Scala analysis: xen10-wilson-purvi-10b-04

Purvi modulation 4 from Figure 10b, Didymus (6/5 25/24 16/15), (25/24 16/15 6/5)

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:         16/9             996.089998 Pythagorean minor seventh
  7:          2/1            1200.000000 octave
SHOW/INTERVAL
  0:          9/8             203.9100 major whole tone
  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:        256/225           223.4626 Neapolitan diminished third
  7:          9/8             203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   2 25/24               70.672 cents   classic chromatic semitone, minor chroma
  1:   1 16/15               111.731 cents  minor diatonic semitone
  1:   2 9/8                 203.910 cents  major whole tone
  1:   1 256/225             223.463 cents  Neapolitan diminished third
  1:   1 6/5                 315.641 cents  minor third
  2:   2 75/64               274.582 cents  classic augmented second
  2:   1 32/27               294.135 cents  Pythagorean minor third
  2:   1 6/5                 315.641 cents  minor third
  2:   1 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:   1 8/5                 813.686 cents  minor sixth
  5:   1 5/3                 884.359 cents  major sixth, BP sixth
  5:   1 27/16               905.865 cents  Pythagorean major sixth
  5:   2 128/75              925.418 cents  diminished seventh
  6:   1 5/3                 884.359 cents  major sixth, BP sixth
  6:   1 225/128             976.537 cents  augmented sixth
  6:   2 16/9                996.090 cents  Pythagorean minor seventh
  6:   1 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: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
         1     2     3     4     5     6      7     
 0.0   : 70.7  386.3 498.0 702.0 772.6 996.1  1200.0
 70.7  : 315.6 427.4 631.3 702.0 925.4 1129.3 1200.0
 386.3 : 111.7 315.6 386.3 609.8 813.7 884.4  1200.0
 498.0 : 203.9 274.6 498.0 702.0 772.6 1088.3 1200.0
 702.0 : 70.7  294.1 498.0 568.7 884.4 996.1  1200.0
 772.6 : 223.5 427.4 498.0 813.7 925.4 1129.3 1200.0
 996.1 : 203.9 274.6 590.2 702.0 905.9 976.5  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:  274.5824  .. 427.3726 cents      2048/1875, 152.7901 cents          125/128,-41.0589 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  .. 925.4176 cents      2048/1875, 152.7901 cents          125/128,-41.0589 cents
  6:  884.3587  .. 1129.3276 cents     144/125, 244.9689 cents            125/128,-41.0589 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         : 9/8, 203.9100 cents, amount: 2
Least squares average step          : 167.03523 cents, oct.:  1169.24660 cents
Scale is not proper
Step pattern alph. order: ABCDAED
Step pattern size order : AEBCADC
Scale is not a Constant Structure
Scale diversity                     : 1.534657
Lumma stability                     : 0.117787
Lumma impropriety factor            : 0.189000
Rothenberg efficiency               : 0.435374   redundancy: 0.564626
Efficiency x scale size             : 3.047619
Number of different interval sizes  : 24 = 4.00000 / class
Number of one step interval sizes   : 5
Highest interval variety            : 5
Mean interval variety               : 4.66667 = 14/3
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
Most common triad is 0.0 498.045 701.955 cents, amount: 2
Number of recognisable fifths       : 4, average 701.9550 cents
Best fifths form a closed circle
Scale contains a complete diamond   : 1 3
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 n-1 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                    : 225 (O: 225 U: 225)
Highest odd numerator or denominator: 25
Scale harmonicity                   : 0.034722
Average absolute harmonicity        : 0.260982
Specific harmonicity                : 0.187609
Fundamental                         : 1/144, -7.1699 octaves, 1.8168 Hz.
Guide tone                          : 1200,  10.2288 octaves, 313950.678 Hz.
Exponens Consonantiae               : 1.728000E+05, 17.39874 octaves
Euler's gradus suavitatis           : 23
Sum of Mann's harmonic distance     : 69.5, average 9.92857
Mersenne's string divisions         : 452025
Sum of van Prooijen's expressibility: 5.40334, average 0.77191
Sum of Tenney's harmonic distance   : 10.99797, average 1.57114
Vogel's harmonic complexity         : 11.85714
Wille's k value                     : 112
Wilson's harmonic complexity        : 19
Rectangular lattice diameter        : 5
Triangular lattice diameter         : 4
Lattice compactness                 : 104.21865, average 3.72209
Lattice compactness (without 2's)   : 47.31590, average 1.68985
Number of different primes          : 3
Prime exponents' range, average, count, tones@limit:
  2:  -4 .. 4        -0.42857   17    1
  3:  -2 .. 1        -0.42857   5     3
  5:   0 .. 2         0.71429   5     3
Average exponent except 2's         : 2 / 7 = 0.28571
Average absolute exponent except 2's: 10 / 7 = 1.42857
Scale is weakly epimorphic with val: <7 11 15|
Scale is weakly epimorphic with val: <7 12 17|
FIT/MODE
  7:  0 2 1 1 1 1 1   N   T3   SD: 47.2206 c. M:-84.5154 c. 
