c. 
 17:  2 2 13   N M DE S SD: 4.5635 c. M: 7.8431 c. 
 21:  3 2 16   N   T3   SD: 3.0738 c. M:-4.7619 c. 
 22:  3 2 17   N   T3   SD: 1.9561 c. M: 3.0303 c. 
 30:  4 3 23   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 x 7    SD: 82.5122 cents
 6 x 7:8  S SD: 75.1085 cents
 7 x 8:9  S SD: 65.8142 cents
 8 x 9:11    SD: 50.6086 cents
 9 x 10:12  S SD: 32.8831 cents
 10 x 11:13    SD: 33.2899 cents
 11 x 12:15  S SD: 25.0965 cents
 12 x 13:16    SD: 10.9965 cents
 13 x 14:17    SD: 18.7128 cents
 14 x 15:19    SD: 14.4106 cents
 15 x 16:20  S SD: 2.6542 cents
 16 x 17:21    SD: 15.7394 cents
 17 x 18:23    SD: 14.6415 cents
 18 x 19:24    SD: 11.5732 cents
 19:20 x 25  S SD: 16.6524 cents
 20:21 x 27    SD: 13.2204 cents
 21:22 x 28    SD: 7.0037 cents
 26:27:28:35  S SD: 6.2412 cents
 27:28:29:36    SD: 2.7324 cents
 57:59:61:76    SD: 2.4237 cents
 71:74:76:95    SD: 2.1906 cents
 72:75:77:96    SD: 1.4928 cents
 99:103:106:132    SD: 1.0566 cents
 101:105:108:135    SD: 0.8276 cents
 128:133:137:171    SD: 0.5847 cents
 200:208:214:267    SD: 0.4450 cents
 203:211:217:271    SD: 0.4154 cents
 230:239:246:307    SD: 0.1095 cents