Scala analysis: 410_D7

  0:          1/1               0.000000 unison, perfect prime
  1:         25/24             70.672427 classic chromatic semitone, minor chroma
  2:         75/64            274.582429 classic augmented second
  3:          4/3             498.044999 perfect fourth

  0:        256/225           223.4626 Neapolitan diminished third
  1:         25/24             70.6724 classic chromatic semitone, minor chroma
  2:          9/8             203.9100 major whole tone
  3:        256/225           223.4626 Neapolitan diminished third

Interval class, Number of incidences, Size:
  1:   1 25/24               70.672 cents   classic chromatic semitone, minor chroma
  1:   1 9/8                 203.910 cents  major whole tone
  1:   1 256/225             223.463 cents  Neapolitan diminished third
  2:   1 75/64               274.582 cents  classic augmented second
  2:   1 32/27               294.135 cents  Pythagorean minor third
  2:   1 32/25               427.373 cents  classic diminished fourth
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  : 70.7  274.6 498.0
 70.7 : 203.9 427.4 498.0
 274.6: 223.5 294.1 498.0
 498.0

Interval class, Interval span, Span size, Gap to prev. class:
  1:  70.6724   .. 223.4626 cents      2048/1875, 152.7901 cents          25/24, 70.6724 cents
  2:  274.5824  .. 427.3726 cents      2048/1875, 152.7901 cents          16875/16384, 51.1199 cents

Number of notes                     : 3
-- Interval properties --
Smallest interval                   : 25/24, 70.6724 cents, class 1
Average step (divided formal octave): 166.0150 cents
Largest one step interval           : 256/225, 223.4626 cents
Average / Smallest step             : 2.349077
Largest / Average step              : 1.346038
Largest / Smallest step             : 3.161948
Median interval of one step         : 9/8, 203.9100 cents, amount: 1
Least squares average step          : 150.99802 cents, oct.:  452.99406 cents
Scale is strictly proper
Scale has trivalence property
Scale is a mode of a 1656-tone equal temperament with octave  4/3
  degrees: 235 913 1656
Least number of segments generator  : 829 of 249.323 cents and inv.
  number of contiguous generator circle segments: 1
Shortest superset generator         : 991 of 298.045 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 : SML
Scale is sum-free (all different intervals)
Scale is a Constant Structure, by a margin of 51.11986 cents
Scale diversity                     : 0.897186
Rothenberg stability                : 1.000000 = 1
Lumma stability                     : 0.386440
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        : 2048/2025, 19.5526 cents
Number of recognisable fifths       : 0
Number of recognisable fourths      : 0
Best minor thirds form a closed circle
Steps are strictly increasing
Length of longest harmonic part     : 1 at degree 0
Length of longest subharmonic part  : 1 at degree 0
Formal octave complements present   : 1 = 33.3333%
2/1 octave complements present      : 0 = 0.0000%
Scale is n-1 differentially coherent in interval class 1
Limited inverse transpositions with margin 133.2376 cents:
 1
-- Rational properties --
Prime limit                         : 5
Odd number limit                    : 225 (O: 75 U: 225)
Highest odd numerator or denominator: 75
Scale harmonicity                   : 0.038265
Average absolute harmonicity        : 0.105007
Specific harmonicity                : 0.165175
Fundamental                         : 1/192, -7.5850 octaves, 1.3626 Hz.
Guide tone                          : 300,  8.2288 octaves, 78487.670 Hz.
Exponens Consonantiae               : 5.760000E+04, 15.81378 octaves
Euler's gradus suavitatis           : 21
Sum of Mann's harmonic distance     : 97.5, average 32.50000
Mersenne's string divisions         : 6811
Sum of van Prooijen's expressibility: 3.75012, average 1.25004
Sum of Tenney's harmonic distance   : 7.53857, average 2.51286
Vogel's harmonic complexity         : 12.33333
Wille's k value                     : 112
Wilson's harmonic complexity        : 16
Rectangular lattice diameter        : 4
Triangular lattice diameter         : 4
Lattice compactness                 : 29.85685, average 4.97614
Lattice compactness (without 2's)   : 12.30056, average 2.05009
Number of different primes          : 3
Prime exponents' range, average, count, tones@limit:
  2:  -6 .. 2        -2.33333   11
  3:  -1 .. 1        -0.33333   3     1
  5:   0 .. 2         1.33333   4     2
Average exponent except 2's         : 3 / 3 = 1.00000
Average absolute exponent except 2's: 7 / 3 = 2.33333
Scale is weakly epimorphic with val: <7 10 17|
Scale is weakly epimorphic with val: <7 11 15|
Scale is weakly epimorphic with val: <7 11 18|
Scale is weakly epimorphic with val: <8 11 19|

