Scala analysis: xen09-wilson-marwa-09-08
Marwa permutation 8 from Figure 9, Hawkins 16/15 135/128 32/27
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 5/4 386.313714 major third 3: 45/32 590.223716 diatonic tritone 4: 3/2 701.955001 perfect fifth 5: 405/256 794.133717 wide augmented fifth 6: 15/8 1088.268715 classic major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 9/8 203.9100 major whole tone 2: 10/9 182.4037 minor whole tone 3: 9/8 203.9100 major whole tone 4: 16/15 111.7313 minor diatonic semitone 5: 135/128 92.1787 major chroma, major limma 6: 32/27 294.1350 Pythagorean minor third 7: 16/15 111.7313 minor diatonic semitone
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: 2 6/5 315.641 cents minor third 2: 3 5/4 386.314 cents major third 2: 1 512/405 405.866 cents narrow diminished 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: 1 405/256 794.134 cents wide augmented fifth 5: 3 8/5 813.686 cents minor sixth 5: 2 5/3 884.359 cents major sixth, BP 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: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 386.3 590.2 702.0 794.1 1088.3 1200.0 203.9 : 182.4 386.3 498.0 590.2 884.4 996.1 1200.0 386.3 : 203.9 315.6 407.8 702.0 813.7 1017.6 1200.0 590.2 : 111.7 203.9 498.0 609.8 813.7 996.1 1200.0 702.0 : 92.2 386.3 498.0 702.0 884.4 1088.3 1200.0 794.1 : 294.1 405.9 609.8 792.2 996.1 1107.8 1200.0 1088.3: 111.7 315.6 498.0 702.0 813.7 905.9 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 .. 405.8663 cents 4096/3645, 201.9563 cents 243/256,-90.2250 cents 3: 407.8200 .. 609.7763 cents 4096/3645, 201.9563 cents 32805/32768, 1.9537 cents 4: 590.2237 .. 792.1800 cents 4096/3645, 201.9563 cents 2025/2048,-19.5526 cents 5: 794.1337 .. 996.0900 cents 4096/3645, 201.9563 cents 32805/32768, 1.9537 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 : 174.68078 cents, oct.: 1222.76547 cents Scale is not proper Step pattern alph. order: ABACDEC Step pattern size order : DCDBAEB Scale is not a Constant Structure Scale diversity : 1.423133 Lumma stability : 0.156887 Lumma impropriety factor : 0.166669 Rothenberg efficiency : 0.451701 redundancy: 0.548299 Efficiency x scale size : 3.161905 Number of different interval sizes : 22 = 3.66667 / 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 : 32805/32768, 1.9537 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 Length of longest harmonic part : 2 at degree 0 Length of longest subharmonic part : 2 at degree 1 Formal octave complements present : 1 = 14.2857% Scale is n-1 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 -- Rational properties -- Prime limit : 5 Odd number limit : 405 (O: 405 U: 405) Highest odd numerator or denominator: 405 Scale harmonicity : 0.038363 Average absolute harmonicity : 0.242043 Specific harmonicity : 0.203346 Fundamental : 1/256, -8.0000 octaves, 1.0220 Hz. Guide tone : 810, 9.6618 octaves, 211916.708 Hz. Exponens Consonantiae : 2.073600E+05, 17.66178 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 397.5, average 56.78571 Mersenne's string divisions : 895532715 Sum of van Prooijen's expressibility: 7.56709, average 1.08101 Sum of Tenney's harmonic distance : 14.49078, average 2.07011 Vogel's harmonic complexity : 12.14286 Wille's k value : 202 Wilson's harmonic complexity : 17 Rectangular lattice diameter : 5 Triangular lattice diameter : 5 Lattice compactness : 110.07383, average 3.93121 Lattice compactness (without 2's) : 51.42383, average 1.83657 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -8 .. 