Scala analysis: 650_T57

Aristoxenian style tetrachord 17/3 + 34/3 + 13, Chapter 4

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

SHOW

  0:          1/1               0.000000 unison, perfect prime
  1:         94.444 cents      94.444440
  2:        283.333 cents     283.333330
  3:        500.000 cents     500.000000

SHOW/INTERVAL

  0:        216.6667 cents    216.6667
  1:         94.4444 cents     94.4444
  2:        188.8889 cents    188.8889
  3:        216.6667 cents    216.6667

SHOW INTERVALS

Interval class, Number of incidences, Size:
  1:   1 94.44444 cents
  1:   1 188.88889 cents
  1:   1 216.66667 cents
  2:   1 283.33333 cents
  2:   1 311.11111 cents
  2:   1 405.55556 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  : 94.4  283.3 500.0
 94.4 : 188.9 405.6 500.0
 283.3: 216.7 311.1 500.0
 500.0

SHOW/SPAN INTERVALS

Interval class, Interval span, Span size, Gap to prev. class:
  1:  94.4444   .. 216.6667 cents      122.22223 cents                    94.44444 cents
  2:  283.3333  .. 405.5556 cents      122.22223 cents                    66.66666 cents

SHOW DATA

Number of notes                     : 3
-- Interval properties --
Smallest interval                   : 94.44444 cents, class 1
Average step (divided formal octave): 166.6667 cents
Largest one step interval           : 216.66667 cents
Average / Smallest step             : 1.764706
Largest / Average step              : 1.300000
Largest / Smallest step             : 2.294118
Median interval of one step         : 188.88889 cents, amount: 1
Least squares average step          : 154.36508 cents, oct.:  463.09524 cents
Scale is strictly proper
Scale has trivalence property
Scale is a mode of a 90-tone equal temperament with octave  500.000 cents
  degrees: 17 51 90
Least number of segments generator  : 47 of 261.111 cents and inv.
  number of contiguous generator circle segments: 1
Shortest superset generator         : 73 of 405.556 cents and inv.
  generated superset size: 4 = 1 more = 133.333%
Number of contiguous 1-step segments: 0
Step pattern alph. order: ABC
Step pattern size order : SML
Interval vector is [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 ]
Scale is sum-free (all different intervals)
Scale is a Constant Structure, by a margin of 66.66666 cents
Scale diversity                     : 1.137579
Rothenberg stability                : 1.000000 = 1
Lumma stability                     : 0.511111
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        : 27.77778 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
Steps are strictly increasing
Formal octave complements present   : 1 = 33.3333%
2/1 octave complements present      : 0 = 0.0000%
-- Rational properties --

FIT/MODE

  3:  0 1 2   N G T3   SD: 86.6619 c. M: 116.6667 c. 
  4:  1 1 2   P M ME S SD: 26.1072 c. M: 33.3333 c. 
  5:  1 2 2  SP M ME S SD: 10.1430 c. M:-16.6667 c. 
  9:  2 3 4  SP   T3   SD: 10.1430 c. M:-16.6667 c. 
 11:  2 4 5  SP   T3   SD: 6.4546 c. M: 10.6061 c. 
 16:  3 6 7  SP   T3   SD: 1.2679 c. M: 2.0833 c. 
 37:  7 14 16  SP   T3   SD: 0.2741 c. M:-0.4505 c. 
 53:  10 20 23  SP   T3   SD: 0.1914 c. M: 0.3145 c. 
 90:  17 34 39  SP   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 5 x  S SD: 102.9804 cents
 5 x 6:7  S SD: 44.3059 cents
 6 x 7:8  S SD: 8.2891 cents
 7 x 8:9  S SD: 41.6373 cents
 8 x 9:11    SD: 47.2800 cents
 9:10:11:12  H SD: 36.2801 cents
 10:11:12:13  H SD: 30.0349 cents
 11:12:13:15    SD: 22.5031 cents
 12:13:14:16  S SD: 15.7132 cents
 15:16:18:20  S SD: 12.2314 cents
 16:17:19:21    SD: 11.3788 cents
 17:18:20:23    SD: 7.9444 cents
 18:19:21:24    SD: 5.5331 cents
 33:35:39:44    SD: 3.2222 cents
 39:41:46:52    SD: 2.8229 cents
 51:54:60:68    SD: 1.7659 cents
 72:76:85:96    SD: 1.5179 cents
 89:94:105:119    SD: 1.3643 cents
 90:95:106:120    SD: 0.7097 cents
 107:113:126:143    SD: 0.7052 cents
 158:167:186:211    SD: 0.6261 cents
 179:189:211:239    SD: 0.5058 cents
 197:208:232:263    SD: 0.1664 cents
 427:451:503:570    SD: 0.1155 cents