Scala analysis: xen09-wilson-marwa-16b-05
Marwa permutation 5 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: 4/3 498.044999 perfect 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: 13/12 138.5727 tridecimal 2/3-tone 4: 15/13 247.7411 tridecimal 5/4-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: 2 13/12 138.573 cents tridecimal 2/3-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 15/13 247.741 cents tridecimal 5/4-tone 2: 2 52/45 250.304 cents 2: 1 6/5 315.641 cents minor third 2: 1 16/13 359.472 cents tridecimal neutral third 2: 2 5/4 386.314 cents major third 2: 1 135/104 451.651 cents 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: 1 208/135 748.349 cents 5: 2 8/5 813.686 cents minor sixth 5: 1 13/8 840.528 cents tridecimal neutral sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 2 45/26 949.696 cents 6: 2 26/15 952.259 cents tridecimal semi-augmented sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 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 : 247.7 359.5 498.0 745.8 949.7 1061.4 1200.0 247.7 : 111.7 250.3 498.0 702.0 813.7 952.3 1200.0 359.5 : 138.6 386.3 590.2 702.0 840.5 1088.3 1200.0 498.0 : 247.7 451.7 563.4 702.0 949.7 1061.4 1200.0 745.8 : 203.9 315.6 454.2 702.0 813.7 952.3 1200.0 949.7 : 111.7 250.3 498.0 609.8 748.3 996.1 1200.0 1061.4: 138.6 386.3 498.0 636.6 884.4 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 .. 451.6511 cents 6075/5408, 201.3471 cents 676/675, 2.5629 cents 3: 454.2139 .. 590.2237 cents 225/208, 136.0098 cents 676/675, 2.5629 cents 4: 609.7763 .. 745.7861 cents 225/208, 136.0098 cents 2048/2025, 19.5526 cents 5: 748.3489 .. 949.6961 cents 6075/5408, 201.3471 cents 676/675, 2.5629 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 : 13/12, 138.5727 cents, amount: 2 Least squares average step : 178.29292 cents, oct.: 1248.05046 cents Scale is strictly proper Step pattern alph. order: ABCADBC Step pattern size order : DABDCAB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 2.56289 cents Scale diversity : 1.515941 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.211056 Rothenberg efficiency : 0.421769 redundancy: 0.578231 Efficiency x scale size : 2.952381 Number of different interval sizes : 26 = 4.33333 / 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 : 676/675, 2.5629 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Number of recognisable fifths : 4, average 701.9550 cents Scale is Phrygian octave species of abstract tetrachord Formal octave complements present : 1 = 14.2857% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval class 3 -- Rational properties -- Prime limit : 13 Odd number limit : 135 (O: 135 U: 135) Highest odd numerator or denominator: 45 Scale harmonicity : 0.024065 Average absolute harmonicity : 0.197412 Specific harmonicity : 0.113749 Fundamental : 1/78, -6.2854 octaves, 3.3542 Hz. Guide tone : 720, 9.4919 octaves, 188370.407 Hz. Exponens Consonantiae : 5.616000E+04, 15.77726 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 104.0, average 14.85714 Mersenne's string divisions : 70393092 Sum of van Prooijen's expressibility: 6.64826, average 0.94975 Sum of Tenney's harmonic distance : 13.96562, average 1.99509 Vogel's harmonic complexity : 12.71429 Wille's k value : 67 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 75.45179, average 2.69471 Lattice compactness (without 2's) : 42.64709, average 1.52311 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 1.57143 13 1 3: -1 .. 