Scala analysis: 245_C17

  0:          1/1               0.000000 unison, perfect prime
  1:         18/17             98.954592 Arabic lute index finger
  2:          9/8             203.910002 major whole tone
  3:          4/3             498.044999 perfect fourth

  0:         32/27            294.1350 Pythagorean minor third
  1:         18/17             98.9546 Arabic lute index finger
  2:         17/16            104.9554 17th harmonic
  3:         32/27            294.1350 Pythagorean minor third

Interval class, Number of incidences, Size:
  1:   1 18/17               98.955 cents   Arabic lute index finger
  1:   1 17/16               104.955 cents  17th harmonic
  1:   1 32/27               294.135 cents  Pythagorean minor third
  2:   1 9/8                 203.910 cents  major whole tone
  2:   1 64/51               393.090 cents  
  2:   1 34/27               399.090 cents  septendecimal 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  : 99.0  203.9 498.0
 99.0 : 105.0 399.1 498.0
 203.9: 294.1 393.1 498.0
 498.0

Interval class, Interval span, Span size, Gap to prev. class:
  1:  98.9546   .. 294.1350 cents      272/243, 195.1804 cents            18/17, 98.9546 cents
  2:  203.9100  .. 399.0904 cents      272/243, 195.1804 cents            243/256,-90.2250 cents

Number of notes                     : 3
-- Interval properties --
Smallest interval                   : 18/17, 98.9546 cents, class 1
Average step (divided formal octave): 166.0150 cents
Largest one step interval           : 32/27, 294.1350 cents
Average / Smallest step             : 1.677689
Largest / Average step              : 1.771737
Largest / Smallest step             : 2.972424
Median interval of one step         : 17/16, 104.9554 cents, amount: 1
Least squares average step          : 142.92211 cents, oct.:  428.76634 cents
Scale is not proper
Scale has trivalence property
Scale is a mode of a 1827-tone equal temperament with octave  4/3
  degrees: 363 748 1827
Least number of segments generator  : 914 of 249.159 cents and inv.
  number of contiguous generator circle segments: 1
Shortest superset generator         : 1724 of 469.967 cents and inv.
  generated superset size: 40 = 37 more = 1333.333%
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 90.22500 cents
Scale diversity                     : 1.093641
Lumma stability                     : 0.397372
Lumma impropriety factor            : 0.181158
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        : 289/288, 6.0008 cents
Number of recognisable fifths       : 0
Number of recognisable fourths      : 0
Steps are strictly increasing
Length of longest harmonic part     : 1 at degree 0
Length of longest subharmonic part  : 2 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 189.1796 cents:
 2
-- Rational properties --
Prime limit                         : 17
Odd number limit                    : 51 (O: 17 U: 51)
Highest odd numerator or denominator: 17
Scale harmonicity                   : 0.023192
Average absolute harmonicity        : 0.120573
Specific harmonicity                : 0.117919
Fundamental                         : 1/408, -8.6724 octaves, 0.6412 Hz.
Guide tone                          : 36,  5.1699 octaves, 9418.520 Hz.
Exponens Consonantiae               : 1.468800E+04, 13.84235 octaves
Euler's gradus suavitatis           : 28
Sum of Mann's harmonic distance     : 29.5, average 9.83333
Mersenne's string divisions         : 595
Sum of van Prooijen's expressibility: 2.66181, average 0.88727
Sum of Tenney's harmonic distance   : 5.42224, average 1.80741
Vogel's harmonic complexity         : 20.33333
Wille's k value                     : 229
Wilson's harmonic complexity        : 26
Rectangular lattice diameter        : 4
Triangular lattice diameter         : 3
Lattice compactness                 : 21.56179, average 3.59363
Lattice compactness (without 2's)   : 12.39835, average 2.06639
Number of different primes          : 3
Prime exponents' range, average, count, tones@limit:
  2:  -3 .. 2         0.00000   6
  3:  -1 .. 2         1.00000   5     2
 17:  -1 .. 0        -0.33333   1     1
Average exponent except 2's         : 2 / 3 = 0.66667
Average absolute exponent except 2's: 6 / 3 = 2.00000
Scale is weakly epimorphic with val: <7 11 27|
Scale is weakly epimorphic with val: <7 11 30| = patent
Scale is weakly epimorphic with val: <7 11 33|
Scale is weakly epimorphic with val: <7 12 27|
Scale is weakly epimorphic with val: <7 12 30|
Scale is weakly epimorphic with val: <7 12 33|
Scale is weakly epimorphic with val: <8 11 27|

