Scala analysis: 406_D6

  0:          1/1               0.000000 unison, perfect prime
  1:        256/243            90.224996 limma, Pythagorean minor second
  2:          7/6             266.870906 septimal minor third
  3:          4/3             498.044999 perfect fourth

  0:          8/7             231.1741 septimal whole tone
  1:        256/243            90.2250 limma, Pythagorean minor second
  2:        567/512           176.6459 
  3:          8/7             231.1741 septimal whole tone

Interval class, Number of incidences, Size:
  1:   1 256/243             90.225 cents   limma, Pythagorean minor second
  1:   1 567/512             176.646 cents  
  1:   1 8/7                 231.174 cents  septimal whole tone
  2:   1 7/6                 266.871 cents  septimal minor third
  2:   1 2048/1701           321.399 cents  
  2:   1 81/64               407.820 cents  Pythagorean major third
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  : 90.2  266.9 498.0
 90.2 : 176.6 407.8 498.0
 266.9: 231.2 321.4 498.0
 498.0

Interval class, Interval span, Span size, Gap to prev. class:
  1:  90.2250   .. 231.1741 cents      243/224, 140.9491 cents            256/243, 90.2250 cents
  2:  266.8709  .. 407.8200 cents      243/224, 140.9491 cents            49/48, 35.6968 cents

Number of notes                     : 3
-- Interval properties --
Smallest interval                   : 256/243, 90.2250 cents, class 1
Average step (divided formal octave): 166.0150 cents
Largest one step interval           : 8/7, 231.1741 cents
Average / Smallest step             : 1.840011
Largest / Average step              : 1.392489
Largest / Smallest step             : 2.562196
Median interval of one step         : 567/512, 176.6459 cents, amount: 1
Least squares average step          : 151.29299 cents, oct.:  453.87896 cents
Scale is strictly proper
Scale has trivalence property
Scale is a mode of a 2219-tone equal temperament with octave  4/3
  degrees: 402 1189 2219
Least number of segments generator  : 1110 of 249.135 cents and inv.
  number of contiguous generator circle segments: 1
Shortest superset generator         : 1457 of 327.017 cents and inv.
  generated superset size: 32 = 29 more = 1066.667%
Number of contiguous 1-step segments: 0
Step pattern alph. order: ABC
Step pattern size order : SML
Scale is sum-free (all different intervals)
Scale is a Constant Structure, by a margin of 35.69681 cents
Scale diversity                     : 1.141936
Rothenberg stability                : 1.000000 = 1
Lumma stability                     : 0.433991
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        : 49/48, 35.6968 cents
Number of recognisable fifths       : 0
Number of recognisable fourths      : 0
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%
Scale is n-1 differentially coherent in interval classes 1 and 2 combined
-- Rational properties --
Prime limit                         : 7
Odd number limit                    : 1701 (O: 567 U: 1701)
Highest odd numerator or denominator: 243
Scale harmonicity                   : 0.030657
Average absolute harmonicity        : 0.110944
Specific harmonicity                : 0.160228
Fundamental                         : 1/486, -8.9248 octaves, 0.5383 Hz.
Guide tone                          : 1792,  10.8074 octaves, 468833.013 Hz.
Exponens Consonantiae               : 8.709120E+05, 19.73217 octaves
Euler's gradus suavitatis           : 26
Sum of Mann's harmonic distance     : 259.5, average 86.50000
Mersenne's string divisions         : 45409
Sum of van Prooijen's expressibility: 3.70783, average 1.23594
Sum of Tenney's harmonic distance   : 7.49628, average 2.49876
Vogel's harmonic complexity         : 14.33333
Wille's k value                     : 283
Wilson's harmonic complexity        : 22
Rectangular lattice diameter        : 6
Triangular lattice diameter         : 5
Lattice compactness                 : 33.67498, average 5.61250
Lattice compactness (without 2's)   : 16.53732, average 2.75622
Number of different primes          : 3
Prime exponents' range, average, count, tones@limit:
  2:  -1 .. 8         3.00000   11
  3:  -5 ..-1        -2.33333   7     2
  7:   0 .. 1         0.33333   1     1
Average exponent except 2's         :-6 / 3 =-2.00000
Average absolute exponent except 2's: 8 / 3 = 2.66667
Scale is weakly epimorphic with val: <6 10 19|
Scale is weakly epimorphic with val: <6 11 20|
Scale is JI-epimorphic with val: <7 11 20| = patent

