Scala analysis: 214_C14

Chromatic tetrachord 30/29 * 29/27 * 6/5

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

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:         30/29             58.691521
  2:         10/9             182.403712 minor whole tone
  3:          4/3             498.044999 perfect fourth
SHOW/INTERVAL
  0:          6/5             315.6413 minor third
  1:         30/29             58.6915 
  2:         29/27            123.7122 
  3:          6/5             315.6413 minor third
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   1 30/29               58.692 cents   
  1:   1 29/27               123.712 cents  
  1:   1 6/5                 315.641 cents  minor third
  2:   1 10/9                182.404 cents  minor whole tone
  2:   1 36/29               374.333 cents  
  2:   1 58/45               439.353 cents  
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  : 58.7  182.4 498.0
 58.7 : 123.7 439.4 498.0
 182.4: 315.6 374.3 498.0
 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  58.6915   .. 315.6413 cents      29/25, 256.9498 cents              30/29, 58.6915 cents
  2:  182.4037  .. 439.3535 cents      29/25, 256.9498 cents              25/27,-133.2376 cents
SHOW DATA
Number of notes                     : 3
-- Interval properties --
Smallest interval                   : 30/29, 58.6915 cents, class 1
Average step (divided formal octave): 166.0150 cents
Largest one step interval           : 6/5, 315.6413 cents
Average / Smallest step             : 2.828603
Largest / Average step              : 1.901282
Largest / Smallest step             : 5.377971
Median interval of one step         : 29/27, 123.7122 cents, amount: 1
Least squares average step          : 136.97385 cents, oct.:  410.92156 cents
Scale is not proper
Scale has trivalence property
Scale is a mode of a 314-tone equal temperament with octave  4/3
  degrees: 37 115 314
Least number of segments generator  : 159 of 252.195 cents and inv.
  number of contiguous generator circle segments: 1
Shortest superset generator         : 275 of 436.186 cents and inv.
  generated superset size: 12 = 9 more = 400.000%
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 58.69152 cents
Scale diversity                     : 0.916105
Lumma stability                     : 0.235688
Lumma impropriety factor            : 0.267521
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        : 30/29, 58.6915 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  : 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                         : 29
Odd number limit                    : 45 (O: 29 U: 45)
Highest odd numerator or denominator: 29
Scale harmonicity                   : 0.014191
Average absolute harmonicity        : 0.102803
Specific harmonicity                : 0.072571
Fundamental                         : 1/261, -8.0279 octaves, 1.0024 Hz.
Guide tone                          : 60,  5.9069 octaves, 15697.534 Hz.
Exponens Consonantiae               : 1.566000E+04, 13.93480 octaves
Euler's gradus suavitatis           : 41
Sum of Mann's harmonic distance     : 42.5, average 14.16667
Mersenne's string divisions         : 7847
Sum of van Prooijen's expressibility: 2.89376, average 0.96459
Sum of Tenney's harmonic distance   : 5.97294, average 1.99098
Vogel's harmonic complexity         : 28.00000
Wille's k value                     : 72
Wilson's harmonic complexity        : 43
Rectangular lattice diameter        : 5
