Scala analysis: xen10-wilson-purvi-09b-02
Purvi modulation 2 from Figure 9b, Hawkins (32/27 16/15 135/128), (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: 16/15 111.731285 minor diatonic semitone 2: 9/8 203.910002 major whole tone 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 8/5 813.686286 minor sixth 6: 27/16 905.865003 Pythagorean major sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 32/27 294.1350 Pythagorean minor third 1: 16/15 111.7313 minor diatonic semitone 2: 135/128 92.1787 major chroma, major limma 3: 32/27 294.1350 Pythagorean minor third 4: 9/8 203.9100 major whole tone 5: 16/15 111.7313 minor diatonic semitone 6: 135/128 92.1787 major chroma, major limma 7: 32/27 294.1350 Pythagorean minor third
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 : 111.7 203.9 498.0 702.0 813.7 905.9 1200.0 111.7 : 92.2 386.3 590.2 702.0 794.1 1088.3 1200.0 203.9 : 294.1 498.0 609.8 702.0 996.1 1107.8 1200.0 498.0 : 203.9 315.6 407.8 702.0 813.7 905.9 1200.0 702.0 : 111.7 203.9 498.0 609.8 702.0 996.1 1200.0 813.7 : 92.2 386.3 498.0 590.2 884.4 1088.3 1200.0 905.9 : 294.1 405.9 498.0 792.2 996.1 1107.8 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 : 162.32234 cents, oct.: 1136.25639 cents Scale is not proper Step pattern alph. order: ABCDABC Step pattern size order : BADCBAD 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 Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Scale contains a complete diamond : 1 3 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% 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: 27 Scale harmonicity : 0.039894 Average absolute harmonicity : 0.267608 Specific harmonicity : 0.216606 Fundamental : 1/240, -7.9069 octaves, 1.0901 Hz. Guide tone : 432, 8.7549 octaves, 113022.244 Hz. Exponens Consonantiae : 1.036800E+05, 16.66178 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 59.5, average 8.50000 Mersenne's string divisions : 30932265 Sum of van Prooijen's expressibility: 5.21491, average 0.74499 Sum of Tenney's harmonic distance : 10.63345, average 1.51906 Vogel's harmonic complexity : 12.57143 Wille's k value : 202 Wilson's harmonic complexity : 17 Rectangular lattice diameter : 5 Triangular lattice diameter : 5 Lattice compactness : 109.93787, average 3.92635 Lattice compactness (without 2's) : 51.57665, average 1.84202 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 4 0.28571 18 1 3: -1 .. 3 0.57143 8 4 5: -1 .. 0 -0.28571 2 2 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 10 / 7 = 1.42857 Scale is weakly epimorphic with val: <7 11 15| Scale is weakly epimorphic with val: <7 12 17|
FIT/MODE
7: 1 0 2 1 1 0 2 N T3 SD: 36.6619 c. M:-59.6973 c. 9: 1 1 2 1 1 1 2 P M ME S SD: 33.4609 c. M:-62.7567 c. Pseudo Pelog, Pelogic-7, Antiionian 10: 1 1 2 2 1 1 2 P D3 S SD: 28.3980 c. M:-54.1350 c. 12: 1 1 3 2 1 1 3 N SD: 7.3898 c. M: 13.6863 c. Chromatic Dorian, Mela Kanakangi, Raga Kanakambari 29: 3 2 7 5 3 2 7 N SD: 7.3735 c. M:-13.8999 c. 34: 3 3 8 6 3 3 8 N SD: 6.2021 c. M:-11.7821 c. 41: 4 3 10 7 4 3 10 N SD: 3.0704 c. M:-5.8259 c. 53: 5 4 13 9 5 4 13 N SD: 0.7775 c. M:-1.4763 c. 65: 6 5 16 11 6 5 16 N SD: 0.8806 c. M: 1.3786 c. 118: 11 9 29 20 11 9 29 N SD: 0.3870 c. M: 0.7803 c. 171: 16 13 42 29 16 13 42 N SD: 0.3831 c. M: 0.6018 c. 289: 27 22 71 49 27 22 71 N SD: 0.3638 c. M: 0.6747 c. 323: 30 25 79 55 30 25 79 N SD: 0.3286 c. M:-0.6365 c. 376: 35 29 92 64 35 29 92 N SD: 0.2587 c. M:-0.5180 c. 388: 36 30 95 66 36 30 95 N SD: 0.2405 c. M: 0.3911 c. 429: 40 33 105 73 40 33 105 N SD: 0.2452 c. M:-0.4287 c. 441: 41 34 108 75 41 34 108 N SD: 0.1438 c. M:-0.2574 c. 494: 46 38 121 84 46 38 121 N SD: 0.1058 c. M:-0.2079 c. 547: 51 42 134 93 51 42 134 N SD: 0.1271 c. M:-0.2077 c. 559: 52 43 137 95 52 43 137 N SD: 0.0552 c. M: 0.1034 c. 612: 57 47 150 104 57 47 150 N SD: 0.0212 c. M:-0.0392 c. 1171: 109 90 287 199 109 90 287 N SD: 0.0199 c. M: 0.0319 c. 1783: 166 137 437 303 166 137 437 N SD: 0.0122 c. M:-0.0239 c. 1901: 177 146 466 323 177 146 466 N SD: 0.0132 c. M: 0.0260 c. 2395: 223 184 587 407 223 184 587 N SD: 0.0114 c. M:-0.0223 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 x 5:6 S SD: 7.1688 cents 4 x x 5:6 x 7:8 S SD: 32.0624 cents 5 x 6:7 x 8 x 10 S SD: 35.0166 cents 6 x 7:8:9 x 10:12 S SD: 13.3065 cents 7 x 8:9 x 11:12:14 SD: 16.0297 cents 8 x 9:11:12:13:14:16 SD: 14.4554 cents 9 x 10:12 x 14:15:18 S SD: 11.4954 cents 10 x 11:13:15:16:17:20 SD: 9.9973 cents 11:12 x 15:17:18:19:22 SD: 15.6689 cents 12:13:14:16:18:19:20:24 S SD: 10.5711 cents 14:15:16:19:21:22:24:28 SD: 8.4009 cents 15:16:17:20:23:24:25:30 SD: 6.5053 cents 16:17:18:21:24:26:27:32 SD: 5.5507 cents 18:19:20:24:27:29:30:36 SD: 5.3399 cents 26:28:29:35:39:42:44:52 SD: 4.6697 cents 30:32:34:40:45:48:51:60 SD: 2.5813 cents 32:34:36:43:48:51:54:64 SD: 2.3619 cents 42:45:47:56:63:67:71:84 SD: 1.9153 cents 48:51:54:64:72:77:81:96 SD: 1.1622 cents 90:96:101:120:135:144:152:180 SD: 0.6444 cents 120:128:135:160:180:192:203:240 SD: 0.6099 cents 138:147:155:184:207:221:233:276 SD: 0.5828 cents 150:160:169:200:225:240:253:300 SD: 0.3860 cents 192:205:216:256:288:307:324:384 SD: 0.2902 cents 240:256:270:320:360:384:405:480 SD: 0.0000 cents