Scala analysis: xen07-london-didymus

Scale for 'Solo in Didymus's Chromatic'

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

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:         25/24             70.672427 classic chromatic semitone, minor chroma
  2:          5/4             386.313714 major third
  3:          4/3             498.044999 perfect fourth
  4:          3/2             701.955001 perfect fifth
  5:         25/16            772.627428 classic augmented fifth
  6:         15/8            1088.268715 classic major seventh
  7:          2/1            1200.000000 octave
SHOW/INTERVAL
  0:         16/15            111.7313 minor diatonic semitone
  1:         25/24             70.6724 classic chromatic semitone, minor chroma
  2:          6/5             315.6413 minor third
  3:         16/15            111.7313 minor diatonic semitone
  4:          9/8             203.9100 major whole tone
  5:         25/24             70.6724 classic chromatic semitone, minor chroma
  6:          6/5             315.6413 minor third
  7:         16/15            111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   2 25/24               70.672 cents   classic chromatic semitone, minor chroma
  1:   2 16/15               111.731 cents  minor diatonic semitone
  1:   1 9/8                 203.910 cents  major whole tone
  1:   2 6/5                 315.641 cents  minor third
  2:   1 10/9                182.404 cents  minor whole tone
  2:   1 75/64               274.582 cents  classic augmented second
  2:   1 6/5                 315.641 cents  minor third
  2:   2 5/4                 386.314 cents  major third
  2:   2 32/25               427.373 cents  classic diminished fourth
  3:   1 5/4                 386.314 cents  major third
  3:   4 4/3                 498.045 cents  perfect fourth
  3:   1 45/32               590.224 cents  diatonic tritone
  3:   1 36/25               631.283 cents  classic diminished fifth
  4:   1 25/18               568.717 cents  classic augmented fourth
  4:   1 64/45               609.776 cents  2nd tritone
  4:   4 3/2                 701.955 cents  perfect fifth
  4:   1 8/5                 813.686 cents  minor sixth
  5:   2 25/16               772.627 cents  classic augmented fifth
  5:   2 8/5                 813.686 cents  minor sixth
  5:   1 5/3                 884.359 cents  major sixth, BP sixth
  5:   1 128/75              925.418 cents  diminished seventh
  5:   1 9/5                 1017.596 cents just minor seventh, BP seventh
  6:   2 5/3                 884.359 cents  major sixth, BP sixth
  6:   1 16/9                996.090 cents  Pythagorean minor seventh
  6:   2 15/8                1088.269 cents classic major seventh
  6:   2 48/25               1129.328 cents classic diminished octave
Highest number of different intervals for one interval class: 5
Average number of different intervals per interval class: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
         1     2     3     4     5      6      7     
 0.0   : 70.7  386.3 498.0 702.0 772.6  1088.3 1200.0
 70.7  : 315.6 427.4 631.3 702.0 1017.6 1129.3 1200.0
 386.3 : 111.7 315.6 386.3 702.0 813.7  884.4  1200.0
 498.0 : 203.9 274.6 590.2 702.0 772.6  1088.3 1200.0
 702.0 : 70.7  386.3 498.0 568.7 884.4  996.1  1200.0
 772.6 : 315.6 427.4 498.0 813.7 925.4  1129.3 1200.0
 1088.3: 111.7 182.4 498.0 609.8 813.7  884.4  1200.0
 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  70.6724   .. 315.6413 cents      144/125, 244.9689 cents            25/24, 70.6724 cents
  2:  182.4037  .. 427.3726 cents      144/125, 244.9689 cents            25/27,-133.2376 cents
  3:  386.3137  .. 631.2826 cents      144/125, 244.9689 cents            125/128,-41.0589 cents
  4:  568.7174  .. 813.6863 cents      144/125, 244.9689 cents            625/648,-62.5651 cents
