Scala analysis: 330_C25

Chromatic tetrachord 117/112 * 56/51 * 136/117

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

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:        117/112            75.611757
  2:         39/34            237.527253
  3:          4/3             498.044999 perfect fourth
SHOW/INTERVAL
  0:        136/117           260.5177 
  1:        117/112            75.6118 
  2:         56/51            161.9155 
  3:        136/117           260.5177 
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   1 117/112             75.612 cents   
  1:   1 56/51               161.915 cents  
  1:   1 136/117             260.518 cents  
  2:   1 39/34               237.527 cents  
  2:   1 17/14               336.130 cents  supraminor third
  2:   1 448/351             422.433 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  : 75.6  237.5 498.0
 75.6 : 161.9 422.4 498.0
 237.5: 260.5 336.1 498.0
 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  75.6118   .. 260.5177 cents      15232/13689, 184.9060 cents        117/112, 75.6118 cents
  2:  237.5273  .. 422.4332 cents      15232/13689, 184.9060 cents        4563/4624,-22.9905 cents
SHOW DATA
Number of notes                     : 3
-- Interval properties --
Smallest interval                   : 117/112, 75.6118 cents, class 1
Average step (divided formal octave): 166.0150 cents
Largest one step interval           : 136/117, 260.5177 cents
Average / Smallest step             : 2.195624
Largest / Average step              : 1.569242
Largest / Smallest step             : 3.445466
Median interval of one step         : 56/51, 161.9155 cents, amount: 1
Least squares average step          : 146.05723 cents, oct.:  438.17170 cents
Scale is not proper
Scale has trivalence property
Scale is a mode of a 2187-tone equal temperament with octave  4/3
  degrees: 332 1043 2187
Least number of segments generator  : 1094 of 249.136 cents and inv.
  number of contiguous generator circle segments: 1
Shortest superset generator         : 1136 of 258.701 cents and inv.
  generated superset size: 86 = 83 more = 2866.667%
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 22.99049 cents
Scale diversity                     : 1.040159
Lumma stability                     : 0.303634
Lumma impropriety factor            : 0.046161
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        : 4624/4563, 22.9905 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%
-- Rational properties --
Prime limit                         : 17
Odd number limit                    : 351 (O: 117 U: 351)
Highest odd numerator or denominator: 117
Scale harmonicity                   : 0.013062
Average absolute harmonicity        : 0.085367
Specific harmonicity                : 0.062624
Fundamental                         : 1/5712, -12.4798 octaves, 0.0458 Hz.
Guide tone                          : 468,  8.8704 octaves, 122440.765 Hz.
Exponens Consonantiae               : 2.673216E+06, 21.35014 octaves
Euler's gradus suavitatis           : 47
Sum of Mann's harmonic distance     : 154.5, average 51.50000
Mersenne's string divisions         : 117019
Sum of van Prooijen's expressibility: 4.13637, average 1.37879
Sum of Tenney's harmonic distance   : 8.31913, average 2.77304
Vogel's harmonic complexity         : 32.66667
Wille's k value                     : 2983
Wilson's harmonic complexity        : 46
Rectangular lattice diameter        : 6
Triangular lattice diameter         : 4
Lattice compactness                 : 23.11922, average 3.85320