2 0.42857 5 1 5: 0 .. 1 0.42857 3 13: -1 .. 0 -0.71429 5 5 Average exponent except 2's : 1 / 7 = 0.14286 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is weakly epimorphic with val: <7 11 15 24| 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: 52.9388 c. M: 92.5532 c. Lebeng 8: 1 1 1 2 1 1 1 P M ME I SD: 50.7327 c. M: 97.7411 c. 9: 2 1 1 2 1 1 1 P M ME S SD: 30.4262 c. M:-54.2139 c. 10: 2 1 1 2 2 1 1 P D3 S SD: 14.6476 c. M: 25.7861 c. Pseudo Rast 19: 4 2 2 4 3 2 2 P SD: 10.4031 c. M:-19.4750 c. 24: 5 2 3 5 4 2 3 P SD: 5.9412 c. M: 11.4273 c. Soft Diatonic Phrygian 34: 7 3 4 7 6 3 4 P SD: 3.7245 c. M: 6.5312 c. 43: 9 4 5 9 7 4 5 P SD: 3.8179 c. M:-7.7023 c. 53: 11 5 6 11 9 5 6 P SD: 1.7079 c. M:-2.7918 c. 77: 16 7 9 16 13 7 9 P SD: 1.3614 c. M:-2.2659 c. 87: 18 8 10 18 15 8 10 P SD: 1.1139 c. M:-2.0281 c. 130: 27 12 15 27 22 12 15 P SD: 1.0330 c. M:-1.9063 c. 140: 29 13 16 29 24 13 16 P SD: 0.9880 c. M:-1.7325 c. 164: 34 15 19 34 28 15 19 P SD: 0.8472 c. M:-1.5235 c. 217: 45 20 25 45 37 20 25 P SD: 0.7697 c. M:-1.4560 c. 241: 50 22 28 50 41 22 28 P SD: 0.9388 c. M:-1.3413 c. 243: 50 23 28 50 41 23 28 SP SD: 0.8233 c. M: 1.5479 c. 253: 52 24 29 52 43 24 29 SP SD: 0.9014 c. M: 1.1220 c. 258: 53 24 30 53 44 24 30 SP SD: 1.0453 c. M: 1.6000 c. 267: 55 25 31 55 45 25 31 SP SD: 0.7126 c. M: 1.3814 c. 277: 57 26 32 57 47 26 32 SP SD: 0.5406 c. M: 0.9596 c. 301: 62 28 35 62 51 28 35 SP SD: 0.6082 c. M: 0.9622 c. 311: 64 29 36 64 53 29 36 SP SD: 0.6176 c. M: 1.0915 c. 320: 66 30 37 66 54 30 37 SP SD: 0.5312 c. M: 0.9461 c. 330: 68 31 38 68 56 31 38 SP SD: 0.4045 c. M: 0.6051 c. 354: 73 33 41 73 60 33 41 SP SD: 0.3012 c. M: 0.5435 c. 407: 84 38 47 84 69 38 47 SP SD: 0.1840 c. M: 0.3103 c. 441: 91 41 51 91 75 41 51 SP SD: 0.1653 c. M: 0.2887 c. 494: 102 46 57 102 84 46 57 SP SD: 0.0672 c. M:-0.1111 c. 935: 193 87 108 193 159 87 108 SP SD: 0.0728 c. M: 0.1176 c. 1342: 277 125 155 277 228 125 155 SP SD: 0.0369 c. M: 0.0686 c. 1836: 379 171 212 379 312 171 212 SP SD: 0.0196 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: 21.7791 cents 4 x 5 x 6:7 x 8 S SD: 13.7103 cents 5 x 6:7:8 x 9:10 S SD: 24.9700 cents 6:7 x 8:9:10:11:12 S SD: 13.6439 cents 7:8 x 9:11:12:13:14 SD: 12.8732 cents 10 x 12:13:15:17:18:20 SD: 15.5000 cents 11:13:14:15:17:19:20:22 SD: 12.2674 cents 12:14:15:16:18:21:22:24 S SD: 8.4745 cents 13:15:16:17:20:23:24:26 SD: 7.2534 cents 18:21:22:24:28:31:33:36 SD: 4.7304 cents 21:24:26:28:32:36:39:42 S SD: 4.5949 cents 26:30:32:35:40:45:48:52 SD: 2.3667 cents 39:45:48:52:60:68:72:78 SD: 1.8252 cents 52:60:64:69:80:90:96:104 SD: 1.1919 cents 78:90:96:104:120:135:144:156 SD: 0.0000 cents