Scala analysis: xen09-wilson-marwa-14a-02
Marwa permutation 2 from Figure 14a, Didymus 16/15 25/24 6/5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 6/5 315.641287 minor third 2: 32/25 427.372572 classic diminished fourth 3: 36/25 631.282574 classic diminished fifth 4: 8/5 813.686286 minor sixth 5: 9/5 1017.596288 just minor seventh, BP seventh 6: 48/25 1129.327573 classic diminished octave 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 25/24 70.6724 classic chromatic semitone, minor chroma 1: 6/5 315.6413 minor third 2: 16/15 111.7313 minor diatonic semitone 3: 9/8 203.9100 major whole tone 4: 10/9 182.4037 minor whole tone 5: 9/8 203.9100 major whole tone 6: 16/15 111.7313 minor diatonic semitone 7: 25/24 70.6724 classic chromatic semitone, minor chroma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 2 16/15 111.731 cents minor diatonic semitone 1: 1 10/9 182.404 cents minor whole tone 1: 2 9/8 203.910 cents major whole tone 1: 1 6/5 315.641 cents minor third 2: 1 10/9 182.404 cents minor whole tone 2: 2 6/5 315.641 cents minor third 2: 3 5/4 386.314 cents major third 2: 1 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: 1 25/16 772.627 cents classic augmented fifth 5: 3 8/5 813.686 cents minor sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 5/3 884.359 cents major sixth, BP sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 2 15/8 1088.269 cents classic major seventh 6: 1 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 : 315.6 427.4 631.3 813.7 1017.6 1129.3 1200.0 315.6 : 111.7 315.6 498.0 702.0 813.7 884.4 1200.0 427.4 : 203.9 386.3 590.2 702.0 772.6 1088.3 1200.0 631.3 : 182.4 386.3 498.0 568.7 884.4 996.1 1200.0 813.7 : 203.9 315.6 386.3 702.0 813.7 1017.6 1200.0 1017.6: 111.7 182.4 498.0 609.8 813.7 996.1 1200.0 1129.3: 70.7 386.3 498.0 702.0 884.4 1088.3 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 : 10/9, 182.4037 cents, amount: 1 Least squares average step : 189.87804 cents, oct.: 1329.14631 cents Scale is not proper Step pattern alph. order: ABCDCBE Step pattern size order : EBDCDBA Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 1.460961 Lumma stability : 0.117787 Lumma impropriety factor : 0.342632 Rothenberg efficiency : 0.478912 redundancy: 0.521088 Efficiency x scale size : 3.352381 Number of different interval sizes : 20 = 3.33333 / class Number of one step interval sizes : 5 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 triad is 0.0 386.314 701.955 cents, amount: 3 Number of recognisable fifths : 4, average 701.9550 cents Scale is fully connected 5-limit major-minor triadic All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 2 Length of longest subharmonic part : 2 at degree 3 Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 Scale is differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined Scale is n-1 differentially coherent in interval class 5 -- Rational properties -- Prime limit : 5 Odd number limit : 45 (O: 45 U: 45) Highest odd numerator or denominator: 25 Scale harmonicity : 0.043228 Average absolute harmonicity : 0.206880 Specific harmonicity : 0.206807 Fundamental : 1/25, -4.6439 octaves, 10.4650 Hz. Guide tone : 288, 8.1699 octaves, 75348.163 Hz. Exponens Consonantiae : 7.200000E+03, 12.81378 octaves Euler's gradus suavitatis : 18 Sum of Mann's harmonic distance : 116.0, average 16.57143 Mersenne's string divisions : 508149642 Sum of van Prooijen's expressibility: 6.54600, average 0.93514 Sum of Tenney's harmonic distance : 13.96994, average 1.99571 Vogel's harmonic complexity : 8.42857 Wille's k value : 22 Wilson's harmonic complexity : 16 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 80.89798, average 2.88921 Lattice compactness (without 2's) : 44.55854, average 1.59138 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 0 .. 5 2.28571 16 1 3: 0 .. 2 0.85714 6 5: -2 .. 0 -1.28571 9 6 Average exponent except 2's :-3 / 7 =-0.42857 Average absolute exponent except 2's: 15 / 7 = 2.14286 Scale is weakly epimorphic with val: <7 10 16| Scale is weakly epimorphic with val: <7 12 15|
FIT/MODE
7: 2 1 1 1 1 1 0 N T3 SD: 51.0755 c. M:-86.9131 c. 8: 2 1 1 1 2 1 0 N D3 SD: 41.1197 c. M:-70.6724 c. 11: 3 1 2 1 2 1 1 N T3 SD: 29.3217 c. M: 50.0499 c. 12: 3 1 2 2 2 1 1 N T3 SD: 21.8094 c. M: 31.2826 c. 15: 4 1 3 2 3 1 1 N SD: 15.2151 c. M: 27.3726 c. 19: 5 2 3 3 3 2 1 N SD: 7.3473 c. M:-14.7327 c. 31: 8 3 5 5 5 3 2 N SD: 7.0774 c. M: 11.9277 c. 34: 9 3 6 5 6 3 2 N SD: 3.2467 c. M:-5.9331 c. 53: 14 5 9 8 9 5 3 N SD: 2.0020 c. M:-2.8161 c. 84: 22 8 14 13 14 8 5 N SD: 1.7935 c. M: 3.3106 c. 99: 26 9 17 15 17 9 6 N SD: 1.6041 c. M: 3.1301 c. 118: 31 11 20 18 20 11 7 N SD: 0.4649 c. M: 0.7741 c. 171: 45 16 29 26 29 16 10 N SD: 0.3718 c. M:-0.6976 c. 270: 71 25 46 41 46 25 16 N SD: 0.3556 c. M: 0.7059 c. 289: 76 27 49 44 49 27 17 N SD: 0.1846 c. M:-0.3091 c. 323: 85 30 55 49 55 30 19 N SD: 0.1954 c. M:-0.3604 c. 441: 116 41 75 67 75 41 26 N SD: 0.0818 c. M: 0.1617 c. 612: 161 57 104 93 104 57 36 N SD: 0.0626 c. M:-0.0900 c. 730: 192 68 124 111 124 68 43 N SD: 0.0335 c. M: 0.0620 c. 1171: 308 109 199 178 199 109 69 N SD: 0.0263 c. M: 0.0455 c. 1342: 353 125 228 204 228 125 79 N SD: 0.0250 c. M:-0.0492 c. 1783: 469 166 303 271 303 166 105 N SD: 0.0081 c. M:-0.0145 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x x 4 S SD: 35.3362 cents 3 x 4 x 5 x x 6 S SD: 33.3153 cents 4 x 5:6 x 7 x 8 S SD: 23.7947 cents 5:6 x 7:8:9 x 10 S SD: 9.7541 cents 6:7:8:9:10:11 x 12 S SD: 22.5902 cents 7:8:9:10:11:13 x 14 SD: 17.7051 cents 8 x 10:12:13:14:15:16 S SD: 17.8460 cents 9:11:12:13:14:16:17:18 SD: 14.0503 cents 10:12:13:14:16:18:19:20 S SD: 8.3637 cents 11:13:14:16:18:20:21:22 SD: 7.8408 cents 14:17:18:20:22:25:27:28 SD: 6.2145 cents 15:18:19:22:24:27:29:30 SD: 5.4982 cents 20:24:26:29:32:36:38:40 SD: 4.9335 cents 21:25:27:30:34:38:40:42 SD: 4.8098 cents 25:30:32:36:40:45:48:50 S SD: 0.0000 cents