Scala analysis: xen09-wilson-marwa-14b-09
Marwa permutation 9 from Figure 14b, Didymus 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: 10/9 182.403712 minor whole tone 2: 5/4 386.313714 major third 3: 4/3 498.044999 perfect fourth 4: 8/5 813.686286 minor sixth 5: 5/3 884.358713 major sixth, BP sixth 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: 10/9 182.4037 minor whole tone 2: 9/8 203.9100 major whole tone 3: 16/15 111.7313 minor diatonic semitone 4: 6/5 315.6413 minor third 5: 25/24 70.6724 classic chromatic semitone, minor chroma 6: 16/15 111.7313 minor diatonic semitone 7: 9/8 203.9100 major whole tone
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 : 182.4 386.3 498.0 813.7 884.4 996.1 1200.0 182.4 : 203.9 315.6 631.3 702.0 813.7 1017.6 1200.0 386.3 : 111.7 427.4 498.0 609.8 813.7 996.1 1200.0 498.0 : 315.6 386.3 498.0 702.0 884.4 1088.3 1200.0 813.7 : 70.7 182.4 386.3 568.7 772.6 884.4 1200.0 884.4 : 111.7 315.6 498.0 702.0 813.7 1129.3 1200.0 996.1 : 203.9 386.3 590.2 702.0 1017.6 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 : 175.01603 cents, oct.: 1225.11224 cents Scale is not proper Step pattern alph. order: ABCDECB Step pattern size order : CDBEABD 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 0.0 498.045 813.686 cents, amount: 3 Number of recognisable fifths : 4, average 701.9550 cents Scale is fully connected 5-limit major-minor triadic Scale contains a complete diamond : 1 5 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 6 Length of longest subharmonic part : 2 at degree 0 Formal octave complements present : 3 = 42.8571% 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 -- Rational properties -- Prime limit : 5 Odd number limit : 45 (O: 45 U: 45) Highest odd numerator or denominator: 9 Scale harmonicity : 0.041436 Average absolute harmonicity : 0.247955 Specific harmonicity : 0.229830 Fundamental : 1/180, -7.4919 octaves, 1.4535 Hz. Guide tone : 80, 6.3219 octaves, 20930.045 Hz. Exponens Consonantiae : 1.440000E+04, 13.81378 octaves Euler's gradus suavitatis : 19 Sum of Mann's harmonic distance : 42.0, average 6.00000 Mersenne's string divisions : 3112200 Sum of van Prooijen's expressibility: 4.48252, average 0.64036 Sum of Tenney's harmonic distance : 9.57200, average 1.36743 Vogel's harmonic complexity : 13.14286 Wille's k value : 112 Wilson's harmonic complexity : 16 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 79.63965, average 2.84427 Lattice compactness (without 2's) : 41.49405, average 1.48193 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 4 1.28571 13 1 3: -2 .. 0 -0.85714 6 2 5: -1 .. 1 0.28571 4 4 Average exponent except 2's :-4 / 7 =-0.57143 Average absolute exponent except 2's: 10 / 7 = 1.42857 Scale is weakly epimorphic with val: <7 10 16| Scale is weakly epimorphic with val: <7 12 15|
FIT/MODE
7: 1 1 1 2 0 1 1 N T3 SD: 29.1717 c. M: 43.4566 c. 12: 2 2 1 3 1 1 2 N T3 SD: 11.6375 c. M:-17.5963 c. 19: 3 3 2 5 1 2 3 N SD: 7.7371 c. M:-14.4363 c. 31: 5 5 3 8 2 3 5 N SD: 6.4940 c. M:-11.1447 c. 34: 5 6 3 9 2 3 6 N SD: 4.2043 c. M: 7.8547 c. 41: 6 7 4 11 2 4 7 N SD: 4.7060 c. M: 6.7940 c. 46: 7 8 4 12 3 4 8 N SD: 3.4894 c. M: 4.9906 c. 53: 8 9 5 14 3 5 9 N SD: 1.0282 c. M: 1.4081 c. 118: 18 20 11 31 7 11 20 N SD: 0.3663 c. M:-0.6471 c. 171: 26 29 16 45 10 16 29 N SD: 0.2589 c. M:-0.4012 c. 289: 44 49 27 76 17 27 49 N SD: 0.2369 c. M:-0.4498 c. 323: 49 55 30 85 19 30 55 N SD: 0.2346 c. M: 0.4244 c. 388: 59 66 36 102 23 36 66 N SD: 0.1909 c. M:-0.2842 c. 441: 67 75 41 116 26 41 75 N SD: 0.0912 c. M: 0.1716 c. 559: 85 95 52 147 33 52 95 N SD: 0.0627 c. M: 0.0906 c. 612: 93 104 57 161 36 57 104 N SD: 0.0335 c. M: 0.0508 c. 1171: 178 199 109 308 69 109 199 N SD: 0.0154 c. M:-0.0228 c. 1783: 271 303 166 469 105 166 303 N SD: 0.0091 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: 55.8656 cents 3 x x 4 x 5 x 6 S SD: 0.0000 cents 4 x 5 x 6 x 7:8 S SD: 28.7524 cents 5 x 6:7:8 x 9:10 S SD: 22.4427 cents 6:7 x 8 x 10:11:12 S SD: 19.9727 cents 7:8:9 x 11:12 x 14 SD: 18.0097 cents 8:9:10:11:13 x 14:16 SD: 11.5040 cents 9:10:11:12:14:15:16:18 S SD: 8.9125 cents 10:11 x 13:16:17:18:20 SD: 10.3572 cents 11:12:14:15 x 18:20:22 S SD: 12.9300 cents 12:13:15:16:19:20:21:24 SD: 7.8156 cents 15:17:19:20:24:25:27:30 SD: 6.6450 cents 17:19:21:23:27:28:30:34 SD: 6.2399 cents 18:20:23:24:29:30:32:36 SD: 5.6989 cents 20:22:25:27:32:33:36:40 SD: 5.5888 cents 24:27:30:32:38:40:43:48 SD: 4.4554 cents 27:30:34:36:43:45:48:54 SD: 2.1561 cents 36:40:45:48:58:60:64:72 SD: 1.7116 cents 45:50:56:60:72:75:80:90 SD: 1.1016 cents 63:70:79:84:101:105:112:126 SD: 0.9246 cents 72:80:90:96:115:120:128:144 SD: 0.4297 cents 108:120:135:144:173:180:192:216 SD: 0.2861 cents 180:200:225:240:288:300:320:360 S SD: 0.0000 cents