Scala analysis: 672_T79

Tempered tetrachord in cents 55 + 170 + 275, Chapter 5

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

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:         55.000 cents      55.000000
  2:        225.000 cents     225.000000
  3:        500.000 cents     500.000000
SHOW/INTERVAL
  0:        275.0000 cents    275.0000
  1:         55.0000 cents     55.0000
  2:        170.0000 cents    170.0000
  3:        275.0000 cents    275.0000
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   1 55.00000 cents
  1:   1 170.00000 cents
  1:   1 275.00000 cents
  2:   1 225.00000 cents
  2:   1 330.00000 cents
  2:   1 445.00000 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  : 55.0  225.0 500.0
 55.0 : 170.0 445.0 500.0
 225.0: 275.0 330.0 500.0
 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  55.0000   .. 275.0000 cents      220.00000 cents                    55.00000 cents
  2:  225.0000  .. 445.0000 cents      220.00000 cents                   -50.00000 cents
SHOW DATA
Number of notes                     : 3
-- Interval properties --
Smallest interval                   : 55.00000 cents, class 1
Average step (divided formal octave): 166.6667 cents
Largest one step interval           : 275.00000 cents
Average / Smallest step             : 3.030303
Largest / Average step              : 1.650000
Largest / Smallest step             : 5.000000
Median interval of one step         : 170.00000 cents, amount: 1
Least squares average step          : 143.21429 cents, oct.:  429.64286 cents
Scale is not proper
Scale has trivalence property
Scale is a mode of a 100-tone equal temperament with octave  500.000 cents
  degrees: 11 45 100
Least number of segments generator  : 51 of 255.000 cents and inv.
  number of contiguous generator circle segments: 1
Shortest superset generator         : 89 of 445.000 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 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 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                     : 0.890016
Lumma stability                     : 0.220000
Lumma impropriety factor            : 0.100000
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        : 50.00000 cents
Number of recognisable fifths       : 0
Number of recognisable fourths      : 0
Best minor thirds form a closed circle
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: 46.2881 c. M: 58.3333 c. 
  4:  0 2 2   P M DE S SD: 34.8807 c. M: 55.0000 c. 
  5:  0 2 3   N G T3   SD: 34.8807 c. M: 55.0000 c. 
  6:  1 2 3   P   T3   SD: 21.8157 c. M:-28.3333 c. 
  7:  1 2 4   N   T3   SD: 11.3239 c. M:-16.4286 c. 
  9:  1 3 5   N   T3   SD: 1.6355 c. M: 2.7778 c. 
 29:  3 10 16   N   T3   SD: 1.9557 c. M: 3.2759 c. 
 38:  4 13 21   N   T3   SD: 1.5643 c. M: 2.3684 c. 
 44:  5 15 24   N   T3   SD: 1.6804 c. M:-2.2727 c. 
 47:  5 16 26   N   T3   SD: 1.3925 c. M: 1.8085 c. 
 53:  6 18 29   N   T3   SD: 1.2349 c. M:-1.6038 c. 
 62:  7 21 34   N   T3   SD: 0.9587 c. M:-1.4516 c. 
 64:  7 22 35   N   T3   SD: 0.9200 c. M:-1.5625 c. 
 71:  8 24 39   N   T3   SD: 0.7988 c. M:-1.3380 c. 
 73:  8 25 40   N   T3   SD: 0.6049 c. M:-1.0274 c. 
 82:  9 28 45   N   T3   SD: 0.3590 c. M:-0.6098 c. 
 91:  10 31 50   N   T3   SD: 0.1618 c. M:-0.2747 c. 
 100: 11 34 55   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: 61.2864 cents
 6 x 7:8  S SD: 20.9583 cents
 7 x 8:9  S SD: 32.6044 cents
 8 x 9:11    SD: 27.7413 cents
 9 x 10:12  S SD: 21.3206 cents
 10 x 11:13    SD: 37.7354 cents
 11 x 13:15    SD: 37.0414 cents
 12:13:14:16  S SD: 31.1651 cents
 13:14:15:17    SD: 28.1961 cents
 14:15:16:19    SD: 23.6031 cents
 15:16:17:20    SD: 19.1235 cents
 18:19:21:24    SD: 18.9947 cents
 19:20:22:25    SD: 16.9689 cents
 20:21:23:27    SD: 13.0734 cents
 21:22:24:28  S SD: 8.7818 cents
 27:28:31:36    SD: 5.4569 cents
 29:30:33:39    SD: 4.4954 cents
 30:31:34:40    SD: 2.9070 cents
 36:37:41:48    SD: 2.6053 cents
 57:59:65:76    SD: 1.8732 cents
 65:67:74:87    SD: 1.7849 cents
 66:68:75:88    SD: 1.7779 cents
 87:90:99:116    SD: 1.4587 cents
 93:96:106:124    SD: 0.8243 cents
 122:126:139:163    SD: 0.6635 cents
 152:157:173:203    SD: 0.5555 cents
 158:163:180:211    SD: 0.4959 cents
 188:194:214:251    SD: 0.3416 cents
 245:253:279:327    SD: 0.2183 cents
 281:290:320:375    SD: 0.1971 cents
 403:416:459:538    SD: 0.1076 cents
 526:543:599:702    SD: 0.1058 cents