Scala analysis: 343_C28

Chromatic tetrachord 19/18 * 12/11 * 22/19, Schlesinger

Generated by Scala: https://www.huygens-fokker.org/scala/

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:         19/18             93.603014 undevicesimal semitone
  2:         38/33            244.240073
  3:          4/3             498.044999 perfect fourth
SHOW/INTERVAL
  0:         22/19            253.8049 Godzilla third
  1:         19/18             93.6030 undevicesimal semitone
  2:         12/11            150.6371 undecimal neutral second, 3/4-tone
  3:         22/19            253.8049 Godzilla third
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   1 19/18               93.603 cents   undevicesimal semitone
  1:   1 12/11               150.637 cents  undecimal neutral second, 3/4-tone
  1:   1 22/19               253.805 cents  Godzilla third
  2:   1 38/33               244.240 cents  
  2:   1 11/9                347.408 cents  undecimal neutral third
  2:   1 24/19               404.442 cents  smaller undevicesimal major third
Highest number of different intervals for one interval class: 3
Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
        1     2     3    
 0.0  : 93.6  244.2 498.0
 93.6 : 150.6 404.4 498.0
 244.2: 253.8 347.4 498.0
 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  93.6030   .. 253.8049 cents      396/361, 160.2019 cents            19/18, 93.6030 cents
  2:  244.2401  .. 404.4420 cents      396/361, 160.2019 cents            361/363,-9.5649 cents
SHOW DATA
Number of notes                     : 3
-- Interval properties --
Smallest interval                   : 19/18, 93.6030 cents, class 1
Average step (divided formal octave): 166.0150 cents
Largest one step interval           : 22/19, 253.8049 cents
Average / Smallest step             : 1.773607
Largest / Average step              : 1.528807
Largest / Smallest step             : 2.711504
Median interval of one step         : 12/11, 150.6371 cents, amount: 1
Least squares average step          : 148.30130 cents, oct.:  444.90389 cents
Scale is not proper
Scale has trivalence property
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 9.56485 cents
Scale diversity                     : 1.126172
Lumma stability                     : 0.375882
Lumma impropriety factor            : 0.019205
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        : 363/361, 9.5649 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
-- Rational properties --
Prime limit                         : 19
Odd number limit                    : 33 (O: 19 U: 33)
Highest odd numerator or denominator: 33
Scale harmonicity                   : 0.016496
Average absolute harmonicity        : 0.085628
Specific harmonicity                : 0.073744
Fundamental                         : 1/198, -7.6294 octaves, 1.3213 Hz.
Guide tone                          : 76,  6.2479 octaves, 19883.543 Hz.
Exponens Consonantiae               : 1.504800E+04, 13.87728 octaves
Euler's gradus suavitatis           : 36
Sum of Mann's harmonic distance     : 57.5, average 19.16667
Mersenne's string divisions         : 18389
Sum of van Prooijen's expressibility: 3.27439, average 1.09146
Sum of Tenney's harmonic distance   : 6.71150, average 2.23717
Vogel's harmonic complexity         : 23.66667
Wille's k value                     : 104
Wilson's harmonic complexity        : 36
Rectangular lattice diameter        : 4
Triangular lattice diameter         : 1
Lattice compactness                 : 14.18372, average 2.36395
