Scala analysis: 598_T5

Aristoxenian style tetrachord 2 + 4 + 24, 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:        100.000 cents     100.000000
  3:        500.000 cents     500.000000
SHOW/INTERVAL
  0:        400.0000 cents    400.0000
  1:         33.3333 cents     33.3333
  2:         66.6667 cents     66.6667
  3:        400.0000 cents    400.0000
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   1 33.33333 cents
  1:   1 66.66667 cents
  1:   1 400.00000 cents
  2:   1 100.00000 cents
  2:   1 433.33333 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  100.0 500.0
 33.3 : 66.7  466.7 500.0
 100.0: 400.0 433.3 500.0
 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  33.3333   .. 400.0000 cents      366.66667 cents                    33.33333 cents
  2:  100.0000  .. 466.6667 cents      366.66667 cents                   -300.00000 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           : 400.00000 cents
Average / Smallest step             : 5.000001
Largest / Average step              : 2.400000
Largest / Smallest step             : 12.000001
Median interval of one step         : 66.66667 cents, amount: 1
Least squares average step          : 123.80952 cents, oct.:  371.42857 cents
Scale is not proper
Scale has trivalence property
Scale is a mode of a 15-tone equal temperament with octave  500.000 cents
  degrees: 1 3 15
Least number of segments generator  : 11 of 366.667 cents and inv.
  number of contiguous generator circle segments: 1
Shortest superset generator         : 14 of 466.667 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 1 1 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                     : 0.393283
Lumma stability                     : 0.133333
Lumma impropriety factor            : 0.600000
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 0 3   N M DE S SD: 60.8581 c. M: 100.0000 c. 
  4:  0 1 3   N G T3   SD: 24.0563 c. M: 33.3333 c. 
  5:  0 1 4   N G T3   SD: 19.2450 c. M: 33.3333 c. 
  6:  0 1 5   N G T3   SD: 21.5166 c. M: 33.3333 c. 
  9:  1 1 7   N M DE S SD: 14.3444 c. M:-22.2222 c. 
 10:  1 1 8   N M DE S SD: 9.6225 c. M:-16.6667 c. 
 11:  1 1 9   N M DE S SD: 8.7477 c. M:-12.1212 c. 
 13:  1 2 10   N   T3   SD: 9.3628 c. M:-15.3846 c. 
 14:  1 2 11   N   T3   SD: 4.3470 c. M:-7.1429 c. 
 15:  1 2 12   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: 83.4412 cents
 7 x 8:9  S SD: 73.1791 cents
 8 x 9:11    SD: 57.9457 cents
 9 x 10:12  S SD: 41.2134 cents
 10 x 11:13    SD: 39.7552 cents
 11 x 12:15  S SD: 31.3427 cents
 12 x 13:16    SD: 19.3111 cents
 13 x 14:17    SD: 22.7276 cents
 14 x 15:19    SD: 17.3275 cents
 15 x 16:20  S SD: 5.9465 cents
 16 x 17:21    SD: 14.8182 cents
 17 x 18:23    SD: 11.6712 cents
 18 x 19:24    SD: 3.3445 cents
 19 x 20:25  S SD: 13.6448 cents
 20 x 21:27    SD: 12.4852 cents
 21 x 22:28    SD: 9.7805 cents
 22 x 23:29    SD: 15.8404 cents
 23 x 24:31    SD: 15.6017 cents
 24 x 25:32    SD: 14.6963 cents
 25 x 26:33    SD: 18.7416 cents
 26:27:28:35  S SD: 15.0501 cents
 27:28:29:36    SD: 12.6662 cents
 28:29:30:37    SD: 12.6288 cents
 29:30:31:39    SD: 10.7938 cents
 30:31:32:40  S SD: 8.7596 cents
 32:33:34:43    SD: 7.8514 cents
 33:34:35:44    SD: 6.1824 cents
 36:37:38:48    SD: 5.2023 cents
 45:46:48:60  S SD: 4.2648 cents
 47:48:50:63    SD: 3.5382 cents
 48:49:51:64    SD: 1.9426 cents
 51:52:54:68    SD: 0.7450 cents
 149:152:158:199    SD: 0.7179 cents
 152:155:161:203    SD: 0.3675 cents
 203:207:215:271    SD: 0.2491 cents
 403:411:427:538    SD: 0.2459 cents
 454:463:481:606    SD: 0.2175 cents
 469:478:497:626    SD: 0.1959 cents
 520:530:551:694    SD: 0.1744 cents
 570:581:604:761    SD: 0.1681 cents