 10:  0 3 1 2 0 2 2   N        SD: 38.5642 c. M: 70.6724 c. 
 11:  0 3 1 2 1 2 2   N        SD: 46.0081 c. M: 70.6724 c. 
 12:  1 3 1 2 1 2 2   P   D3   SD: 16.1228 c. M:-29.3276 c.  Phrygian Dominant, Phrygian Major, Mela Vakulabharanam, Raga Ahiri, Basant Mukhari, Jogiya, Vativasantabhairavi, Zilof, Ahava Rabba, Freygish: Jewish, Maqam Hijaz-Nahawand, Humayun, Spanish Gipsy, Dorico Flamenco: Spain, Hitzaz: Greece, Harmonic Major inverse, Mixolydian flat 2 flat 6
 17:  1 4 2 3 1 3 3   N        SD: 13.2074 c. M: 33.3725 c. 
 19:  1 5 2 3 1 4 3   N        SD: 9.5648 c. M: 14.7327 c. 
 22:  1 6 2 4 1 4 4   N        SD: 9.7589 c. M: 16.1270 c. 
 29:  2 7 3 5 2 5 5   N        SD: 8.7592 c. M: 13.8999 c. 
 31:  2 8 3 5 2 6 5   N        SD: 5.4724 c. M:-10.3616 c. 
 34:  2 9 3 6 2 6 6   N        SD: 3.9824 c. M: 7.8547 c. 
 53:  3 14 5 9 3 10 9   N        SD: 1.5808 c. M: 2.8161 c. 
 87:  5 23 8 15 5 16 15   N        SD: 1.5283 c. M: 2.9865 c. 
 118: 7 31 11 20 7 22 20   N        SD: 0.3275 c. M:-0.5202 c. 
 289: 17 76 27 49 17 54 49   N        SD: 0.2478 c. M:-0.4498 c. 
 323: 19 85 30 55 19 60 55   N        SD: 0.2062 c. M: 0.4244 c. 
 441: 26 116 41 75 26 82 75   N        SD: 0.1086 c. M: 0.1716 c. 
 494: 29 130 46 84 29 92 84   N        SD: 0.1262 c. M: 0.2271 c. 
 559: 33 147 52 95 33 104 95   N        SD: 0.1003 c. M:-0.1812 c. 
 612: 36 161 57 104 36 114 104   N        SD: 0.0463 c. M: 0.0842 c. 
 730: 43 192 68 124 43 136 124   N        SD: 0.0363 c. M:-0.0744 c. 
 1171: 69 308 109 199 69 218 199   N        SD: 0.0251 c. M:-0.0455 c. 
 1783: 105 469 166 303 105 332 303   N        SD: 0.0077 c. M: 0.0160 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 x 5:6  S SD: 37.2438 cents
 4 x 5 x 6 x 7:8  S SD: 6.8160 cents
 5 x 6:7 x 8:9:10  S SD: 23.8978 cents
 6 x x 8:9 x 11:12    SD: 13.3182 cents
 7 x 9 x x 11:12:14    SD: 20.0623 cents
 9:10:11:12 x 14:16:18  S SD: 19.7604 cents
 10:11 x 13:15:16:18:20    SD: 18.9795 cents
 11:12:14:15 x 17:20:22    SD: 17.2847 cents
 12:13:15:16:18:19:21:24    SD: 10.9541 cents
 13:14:16:17 x 20:23:26    SD: 12.8683 cents
 14:15:18:19:21:22:25:28    SD: 10.9291 cents
 15:16:19:20 x 23:27:30    SD: 10.1903 cents
 16:17:20:21:24:25:28:32    SD: 7.3706 cents
 18:19:23:24:27:28:32:36    SD: 6.4415 cents
 20:21:25:27:30:31:36:40    SD: 5.1680 cents
 23:24:29:31:35:36:41:46    SD: 5.0217 cents
 24:25:30:32:36:38:43:48    SD: 3.7994 cents
 28:29:35:37:42:44:50:56    SD: 3.1825 cents
 32:33:40:43:48:50:57:64    SD: 3.1805 cents
 44:46:55:59:66:69:78:88    SD: 2.0175 cents
 48:50:60:64:72:75:85:96    SD: 0.9680 cents
 96:100:120:128:144:150:171:192    SD: 0.4826 cents
 144:150:180:192:216:225:256:288    SD: 0.0000 cents