  3:  0 2 1   N G T3   SD: 52.5827 c. M: 70.6724 c. 
  4:  0 2 2   P M DE S SD: 43.3893 c. M: 70.6724 c. 
  5:  1 2 2  SP M ME S SD: 21.7954 c. M:-28.9366 c. 
  6:  1 2 3   P   T3   SD: 16.3856 c. M: 25.5599 c. 
  7:  1 3 3  SP M DE S SD: 5.7885 c. M:-10.0147 c. 
 13:  2 5 6  SP   T3   SD: 5.0470 c. M: 6.4044 c. 
 15:  2 6 7  SP   T3   SD: 5.7288 c. M: 8.9584 c. 
 20:  3 8 9  SP   T3   SD: 2.3600 c. M:-4.0343 c. 
 22:  3 9 10  SP   T3   SD: 2.3193 c. M: 2.9215 c. 
 27:  4 11 12  SP   T3   SD: 2.1705 c. M:-3.1120 c. 
 29:  4 12 13  SP   T3   SD: 1.1471 c. M: 1.9766 c. 
 42:  6 17 19  SP   T3   SD: 1.0994 c. M: 1.8435 c. 
 49:  7 20 22  SP   T3   SD: 0.2885 c. M:-0.4769 c. 
 78:  11 32 35  SP   T3   SD: 0.2516 c. M: 0.4353 c. 
 127: 18 52 57  SP   T3   SD: 0.0626 c. M: 0.0834 c. 
 303: 43 124 136  SP   T3   SD: 0.0477 c. M: 0.0824 c. 
 430: 61 176 193  SP   T3   SD: 0.0467 c. M: 0.0786 c. 
 486: 69 199 218  SP   T3   SD: 0.0407 c. M:-0.0597 c. 
 564: 80 231 253  SP   T3   SD: 0.0324 c. M:-0.0488 c. 
 613: 87 251 275  SP   T3   SD: 0.0203 c. M:-0.0329 c. 
 740: 105 303 332  SP   T3   SD: 0.0091 c. M:-0.0154 c. 
 867: 123 355 389  SP   T3   SD: 0.0091 c. M: 0.0155 c. 
 916: 130 375 411  SP   T3   SD: 0.0069 c. M:-0.0108 c. 
 1043: 148 427 468  SP   T3   SD: 0.0075 c. M: 0.0130 c. 
 1529: 217 626 686  SP   T3   SD: 0.0088 c. M:-0.0115 c. 
 1607: 228 658 721  SP   T3   SD: 0.0077 c. M: 0.0102 c. 
 1656: 235 678 743  SP   T3   SD: 0.0034 c. M:-0.0042 c. 
 1783: 253 730 800  SP   T3   SD: 0.0014 c. M: 0.0020 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: 46.9589 cents
 6 x 7:8  S SD: 3.8558 cents
 7 x 8:9  S SD: 38.2373 cents
 8 x 9:11    SD: 44.2510 cents
 9 x 11:12    SD: 36.4128 cents
 11:12:13:15    SD: 30.0406 cents
 12:13:14:16  S SD: 22.7789 cents
 15:16:18:20  S SD: 19.3553 cents
 16:17:19:21    SD: 16.4805 cents
 17:18:20:23    SD: 12.8434 cents
 18:19:21:24    SD: 8.0642 cents
 23:24:27:31    SD: 6.3979 cents
 24:25:28:32    SD: 2.5705 cents
 69:72:81:92    SD: 1.4181 cents
 75:78:88:100    SD: 1.1700 cents
 93:97:109:124    SD: 0.7487 cents
 99:103:116:132    SD: 0.7042 cents
 168:175:197:224    SD: 0.3663 cents
 192:200:225:256    SD: 0.0000 cents