Scala analysis: xen09-wilson-marwa-11b-10
Marwa permutation 10 from Figure 11b, Hawkins 135/128 16/15 32/27
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: 32/27 294.134997 Pythagorean minor third 3: 4/3 498.044999 perfect fourth 4: 128/81 792.179997 Pythagorean 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: 16/15 111.7313 minor diatonic semitone 3: 9/8 203.9100 major whole tone 4: 32/27 294.1350 Pythagorean minor third 5: 135/128 92.1787 major chroma, major limma 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: 1 135/128 92.179 cents major chroma, major limma 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 32/27 294.135 cents Pythagorean minor third 2: 1 9/8 203.910 cents major whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 2 6/5 315.641 cents minor third 2: 2 5/4 386.314 cents major third 2: 1 4/3 498.045 cents perfect fourth 3: 1 81/64 407.820 cents Pythagorean major third 3: 4 4/3 498.045 cents perfect fourth 3: 1 45/32 590.224 cents diatonic tritone 3: 1 64/45 609.776 cents 2nd tritone 4: 1 45/32 590.224 cents diatonic tritone 4: 1 64/45 609.776 cents 2nd tritone 4: 4 3/2 701.955 cents perfect fifth 4: 1 128/81 792.180 cents Pythagorean minor sixth 5: 1 3/2 701.955 cents perfect fifth 5: 2 8/5 813.686 cents minor sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 1 16/9 996.090 cents Pythagorean minor seventh 6: 1 27/16 905.865 cents Pythagorean major 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: 1 256/135 1107.821 cents octave - major chroma 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 : 182.4 294.1 498.0 792.2 884.4 996.1 1200.0 182.4 : 111.7 315.6 609.8 702.0 813.7 1017.6 1200.0 294.1 : 203.9 498.0 590.2 702.0 905.9 1088.3 1200.0 498.0 : 294.1 386.3 498.0 702.0 884.4 996.1 1200.0 792.2 : 92.2 203.9 407.8 590.2 702.0 905.9 1200.0 884.4 : 111.7 315.6 498.0 609.8 813.7 1107.8 1200.0 996.1 : 203.9 386.3 498.0 702.0 996.1 1088.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 92.1787 .. 294.1350 cents 4096/3645, 201.9563 cents 135/128, 92.1787 cents 2: 203.9100 .. 498.0450 cents 32/27, 294.1350 cents 243/256,-90.2250 cents 3: 407.8200 .. 609.7763 cents 4096/3645, 201.9563 cents 243/256,-90.2250 cents 4: 590.2237 .. 792.1800 cents 4096/3645, 201.9563 cents 2025/2048,-19.5526 cents 5: 701.9550 .. 996.0900 cents 32/27, 294.1350 cents 243/256,-90.2250 cents 6: 905.8650 .. 1107.8213 cents 4096/3645, 201.9563 cents 243/256,-90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 135/128, 92.1787 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 32/27, 294.1350 cents Average / Smallest step : 1.859741 Largest / Average step : 1.715787 Largest / Smallest step : 3.190921 Median interval of one step : 10/9, 182.4037 cents, amount: 1 Least squares average step : 173.08473 cents, oct.: 1211.59311 cents Scale is not proper Step pattern alph. order: ABCDEBC Step pattern size order : CBDEABD Scale is not a Constant Structure Scale diversity : 1.422264 Lumma stability : 0.153631 Lumma impropriety factor : 0.317044 Rothenberg efficiency : 0.540136 redundancy: 0.459864 Efficiency x scale size : 3.780952 Number of different interval sizes : 20 = 3.33333 / 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 : 2048/2025, 19.5526 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 5, average 701.9550 cents Length of longest harmonic part : 2 at degree 6 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval classes 3 