Scala analysis: 277_C19

Chromatic tetrachord 28/27 * 99/91 * 13/11

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

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:         28/27             62.960904 Archytas' 1/3-tone
  2:         44/39            208.835280
  3:          4/3             498.044999 perfect fourth
SHOW/INTERVAL
  0:         13/11            289.2097 tridecimal minor third
  1:         28/27             62.9609 Archytas' 1/3-tone
  2:         99/91            145.8744 
  3:         13/11            289.2097 tridecimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   1 28/27               62.961 cents   Archytas' 1/3-tone
  1:   1 99/91               145.874 cents  
  1:   1 13/11               289.210 cents  tridecimal minor third
  2:   1 44/39               208.835 cents  
  2:   1 364/297             352.171 cents  
  2:   1 9/7                 435.084 cents  septimal major third, BP 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  : 63.0  208.8 498.0
 63.0 : 145.9 435.1 498.0
 208.8: 289.2 352.2 498.0
 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  62.9609   .. 289.2097 cents      351/308, 226.2488 cents            28/27, 62.9609 cents
  2:  208.8353  .. 435.0841 cents      351/308, 226.2488 cents            484/507,-80.3744 cents
SHOW DATA
Number of notes                     : 3
-- Interval properties --
Smallest interval                   : 28/27, 62.9609 cents, class 1
Average step (divided formal octave): 166.0150 cents
Largest one step interval           : 13/11, 289.2097 cents
Average / Smallest step             : 2.636795
Largest / Average step              : 1.742070
Largest / Smallest step             : 4.593481
Median interval of one step         : 99/91, 145.8744 cents, amount: 1
Least squares average step          : 141.05475 cents, oct.:  423.16424 cents
Scale is not proper
Scale has trivalence property
Scale is a mode of a 973-tone equal temperament with octave  4/3
  degrees: 123 408 973
Least number of segments generator  : 487 of 249.278 cents and inv.
  number of contiguous generator circle segments: 1
Shortest superset generator         : 801 of 410.004 cents and inv.
  generated superset size: 30 = 27 more = 1000.000%
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 62.96090 cents
Scale diversity                     : 0.982829
Lumma stability                     : 0.252832
Lumma impropriety factor            : 0.161380
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        : 28/27, 62.9609 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%
-- Rational properties --
Prime limit                         : 13
Odd number limit                    : 297 (O: 99 U: 297)
Highest odd numerator or denominator: 39
Scale harmonicity                   : 0.016496
Average absolute harmonicity        : 0.095267
Specific harmonicity                : 0.087977
Fundamental                         : 1/351, -8.4553 octaves, 0.7454 Hz.
Guide tone                          : 308,  8.2668 octaves, 80580.674 Hz.
Exponens Consonantiae               : 1.081080E+05, 16.72211 octaves
Euler's gradus suavitatis           : 37
Sum of Mann's harmonic distance     : 72.5, average 24.16667
Mersenne's string divisions         : 31955
Sum of van Prooijen's expressibility: 3.49955, average 1.16652
Sum of Tenney's harmonic distance   : 7.19222, average 2.39741
Vogel's harmonic complexity         : 20.66667
Wille's k value                     : 58
Wilson's harmonic complexity        : 40
Rectangular lattice diameter        : 6
Triangular lattice diameter         : 3
Lattice compactness                 : 14.91951, average 2.48658
Lattice compactness (without 2's)   : 12.19036, average 2.03173
Number of different primes          : 5
Prime exponents' range, average, count, tones@limit:
  2:   2 .. 2         2.00000   6
  3:  -3 ..-1        -1.66667   5     1
  7:   0 .. 1         0.33333   1     1
 11:   0 .. 1         0.33333   1
 13:  -1 .. 0        -0.33333   1     1
Average exponent except 2's         :-4 / 3 =-1.33333
