Scala analysis: xen09-wilson-marwa-16b-03
Marwa permutation 3 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: 64/39 857.517337 39th subharmonic 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: 16/15 111.7313 minor diatonic semitone 6: 9/8 203.9100 major whole tone 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 32/27 294.135 cents Pythagorean minor third 2: 2 6/5 315.641 cents minor third 2: 1 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 2: 1 16/13 359.472 cents tridecimal neutral third 2: 2 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: 2 8/5 813.686 cents minor sixth 5: 1 13/8 840.528 cents tridecimal neutral sixth 5: 1 64/39 857.517 cents 39th subharmonic 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 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: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 247.7 359.5 563.4 745.8 857.5 1061.4 1200.0 247.7 : 111.7 315.6 498.0 609.8 813.7 952.3 1200.0 359.5 : 203.9 386.3 498.0 702.0 840.5 1088.3 1200.0 563.4 : 182.4 294.1 498.0 636.6 884.4 996.1 1200.0 745.8 : 111.7 315.6 454.2 702.0 813.7 1017.6 1200.0 857.5 : 203.9 342.5 590.2 702.0 905.9 1088.3 1200.0 1061.4: 138.6 386.3 498.0 702.0 884.4 996.1 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: 294.1350 .. 386.3137 cents 135/128, 92.1787 cents 416/405, 46.3939 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 .. 905.8650 cents 135/128, 92.1787 cents 26/25, 67.9002 cents 6: 952.2589 .. 1088.2687 cents 225/208, 136.0098 cents 416/405, 46.3939 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 : 176.40091 cents, oct.: 1234.80638 cents Scale is strictly proper Step pattern alph. order: ABCDBCE Step pattern size order : EADCADB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.575480 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.393003 Rothenberg efficiency : 0.408163 redundancy: 0.591837 Efficiency x scale size : 2.857143 Number of different interval sizes : 28 = 4.66667 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.66667 = 14/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 512/507, 16.9897 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 Formal octave complements present : 1 = 14.2857% Scale is 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 Scale is n-1 differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 13 Odd number limit : 45 (O: 45 U: 45) Highest odd numerator or denominator: 39 Scale harmonicity : 0.023500 Average absolute harmonicity : 0.172355 Specific harmonicity : 0.130884 Fundamental : 1/39, -5.2854 octaves, 6.7083 Hz. Guide tone : 2880, 11.4919 octaves, 753481.628 Hz. Exponens Consonantiae : 1.123200E+05, 16.77726 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 132.0, average 18.85714 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.22293, average 1.03185 Sum of Tenney's harmonic distance : 15.58472, average 2.22639 Vogel's harmonic complexity : 10.00000 Wille's k value : 22 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 85.37603, average 3.04914 Lattice compactness (without 2's) : 41.55051, average 1.48395 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 6 2.42857 17 1 3: -1 .. 2 0.42857 5 5: 0 .. 1 0.28571 2 13: -1 .. 0 -0.85714 6 6 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 10 16 29| Scale is JI-epimorphic with val: <7 11 16 26| = patent Scale is weakly epimorphic with val: <7 12 15 25|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 43.4222 c. M: 76.3125 c. Lebeng 8: 2 0 2 1 1 1 1 P D3 S SD: 36.9593 c. M: 59.4723 c. 9: 2 1 1 2 0 2 1 N D3 SD: 36.2106 c. M: 57.5173 c. 10: 2 1 2 1 1 2 1 P M ME S SD: 19.7042 c. M:-36.6177 c. 11: 2 1 2 2 1 2 1 P M ME S SD: 22.8383 c. M: 32.1996 c. 14: 3 1 3 2 1 2 2 P T3 SD: 22.1762 c. M:-36.6177 c. 15: 3 1 3 2 2 2 2 SP D3 S SD: 21.5769 c. M: 39.4723 c. 16: 3 2 2 3 1 3 2 P D3 SD: 22.1591 c. M: 38.3823 c. 17: 4 1 3 3 1 3 2 N SD: 18.1269 c. M:-34.6119 c. 18: 4 1 3 3 2 3 2 P SD: 17.7708 c. M: 30.0490 c. 19: 4 2 3 3 2 3 2 SP D3 SD: 14.3326 c. M:-26.6932 c. 21: 4 2 4 3 2 4 2 SP T3 SD: 13.6636 c. M:-24.2869 c. 23: 5 2 4 3 2 4 3 N SD: 14.0964 c. M: 22.7347 c. 24: 5 2 4 4 2 4 3 P SD: 8.2701 c. M: 13.3823 c. 34: 7 3 6 5 3 6 4 P SD: 5.1030 c. M: 10.4585 c. 43: 9 4 7 7 4 7 5 SP SD: 4.9019 c. M:-7.7023 c. 53: 11 5 9 8 5 9 6 SP SD: 2.2068 c. M:-2.8600 c. 77: 16 7 13 12 7 13 9 SP SD: 1.5705 c. M: 2.3434 c. 87: 18 8 15 13 8 15 10 SP SD: 1.3309 c. M: 2.3449 c. 130: 27 12 22 20 12 22 15 SP SD: 1.0091 c. M:-1.9063 c. 164: 34 15 28 25 15 28 19 SP SD: 0.8005 c. M: 1.4198 c. 217: 45 20 37 33 20 37 25 SP SD: 0.5974 c. M:-1.1069 c. 277: 57 26 47 42 26 47 32 SP SD: 0.4148 c. M: 0.8096 c. 330: 68 31 56 50 31 56 38 SP SD: 0.4254 c. M:-0.6645 c. 354: 73 33 60 54 33 60 41 SP SD: 0.3237 c. M: 0.6705 c. 407: 84 38 69 62 38 69 47 SP SD: 0.2270 c. M:-0.4679 c. 441: 91 41 75 67 41 75 51 SP SD: 0.2192 c. M: 0.3745 c. 494: 102 46 84 75 46 84 57 SP SD: 0.0844 c. M:-0.1804 c. 848: 175 79 144 129 79 144 98 SP SD: 0.0888 c. M: 0.1748 c. 1065: 220 99 181 162 99 181 123 SP SD: 0.0780 c. M:-0.1463 c. 1342: 277 125 228 204 125 228 155 SP SD: 0.0305 c. M: 0.0510 c. 1836: 379 171 312 279 171 312 212 SP SD: 0.0185 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: 23.5453 cents 4 x 5 x 6 x 7:8 S SD: 26.4772 cents 5 x 6:7 x 8:9:10 S SD: 15.6581 cents 6:7 x 8:9:10:11:12 S SD: 14.3586 cents 7:8:9:10:11 x 13:14 SD: 16.9738 cents 8:9:10:11:12:13:15:16 SD: 10.8020 cents 10 x 12:14:15:16:18:20 S SD: 14.9542 cents 11:13:14:15:17:18:20:22 SD: 11.5802 cents 12:14:15:17:18:20:22:24 SD: 10.5397 cents 13:15:16:18:20:21:24:26 SD: 3.8949 cents 26:30:32:36:40:43:48:52 SD: 1.9247 cents 39:45:48:54:60:64:72:78 SD: 0.0000 cents