Scala analysis: 673_T80

Tempered tetrachord in cents 66.7 + 266.7 + 166.7, Chapter 5

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

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:         66.700 cents      66.700000
  2:        333.400 cents     333.400000
  3:        500.100 cents     500.100000
SHOW/INTERVAL
  0:        166.7000 cents    166.7000
  1:         66.7000 cents     66.7000
  2:        266.7000 cents    266.7000
  3:        166.7000 cents    166.7000
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   1 66.70000 cents
  1:   1 166.70000 cents
  1:   1 266.70000 cents
  2:   1 233.40000 cents
  2:   1 333.40000 cents
  2:   1 433.40000 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  333.4 500.1
 66.7 : 266.7 433.4 500.1
 333.4: 166.7 233.4 500.1
 500.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  66.7000   .. 266.7000 cents      200.00000 cents                    66.70000 cents
  2:  233.4000  .. 433.4000 cents      200.00000 cents                   -33.30000 cents
SHOW DATA
Number of notes                     : 3
-- Interval properties --
Smallest interval                   : 66.70000 cents, class 1
Average step (divided formal octave): 166.7000 cents
Largest one step interval           : 266.70000 cents
Average / Smallest step             : 2.499250
Largest / Average step              : 1.599880
Largest / Smallest step             : 3.998501
Median interval of one step         : 166.70000 cents, amount: 1
Least squares average step          : 159.55714 cents, oct.:  478.67143 cents
Scale is not proper
Scale has trivalence property
Step pattern alph. order: ABC
Step pattern size order : SLM
Scale is sum-free (all different intervals)
Scale is a Constant Structure, by a margin of 33.30000 cents
Scale diversity                     : 0.981557
Lumma stability                     : 0.266747
Lumma impropriety factor            : 0.066587
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        : 33.30000 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%
-- Rational properties --
FIT/MODE
  3:  0 2 1   N G T3   SD: 38.5093 c. M: 66.7000 c. 
  5:  1 2 2  SP M ME S SD: 27.2138 c. M: 33.3400 c. 
  6:  1 3 2   P   T3   SD: 9.6129 c. M:-16.6500 c. 
  9:  1 5 3   N   T3   SD: 6.4278 c. M: 11.1333 c. 
 15:  2 8 5   N   T3   SD: 0.0115 c. M: 0.0200 c. 
FIT/HARMONIC
 1 x x 2  S SD: 699.9000 cents
 2 x x 3  S SD: 201.8550 cents
 3 x x 4  S SD: 2.0550 cents
 4 x 5 x  S SD: 52.9137 cents
 5 x 6:7  S SD: 42.1519 cents
 6 x 7:8  S SD: 33.2804 cents
 7 x x 9    SD: 65.0159 cents
 8 x 10:11  S SD: 36.8210 cents
 10:11:12:13  H SD: 36.6434 cents
 11:12:13:15    SD: 33.9218 cents
 12:13:15:16    SD: 29.7578 cents
 13:14:16:17  S SD: 25.2688 cents
 14:15:17:19    SD: 20.0180 cents
 15:16:18:20  S SD: 16.1500 cents
 18:19:22:24    SD: 10.1336 cents
 23:24:28:31    SD: 6.4762 cents
 24:25:29:32    SD: 2.4355 cents
 51:53:62:68    SD: 1.7179 cents
 75:78:91:100    SD: 0.9155 cents
 128:133:155:171    SD: 0.8223 cents
 155:161:188:207    SD: 0.4731 cents
 179:186:217:239    SD: 0.1590 cents
 433:450:525:578    SD: 0.0515 cents