Triangular lattice diameter         : 3
Lattice compactness                 : 14.22564, average 2.37094
Lattice compactness (without 2's)   : 11.99410, average 1.99902
Number of different primes          : 4
Prime exponents' range, average, count, tones@limit:
  2:   1 .. 2         1.33333   4
  3:  -2 .. 1        -0.66667   4     1
  5:   0 .. 1         0.66667   2     1
 29:  -1 .. 0        -0.33333   1     1
Average exponent except 2's         :-1 / 3 =-0.33333
Average absolute exponent except 2's: 7 / 3 = 2.33333
Scale is weakly epimorphic with val: <6 10 17 32|
Scale is weakly epimorphic with val: <6 10 17 35|
Scale is weakly epimorphic with val: <6 10 17 38|
Scale is weakly epimorphic with val: <6 11 18 32|
Scale is weakly epimorphic with val: <6 11 19 34|
Scale is weakly epimorphic with val: <6 11 19 37|
Scale is weakly epimorphic with val: <7 10 16 34|
Scale is weakly epimorphic with val: <7 10 16 37|
Scale is weakly epimorphic with val: <7 10 18 32|
Scale is weakly epimorphic with val: <7 11 16 32|
Scale is weakly epimorphic with val: <7 11 16 35|
Scale is weakly epimorphic with val: <7 11 16 38|
Scale is JI-epimorphic with val: <7 11 17 34|
Scale is weakly epimorphic with val: <7 11 17 37|
Scale is weakly epimorphic with val: <7 11 19 32|
Scale is weakly epimorphic with val: <7 11 19 35|
Scale is weakly epimorphic with val: <7 11 19 38|
Scale is weakly epimorphic with val: <7 12 18 34|
Scale is weakly epimorphic with val: <8 11 17 32|
Scale is weakly epimorphic with val: <8 11 17 35|
Scale is weakly epimorphic with val: <8 11 17 38|
Scale is weakly epimorphic with val: <8 11 18 34|
Scale is weakly epimorphic with val: <8 12 15 32|
Scale is weakly epimorphic with val: <8 12 18 35|
Scale is weakly epimorphic with val: <8 12 19 34|
Scale is weakly epimorphic with val: <8 12 19 37|
FIT/MODE
  3:  0 1 2   N G T3   SD: 35.1818 c. M: 58.6915 c. 
  5:  1 1 3   N M DE S SD: 25.5406 c. M:-40.9175 c. 
  6:  1 1 4   N M DE S SD: 16.9298 c. M:-24.3160 c. 
  7:  1 2 4   N   T3   SD: 19.3126 c. M:-31.0441 c. 
  8:  1 2 5   N   T3   SD: 3.2527 c. M:-4.3632 c. 
 25:  3 6 16   N   T3   SD: 1.8982 c. M: 3.1075 c. 
 33:  4 8 21   N   T3   SD: 1.2241 c. M:-1.6776 c. 
 41:  5 10 26   N   T3   SD: 1.1863 c. M:-2.0457 c. 
 44:  5 11 28   N   T3   SD: 1.4227 c. M: 2.0955 c. 
 49:  6 12 31   N   T3   SD: 1.3620 c. M:-2.2936 c. 
 52:  6 13 33   N   T3   SD: 0.7486 c. M: 1.2248 c. 
 60:  7 15 38   N   T3   SD: 0.3601 c. M: 0.5863 c. 
 93:  11 23 59   N   T3   SD: 0.2245 c. M: 0.3227 c. 
 153: 18 38 97   N   T3   SD: 0.0862 c. M: 0.1127 c. 
 161: 19 40 102   N   T3   SD: 0.0797 c. M:-0.1097 c. 
 314: 37 78 199   N   T3   SD: 0.0028 c. M: 0.0047 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: 78.8780 cents
 6 x 7:8  S SD: 42.2336 cents
 7 x 8:9  S SD: 39.8203 cents
 8 x 9:11    SD: 28.7251 cents
 9 x 10:12  S SD: 0.0000 cents
 10 x 11:13    SD: 23.5791 cents
 11 x 12:15  S SD: 25.1136 cents
 12 x 13:16    SD: 21.9155 cents
 13 x 14:17    SD: 31.8493 cents
 14:15:16:19    SD: 27.9050 cents
 15:16:17:20    SD: 21.0516 cents
 16:17:18:21  S SD: 19.2821 cents
 17:18:19:23    SD: 16.2035 cents
 18:19:20:24  S SD: 11.6372 cents
 21:22:23:28    SD: 11.0441 cents
 24:25:27:32    SD: 8.2061 cents
 25:26:28:33    SD: 8.0128 cents
 26:27:29:35    SD: 6.3491 cents
 27:28:30:36  S SD: 1.4231 cents
 90:93:100:120    SD: 0.6416 cents
 117:121:130:156    SD: 0.1644 cents
 144:149:160:192    SD: 0.1336 cents
 261:270:290:348    SD: 0.0000 cents