  3:  0 1 2   N G T3   SD: 61.1775 c. M: 98.9546 c. 
  4:  1 1 2   P M ME S SD: 29.9348 c. M:-45.1125 c. 
  5:  1 1 3   N M DE S SD: 2.7351 c. M: 4.6920 c. 
 29:  6 6 17   N M DE S SD: 2.6748 c. M:-4.0892 c. 
 34:  7 7 20   N M DE S SD: 2.1763 c. M:-3.5841 c. 
 39:  8 8 23   N M DE S SD: 1.8679 c. M:-3.2085 c. 
 41:  8 9 24   N   T3   SD: 1.8159 c. M:-2.5965 c. 
 44:  9 9 26   N M DE S SD: 1.6875 c. M:-2.9182 c. 
 46:  9 10 27   N   T3   SD: 1.3587 c. M:-1.8042 c. 
 51:  10 11 30   N   T3   SD: 1.0082 c. M: 1.2987 c. 
 56:  11 12 33   N   T3   SD: 0.7481 c. M: 1.1243 c. 
 61:  12 13 36   N   T3   SD: 0.5774 c. M: 0.9785 c. 
 66:  13 14 39   N   T3   SD: 0.5026 c. M: 0.8548 c. 
 71:  14 15 42   N   T3   SD: 0.5144 c. M: 0.7485 c. 
 95:  19 20 56   N   T3   SD: 0.4938 c. M:-0.6544 c. 
 100: 20 21 59   N   T3   SD: 0.4129 c. M:-0.6544 c. 
 105: 21 22 62   N   T3   SD: 0.3790 c. M:-0.6544 c. 
 151: 30 32 89   N   T3   SD: 0.3379 c. M:-0.5853 c. 
 156: 31 33 92   N   T3   SD: 0.2404 c. M:-0.4162 c. 
 161: 32 34 95   N   T3   SD: 0.1501 c. M:-0.2575 c. 
 166: 33 35 98   N   T3   SD: 0.0700 c. M:-0.1084 c. 
 171: 34 36 101   N   T3   SD: 0.0454 c. M:-0.0719 c. 
 337: 67 71 199   N   T3   SD: 0.0424 c. M:-0.0633 c. 
 503: 100 106 297   N   T3   SD: 0.0494 c. M:-0.0607 c. 
 508: 101 107 300   N   T3   SD: 0.0390 c. M:-0.0662 c. 
 569: 113 120 336   N   T3   SD: 0.0332 c. M: 0.0458 c. 
 574: 114 121 339   N   T3   SD: 0.0232 c. M: 0.0397 c. 
 740: 147 156 437   N   T3   SD: 0.0155 c. M:-0.0192 c. 
 745: 148 157 440   N   T3   SD: 0.0108 c. M: 0.0141 c. 
 911: 181 192 538   N   T3   SD: 0.0056 c. M:-0.0096 c. 
 1082: 215 228 639   N   T3   SD: 0.0060 c. M:-0.0100 c. 
 1656: 329 349 978   N   T3   SD: 0.0042 c. M: 0.0072 c. 
 1827: 363 385 1079   N   T3   SD: 0.0019 c. M: 0.0032 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: 70.0332 cents
 6 x 7:8  S SD: 31.4805 cents
 7 x 8:9  S SD: 34.3053 cents
 8 x 9:11    SD: 26.6365 cents
 9 x 10:12  S SD: 10.7531 cents
 10 x 11:13    SD: 29.3037 cents
 11:12 x 15  S SD: 32.3448 cents
 12:13:14:16  S SD: 24.7962 cents
 13:14:15:17    SD: 20.8495 cents
 14:15:16:19    SD: 15.2827 cents
 15:16:17:20    SD: 6.0230 cents
 31:33:35:41    SD: 5.9726 cents
 32:34:36:43    SD: 4.9162 cents
 33:35:37:44    SD: 2.1749 cents
 48:51:54:64    SD: 2.0003 cents
 72:76:81:96    SD: 1.7839 cents
 81:86:91:108    SD: 1.7684 cents
 87:92:98:116    SD: 1.0423 cents
 120:127:135:160    SD: 0.2672 cents
 255:270:287:340    SD: 0.2514 cents
 288:305:324:384    SD: 0.1113 cents
 408:432:459:544    SD: 0.0000 cents