Scala analysis: xen09-wilson-marwa-16b-02
Marwa permutation 2 from Figure 16b, Schlesinger 13/12 15/13 16/15
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 15/13 247.741053 tridecimal 5/4-tone 2: 16/13 359.472338 tridecimal neutral third 3: 18/13 563.382340 tridecimal augmented fourth 4: 20/13 745.786052 tridecimal semi-augmented fifth 5: 45/26 949.696054 6: 24/13 1061.427339 tridecimal neutral seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 13/12 138.5727 tridecimal 2/3-tone 1: 15/13 247.7411 tridecimal 5/4-tone 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: 13/12 138.5727 tridecimal 2/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 16/15 111.731 cents minor diatonic semitone 1: 1 13/12 138.573 cents tridecimal 2/3-tone 1: 1 10/9 182.404 cents minor whole tone 1: 2 9/8 203.910 cents major whole tone 1: 1 15/13 247.741 cents tridecimal 5/4-tone 2: 1 52/45 250.304 cents 2: 2 6/5 315.641 cents minor third 2: 1 16/13 359.472 cents tridecimal neutral third 2: 3 5/4 386.314 cents major third 3: 1 13/10 454.214 cents tridecimal semi-diminished fourth 3: 4 4/3 498.045 cents perfect fourth 3: 1 18/13 563.382 cents tridecimal augmented fourth 3: 1 45/32 590.224 cents diatonic tritone 4: 1 64/45 609.776 cents 2nd tritone 4: 1 13/9 636.618 cents tridecimal diminished fifth 4: 4 3/2 701.955 cents perfect fifth 4: 1 20/13 745.786 cents tridecimal semi-augmented fifth 5: 3 8/5 813.686 cents minor sixth 5: 1 13/8 840.528 cents tridecimal neutral sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 1 45/26 949.696 cents 6: 1 26/15 952.259 cents tridecimal semi-augmented sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 24/13 1061.427 cents tridecimal neutral seventh 6: 2 15/8 1088.269 cents classic major seventh 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 : 247.7 359.5 563.4 745.8 949.7 1061.4 1200.0 247.7 : 111.7 315.6 498.0 702.0 813.7 952.3 1200.0 359.5 : 203.9 386.3 590.2 702.0 840.5 1088.3 1200.0 563.4 : 182.4 386.3 498.0 636.6 884.4 996.1 1200.0 745.8 : 203.9 315.6 454.2 702.0 813.7 1017.6 1200.0 949.7 : 111.7 250.3 498.0 609.8 813.7 996.1 1200.0 1061.4: 138.6 386.3 498.0 702.0 884.4 1088.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 247.7411 cents 225/208, 136.0098 cents 16/15, 111.7313 cents 2: 250.3039 .. 386.3137 cents 225/208, 136.0098 cents 676/675, 2.5629 cents 3: 454.2139 .. 590.2237 cents 225/208, 136.0098 cents 26/25, 67.9002 cents 4: 609.7763 .. 745.7861 cents 225/208, 136.0098 cents 2048/2025, 19.5526 cents 5: 813.6863 .. 949.6961 cents 225/208, 136.0098 cents 26/25, 67.9002 cents 6: 952.2589 .. 1088.2687 cents 225/208, 136.0098 cents 676/675, 2.5629 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 15/13, 247.7411 cents Average / Smallest step : 1.534293 Largest / Average step : 1.445156 Largest / Smallest step : 2.217294 Median interval of one step : 10/9, 182.4037 cents, amount: 1 Least squares average step : 179.69301 cents, oct.: 1257.85106 cents Scale is strictly proper Step pattern alph. order: ABCDCBE Step pattern size order : EADCDAB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 2.56289 cents Scale diversity : 1.537528 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.319951 Rothenberg efficiency : 0.423129 redundancy: 0.576871 Efficiency x scale size : 2.961905 Number of different interval sizes : 26 = 4.33333 / 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 : 676/675, 2.5629 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 Best minor thirds form a closed circle 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 class 3 -- Rational properties -- Prime limit : 13 