  5:  772.6274  .. 1017.5963 cents     144/125, 244.9689 cents            125/128,-41.0589 cents
  6:  884.3587  .. 1129.3276 cents     144/125, 244.9689 cents            25/27,-133.2376 cents
SHOW DATA
Number of notes                     : 7
-- Interval properties --
Smallest interval                   : 25/24, 70.6724 cents, class 1
Average step (divided formal octave): 171.4286 cents
Largest one step interval           : 6/5, 315.6413 cents
Average / Smallest step             : 2.425678
Largest / Average step              : 1.841241
Largest / Smallest step             : 4.466258
Median interval of one step         : 16/15, 111.7313 cents, amount: 2
Least squares average step          : 170.98574 cents, oct.:  1196.90021 cents
Scale is not proper
Step pattern alph. order: ABCDABC
Step pattern size order : ADBCADB
Scale is not a Constant Structure
Scale diversity                     : 1.537490
Lumma stability                     : 0.117787
Lumma impropriety factor            : 0.342632
Rothenberg efficiency               : 0.451701   redundancy: 0.548299
Efficiency x scale size             : 3.161905
Number of different interval sizes  : 22 = 3.66667 / class
Number of one step interval sizes   : 4
Highest interval variety            : 5
Mean interval variety               : 4.33333 = 13/3
Median interval variety             : 4
Lowest interval variety             : 4
Smallest interval difference        : 2048/2025, 19.5526 cents
Most common intervals               : 4/3, 498.0450 cents & inv., amount: 4
Number of recognisable fifths       : 4, average 701.9550 cents
Scale is Dorian octave species of abstract tetrachord
Scale contains two identical disjunct tetrachords
Best fifths form a closed circle
Scale contains a complete diamond   : 1 3
All steps are superparticular (epimoric)
Length of longest harmonic part     : 1 at degree 0
Length of longest subharmonic part  : 1 at degree 0
Formal octave complements present   : 3 = 42.8571%
Scale is differentially coherent in interval class 1
Scale is differentially coherent in interval classes 3 and 4 combined
Scale is n-1 differentially coherent in interval classes 4 and 5 combined
-- Rational properties --
Prime limit                         : 5
Odd number limit                    : 75 (O: 75 U: 75)
Highest odd numerator or denominator: 25
Scale harmonicity                   : 0.041436
Average absolute harmonicity        : 0.257515
Specific harmonicity                : 0.203045
Fundamental                         : 1/48, -5.5850 octaves, 5.4505 Hz.
Guide tone                          : 300,  8.2288 octaves, 78487.670 Hz.
Exponens Consonantiae               : 1.440000E+04, 13.81378 octaves
Euler's gradus suavitatis           : 19
Sum of Mann's harmonic distance     : 68.5, average 9.78571
Mersenne's string divisions         : 2079315
Sum of van Prooijen's expressibility: 5.62518, average 0.80360
Sum of Tenney's harmonic distance   : 10.91878, average 1.55983
Vogel's harmonic complexity         : 9.85714
Wille's k value                     : 37
Wilson's harmonic complexity        : 16
Rectangular lattice diameter        : 4
Triangular lattice diameter         : 3
Lattice compactness                 : 86.49196, average 3.08900
Lattice compactness (without 2's)   : 42.73012, average 1.52608
Number of different primes          : 3
Prime exponents' range, average, count, tones@limit:
  2:  -4 .. 2        -1.42857   16    1
  3:  -1 .. 1         0.00000   4     2
  5:   0 .. 2         0.85714   6     4
Average exponent except 2's         : 6 / 7 = 0.85714
Average absolute exponent except 2's: 10 / 7 = 1.42857
FIT/MODE
  7:  0 2 1 1 0 2 1   N   T3   SD: 51.4480 c. M: 86.9131 c. 
  9:  1 2 1 1 1 2 1   P M ME I SD: 33.4240 c. M:-62.6609 c. 
 10:  0 3 1 2 0 3 1   N        SD: 36.2063 c. M: 70.6724 c. 