Average absolute exponent except 2's: 8 / 3 = 2.66667
Scale is weakly epimorphic with val: <6 10 21 23 27|
Scale is weakly epimorphic with val: <6 10 21 23 30|
Scale is weakly epimorphic with val: <6 10 21 24 25|
Scale is weakly epimorphic with val: <6 10 21 24 28|
Scale is weakly epimorphic with val: <6 10 21 25 26|
Scale is weakly epimorphic with val: <6 10 21 25 29|
Scale is weakly epimorphic with val: <6 10 21 26 27|
Scale is weakly epimorphic with val: <6 10 21 26 30|
Scale is weakly epimorphic with val: <6 10 21 27 28|
Scale is weakly epimorphic with val: <7 10 18 24 25|
Scale is weakly epimorphic with val: <7 10 18 25 26|
Scale is weakly epimorphic with val: <7 10 18 26 27|
Scale is weakly epimorphic with val: <7 10 18 27 28|
Scale is weakly epimorphic with val: <7 10 19 23 25|
Scale is weakly epimorphic with val: <7 10 19 23 28|
Scale is weakly epimorphic with val: <7 10 19 24 26|
Scale is weakly epimorphic with val: <7 10 19 24 29|
Scale is weakly epimorphic with val: <7 10 19 25 27|
Scale is weakly epimorphic with val: <7 10 19 25 30|
Scale is weakly epimorphic with val: <7 10 19 26 28|
Scale is weakly epimorphic with val: <7 10 19 27 29|
Scale is weakly epimorphic with val: <7 10 21 24 25|
Scale is weakly epimorphic with val: <7 10 21 25 26|
Scale is weakly epimorphic with val: <7 10 21 26 27|
Scale is weakly epimorphic with val: <7 10 21 27 28|
Scale is weakly epimorphic with val: <7 11 18 23 25|
Scale is weakly epimorphic with val: <7 11 18 23 28|
Scale is weakly epimorphic with val: <7 11 18 24 26|
Scale is weakly epimorphic with val: <7 11 18 24 29|
Scale is weakly 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 26 28|
Scale is weakly epimorphic with val: <7 11 18 27 29|
Scale is weakly epimorphic with val: <7 11 20 23 27|
Scale is weakly epimorphic with val: <7 11 20 23 30|
Scale is JI-epimorphic with val: <7 11 20 24 25|
Scale is weakly epimorphic with val: <7 11 20 24 28|
Scale is JI-epimorphic with val: <7 11 20 25 26|
Scale is weakly epimorphic with val: <7 11 20 25 29|
Scale is JI-epimorphic with val: <7 11 20 26 27|
Scale is weakly epimorphic with val: <7 11 20 26 30|
Scale is JI-epimorphic with val: <7 11 20 27 28|
Scale is weakly epimorphic with val: <7 11 21 23 25|
Scale is weakly epimorphic with val: <7 11 21 23 28|
Scale is weakly epimorphic with val: <7 11 21 24 26|
Scale is weakly epimorphic with val: <7 11 21 24 29|
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 26 28|
Scale is weakly epimorphic with val: <7 11 21 27 29|
Scale is weakly epimorphic with val: <8 11 18 23 25|
Scale is weakly epimorphic with val: <8 11 18 24 26|
Scale is weakly epimorphic with val: <8 11 18 25 27|
Scale is weakly epimorphic with val: <8 11 18 26 28|
Scale is weakly epimorphic with val: <8 11 18 27 29|
Scale is weakly epimorphic with val: <8 11 20 23 27|
Scale is weakly epimorphic with val: <8 11 20 23 30|
Scale is weakly epimorphic with val: <8 11 20 24 25|
Scale is weakly epimorphic with val: <8 11 20 24 28|
Scale is weakly epimorphic with val: <8 11 20 25 26|
Scale is weakly epimorphic with val: <8 11 20 25 29|
Scale is weakly epimorphic with val: <8 11 20 26 27|
Scale is weakly epimorphic with val: <8 11 20 26 30|
Scale is weakly epimorphic with val: <8 11 20 27 28|
Scale is weakly epimorphic with val: <8 11 21 23 25|
Scale is weakly epimorphic with val: <8 11 21 24 26|
Scale is weakly epimorphic with val: <8 11 21 25 27|
Scale is weakly epimorphic with val: <8 11 21 26 28|
Scale is weakly epimorphic with val: <8 11 21 27 29|
Scale is weakly epimorphic with val: <8 12 19 24 25|
Scale is weakly epimorphic with val: <8 12 19 25 26|
Scale is weakly epimorphic with val: <8 12 19 26 27|
Scale is weakly epimorphic with val: <8 12 19 27 28|
Scale is weakly epimorphic with val: <8 12 22 24 25|
Scale is weakly epimorphic with val: <8 12 22 25 26|
Scale is weakly epimorphic with val: <8 12 22 26 27|
Scale is weakly epimorphic with val: <8 12 22 27 28|
FIT/MODE
  3:  0 1 2   N G T3   SD: 43.9608 c. M: 62.9609 c. 