Odd number limit : 45 (O: 45 U: 45) Highest odd numerator or denominator: 45 Scale harmonicity : 0.025715 Average absolute harmonicity : 0.171815 Specific harmonicity : 0.129945 Fundamental : 1/26, -4.7004 octaves, 10.0625 Hz. Guide tone : 720, 9.4919 octaves, 188370.407 Hz. Exponens Consonantiae : 1.872000E+04, 14.19229 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 116.0, average 16.57143 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.28508, average 1.04073 Sum of Tenney's harmonic distance : 15.25566, average 2.17938 Vogel's harmonic complexity : 9.00000 Wille's k value : 22 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 74.48085, average 2.66003 Lattice compactness (without 2's) : 41.62106, average 1.48647 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 1.42857 12 1 3: 0 .. 2 0.85714 6 5: 0 .. 1 0.42857 3 13: -1 .. 0 -0.85714 6 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 25| Scale is JI-epimorphic with val: <7 11 16 26| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 55.7602 c. M: 92.5532 c. Lebeng 8: 2 0 2 1 1 1 1 P D3 S SD: 38.2227 c. M: 59.4723 c. 9: 2 1 1 2 1 1 1 P M ME S SD: 29.6117 c. M:-54.2139 c. 10: 2 1 2 1 2 1 1 P M ME S SD: 18.9627 c. M:-36.6177 c. 11: 2 1 2 2 2 1 1 N D3 SD: 25.2179 c. M: 32.1996 c. 13: 3 1 2 2 2 1 2 P D3 SD: 23.6641 c. M: 46.0427 c. 14: 3 1 3 2 2 1 2 P T3 SD: 22.3259 c. M:-36.6177 c. 15: 3 1 3 2 3 1 2 N T3 SD: 20.2119 c. M: 39.4723 c. 19: 4 2 3 3 3 2 2 P T3 SD: 10.2180 c. M:-19.4750 c. 23: 5 2 4 3 4 2 3 P SD: 11.8667 c. M: 17.9491 c. 24: 5 2 4 4 4 2 3 P SD: 7.7676 c. M: 13.3823 c. 34: 7 3 6 5 6 3 4 P SD: 3.4524 c. M: 6.5312 c. 53: 11 5 9 8 9 5 6 P SD: 1.9808 c. M:-2.7918 c. 77: 16 7 13 12 13 7 9 P SD: 1.6051 c. M: 2.3434 c. 87: 18 8 15 13 15 8 10 P SD: 1.2543 c. M:-2.1349 c. 130: 27 12 22 20 22 12 15 P SD: 1.0274 c. M:-1.9063 c. 164: 34 15 28 25 28 15 19 P SD: 0.8273 c. M:-1.5235 c. 217: 45 20 37 33 37 20 25 P SD: 0.7998 c. M:-1.4560 c. 241: 50 22 41 37 41 22 28 P SD: 0.9771 c. M:-1.3413 c. 243: 50 23 41 37 41 23 28 SP SD: 0.7930 c. M: 1.5479 c. 253: 52 24 43 38 43 24 29 SP SD: 0.9840 c. M: 1.1220 c. 267: 55 25 45 41 45 25 31 SP SD: 0.8762 c. M: 1.5846 c. 270: 56 25 46 41 46 25 31 P SD: 0.9361 c. M:-1.4151 c. 277: 57 26 47 42 47 26 32 SP SD: 0.5432 c. M: 0.9596 c. 311: 64 29 53 47 53 29 36 SP SD: 0.6076 c. M: 1.0915 c. 320: 66 30 54 49 54 30 37 SP SD: 0.5678 c. M: 0.9461 c. 330: 68 31 56 50 56 31 38 SP SD: 0.4125 c. M: 0.6051 c. 354: 73 33 60 54 60 33 41 SP SD: 0.3811 c. M: 0.6705 c. 364: 75 34 62 55 62 34 42 SP SD: 0.3757 c. M: 0.7311 c. 407: 84 38 69 62 69 38 47 SP SD: 0.1844 c. M: 0.3103 c. 441: 91 41 75 67 75 41 51 SP SD: 0.1680 c. M: 0.2887 c. 494: 102 46 84 75 84 46 57 SP SD: 0.0921 c. M:-0.1804 c. 848: 175 79 144 129 144 79 98 SP SD: 0.1085 c. M: 0.1748 c. 901: 186 84 153 137 153 84 104 SP SD: 0.0657 c. M:-0.1281 c. 935: 193 87 159 142 159 87 108 SP SD: 0.0684 c. M: 0.1176 c. 1342: 277 125 228 204 228 125 155 SP SD: 0.0399 c. M: 0.0686 c. 1836: 379 171 312 279 312 171 212 SP SD: 0.0205 c. M: 0.0344 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: 21.9155 cents 3 x x 4 x 5 x 6 S SD: 30.8003 cents 4 x 5 x 6:7 x 8 S SD: 13.7103 cents 5 x 6:7:8 x 9:10 S SD: 18.7816 cents 6:7 x 8:9:10:11:12 S SD: 17.4568 cents 7:8:9:10:11:12:13:14 H SD: 14.7402 cents 8:9:10:11:12:14:15:16 S SD: 10.8747 cents 10 x 12:14:15:17:18:20 SD: 14.0375 cents 11:13:14:15:17:19:20:22 SD: 11.5696 cents 12:14:15:17:18:21:22:24 SD: 10.1907 cents 13:15:16:18:20:23:24:26 SD: 5.4358 cents 18:21:22:25:28:31:33:36 SD: 4.7914 cents 21:24:26:29:32:36:39:42 SD: 4.6413 cents 26:30:32:36:40:45:48:52 SD: 0.0000 cents