  3:  0 1 2   N G T3   SD: 78.1291 c. M: 100.8559 c. 
  4:  1 1 2   P M ME S SD: 22.3168 c. M:-34.2863 c. 
  5:  1 2 2  SP M ME S SD: 19.2289 c. M:-31.9561 c. 
  6:  1 2 3   P   T3   SD: 11.1154 c. M: 17.8484 c. 
 11:  2 4 5  SP   T3   SD: 2.7720 c. M:-4.7900 c. 
 17:  3 6 8  SP   T3   SD: 2.2870 c. M: 3.2000 c. 
 28:  5 10 13  SP   T3   SD: 0.7447 c. M: 1.2884 c. 
 60:  11 21 28  SP   T3   SD: 0.9536 c. M: 1.2469 c. 
 67:  12 24 31  SP   T3   SD: 0.7273 c. M: 1.0229 c. 
 71:  13 25 33  SP   T3   SD: 0.5862 c. M:-0.9663 c. 
 82:  15 29 38  SP   T3   SD: 0.5522 c. M:-0.8808 c. 
 88:  16 31 41  SP   T3   SD: 0.5367 c. M: 0.8696 c. 
 99:  18 35 46  SP   T3   SD: 0.2352 c. M:-0.3286 c. 
 110: 20 39 51  SP   T3   SD: 0.2428 c. M:-0.3286 c. 
 127: 23 45 59  SP   T3   SD: 0.1172 c. M: 0.2011 c. 
 138: 25 49 64  SP   T3   SD: 0.1136 c. M:-0.1967 c. 
 237: 43 84 110  SP   T3   SD: 0.0799 c. M:-0.1376 c. 
 265: 48 94 123  SP   T3   SD: 0.0083 c. M: 0.0131 c. 
 1297: 235 460 602  SP   T3   SD: 0.0094 c. M:-0.0145 c. 
 1424: 258 505 661  SP   T3   SD: 0.0089 c. M: 0.0111 c. 
 1562: 283 554 725  SP   T3   SD: 0.0070 c. M:-0.0098 c. 
 1689: 306 599 784  SP   T3   SD: 0.0063 c. M: 0.0084 c. 
 1827: 331 648 848  SP   T3   SD: 0.0055 c. M:-0.0071 c. 
 1954: 354 693 907  SP   T3   SD: 0.0045 c. M: 0.0065 c. 
 2092: 379 742 971  SP   T3   SD: 0.0046 c. M:-0.0069 c. 
 2219: 402 787 1030  SP   T3   SD: 0.0031 c. M: 0.0050 c. 

 1 x x 2  S SD: 701.9550 cents
 2 x x 3  S SD: 203.9100 cents
 3 x x 4  S SD: 0.0000 cents
 4 x x 5  S SD: 111.7313 cents
 5 x 6:7  S SD: 48.7680 cents
 6 x 7:8  S SD: 0.0000 cents
 7 x 8:9  S SD: 36.1882 cents
 8 x 9:11    SD: 41.2374 cents
 9 x 11:12    SD: 40.2685 cents
 10:11:12:13  H SD: 33.1522 cents
 11:12:13:15    SD: 25.0827 cents
 12:13:14:16  S SD: 16.1159 cents
 16:17:19:21    SD: 14.5268 cents
 17:18:20:23    SD: 10.1372 cents
 18:19:21:24    SD: 1.1260 cents
 96:101:112:128    SD: 0.7754 cents
 114:120:133:152    SD: 0.4748 cents
 132:139:154:176    SD: 0.2562 cents
 150:158:175:200    SD: 0.0902 cents
 168:177:196:224    SD: 0.0403 cents
 318:335:371:424    SD: 0.0213 cents
 486:512:567:648    SD: 0.0000 cents