  5:  1 1 3   N M DE S SD: 21.8752 c. M:-36.6481 c. 
  6:  1 2 3   P   T3   SD: 25.9286 c. M:-40.1872 c. 
  7:  1 2 4   N   T3   SD: 5.4260 c. M:-8.1884 c. 
 16:  2 5 9   N   T3   SD: 5.2463 c. M:-9.0594 c. 
 17:  2 5 10   N   T3   SD: 3.3265 c. M: 4.3674 c. 
 24:  3 7 14   N   T3   SD: 0.8623 c. M: 1.3165 c. 
 31:  4 9 18   N   T3   SD: 0.7524 c. M:-1.3030 c. 
 55:  7 16 32   N   T3   SD: 0.4073 c. M: 0.5619 c. 
 79:  10 23 46   N   T3   SD: 0.4593 c. M: 0.7912 c. 
 112: 14 33 65   N   T3   SD: 0.4183 c. M: 0.7053 c. 
 119: 15 35 69   N   T3   SD: 0.2682 c. M:-0.4273 c. 
 143: 18 42 83   N   T3   SD: 0.1742 c. M: 0.2699 c. 
 174: 22 51 101   N   T3   SD: 0.0665 c. M:-0.1146 c. 
 198: 25 58 115   N   T3   SD: 0.0557 c. M: 0.0764 c. 
 372: 47 109 216   N   T3   SD: 0.0244 c. M: 0.0359 c. 
 570: 72 167 331   N   T3   SD: 0.0290 c. M: 0.0500 c. 
 601: 76 176 349   N   T3   SD: 0.0117 c. M:-0.0198 c. 
 799: 101 234 464   N   T3   SD: 0.0106 c. M: 0.0179 c. 
 973: 123 285 565   N   T3   SD: 0.0034 c. M:-0.0058 c. 
 1574: 199 461 914   N   T3   SD: 0.0040 c. M:-0.0067 c. 
 1772: 224 519 1029   N   T3   SD: 0.0032 c. M: 0.0049 c. 
 2373: 300 695 1378   N   T3   SD: 0.0033 c. M: 0.0048 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: 68.0849 cents
 6 x 7:8  S SD: 29.0178 cents
 7 x 8:9  S SD: 33.4032 cents
 8 x 9:11    SD: 26.7501 cents
 9 x 10:12  S SD: 13.2158 cents
 10 x 11:13    SD: 30.9932 cents
 11 x 12:15  S SD: 35.0025 cents
 12 x 14:16  S SD: 29.0178 cents
 13:14:15:17    SD: 27.7143 cents
 14:15:16:19    SD: 22.6769 cents
 15:16:17:20    SD: 16.4661 cents
 17:18:19:23    SD: 15.6322 cents
 18:19:20:24  S SD: 13.4890 cents
 21:22:24:28  S SD: 9.4748 cents
 22:23:25:29    SD: 9.0857 cents
 23:24:26:31    SD: 7.2793 cents
 24:25:27:32    SD: 3.0501 cents
 54:56:61:72    SD: 0.7282 cents
 132:137:149:176    SD: 0.5550 cents
 186:193:210:248    SD: 0.5379 cents
 219:227:247:292    SD: 0.3347 cents
 243:252:274:324    SD: 0.3239 cents
 273:283:308:364    SD: 0.2265 cents
 297:308:335:396    SD: 0.1325 cents
 351:364:396:468    SD: 0.0000 cents