Lattice compactness (without 2's)   : 12.67971, average 2.11328
Number of different primes          : 5
Prime exponents' range, average, count, tones@limit:
  2:  -4 .. 2        -1.00000   7
  3:  -1 .. 2         0.66667   4     1
  7:  -1 .. 0        -0.33333   1
 13:   0 .. 1         0.66667   2     1
 17:  -1 .. 0        -0.33333   1     1
Average exponent except 2's         : 2 / 3 = 0.66667
Average absolute exponent except 2's: 8 / 3 = 2.66667
Scale is weakly epimorphic with val: <6 10 18 25 28|
Scale is weakly epimorphic with val: <6 10 18 25 31|
Scale is weakly epimorphic with val: <6 10 18 26 27|
Scale is weakly epimorphic with val: <6 10 18 29 30|
Scale is weakly epimorphic with val: <6 10 19 26 29|
Scale is weakly epimorphic with val: <6 10 19 26 32|
Scale is weakly epimorphic with val: <6 10 19 27 28|
Scale is weakly epimorphic with val: <6 10 19 30 31|
Scale is weakly epimorphic with val: <6 10 20 27 27|
Scale is weakly epimorphic with val: <6 10 20 27 30|
Scale is weakly epimorphic with val: <6 10 20 27 33|
Scale is weakly epimorphic with val: <6 10 20 28 29|
Scale is weakly epimorphic with val: <6 10 21 26 27|
Scale is weakly epimorphic with val: <6 10 21 28 28|
Scale is weakly epimorphic with val: <6 10 21 28 31|
Scale is weakly epimorphic with val: <6 10 21 29 30|
Scale is weakly epimorphic with val: <6 10 22 27 28|
Scale is weakly epimorphic with val: <6 10 22 29 29|
Scale is weakly epimorphic with val: <6 10 22 29 32|
Scale is weakly epimorphic with val: <6 10 22 30 31|
Scale is weakly epimorphic with val: <6 11 18 25 27|
Scale is weakly epimorphic with val: <6 11 18 28 30|
Scale is weakly epimorphic with val: <6 11 19 26 28|
Scale is weakly epimorphic with val: <6 11 19 29 31|
Scale is weakly epimorphic with val: <6 11 20 25 28|
Scale is weakly epimorphic with val: <6 11 20 25 31|
Scale is weakly epimorphic with val: <6 11 20 27 29|
Scale is weakly epimorphic with val: <6 11 20 30 32|
Scale is weakly epimorphic with val: <6 11 21 25 27|
Scale is weakly epimorphic with val: <6 11 21 26 29|
Scale is weakly epimorphic with val: <6 11 21 26 32|
Scale is weakly epimorphic with val: <6 11 21 28 30|
Scale is weakly epimorphic with val: <6 11 22 26 28|
Scale is weakly epimorphic with val: <6 11 22 27 27|
Scale is weakly epimorphic with val: <6 11 22 27 30|
Scale is weakly epimorphic with val: <6 11 22 27 33|
Scale is weakly epimorphic with val: <6 11 22 29 31|
Scale is weakly epimorphic with val: <7 10 18 28 28|
Scale is weakly epimorphic with val: <7 10 18 29 30|
Scale is weakly epimorphic with val: <7 10 18 29 33|
Scale is weakly epimorphic with val: <7 10 19 29 29|
Scale is weakly epimorphic with val: <7 10 19 30 31|
Scale is weakly epimorphic with val: <7 10 20 27 27|
Scale is weakly epimorphic with val: <7 10 20 30 30|
Scale is weakly epimorphic with val: <7 10 21 28 28|
Scale is weakly epimorphic with val: <7 10 22 29 29|
Scale is JI-epimorphic with val: <7 11 18 25 27|
Scale is weakly epimorphic with val: <7 11 18 25 30|
Scale is weakly epimorphic with val: <7 11 18 25 33|
Scale is weakly epimorphic with val: <7 11 18 26 29|
Scale is weakly epimorphic with val: <7 11 18 26 32|
Scale is weakly epimorphic with val: <7 11 18 28 30|
Scale is weakly epimorphic with val: <7 11 18 28 33|
Scale is weakly epimorphic with val: <7 11 18 29 29|
Scale is weakly epimorphic with val: <7 11 18 29 32|
Scale is JI-epimorphic with val: <7 11 19 26 28|
Scale is weakly epimorphic with val: <7 11 19 26 31|
Scale is weakly epimorphic with val: <7 11 19 27 27|
Scale is weakly epimorphic with val: <7 11 19 27 30|
