Scala analysis: xen09-wilson-marwa-09-09
Marwa permutation 9 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: 135/128 92.178716 major chroma, major limma 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: 135/128 92.1787 major chroma, major limma 2: 32/27 294.1350 Pythagorean minor third 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: 2 135/128 92.179 cents major chroma, major limma 1: 2 16/15 111.731 cents minor diatonic semitone 1: 1 9/8 203.910 cents major whole tone 1: 2 32/27 294.135 cents Pythagorean minor third 2: 2 9/8 203.910 cents major whole tone 2: 1 6/5 315.641 cents minor third 2: 2 5/4 386.314 cents major third 2: 1 512/405 405.866 cents narrow diminished fourth 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: 1 405/256 794.134 cents wide augmented fifth 5: 2 8/5 813.686 cents minor sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 2 16/9 996.090 cents Pythagorean minor seventh 6: 2 27/16 905.865 cents Pythagorean major sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 15/8 1088.269 cents classic major seventh 6: 2 256/135 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 : 92.2 386.3 590.2 702.0 794.1 1088.3 1200.0 92.2 : 294.1 498.0 609.8 702.0 996.1 1107.8 1200.0 386.3 : 203.9 315.6 407.8 702.0 813.7 905.9 1200.0 590.2 : 111.7 203.9 498.0 609.8 702.0 996.1 1200.0 702.0 : 92.2 386.3 498.0 590.2 884.4 1088.3 1200.0 794.1 : 294.1 405.9 498.0 792.2 996.1 1107.8 1200.0 1088.3: 111.7 203.9 498.0 702.0 813.7 905.9 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 .. 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 : 16/15, 111.7313 cents, amount: 2 Least squares average step : 173.88270 cents, oct.: 1217.17891 cents Scale is not proper Step pattern alph. order: ABCDABD Step pattern size order : ADCBADB Scale is not a Constant Structure Scale diversity : 1.389648 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 : 4 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: 5 Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 5, average 701.9550 cents Scale is Hypolydian octave species of abstract tetrachord 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 differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 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 : 0.231575 Specific harmonicity : 0.189536 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 : 520.5, average 74.35714 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.74318, average 1.24903 Sum of Tenney's harmonic distance : 16.87099, average 2.41014 Vogel's harmonic complexity : 12.71429 Wille's k value : 202 Wilson's harmonic complexity : 17 Rectangular lattice diameter : 5 Triangular lattice diameter : 5 Lattice compactness : 124.82305, average 4.45797 Lattice compactness (without 2's) : 55.09810, average 1.96779 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -8 .. 1 -3.57143 27 1 3: 0 .. 4 1.57143 11 1 5: 0 .. 1 0.71429 5 5 Average exponent except 2's : 16 / 7 = 2.28571 Average absolute exponent except 2's: 16 / 7 = 2.28571 Scale is weakly epimorphic with val: <7 11 15| Scale is weakly epimorphic with val: <7 12 17|
FIT/MODE
7: 0 2 1 1 0 2 1 N T3 SD: 67.3310 c. M: 108.4194 c. 8: 1 2 1 1 0 2 1 N T3 SD: 43.4502 c. M:-63.6863 c. 9: 1 2 1 1 1 2 1 P M ME I SD: 31.3138 c. M: 56.8904 c. 10: 1 2 2 1 1 2 1 P D3 S SD: 24.0824 c. M:-45.8663 c. 12: 1 3 2 1 1 3 1 N SD: 8.6183 c. M:-13.6863 c. Chromatic Hypolydian, Purvi (Poorvi) That, Mela Kamavardhani, Raga Shri, Basant, Dhipaka, Pantuvarali, Jaitshree, Kasiramakriya, Maligaura, Puriya Dhanashri, Suddharamakriya, Tanki, Pireotikos: Greece 38: 3 9 7 3 3 9 4 N SD: 7.9544 c. M: 14.5845 c. 39: 3 10 6 4 3 9 4 N SD: 7.6982 c. M:-13.6863 c. 41: 3 10 7 4 3 10 4 N SD: 4.1502 c. M: 5.8259 c. 53: 4 13 9 5 4 13 5 N SD: 1.3081 c. M: 1.6809 c. 65: 5 16 11 6 5 16 6 N SD: 0.6966 c. M:-1.3786 c. 118: 9 29 20 11 9 29 11 N SD: 0.4655 c. M: 0.9134 c. 183: 14 45 31 17 14 45 17 N SD: 0.3989 c. M: 0.6911 c. 311: 24 76 53 29 24 76 29 N SD: 0.3867 c. M:-0.7216 c. 364: 28 89 62 34 28 89 34 N SD: 0.3192 c. M: 0.5994 c. 376: 29 92 64 35 29 92 35 N SD: 0.2756 c. M:-0.5471 c. 429: 33 105 73 40 33 105 40 N SD: 0.1795 c. M: 0.2997 c. 494: 38 121 84 46 38 121 46 N SD: 0.1004 c. M:-0.1983 c. 559: 43 137 95 52 43 137 52 N SD: 0.0995 c. M:-0.1418 c. 612: 47 150 104 57 47 150 57 N SD: 0.0245 c. M: 0.0392 c. 1289: 99 316 219 120 99 316 120 N SD: 0.0195 c. M:-0.0323 c. 1783: 137 437 303 166 137 437 166 N SD: 0.0178 c. M:-0.0334 c. 1901: 146 466 323 177 146 466 177 N SD: 0.0128 c. M: 0.0254 c. 2395: 184 587 407 223 184 587 223 N SD: 0.0106 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 x x 8:9:10:11:12 S SD: 26.9452 cents 7:8:9:10 x 11:13:14 SD: 25.1946 cents 8:9:10:11:12:13:15:16 SD: 18.1546 cents 9:10:11:13 x 14:17:18 SD: 18.8735 cents 10:11:13:14:15:16:19:20 SD: 14.9021 cents 11:12:14:15 x 17:21:22 SD: 16.5340 cents 12:13:15:17:18:19:23:24 SD: 8.7663 cents 15:16:19:21:23:24:28:30 SD: 7.6361 cents 16:17:20:23:24:25:30:32 SD: 6.5053 cents 17:18:21:24:26:27:32:34 SD: 5.9480 cents 20:21:25:28:30:32:38:40 SD: 4.5782 cents 24:25:30:34:36:38:45:48 SD: 3.5794 cents 32:34:40:45:48:51:60:64 SD: 2.5813 cents 40:42:50:56:60:63:75:80 SD: 1.9081 cents 52:55:65:73:78:82:98:104 SD: 1.7071 cents 56:59:70:79:84:89:105:112 SD: 1.4012 cents 72:76:90:101:108:114:135:144 SD: 0.6757 cents 96:101:120:135:144:152:180:192 SD: 0.6444 cents 128:135:160:180:192:203:240:256 SD: 0.6099 cents 148:156:185:208:222:234:278:296 SD: 0.5142 cents 160:169:200:225:240:253:300:320 SD: 0.3860 cents 184:194:230:259:276:291:345:368 SD: 0.2641 cents 256:270:320:360:384:405:480:512 SD: 0.0000 cents