Scala analysis: 714_S23

  0:          1/1               0.000000 unison, perfect prime
  1:        216.407 cents     216.406620
  2:        420.317 cents     420.316620
  3:        498.093 cents     498.093290

  0:         77.7767 cents     77.7767
  1:        216.4066 cents    216.4066
  2:        203.9100 cents    203.9100
  3:         77.7767 cents     77.7767

Interval class, Number of incidences, Size:
  1:   1 77.77667 cents
  1:   1 203.91000 cents
  1:   1 216.40662 cents
  2:   1 281.68667 cents
  2:   1 294.18329 cents
  2:   1 420.31662 cents
Highest number of different intervals for one interval class: 3
Average number of different intervals per interval class: 3.00000 = 3

        1     2     3    
 0.0  : 216.4 420.3 498.1
 216.4: 203.9 281.7 498.1
 420.3: 77.8  294.2 498.1
 498.1

Interval class, Interval span, Span size, Gap to prev. class:
  1:  77.7767   .. 216.4066 cents      138.62995 cents                    77.77667 cents
  2:  281.6867  .. 420.3166 cents      138.62995 cents                    65.28005 cents

Number of notes                     : 3
-- Interval properties --
Smallest interval                   : 77.77667 cents, class 1
Average step (divided formal octave): 166.0311 cents
Largest one step interval           : 216.40662 cents
Average / Smallest step             : 2.134716
Largest / Average step              : 1.303410
Largest / Smallest step             : 2.782410
Median interval of one step         : 203.91000 cents, amount: 1
Least squares average step          : 182.23712 cents, oct.:  546.71137 cents
Scale is strictly proper
Scale has trivalence property
Scale is a mode of a 1236-tone equal temperament with octave  498.093 cents
  degrees: 537 1043 1236
Least number of segments generator  : 619 of 249.450 cents and inv.
  number of contiguous generator circle segments: 1
Shortest superset generator         : 1003 of 404.197 cents and inv.
  generated superset size: 35 = 32 more = 1166.667%
Number of contiguous 1-step segments: 0
Step pattern alph. order: ABC
Step pattern size order : LMS
Scale is sum-free (all different intervals)
Scale is a Constant Structure, by a margin of 65.28005 cents
Scale diversity                     : 0.942888
Rothenberg stability                : 1.000000 = 1
Lumma stability                     : 0.443357
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        : 12.49662 cents
Number of recognisable fifths       : 0
Number of recognisable fourths      : 0
Best major thirds form a closed circle
Steps are strictly decreasing
Formal octave complements present   : 1 = 33.3333%
2/1 octave complements present      : 0 = 0.0000%
Limited inverse transpositions with margin 126.1333 cents:
 2
-- Rational properties --

  3:  1 1 1  SP B ME I SD: 58.6701 c. M: 88.2544 c. 
  4:  2 1 1   P M ME S SD: 32.9172 c. M: 46.7467 c. 
  5:  2 2 1  SP M ME S SD: 16.0401 c. M: 21.8420 c. 
  7:  3 3 1  SP M DE S SD: 4.1818 c. M:-6.6205 c. 
 18:  8 7 3  SP   T3   SD: 4.1685 c. M: 5.2389 c. 
 19:  8 8 3  SP M DE S SD: 3.8910 c. M: 6.6831 c. 
 25:  11 10 4  SP   T3   SD: 1.9379 c. M:-2.7544 c. 
 32:  14 13 5  SP   T3   SD: 0.8718 c. M:-1.5092 c. 
 39:  17 16 6  SP   T3   SD: 0.7791 c. M:-1.1469 c. 
 71:  31 29 11  SP   T3   SD: 0.7107 c. M:-1.0707 c. 
 76:  33 31 12  SP   T3   SD: 0.5076 c. M: 0.8696 c. 
 83:  36 34 13  SP   T3   SD: 0.2521 c. M: 0.3662 c. 
 115: 50 47 18  SP   T3   SD: 0.1399 c. M: 0.1858 c. 
 122: 53 50 19  SP   T3   SD: 0.1189 c. M:-0.2048 c. 
 198: 86 81 31  SP   T3   SD: 0.1253 c. M: 0.2076 c. 
 205: 89 84 32  SP   T3   SD: 0.0943 c. M: 0.1612 c. 
 237: 103 97 37  SP   T3   SD: 0.0382 c. M:-0.0643 c. 
 320: 139 131 50  SP   T3   SD: 0.0399 c. M: 0.0504 c. 
 442: 192 181 69  SP   T3   SD: 0.0260 c. M: 0.0403 c. 
 557: 242 228 87  SP   T3   SD: 0.0130 c. M: 0.0225 c. 
 679: 295 278 106  SP   T3   SD: 0.0108 c. M:-0.0184 c. 
 916: 398 375 143  SP   T3   SD: 0.0129 c. M:-0.0176 c. 
 999: 434 409 156  SP   T3   SD: 0.0105 c. M: 0.0177 c. 
 1236: 537 506 193  SP   T3   SD: 0.0012 c. M: 0.0020 c. 

 1 x x 2  S SD: 701.9067 cents
 2 x x 3  S SD: 203.8617 cents
 3 x x 4  S SD: 0.0483 cents
 4 x 5 x  S SD: 34.0029 cents
 5:6 x 7  S SD: 65.1423 cents
 6:7 x 8  S SD: 25.2322 cents
 7:8:9 x  S SD: 10.4422 cents
 10:11:13 x    SD: 30.7865 cents
 11:12:14:15  S SD: 25.4808 cents
 12:14:15:16  S SD: 20.2837 cents
 13:15 x 17    SD: 22.9957 cents
 14:16:18:19  S SD: 12.3475 cents
 15:17:19:20    SD: 3.6920 cents
 36:41:46:48    SD: 3.2124 cents
 51:58:65:68    SD: 2.0907 cents
 66:75:84:88    SD: 1.8835 cents
 69:78:88:92    SD: 1.4082 cents
 84:95:107:112    SD: 1.2058 cents
 105:119:134:140    SD: 0.6390 cents
 120:136:153:160    SD: 0.1330 cents
 375:425:478:500    SD: 0.1108 cents
 495:561:631:660    SD: 0.0970 cents
 564:639:719:752    SD: 0.0897 cents