Scala analysis: 662_T69

Aristoxenian style tetrachord 9 + 12 + 7, Tiby

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

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:        158.786 cents     158.785710
  2:        370.500 cents     370.500000
  3:        494.000 cents     494.000000
SHOW/INTERVAL
  0:        123.5000 cents    123.5000
  1:        158.7857 cents    158.7857
  2:        211.7143 cents    211.7143
  3:        123.5000 cents    123.5000
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   1 123.50000 cents
  1:   1 158.78571 cents
  1:   1 211.71429 cents
  2:   1 282.28571 cents
  2:   1 335.21429 cents
  2:   1 370.50000 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  : 158.8 370.5 494.0
 158.8: 211.7 335.2 494.0
 370.5: 123.5 282.3 494.0
 494.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  123.5000  .. 211.7143 cents      88.21429 cents                     123.50000 cents
  2:  282.2857  .. 370.5000 cents      88.21429 cents                     70.57142 cents
SHOW DATA
Number of notes                     : 3
-- Interval properties --
Smallest interval                   : 123.50000 cents, class 1
Average step (divided formal octave): 164.6667 cents
Largest one step interval           : 211.71429 cents
Average / Smallest step             : 1.333333
Largest / Average step              : 1.285714
Largest / Smallest step             : 1.714286
Median interval of one step         : 158.78571 cents, amount: 1
Least squares average step          : 170.12755 cents, oct.:  510.38265 cents
Scale is strictly proper
Scale has trivalence property
Scale is a mode of a 28-tone equal temperament with octave  494.000 cents
  degrees: 9 21 28
Least number of segments generator  : 15 of 264.643 cents and inv.
  number of contiguous generator circle segments: 1
Shortest superset generator         : 25 of 441.071 cents and inv.
  generated superset size: 8 = 5 more = 266.667%
Number of contiguous 1-step segments: 0
Step pattern alph. order: ABC
Step pattern size order : MLS
Interval vector is [ 0 0 0 0 0 0 1 0 1 0 0 1 0 0 ]
Scale is sum-free (all different intervals)
Scale is a Constant Structure, by a margin of 70.57142 cents
Scale diversity                     : 1.335619
Rothenberg stability                : 1.000000 = 1
Lumma stability                     : 0.642857
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        : 35.28571 cents
Number of recognisable fifths       : 0
Number of recognisable fourths      : 0
Best major thirds form a closed circle
Best minor thirds form a closed circle
Formal octave complements present   : 1 = 33.3333%
2/1 octave complements present      : 0 = 0.0000%
-- Rational properties --
FIT/MODE
  3:  1 1 1  SP B ME I SD: 24.0089 c. M: 41.1667 c. 
  4:  1 2 1   P M ME I SD: 20.3722 c. M: 35.2857 c. 
  7:  2 3 2  SP M ME I SD: 14.4053 c. M: 17.6429 c. 
  9:  3 4 2  SP   T3   SD: 8.6195 c. M:-13.7222 c. 
 12:  4 5 3  SP   T3   SD: 3.3954 c. M:-5.8810 c.  Raga Bilwadala
 16:  5 7 4  SP   T3   SD: 2.5465 c. M: 4.4107 c. 
 28:  9 12 7  SP   T3   SD: 0.0000 c. M:-0.0000 c. 
FIT/HARMONIC
 1 x x 2  S SD: 706.0000 cents
 2 x x 3  S SD: 207.9550 cents
 3 x x 4  S SD: 4.0450 cents
 4 x 5 x  S SD: 15.8137 cents
 5 x 6:7  S SD: 52.0670 cents
 6 x 7:8  S SD: 51.8540 cents
 7:8 x 9  S SD: 46.6668 cents
 8:9:10:11  H SD: 24.8811 cents
 9:10:11:12  H SD: 11.0926 cents
 12:13:15:16    SD: 8.6603 cents
 21:23:26:28    SD: 1.4376 cents
 113:124:140:150    SD: 1.3951 cents
 125:137:155:166    SD: 1.1558 cents
 134:147:166:178    SD: 0.9569 cents
 146:160:181:194    SD: 0.8154 cents
 155:170:192:206    SD: 0.6408 cents
 167:183:207:222    SD: 0.5776 cents
 176:193:218:234    SD: 0.4067 cents
 197:216:244:262    SD: 0.2386 cents
 218:239:270:290    SD: 0.1538 cents
 406:445:503:540    SD: 0.1513 cents
 427:468:529:568    SD: 0.1144 cents