Scale is weakly epimorphic with val: <7 11 19 27 33|
Scale is weakly epimorphic with val: <7 11 19 29 31|
Scale is weakly epimorphic with val: <7 11 19 30 30|
Scale is weakly epimorphic with val: <7 11 19 30 33|
Scale is weakly epimorphic with val: <7 11 20 25 28|
Scale is weakly epimorphic with val: <7 11 20 25 31|
Scale is JI-epimorphic with val: <7 11 20 27 29|
Scale is weakly epimorphic with val: <7 11 20 27 32|
Scale is weakly epimorphic with val: <7 11 20 28 28|
Scale is weakly epimorphic with val: <7 11 20 28 31|
Scale is weakly epimorphic with val: <7 11 20 30 32|
Scale is weakly epimorphic with val: <7 11 21 25 27|
Scale is weakly epimorphic with val: <7 11 21 25 30|
Scale is weakly epimorphic with val: <7 11 21 25 33|
Scale is weakly epimorphic with val: <7 11 21 26 29|
Scale is weakly epimorphic with val: <7 11 21 26 32|
Scale is JI-epimorphic with val: <7 11 21 28 30|
Scale is weakly epimorphic with val: <7 11 21 28 33|
Scale is weakly epimorphic with val: <7 11 21 29 29|
Scale is weakly epimorphic with val: <7 11 21 29 32|
Scale is weakly epimorphic with val: <7 11 22 26 28|
Scale is weakly epimorphic with val: <7 11 22 26 31|
Scale is weakly epimorphic with val: <7 11 22 27 27|
Scale is weakly epimorphic with val: <7 11 22 27 30|
Scale is weakly epimorphic with val: <7 11 22 27 33|
Scale is JI-epimorphic with val: <7 11 22 29 31|
Scale is weakly epimorphic with val: <7 11 22 30 30|
Scale is weakly epimorphic with val: <7 11 22 30 33|
Scale is weakly epimorphic with val: <7 12 18 25 29|
Scale is weakly epimorphic with val: <7 12 18 25 32|
Scale is weakly epimorphic with val: <7 12 18 26 28|
Scale is weakly epimorphic with val: <7 12 18 29 31|
Scale is weakly epimorphic with val: <7 12 19 26 27|
Scale is weakly epimorphic with val: <7 12 19 26 30|
Scale is weakly epimorphic with val: <7 12 19 26 33|
Scale is weakly epimorphic with val: <7 12 19 27 29|
Scale is weakly epimorphic with val: <7 12 19 30 32|
Scale is weakly epimorphic with val: <7 12 20 25 27|
Scale is weakly epimorphic with val: <7 12 20 27 28|
Scale is weakly epimorphic with val: <7 12 20 27 31|
Scale is weakly epimorphic with val: <7 12 20 28 30|
Scale is weakly epimorphic with val: <7 12 21 26 28|
Scale is weakly epimorphic with val: <7 12 21 28 29|
Scale is weakly epimorphic with val: <7 12 21 28 32|
Scale is weakly epimorphic with val: <7 12 21 29 31|
Scale is weakly epimorphic with val: <7 12 22 27 29|
Scale is weakly epimorphic with val: <7 12 22 29 30|
Scale is weakly epimorphic with val: <7 12 22 29 33|
Scale is weakly epimorphic with val: <7 12 22 30 32|
Scale is weakly epimorphic with val: <8 11 18 29 29|
Scale is weakly epimorphic with val: <8 11 19 27 27|
Scale is weakly epimorphic with val: <8 11 19 30 30|
Scale is weakly epimorphic with val: <8 11 20 28 28|
Scale is weakly epimorphic with val: <8 11 21 29 29|
Scale is weakly epimorphic with val: <8 11 22 27 27|
Scale is weakly epimorphic with val: <8 11 22 30 30|
Scale is weakly epimorphic with val: <8 12 18 28 29|
Scale is weakly epimorphic with val: <8 12 18 29 31|
Scale is weakly epimorphic with val: <8 12 19 26 27|
Scale is weakly epimorphic with val: <8 12 19 29 30|
Scale is weakly epimorphic with val: <8 12 19 30 32|
Scale is weakly epimorphic with val: <8 12 20 27 28|
Scale is weakly epimorphic with val: <8 12 20 30 31|
Scale is weakly epimorphic with val: <8 12 21 28 29|
Scale is weakly epimorphic with val: <8 12 22 26 27|
Scale is weakly epimorphic with val: <8 12 22 29 30|
FIT/MODE
  3:  0 1 2   N G T3   SD: 60.0864 c. M: 75.6118 c. 