Lattice compactness (without 2's)   : 9.21076, average 1.53513
Number of different primes          : 4
Prime exponents' range, average, count, tones@limit:
  2:  -1 .. 2         0.66667   4
  3:  -2 ..-1        -1.33333   4     1
 11:  -1 .. 0        -0.33333   1
 19:   0 .. 1         0.66667   2     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: <6 10 23 30|
Scale is weakly epimorphic with val: <6 10 24 29|
Scale is weakly epimorphic with val: <6 10 26 33|
Scale is weakly epimorphic with val: <6 10 27 29|
Scale is weakly epimorphic with val: <6 11 24 31|
Scale is weakly epimorphic with val: <6 11 25 33|
Scale is weakly epimorphic with val: <6 11 27 31|
Scale is weakly epimorphic with val: <7 10 23 29|
Scale is weakly epimorphic with val: <7 10 25 30|
Scale is weakly epimorphic with val: <7 10 26 32|
Scale is weakly epimorphic with val: <7 11 23 28|
Scale is weakly epimorphic with val: <7 11 23 31|
Scale is weakly epimorphic with val: <7 11 23 34|
Scale is JI-epimorphic with val: <7 11 24 30|
Scale is weakly epimorphic with val: <7 11 24 33|
Scale is weakly epimorphic with val: <7 11 26 28|
Scale is weakly epimorphic with val: <7 11 26 31|
Scale is weakly epimorphic with val: <7 11 26 34|
Scale is weakly epimorphic with val: <7 11 27 30|
Scale is weakly epimorphic with val: <7 11 27 33|
Scale is weakly epimorphic with val: <7 12 24 32|
Scale is weakly epimorphic with val: <7 12 25 34|
Scale is weakly epimorphic with val: <8 11 23 33|
Scale is weakly epimorphic with val: <8 11 25 31|
Scale is weakly epimorphic with val: <8 11 26 33|
Scale is weakly epimorphic with val: <8 12 24 31|
Scale is weakly epimorphic with val: <8 12 27 34|
FIT/MODE
  3:  0 1 2   N G T3   SD: 70.4289 c. M: 93.6030 c. 
  4:  1 1 2   P M ME S SD: 18.0572 c. M:-30.9082 c. 
  6:  1 2 3   P   T3   SD: 6.7116 c. M: 10.5955 c. 
 10:  2 3 5   P   T3   SD: 4.4326 c. M:-6.0060 c. 
 16:  3 5 8   P   T3   SD: 2.7640 c. M:-4.7824 c. 
 26:  5 8 13   P   T3   SD: 3.0332 c. M:-4.7824 c. 
 27:  5 8 14   N   T3   SD: 2.6835 c. M: 4.4406 c. 
 31:  6 9 16   N   T3   SD: 2.4743 c. M: 3.2506 c. 
 33:  6 10 17   N   T3   SD: 2.3760 c. M: 3.0494 c. 
 37:  7 11 19   N   T3   SD: 1.1805 c. M: 1.9479 c. 
 43:  8 13 22   N   T3   SD: 0.7975 c. M: 1.0088 c. 
 53:  10 16 27   N   T3   SD: 0.2178 c. M:-0.3677 c. 
 112: 21 34 57   N   T3   SD: 0.2315 c. M:-0.3356 c. 
 149: 28 45 76   N   T3   SD: 0.1338 c. M: 0.2314 c. 
 202: 38 61 103   N   T3   SD: 0.0999 c. M: 0.1487 c. 
 255: 48 77 130   N   T3   SD: 0.1026 c. M:-0.1466 c. 
 261: 49 79 133   N   T3   SD: 0.0583 c. M: 0.1003 c. 
 314: 59 95 160   N   T3   SD: 0.0185 c. M:-0.0240 c. 
 681: 128 206 347   N   T3   SD: 0.0174 c. M:-0.0287 c. 
 777: 146 235 396   N   T3   SD: 0.0182 c. M: 0.0250 c. 
 830: 156 251 423   N   T3   SD: 0.0109 c. M: 0.0180 c. 
 1144: 215 346 583   N   T3   SD: 0.0039 c. M: 0.0065 c. 
 1458: 274 441 743   N   T3   SD: 0.0035 c. M: 0.0061 c. 
FIT/HARMONIC
 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: 55.3011 cents
 6 x 7:8  S SD: 11.3154 cents
 7 x 8:9  S SD: 32.1512 cents
 8 x 9:11    SD: 33.4085 cents
 9 x 10:12  S SD: 30.9182 cents
 11:12:13:15    SD: 27.4647 cents
 12:13:14:16  S SD: 16.7810 cents
 13:14:15:17    SD: 16.1456 cents
 14:15:16:19    SD: 14.0529 cents
 15:16:17:20    SD: 10.9941 cents
 18:19:21:24    SD: 7.5436 cents
 21:22:24:28  S SD: 6.1594 cents
 33:35:38:44    SD: 2.7546 cents
 39:41:45:52    SD: 2.6158 cents
 54:57:62:72    SD: 1.6898 cents
 72:76:83:96    SD: 0.6324 cents
 126:133:145:168    SD: 0.3617 cents
 198:209:228:264    SD: 0.0000 cents