Scala analysis: 675_T82

Tempered tetrachord in cents 225 + 25 + 250, Chapter 5

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

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:        225.000 cents     225.000000
  2:        250.000 cents     250.000000
  3:        500.000 cents     500.000000
SHOW/INTERVAL
  0:        250.0000 cents    250.0000
  1:        225.0000 cents    225.0000
  2:         25.0000 cents     25.0000
  3:        250.0000 cents    250.0000
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   1 25.00000 cents
  1:   1 225.00000 cents
  1:   1 250.00000 cents
  2:   1 250.00000 cents
  2:   1 275.00000 cents
  2:   1 475.00000 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  : 225.0 250.0 500.0
 225.0: 25.0  275.0 500.0
 250.0: 250.0 475.0 500.0
 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  25.0000   .. 250.0000 cents      225.00000 cents                    25.00000 cents
  2:  250.0000  .. 475.0000 cents      225.00000 cents                    1/1, 0.0000 cents
SHOW DATA
Number of notes                     : 3
-- Interval properties --
Smallest interval                   : 25.00000 cents, class 1
Average step (divided formal octave): 166.6667 cents
Largest one step interval           : 250.00000 cents
Average / Smallest step             : 6.666667
Largest / Average step              : 1.500000
Largest / Smallest step             : 10.000000
Median interval of one step         : 225.00000 cents, amount: 1
Least squares average step          : 158.92857 cents, oct.:  476.78571 cents
Scale is proper
Scale has trivalence property
Scale is a mode of a 20-tone equal temperament with octave  500.000 cents
  degrees: 9 10 20
Least number of segments generator  : 11 of 275.000 cents and inv.
  number of contiguous generator circle segments: 1
Shortest superset generator         : 11 of 275.000 cents and inv.
  generated superset size: 11 = 8 more = 366.667%
Number of contiguous 1-step segments: 1
Step pattern alph. order: ABC
Step pattern size order : MSL
Interval vector is [ 1 0 0 0 0 0 0 0 1 1 ]
Scale is sum-free (all different intervals)
Scale is not a Constant Structure
Scale diversity                     : 0.447031
Rothenberg stability                : 0.666667 = 2/3
Lumma stability                     : 0.100000
Rothenberg efficiency               : 0.777778   redundancy: 0.222222
Efficiency x scale size             : 2.333333
Number of different interval sizes  : 5 = 2.50000 / 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        : 25.00000 cents
Most common intervals               : 250.00000 cents & inv., amount: 2
Number of recognisable fifths       : 0
Number of recognisable fourths      : 0
Formal octave complements present   : 2 = 66.6667%
2/1 octave complements present      : 0 = 0.0000%
-- Rational properties --
FIT/MODE
  3:  1 0 2   N G T3   SD: 58.7288 c. M: 83.3333 c. 
  4:  2 0 2   P M DE I SD: 14.4338 c. M:-25.0000 c. 
 10:  4 1 5   P   T3   SD: 14.4338 c. M: 25.0000 c. 
 11:  5 0 6   N G T3   SD: 13.1870 c. M: 22.7273 c. 
 12:  5 1 6   P   T3   SD: 9.6225 c. M: 16.6667 c. 
 14:  6 1 7   P   T3   SD: 6.1859 c. M: 10.7143 c. 
 16:  7 1 8   P   T3   SD: 3.6084 c. M: 6.2500 c. 
 18:  8 1 9   P   T3   SD: 1.6038 c. M: 2.7778 c. 
 20:  9 1 10   P   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: 52.7187 cents
 6 x 7:8  S SD: 8.4919 cents
 7:8 x 9  S SD: 32.6044 cents
 8:9 x 11    SD: 27.7413 cents
 9:10 x 12  S SD: 21.3206 cents
 11 x 13:15    SD: 26.9386 cents
 12 x 14:16  S SD: 8.4919 cents
 13 x 15:17    SD: 17.8220 cents
 14:16 x 19    SD: 14.6720 cents
 15:17 x 20    SD: 4.2700 cents
 16:18 x 21  S SD: 18.0177 cents
 17:19:20:23    SD: 16.9300 cents
 18 x 21:24  S SD: 8.4919 cents
 19 x 22:25    SD: 12.5874 cents
 20 x 23:27    SD: 10.5698 cents
 21:24 x 28  S SD: 3.2381 cents
 22:25 x 29    SD: 11.0259 cents
 24:27:28:32  S SD: 9.0261 cents
 26 x 30:35    SD: 7.3928 cents
 27 x 31:36    SD: 5.5022 cents
 28:32 x 37    SD: 9.2700 cents
 30:34:35:40    SD: 6.3031 cents
 33 x 38:44    SD: 3.0413 cents
 34 x 39:45    SD: 9.6513 cents
 35:40 x 47    SD: 6.0331 cents
 36:41:42:48    SD: 5.6615 cents
 38:43:44:51    SD: 4.9854 cents
 40 x 46:53    SD: 7.5615 cents
 41:47 x 55    SD: 7.1485 cents
 42:48:49:56  S SD: 6.0237 cents
 43:49:50:57    SD: 5.4763 cents
 44:50:51:59    SD: 3.4412 cents
 45:51:52:60    SD: 2.8485 cents
 47 x 54:63    SD: 6.0254 cents
 48:55 x 64    SD: 5.4271 cents
 50:57:58:67    SD: 3.2712 cents
 51:58:59:68    SD: 1.2640 cents
 108:123:125:144    SD: 1.2160 cents
 116:132:134:155    SD: 0.7389 cents
 122:139:141:163    SD: 0.6299 cents
 167:190:193:223    SD: 0.6033 cents
 173:197:200:231    SD: 0.4025 cents
 245:279:283:327    SD: 0.1404 cents
 418:476:483:558    SD: 0.0856 cents