1 -3.00000 23 1 3: 0 .. 4 1.42857 10 2 5: 0 .. 1 0.57143 4 4 Average exponent except 2's : 14 / 7 = 2.00000 Average absolute exponent except 2's: 14 / 7 = 2.00000
FIT/MODE
7: 1 1 1 1 0 2 1 N T3 SD: 58.9096 c. M: 108.4194 c. 8: 1 2 1 1 0 2 1 N T3 SD: 42.7257 c. M:-63.6863 c. 9: 1 2 1 1 1 2 1 P M ME I SD: 38.0812 c. M: 70.5767 c. 10: 2 1 2 1 1 2 1 P M ME S SD: 25.6019 c. M:-45.8663 c. 12: 2 2 2 1 1 3 1 N T3 SD: 8.2292 c. M:-13.6863 c. Harmonic Lydian, Mela Latangi, Raga Gitapriya, Hamsalata 34: 6 5 6 3 3 8 3 N SD: 8.6309 c. M:-17.6310 c. 35: 6 5 6 3 3 9 3 N SD: 8.5780 c. M: 16.2407 c. 41: 7 6 7 4 3 10 4 N SD: 3.8243 c. M: 5.8259 c. 53: 9 8 9 5 4 13 5 N SD: 1.1586 c. M: 1.6809 c. 65: 11 10 11 6 5 16 6 N SD: 0.7629 c. M:-1.3786 c. 118: 20 18 20 11 9 29 11 N SD: 0.4409 c. M: 0.9134 c. 183: 31 28 31 17 14 45 17 N SD: 0.4426 c. M: 0.6911 c. 289: 49 44 49 27 22 71 27 N SD: 0.5206 c. M: 1.0541 c. 301: 51 46 51 28 23 74 28 N SD: 0.4213 c. M: 0.7782 c. 311: 53 47 53 29 24 76 29 N SD: 0.4167 c. M:-0.7216 c. 323: 55 49 55 30 25 79 30 N SD: 0.4435 c. M:-0.9127 c. 364: 62 55 62 34 28 89 34 N SD: 0.3650 c. M: 0.5994 c. 376: 64 57 64 35 29 92 35 N SD: 0.2701 c. M:-0.5471 c. 429: 73 65 73 40 33 105 40 N SD: 0.2038 c. M: 0.2997 c. 441: 75 67 75 41 34 108 41 N SD: 0.2120 c. M:-0.4241 c. 494: 84 75 84 46 38 121 46 N SD: 0.1023 c. M:-0.1983 c. 559: 95 85 95 52 43 137 52 N SD: 0.0873 c. M:-0.1418 c. 612: 104 93 104 57 47 150 57 N SD: 0.0234 c. M: 0.0392 c. 1289: 219 196 219 120 99 316 120 N SD: 0.0221 c. M:-0.0323 c. 1783: 303 271 303 166 137 437 166 N SD: 0.0162 c. M:-0.0334 c. 1901: 323 289 323 177 146 466 177 N SD: 0.0129 c. M: 0.0254 c. 2395: 407 364 407 223 184 587 223 N SD: 0.0108 c. M:-0.0208 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: 0.0000 cents 3 x x 4 x 5 x 6 S SD: 42.9954 cents 4 x 5 x 6 x x 8 S SD: 0.0000 cents 5 x 6:7 x 8:9:10 S SD: 20.4264 cents 6:7 x 8:9:10:11:12 S SD: 24.7853 cents 7:8:9:10 x 11:13:14 SD: 10.8975 cents 8:9:10:11:12:13:15:16 SD: 8.6497 cents 9:10:11:13 x 14:17:18 SD: 11.9554 cents 11:12:14:15 x 17:21:22 SD: 16.0400 cents 12:14:15:17:18:19:23:24 SD: 10.6687 cents 14:16:18:20:21:22:26:28 SD: 9.3407 cents 15:17:19:21:23:24:28:30 SD: 7.3376 cents 16:18:20:23:24:25:30:32 SD: 6.2440 cents 17:19:21:24:26:27:32:34 SD: 6.0886 cents 22:25:28:31:33:35:41:44 SD: 5.5193 cents 24:27:30:34:36:38:45:48 SD: 1.8365 cents 32:36:40:45:48:51:60:64 SD: 1.8252 cents 40:45:50:56:60:63:75:80 SD: 1.5580 cents 56:63:70:79:84:89:105:112 SD: 1.3765 cents 64:72:80:90:96:101:120:128 SD: 0.6114 cents 96:108:120:135:144:152:180:192 SD: 0.2035 cents 160:180:200:225:240:253:300:320 SD: 0.1222 cents 256:288:320:360:384:405:480:512 SD: 0.0000 cents