Scala analysis: 655_T62

Aristoxenian style tetrachord 12 + 9 + 9, Al-Farabi; Chapter 4

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

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:        200.000 cents     200.000000
  2:        350.000 cents     350.000000
  3:        500.000 cents     500.000000
SHOW/INTERVAL
  0:        150.0000 cents    150.0000
  1:        200.0000 cents    200.0000
  2:        150.0000 cents    150.0000
  3:        150.0000 cents    150.0000
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   2 150.00000 cents
  1:   1 200.00000 cents
  2:   1 300.00000 cents
  2:   2 350.00000 cents
Highest number of different intervals for one interval class: 2
Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
        1     2     3    
 0.0  : 200.0 350.0 500.0
 200.0: 150.0 300.0 500.0
 350.0: 150.0 350.0 500.0
 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  150.0000  .. 200.0000 cents      50.00000 cents                     150.00000 cents
  2:  300.0000  .. 350.0000 cents      50.00000 cents                     100.00000 cents
SHOW DATA
Number of notes                     : 3
-- Interval properties --
Smallest interval                   : 150.00000 cents, class 1
Average step (divided formal octave): 166.6667 cents
Largest one step interval           : 200.00000 cents
Average / Smallest step             : 1.111111
Largest / Average step              : 1.200000
Largest / Smallest step             : 1.333333
Median interval of one step         : 150.00000 cents, amount: 2
Most common interval of one step    : 150.00000 cents, amount: 2
Least squares average step          : 171.42857 cents, oct.:  514.28571 cents
Scale is strictly proper
Scale has Myhill's property
  chromas: 50.00000 cents and 100.00000 cents, ratio: 2.000000
  generators: 150.00000 cents and 2 of 350.00000 cents
Scale is maximally even in 10-tone equal temperament
ET pair of linear temperament       : 20&20
Scale is maximally even for L / S <= 2
Scale is distributional even
Scale is a mode of a 10-tone equal temperament with octave  500.000 cents
  degrees: 4 7 10
  generators: 3 and 7
Number of contiguous 1-step segments: 0
Step pattern alph. order: ABB
Step pattern size order : LSS
Interval vector is [ 0 0 2 1 0 ]
Scale is sum-free (all different intervals)
Scale is a Constant Structure, by a margin of 100.00000 cents
Scale diversity                     : 1.336658
Rothenberg stability                : 1.000000 = 1
Lumma stability                     : 0.800000
Rothenberg efficiency               : 0.888889   redundancy: 0.111111
Efficiency x scale size             : 2.666667
Number of different interval sizes  : 4 = 2.00000 / class
Number of one step interval sizes   : 2
Highest interval variety            : 2
Mean interval variety               : 2.00000 = 2
Median interval variety             : 2
Lowest interval variety             : 2
Smallest interval difference        : 50.00000 cents
Most common intervals               : 150.00000 cents & inv., amount: 2
Number of recognisable fifths       : 0
Number of recognisable fourths      : 0
Best fifths form a closed circle
Best major thirds form a closed circle
Best minor thirds form a closed circle
Steps are decreasing
Formal octave complements present   : 1 = 33.3333%
2/1 octave complements present      : 0 = 0.0000%
Limited inverse transpositions      :
 1
Inversional symmetry on degrees     :
 2
Inversional symmetry on intervals   :
 0-1
-- Rational properties --
FIT/MODE
  3:  1 1 1  SP B ME I SD: 21.5166 c. M: 33.3333 c. 
  7:  3 2 2  SP M ME S SD: 9.2214 c. M:-14.2857 c. 
 10:  4 3 3  SP M ME S 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 5 x  S SD: 36.3137 cents
 5 x 6:7  S SD: 44.6900 cents
 6:7 x 8  S SD: 33.4497 cents
 7:8 x 9  S SD: 36.0066 cents
 8:9:10:11  H SD: 20.9960 cents
 9:10:11:12  H SD: 5.9644 cents
 32:36:39:43    SD: 4.7663 cents
 39:44:48:52    SD: 4.3667 cents
 41:46:50:55    SD: 3.5818 cents
 48:54:59:64    SD: 2.8125 cents
 57:64:70:76    SD: 2.0075 cents
 66:74:81:88    SD: 1.7707 cents
 72:81:88:96    SD: 1.6941 cents
 81:91:99:108    SD: 1.1969 cents
 89:100:109:119    SD: 1.1717 cents
 90:101:110:120    SD: 1.0892 cents
 98:110:120:131    SD: 0.8441 cents
 138:155:169:184    SD: 0.7999 cents
 147:165:180:196    SD: 0.6834 cents
 170:191:208:227    SD: 0.6328 cents
 179:201:219:239    SD: 0.3910 cents
 188:211:230:251    SD: 0.3331 cents
 236:265:289:315    SD: 0.3299 cents
 245:275:300:327    SD: 0.2152 cents
 424:476:519:566    SD: 0.0966 cents
 433:486:530:578    SD: 0.0379 cents