Scala analysis: xen10-wilson-purvi-09a-06
Purvi modulation 6 from Figure 9a, Hawkins (135/128 16/15 32/27), (32/27 135/128 16/15)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 32/27 294.134997 Pythagorean minor third 2: 5/4 386.313714 major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 16/9 996.089998 Pythagorean minor seventh 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: 32/27 294.1350 Pythagorean minor third 2: 135/128 92.1787 major chroma, major limma 3: 16/15 111.7313 minor diatonic semitone 4: 9/8 203.9100 major whole tone 5: 32/27 294.1350 Pythagorean minor third 6: 135/128 92.1787 major chroma, major limma 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 : 294.1 386.3 498.0 702.0 996.1 1088.3 1200.0 294.1 : 92.2 203.9 407.8 702.0 794.1 905.9 1200.0 386.3 : 111.7 315.6 609.8 702.0 813.7 1107.8 1200.0 498.0 : 203.9 498.0 590.2 702.0 996.1 1088.3 1200.0 702.0 : 294.1 386.3 498.0 792.2 884.4 996.1 1200.0 996.1 : 92.2 203.9 498.0 590.2 702.0 905.9 1200.0 1088.3: 111.7 405.9 498.0 609.8 813.7 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 : 180.56271 cents, oct.: 1263.93899 cents Scale is not proper Step pattern alph. order: ABCDABC Step pattern size order : DABCDAB 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 Formal octave complements present : 3 = 42.8571% Scale is 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 : 0.267571 Specific harmonicity : 0.216606 Fundamental : 1/216, -7.7549 octaves, 1.2112 Hz. Guide tone : 480, 8.9069 octaves, 125580.271 Hz. Exponens Consonantiae : 1.036800E+05, 16.66178 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 65.5, average 9.35714 Mersenne's string divisions : 2137275 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: -3 .. 5 0.85714 18 1 3: -3 .. 1 -0.57143 8 4 5: 0 .. 1 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: 2 0 1 1 2 0 1 N T3 SD: 36.6619 c. M: 59.6973 c. 9: 2 1 1 1 2 1 1 P M ME S SD: 33.4609 c. M: 62.7567 c. 10: 2 1 1 2 2 1 1 P D3 S SD: 28.3980 c. M: 54.1350 c. Pseudo Rast 12: 3 1 1 2 3 1 1 N SD: 7.3898 c. M:-13.6863 c. Mela Calanata, Raga None, Chromatic Dorian inverse 29: 7 2 3 5 7 2 3 N SD: 7.3735 c. M: 13.8999 c. 34: 8 3 3 6 8 3 3 N SD: 6.2021 c. M: 11.7821 c. 41: 10 3 4 7 10 3 4 N SD: 3.0704 c. M: 5.8259 c. 53: 13 4 5 9 13 4 5 N SD: 0.7775 c. M: 1.4763 c. 65: 16 5 6 11 16 5 6 N SD: 0.8806 c. M:-1.3786 c. 118: 29 9 11 20 29 9 11 N SD: 0.3870 c. M:-0.7803 c. 171: 42 13 16 29 42 13 16 N SD: 0.3831 c. M:-0.6018 c. 289: 71 22 27 49 71 22 27 N SD: 0.3638 c. M:-0.6747 c. 323: 79 25 30 55 79 25 30 N SD: 0.3286 c. M: 0.6365 c. 376: 92 29 35 64 92 29 35 N SD: 0.2587 c. M: 0.5180 c. 388: 95 30 36 66 95 30 36 N SD: 0.2405 c. M:-0.3911 c. 429: 105 33 40 73 105 33 40 N SD: 0.2452 c. M: 0.4287 c. 441: 108 34 41 75 108 34 41 N SD: 0.1438 c. M: 0.2574 c. 494: 121 38 46 84 121 38 46 N SD: 0.1058 c. M: 0.2079 c. 547: 134 42 51 93 134 42 51 N SD: 0.1271 c. M: 0.2077 c. 559: 137 43 52 95 137 43 52 N SD: 0.0552 c. M:-0.1034 c. 612: 150 47 57 104 150 47 57 N SD: 0.0212 c. M: 0.0392 c. 1171: 287 90 109 199 287 90 109 N SD: 0.0199 c. M:-0.0319 c. 1783: 437 137 166 303 437 137 166 N SD: 0.0122 c. M: 0.0239 c. 1901: 466 146 177 323 466 146 177 N SD: 0.0132 c. M:-0.0260 c. 2395: 587 184 223 407 587 184 223 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 5 x 6 S SD: 37.2438 cents 4 x 5 x 6:7 x 8 S SD: 6.8160 cents 5:6 x 7:8:9 x 10 S SD: 28.6661 cents 6:7 x 8:9 x 11:12 SD: 9.5016 cents 7:8:9 x 11:12:13:14 SD: 21.7737 cents 8:9:10:11:12:14:15:16 S SD: 15.4668 cents 9 x 11:12:14:16:17:18 SD: 12.5177 cents 10:12 x 13:15:18:19:20 SD: 9.6782 cents 12:14:15:16:18:21:23:24 SD: 7.7387 cents 16:19:20:21:24:28:30:32 SD: 5.5293 cents 24:28:30:32:36:43:45:48 SD: 4.3445 cents 27:32:34:36:41:48:51:54 SD: 3.9840 cents 28:33:35:37:42:50:53:56 SD: 3.6803 cents 32:38:40:43:48:57:60:64 SD: 2.0421 cents 48:57:60:64:72:85:90:96 SD: 1.0816 cents 72:85:90:96:108:128:135:144 SD: 0.9680 cents 96:114:120:128:144:171:180:192 SD: 0.6825 cents 108:128:135:144:162:192:203:216 SD: 0.6099 cents 120:142:150:160:180:213:225:240 SD: 0.5469 cents 144:171:180:192:216:256:270:288 SD: 0.4826 cents 168:199:210:224:252:299:315:336 SD: 0.3085 cents 216:256:270:288:324:384:405:432 SD: 0.0000 cents