 12:  1 3 1 2 1 3 1   N   T3 I SD: 16.6560 c. M:-29.3276 c.  Double Harmonic Major, Major Gipsy, Bhairav That, Mela Mayamalavagaula, Raga Paraj, Kalingada, Gaulipantu, Lalitapancamam, Gandhakriya, Kalingda, Manjiri, Chromatic 2nd Byzantine Liturgical, Hitzazkiar: Greece, Maqam Zengule, Hijaz Kar, Suzidil
 19:  1 5 2 3 1 5 2   N        SD: 9.5968 c. M: 14.7327 c. 
 22:  1 6 2 4 1 6 2   N        SD: 8.1936 c. M: 16.1270 c. 
 29:  2 7 3 5 2 7 3   N        SD: 9.8711 c. M: 13.8999 c. 
 31:  2 8 3 5 2 8 3   N        SD: 4.1681 c. M:-6.7469 c. 
 34:  2 9 3 6 2 9 3   N        SD: 3.4543 c. M:-5.8489 c. 
 53:  3 14 5 9 3 14 5   N        SD: 1.6756 c. M: 2.8161 c. 
 84:  5 22 8 14 5 22 8   N        SD: 1.5370 c. M: 2.5544 c. 
 87:  5 23 8 15 5 23 8   N        SD: 1.1559 c. M: 1.7069 c. 
 118: 7 31 11 20 7 31 11   N        SD: 0.2667 c. M:-0.5140 c. 
 205: 12 54 19 35 12 54 19   N        SD: 0.3621 c. M:-0.5118 c. 
 289: 17 76 27 49 17 76 27   N        SD: 0.2304 c. M: 0.3794 c. 
 323: 19 85 30 55 19 85 30   N        SD: 0.1664 c. M:-0.2762 c. 
 441: 26 116 41 75 26 116 41   N        SD: 0.1075 c. M:-0.1667 c. 
 559: 33 147 52 95 33 147 52   N        SD: 0.1072 c. M:-0.1812 c. 
 612: 36 161 57 104 36 161 57   N        SD: 0.0477 c. M: 0.0842 c. 
 730: 43 192 68 124 43 192 68   N        SD: 0.0296 c. M: 0.0495 c. 
 1171: 69 308 109 199 69 308 109   N        SD: 0.0270 c. M:-0.0455 c. 
 1665: 98 438 155 283 98 438 155   N        SD: 0.0235 c. M: 0.0418 c. 
 1783: 105 469 166 303 105 469 166   N        SD: 0.0060 c. M:-0.0095 c. 
FIT/HARMONIC
 1 x x x x x x 2  S SD: 0.0000 cents
 2 x x x 3 x x 4  S SD: 0.0000 cents
 3 x x 4 x 5 x 6  S SD: 37.2438 cents
 4 x 5 x 6 x x 8  S SD: 0.0000 cents
 5 x 6:7 x 8:9:10  S SD: 27.4297 cents
 6 x x 8:9 x 11:12    SD: 9.7264 cents
 7 x 9 x x 11:13:14    SD: 13.1109 cents
 9:10:11:12 x 14:17:18    SD: 19.8748 cents
 10:11 x 13:15:16:19:20    SD: 19.0258 cents
 11:12:14:15 x 17:21:22    SD: 16.8447 cents
 12:13:15:16:18:19:23:24    SD: 11.5918 cents
 13:14:16:17 x 20:24:26    SD: 13.5526 cents
 14:15:18:19:21:22:26:28    SD: 11.1280 cents
 15:16:19:20 x 23:28:30    SD: 9.6253 cents
 16:17:20:21:24:25:30:32    SD: 6.2575 cents
 20:21:25:27:30:31:38:40    SD: 5.2915 cents
 23:24:29:31:35:36:43:46    SD: 5.0282 cents
 24:25:30:32:36:38:45:48    SD: 3.2758 cents
 32:33:40:43:48:50:60:64    SD: 3.1437 cents
 44:46:55:59:66:69:83:88    SD: 2.4101 cents
 48:50:60:64:72:75:90:96  S SD: 0.0000 cents