Scala analysis: 608_T15

Aristoxenian style tetrachord 2 + 7 + 21, Chapter 4

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

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:         33.333 cents      33.333330
  2:        150.000 cents     150.000000
  3:        500.000 cents     500.000000
SHOW/INTERVAL
  0:        350.0000 cents    350.0000
  1:         33.3333 cents     33.3333
  2:        116.6667 cents    116.6667
  3:        350.0000 cents    350.0000
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   1 33.33333 cents
  1:   1 116.66667 cents
  1:   1 350.00000 cents
  2:   1 150.00000 cents
  2:   1 383.33333 cents
  2:   1 466.66667 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  : 33.3  150.0 500.0
 33.3 : 116.7 466.7 500.0
 150.0: 350.0 383.3 500.0
 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  33.3333   .. 350.0000 cents      316.66667 cents                    33.33333 cents
  2:  150.0000  .. 466.6667 cents      316.66667 cents                   -200.00000 cents
SHOW DATA
Number of notes                     : 3
-- Interval properties --
Smallest interval                   : 33.33333 cents, class 1
Average step (divided formal octave): 166.6667 cents
Largest one step interval           : 350.00000 cents
Average / Smallest step             : 5.000001
Largest / Average step              : 2.100000
Largest / Smallest step             : 10.500001
Median interval of one step         : 116.66667 cents, amount: 1
Least squares average step          : 130.95238 cents, oct.:  392.85714 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: 2 9 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: 5 = 2 more = 166.667%
Number of contiguous 1-step segments: 0
Step pattern alph. order: ABC
Step pattern size order : SML
Interval vector is [ 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 ]
Scale is sum-free (all different intervals)
Scale is a Constant Structure, by a margin of 33.33333 cents
Scale diversity                     : 0.638547
Lumma stability                     : 0.133333
Lumma impropriety factor            : 0.400000
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        : 33.33333 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: 21.5166 c. M: 33.3333 c. 
  4:  0 1 3   N G T3   SD: 24.0563 c. M: 33.3333 c. 
  6:  0 2 4   N G T3   SD: 21.5166 c. M: 33.3333 c. 
  7:  0 2 5   N G T3   SD: 19.6819 c. M: 33.3333 c. 
  9:  1 2 6   N   T3   SD: 16.0375 c. M:-22.2222 c. 
 10:  1 2 7   N   T3   SD: 9.6225 c. M:-16.6667 c. 
 11:  1 2 8   N   T3   SD: 10.5337 c. M: 13.6364 c. 
 12:  1 3 8   N   T3   SD: 10.7583 c. M:-16.6667 c. 
 13:  1 3 9   N   T3   SD: 3.7010 c. M:-5.1282 c. 
 17:  1 4 12   N   T3   SD: 2.8301 c. M: 3.9216 c. 
 27:  2 6 19   N   T3   SD: 2.3907 c. M:-3.7037 c. 
 30:  2 7 21   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: 92.5274 cents
 6 x 7:8  S SD: 58.4436 cents
 7 x 8:9  S SD: 51.9695 cents
 8 x 9:11    SD: 37.2150 cents
 9 x 10:12  S SD: 16.2313 cents
 10 x 11:13    SD: 24.0909 cents
 11 x 12:15  S SD: 18.4781 cents
 12 x 13:16    SD: 5.7967 cents
 13 x 14:17    SD: 20.8348 cents
 14 x 15:19    SD: 20.9565 cents
 15 x 16:20  S SD: 19.1593 cents
 16 x 17:21    SD: 26.8457 cents
 17 x 19:23    SD: 24.2638 cents
 18 x 20:24  S SD: 16.2313 cents
 21:22:23:28    SD: 15.9449 cents
 23:24:25:31    SD: 14.6846 cents
 24:25:26:32    SD: 13.0325 cents
 29:30:32:39    SD: 11.6747 cents
 30:31:33:40    SD: 9.2980 cents
 32:33:35:43    SD: 7.8646 cents
 33:34:36:44    SD: 6.1547 cents
 36:37:39:48    SD: 6.0849 cents
 41:42:45:55    SD: 5.4601 cents
 42:43:46:56    SD: 3.5713 cents
 44:45:48:59    SD: 3.2169 cents
 45:46:49:60    SD: 1.9058 cents
 54:55:59:72    SD: 1.3829 cents
 98:100:107:131    SD: 1.2099 cents
 99:101:108:132    SD: 0.8096 cents
 155:158:169:207    SD: 0.2991 cents
 209:213:228:279    SD: 0.2753 cents
 254:259:277:339    SD: 0.1634 cents
 409:417:446:546    SD: 0.0890 cents