Scala analysis: xen10-wilson-purvi-10c-01
Purvi modulation 1 from Figure 10c, Didymus (25/24 6/5 16/15), (16/15 6/5 25/24)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 16/15 111.731285 minor diatonic semitone 2: 6/5 315.641287 minor third 3: 5/4 386.313714 major third 4: 3/2 701.955001 perfect fifth 5: 8/5 813.686286 minor sixth 6: 5/3 884.358713 major sixth, BP sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 6/5 315.6413 minor third 1: 16/15 111.7313 minor diatonic semitone 2: 9/8 203.9100 major whole tone 3: 25/24 70.6724 classic chromatic semitone, minor chroma 4: 6/5 315.6413 minor third 5: 16/15 111.7313 minor diatonic semitone 6: 25/24 70.6724 classic chromatic semitone, minor chroma 7: 6/5 315.6413 minor third
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 : 111.7 315.6 386.3 702.0 813.7 884.4 1200.0 111.7 : 203.9 274.6 590.2 702.0 772.6 1088.3 1200.0 315.6 : 70.7 386.3 498.0 568.7 884.4 996.1 1200.0 386.3 : 315.6 427.4 498.0 813.7 925.4 1129.3 1200.0 702.0 : 111.7 182.4 498.0 609.8 813.7 884.4 1200.0 813.7 : 70.7 386.3 498.0 702.0 772.6 1088.3 1200.0 884.4 : 315.6 427.4 631.3 702.0 1017.6 1129.3 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 : 160.60256 cents, oct.: 1124.21794 cents Scale is not proper Step pattern alph. order: ABCDACD Step pattern size order : BCADBAD 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 Hypophrygian octave species of abstract tetrachord Best fifths form a closed circle Scale contains a complete diamond : 1 5 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 : 5 = 71.4286% 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: 15 Scale harmonicity : 0.041436 Average absolute harmonicity : 0.254902 Specific harmonicity : 0.211360 Fundamental : 1/60, -5.9069 octaves, 4.3604 Hz. Guide tone : 240, 7.9069 octaves, 62790.136 Hz. Exponens Consonantiae : 1.440000E+04, 13.81378 octaves Euler's gradus suavitatis : 19 Sum of Mann's harmonic distance : 40.0, average 5.71429 Mersenne's string divisions : 1595880 Sum of van Prooijen's expressibility: 4.44909, average 0.63558 Sum of Tenney's harmonic distance : 9.01569, average 1.28796 Vogel's harmonic complexity : 10.14286 Wille's k value : 37 Wilson's harmonic complexity : 16 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 81.67188, average 2.91685 Lattice compactness (without 2's) : 41.32248, average 1.47580 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 4 0.85714 12 1 3: -1 .. 1 0.00000 4 1 5: -1 .. 1 -0.14286 5 5 Average exponent except 2's :-1 / 7 =-0.14286 Average absolute exponent except 2's: 9 / 7 = 1.28571
FIT/MODE
7: 1 1 0 2 1 0 2 N T3 SD: 36.0275 c. M:-59.6973 c. 9: 1 1 1 2 1 1 2 P M ME S SD: 31.3587 c. M: 48.9746 c. 10: 1 2 0 3 1 0 3 N SD: 28.5712 c. M:-44.3587 c. 12: 1 2 1 3 1 1 3 N T3 S SD: 11.9844 c. M: 15.6413 c. 19: 2 3 1 5 2 1 5 N SD: 7.3034 c. M:-14.5845 c. 22: 2 4 1 6 2 1 6 N SD: 7.2594 c. M:-11.6314 c. 31: 3 5 2 8 3 2 8 N SD: 4.1152 c. M: 5.9639 c. 34: 3 6 2 9 3 2 9 N SD: 3.0488 c. M: 5.8489 c. 53: 5 9 3 14 5 3 14 N SD: 1.1796 c. M:-1.4763 c. 87: 8 15 5 23 8 5 23 N SD: 1.1524 c. M:-1.6001 c. 118: 11 20 7 31 11 7 31 N SD: 0.2441 c. M:-0.3870 c. 289: 27 49 17 76 27 17 76 N SD: 0.1898 c. M:-0.3794 c. 323: 30 55 19 85 30 19 85 N SD: 0.1574 c. M: 0.2762 c. 441: 41 75 26 116 41 26 116 N SD: 0.0830 c. M: 0.1667 c. 494: 46 84 29 130 46 29 130 N SD: 0.0935 c. M: 0.1482 c. 559: 52 95 33 147 52 33 147 N SD: 0.0750 c. M: 0.1034 c. 612: 57 104 36 161 57 36 161 N SD: 0.0344 c. M:-0.0450 c. 730: 68 124 43 192 68 43 192 N SD: 0.0277 c. M:-0.0495 c. 1171: 109 199 69 308 109 69 308 N SD: 0.0189 c. M: 0.0319 c. 1783: 166 303 105 469 166 105 469 N SD: 0.0059 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 x 5:6 S SD: 37.2438 cents 4 x x 5:6 x 7:8 S SD: 21.1168 cents 5 x 6 x x 8 x 10 S SD: 0.0000 cents 6 x 7:8:9 x 10:12 S SD: 24.3823 cents 7 x 8:9 x 11:12:14 SD: 22.6847 cents 8:9 x 10:12:13 x 16 SD: 19.2014 cents 9:10:11 x x 14:15:18 SD: 18.3109 cents 10:11:12:13:15:16:17:20 SD: 13.2663 cents 11:12:13:14:17 x 18:22 SD: 13.8098 cents 12:13:14:15:18:19:20:24 S SD: 8.3637 cents 13:14 x 16:20:21:22:26 SD: 10.3939 cents 14:15:17:18:21:22:23:28 SD: 9.5312 cents 15:16:18:19:23:24:25:30 SD: 6.3466 cents 16:17:19:20:24:26:27:32 SD: 5.6379 cents 20:21:24:25:30:32:33:40 SD: 4.6204 cents 28:30:34:35:42:45:47:56 SD: 3.7540 cents 30:32:36:38:45:48:50:60 SD: 3.2758 cents 40:43:48:50:60:64:67:80 SD: 2.2860 cents 44:47:53:55:66:70:73:88 SD: 2.0623 cents 56:60:67:70:84:90:93:112 SD: 1.9374 cents 60:64:72:75:90:96:100:120 S SD: 0.0000 cents