  4:  1 1 2   P M ME S SD: 29.0017 c. M:-48.8995 c. 
  5:  1 1 3   N M DE S SD: 26.0990 c. M: 38.3093 c. 
  6:  1 2 3   P   T3   SD: 7.8917 c. M:-11.4952 c. 
 13:  2 4 7   N   T3   SD: 4.4610 c. M: 7.6603 c. 
 19:  3 6 10   N   T3   SD: 1.9798 c. M:-3.0269 c. 
 27:  4 9 14   N   T3   SD: 1.6834 c. M:-2.2722 c. 
 40:  6 13 21   N   T3   SD: 0.7600 c. M: 0.9559 c. 
 46:  7 15 24   N   T3   SD: 0.3992 c. M:-0.6682 c. 
 86:  13 28 45   N   T3   SD: 0.1948 c. M: 0.3259 c. 
 132: 20 43 69   N   T3   SD: 0.1337 c. M:-0.1760 c. 
 151: 23 49 79   N   T3   SD: 0.1467 c. M:-0.2494 c. 
 191: 29 62 100   N   T3   SD: 0.1379 c. M: 0.2388 c. 
 197: 30 64 103   N   T3   SD: 0.1508 c. M:-0.2327 c. 
 218: 33 71 114   N   T3   SD: 0.1335 c. M: 0.2196 c. 
 237: 36 77 124   N   T3   SD: 0.0432 c. M: 0.0628 c. 
 283: 43 92 148   N   T3   SD: 0.0487 c. M:-0.0629 c. 
 369: 56 120 193   N   T3   SD: 0.0207 c. M: 0.0277 c. 
 606: 92 197 317   N   T3   SD: 0.0062 c. M: 0.0107 c. 
 1581: 240 514 827   N   T3   SD: 0.0045 c. M: 0.0072 c. 
 1864: 283 606 975   N   T3   SD: 0.0040 c. M:-0.0060 c. 
 2187: 332 711 1144   N   T3   SD: 0.0043 c. M: 0.0055 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: 57.5250 cents
 6 x 7:8  S SD: 14.6718 cents
 7 x 8:9  S SD: 31.6403 cents
 8 x 9:11    SD: 31.4965 cents
 9 x 10:12  S SD: 27.5618 cents
 10 x 11:13    SD: 42.3697 cents
 11:12:13:15    SD: 33.0211 cents
 12:13:14:16  S SD: 23.1544 cents
 13:14:15:17    SD: 21.1090 cents
 14:15:16:19    SD: 17.9520 cents
 15:16:17:20    SD: 13.9002 cents
 18:19:21:24    SD: 11.4733 cents
 19:20:22:25    SD: 10.3533 cents
 20:21:23:27    SD: 7.8923 cents
 21:22:24:28  S SD: 2.6796 cents
 48:50:55:64    SD: 1.7582 cents
 69:72:79:92    SD: 1.2515 cents
 108:113:124:144    SD: 1.0644 cents
 129:135:148:172    SD: 1.0378 cents
 135:141:155:180    SD: 0.5586 cents
 156:163:179:208    SD: 0.2280 cents
 225:235:258:300    SD: 0.2257 cents
 360:376:413:480    SD: 0.1370 cents
 381:398:437:508    SD: 0.0409 cents
 537:561:616:716    SD: 0.0390 cents