Scala analysis: 669_T76

Tempered tetrachord in cents 83.3 + 283.3 + 133.3, Chapter 5

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

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:         83.300 cents      83.300000
  2:        366.600 cents     366.600000
  3:        499.900 cents     499.900000
SHOW/INTERVAL
  0:        133.3000 cents    133.3000
  1:         83.3000 cents     83.3000
  2:        283.3000 cents    283.3000
  3:        133.3000 cents    133.3000
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   1 83.30000 cents
  1:   1 133.30000 cents
  1:   1 283.30000 cents
  2:   1 216.60000 cents
  2:   1 366.60000 cents
  2:   1 416.60000 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  : 83.3  366.6 499.9
 83.3 : 283.3 416.6 499.9
 366.6: 133.3 216.6 499.9
 499.9
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  83.3000   .. 283.3000 cents      200.00000 cents                    83.30000 cents
  2:  216.6000  .. 416.6000 cents      200.00000 cents                   -66.70000 cents
SHOW DATA
Number of notes                     : 3
-- Interval properties --
Smallest interval                   : 83.30000 cents, class 1
Average step (divided formal octave): 166.6333 cents
Largest one step interval           : 283.30000 cents
Average / Smallest step             : 2.000400
Largest / Average step              : 1.700140
Largest / Smallest step             : 3.400960
Median interval of one step         : 133.30000 cents, amount: 1
Least squares average step          : 165.44286 cents, oct.:  496.32857 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 66.70000 cents
Scale diversity                     : 1.111760
Lumma stability                     : 0.333267
Lumma impropriety factor            : 0.133427
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
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: 51.8009 c. M: 83.3000 c. 
  4:  1 2 1   P M ME I SD: 24.5364 c. M:-41.6750 c. 
  5:  1 3 1   N M DE I SD: 21.5131 c. M:-33.3200 c. 
  6:  1 3 2   P   T3   SD: 19.2450 c. M: 33.3333 c. 
  7:  1 4 2   N   T3   SD: 8.7951 c. M: 11.8857 c. 
 11:  2 6 3   N   T3   SD: 4.7202 c. M:-7.5909 c. 
 12:  2 7 3   N   T3   SD: 4.8065 c. M:-8.3250 c. 
 18:  3 10 5   N   T3   SD: 3.2107 c. M: 5.5611 c. 
 19:  3 11 5   N   T3   SD: 2.7164 c. M: 4.3684 c. 
 23:  4 13 6   N   T3   SD: 2.6835 c. M:-3.6391 c. 
 30:  5 17 8   N   T3   SD: 0.0104 c. M:-0.0167 c. 
FIT/HARMONIC
 1 x x 2  S SD: 700.1000 cents
 2 x x 3  S SD: 202.0550 cents
 3 x x 4  S SD: 1.8550 cents
 4 x 5 x  S SD: 19.7137 cents
 5 x 6:7  S SD: 48.5324 cents
 6 x 7:8  S SD: 49.8732 cents
 7 x x 9    SD: 64.8159 cents
 8:9:10:11  H SD: 44.1955 cents
 9:10:11:12  H SD: 33.6540 cents
 11:12:14:15  S SD: 30.7294 cents
 12:13:15:16    SD: 19.5708 cents
 13:14:16:17  S SD: 19.2467 cents
 14:15:17:19    SD: 18.4495 cents
 15:16:19:20    SD: 17.0955 cents
 16:17:20:21    SD: 13.7659 cents
 17:18:21:23    SD: 9.3933 cents
 18:19:22:24    SD: 7.2872 cents
 21:22:26:28    SD: 1.5267 cents
 60:63:74:80    SD: 1.3835 cents
 81:85:100:108    SD: 0.8613 cents
 102:107:126:136    SD: 0.6867 cents
 123:129:152:164    SD: 0.6803 cents
 140:147:173:187    SD: 0.5695 cents
 161:169:199:215    SD: 0.3624 cents
 182:191:225:243    SD: 0.2751 cents
 242:254:299:323    SD: 0.2183 cents
 263:276:325:351    SD: 0.1142 cents
 445:467:550:594    SD: 0.0993 cents
 547:574:676:730    SD: 0.0987 cents