Scala analysis: 719_S28

  0:          1/1               0.000000 unison, perfect prime
  1:        210.821 cents     210.821120
  2:        414.731 cents     414.731130
  3:        498.044 cents     498.043780

  0:         83.3127 cents     83.3127
  1:        210.8211 cents    210.8211
  2:        203.9100 cents    203.9100
  3:         83.3127 cents     83.3127

Interval class, Number of incidences, Size:
  1:   1 83.31265 cents
  1:   1 203.91001 cents
  1:   1 210.82112 cents
  2:   1 287.22266 cents
  2:   1 294.13377 cents
  2:   1 414.73113 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  : 210.8 414.7 498.0
 210.8: 203.9 287.2 498.0
 414.7: 83.3  294.1 498.0
 498.0

Interval class, Interval span, Span size, Gap to prev. class:
  1:  83.3127   .. 210.8211 cents      127.50847 cents                    83.31265 cents
  2:  287.2227  .. 414.7311 cents      127.50847 cents                    76.40154 cents

Number of notes                     : 3
-- Interval properties --
Smallest interval                   : 83.31265 cents, class 1
Average step (divided formal octave): 166.0146 cents
Largest one step interval           : 210.82112 cents
Average / Smallest step             : 1.992670
Largest / Average step              : 1.269895
Largest / Smallest step             : 2.530482
Median interval of one step         : 203.91001 cents, amount: 1
Least squares average step          : 181.02962 cents, oct.:  543.08887 cents
Scale is strictly proper
Scale has trivalence property
Scale is a mode of a 1082-tone equal temperament with octave  498.044 cents
  degrees: 458 901 1082
Least number of segments generator  : 543 of 249.942 cents and inv.
  number of contiguous generator circle segments: 1
Shortest superset generator         : 619 of 284.925 cents and inv.
  generated superset size: 38 = 35 more = 1266.667%
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 76.40154 cents
Scale diversity                     : 0.972320
Rothenberg stability                : 1.000000 = 1
Lumma stability                     : 0.487963
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        : 6.91111 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 decreasing
Formal octave complements present   : 1 = 33.3333%
2/1 octave complements present      : 0 = 0.0000%
Limited inverse transpositions with margin 120.5974 cents:
 2
-- Rational properties --

  3:  1 1 1  SP B ME I SD: 54.3054 c. M: 82.7019 c. 
  4:  2 1 1   P M ME S SD: 32.4376 c. M: 41.1983 c. 
  5:  2 2 1  SP M ME S SD: 11.5500 c. M: 16.2961 c. 
  7:  3 3 1  SP M DE S SD: 7.1844 c. M:-12.1635 c. 
 12:  5 5 2  SP M DE S SD: 1.9150 c. M: 3.3029 c.  Sansagari: Japan
 31:  13 13 5  SP M DE S SD: 2.0620 c. M:-2.9830 c. 
 35:  15 14 6  SP   T3   SD: 1.9293 c. M:-2.6262 c. 
 42:  18 17 7  SP   T3   SD: 1.5265 c. M:-2.6262 c. 
 43:  18 18 7  SP M DE S SD: 1.8676 c. M: 2.3377 c. 
 47:  20 19 8  SP   T3   SD: 1.0601 c. M: 1.4608 c. 
 54:  23 22 9  SP   T3   SD: 0.7758 c. M:-1.3086 c. 
 59:  25 24 10  SP   T3   SD: 0.6479 c. M: 1.1015 c. 
 66:  28 27 11  SP   T3   SD: 0.3237 c. M:-0.4702 c. 
 78:  33 32 13  SP   T3   SD: 0.1874 c. M:-0.3054 c. 
 137: 58 56 23  SP   T3   SD: 0.1744 c. M: 0.3005 c. 
 144: 61 59 24  SP   T3   SD: 0.1979 c. M:-0.3054 c. 
 149: 63 61 25  SP   T3   SD: 0.2004 c. M: 0.2517 c. 
 203: 86 83 34  SP   T3   SD: 0.1163 c. M:-0.1728 c. 
 215: 91 88 36  SP   T3   SD: 0.0482 c. M: 0.0807 c. 
 293: 124 120 49  SP   T3   SD: 0.0289 c. M: 0.0449 c. 
 496: 210 203 83  SP   T3   SD: 0.0306 c. M:-0.0442 c. 
 508: 215 208 85  SP   T3   SD: 0.0236 c. M: 0.0349 c. 
 574: 243 235 96  SP   T3   SD: 0.0163 c. M:-0.0232 c. 
 789: 334 323 132  SP   T3   SD: 0.0087 c. M:-0.0111 c. 
 867: 367 355 145  SP   T3   SD: 0.0105 c. M:-0.0181 c. 
 1082: 458 443 181  SP   T3   SD: 0.0025 c. M: 0.0041 c. 

 1 x x 2  S SD: 701.9562 cents
 2 x x 3  S SD: 203.9112 cents
 3 x x 4  S SD: 0.0012 cents
 4 x 5 x  S SD: 28.4174 cents
 5 x 6:7  S SD: 65.1032 cents
 6:7 x 8  S SD: 28.0249 cents
 7:8:9 x  S SD: 14.3917 cents
 10:11:13 x    SD: 30.2410 cents
 11:12:14:15  S SD: 23.9063 cents
 12:14:15:16  S SD: 20.9474 cents
 13:15 x 17    SD: 24.9656 cents
 14:16:18:19  S SD: 14.0139 cents
 15:17:19:20    SD: 2.6773 cents
 48:54:61:64    SD: 2.3047 cents
 63:71:80:84    SD: 1.3430 cents
 78:88:99:104    SD: 0.9361 cents
 93:105:118:124    SD: 0.8830 cents
 147:166:187:196    SD: 0.6575 cents
 162:183:206:216    SD: 0.4217 cents
 177:200:225:236    SD: 0.3204 cents
 240:271:305:320    SD: 0.1828 cents
 255:288:324:340    SD: 0.0638 cents