and 4 combined Scale is differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 5 Odd number limit : 135 (O: 135 U: 135) Highest odd numerator or denominator: 81 Scale harmonicity : 0.041551 Average absolute harmonicity : 0.234826 Specific harmonicity : 0.223671 Fundamental : 1/81, -6.3399 octaves, 3.2299 Hz. Guide tone : 640, 9.3219 octaves, 167440.362 Hz. Exponens Consonantiae : 5.184000E+04, 15.66178 octaves Euler's gradus suavitatis : 20 Sum of Mann's harmonic distance : 165.0, average 23.57143 Mersenne's string divisions : 51790200 Sum of van Prooijen's expressibility: 6.42443, average 0.91778 Sum of Tenney's harmonic distance : 13.62112, average 1.94587 Vogel's harmonic complexity : 10.71429 Wille's k value : 67 Wilson's harmonic complexity : 17 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 102.18389, average 3.64942 Lattice compactness (without 2's) : 52.17762, average 1.86349 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 0 .. 7 2.85714 20 1 3: -4 .. 0 -1.85714 13 4 5: 0 .. 1 0.28571 2 2 Average exponent except 2's :-11 / 7 =-1.57143 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: 1 1 1 2 0 1 1 N T3 SD: 35.4038 c. M:-64.9629 c. 8: 1 1 1 2 1 1 1 P M ME I SD: 34.4815 c. M:-53.9100 c. 11: 2 1 2 2 1 1 2 P D3 S SD: 28.7342 c. M:-47.4095 c. 12: 2 1 2 3 1 1 2 N SD: 9.7756 c. M:-17.5963 c. 29: 4 3 5 7 2 3 5 N SD: 9.1729 c. M: 16.8865 c. 32: 5 3 5 8 3 3 5 N SD: 10.0528 c. M:-16.4100 c. 33: 5 3 6 8 2 3 6 N SD: 8.7251 c. M: 14.2718 c. 34: 5 3 6 8 3 3 6 N SD: 8.4680 c. M: 15.7094 c. 38: 6 3 7 9 3 4 6 N SD: 7.7121 c. M:-14.4363 c. 39: 6 4 6 10 3 3 7 N SD: 8.2602 c. M:-13.5573 c. 41: 6 4 7 10 3 4 7 N SD: 3.6450 c. M: 6.7940 c. 53: 8 5 9 13 4 5 9 N SD: 0.7123 c. M: 1.3398 c. 118: 18 11 20 29 9 11 20 N SD: 0.6092 c. M:-1.0403 c. 171: 26 16 29 42 13 16 29 N SD: 0.4195 c. M:-0.8025 c. 224: 34 21 38 55 17 21 38 N SD: 0.3987 c. M:-0.6771 c. 277: 42 26 47 68 21 26 47 N SD: 0.4219 c. M: 0.6042 c. 289: 44 27 49 71 22 27 49 N SD: 0.4795 c. M:-0.8996 c. 323: 49 30 55 79 25 30 55 N SD: 0.4633 c. M: 0.8487 c. 330: 50 31 56 81 25 31 56 N SD: 0.4514 c. M: 0.7223 c. 335: 51 31 57 82 26 31 57 N SD: 0.3375 c. M: 0.5382 c. 388: 59 36 66 95 30 36 66 N SD: 0.2327 c. M: 0.4274 c. 441: 67 41 75 108 34 41 75 N SD: 0.1809 c. M: 0.3433 c. 494: 75 46 84 121 38 46 84 N SD: 0.1746 c. M: 0.2772 c. 506: 77 47 86 124 39 47 86 N SD: 0.1235 c. M:-0.2263 c. 559: 85 52 95 137 43 52 95 N SD: 0.0466 c. M:-0.0778 c. 612: 93 57 104 150 47 57 104 N SD: 0.0283 c. M: 0.0508 c. 1171: 178 109 199 287 90 109 199 N SD: 0.0197 c. M: 0.0365 c. 1783: 271 166 303 437 137 166 303 N SD: 0.0176 c. M: 0.0319 c. 2395: 364 223 407 587 184 223 407 N SD: 0.0188 c. M: 0.0297 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: 45.1125 cents 3 x x 4 x 5 x 6 S SD: 0.0000 cents 4 x 5 x 6 x 7:8 S SD: 32.9591 cents 5 x 6:7:8 x 9:10 S SD: 18.4632 cents 6 x 7:8:9:10:11:12 S SD: 18.0446 cents 7:8 x 9:11:12 x 14 SD: 18.7777 cents 8:9 x 11 x 13:14:16 SD: 15.4467 cents 9:10:11:12:14:15:16:18 S SD: 8.5492 cents 12:13:14:16:19:20:21:24 SD: 8.3535 cents 15:17:18:20:24:25:27:30 SD: 7.2321 cents 17:19:20:23:27:28:30:34 SD: 5.6502 cents 18:20:21:24:28:30:32:36 S SD: 5.5082 cents 21:23:25:28:33:35:37:42 SD: 4.5511 cents 26:29:31:35:41:43:46:52 SD: 3.7467 cents 27:30:32:36:43:45:48:54 SD: 1.9247 cents 45:50:53:60:71:75:80:90 SD: 1.5981 cents 54:60:64:72:85:90:96:108 SD: 0.9680 cents 81:90:96:108:128:135:144:162 SD: 0.0000 cents