Scala analysis: xen10-wilson-purvi-09c-02
Purvi modulation 2 from Figure 9c, Hawkins (135/128 32/27 16/15) (16/15 32/27 135/128)
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: 6/5 315.641287 minor third 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: 9/8 203.9100 major whole tone 3: 10/9 182.4037 minor whole tone 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: 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 : 111.7 315.6 498.0 702.0 813.7 905.9 1200.0 111.7 : 203.9 386.3 590.2 702.0 794.1 1088.3 1200.0 315.6 : 182.4 386.3 498.0 590.2 884.4 996.1 1200.0 498.0 : 203.9 315.6 407.8 702.0 813.7 1017.6 1200.0 702.0 : 111.7 203.9 498.0 609.8 813.7 996.1 1200.0 813.7 : 92.2 386.3 498.0 702.0 884.4 1088.3 1200.0 905.9 : 294.1 405.9 609.8 792.2 996.1 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 .. 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 : 163.91850 cents, oct.: 1147.42952 cents Scale is not proper Step pattern alph. order: ABCBADE Step pattern size order : BDCDBAE 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 Scale contains a complete diamond : 1 3 Length of longest harmonic part : 2 at degree 1 Length of longest subharmonic part : 2 at degree 2 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 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: 27 Scale harmonicity : 0.039894 Average absolute harmonicity : 0.264656 Specific harmonicity : 0.222737 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 : 56.5, average 8.07143 Mersenne's string divisions : 20014995 Sum of van Prooijen's expressibility: 4.95964, average 0.70852 Sum of Tenney's harmonic distance : 10.25324, average 1.46475 Vogel's harmonic complexity : 12.00000 Wille's k value : 202 Wilson's harmonic complexity : 17 Rectangular lattice diameter : 5 Triangular lattice diameter : 5 Lattice compactness : 97.44534, average 3.48019 Lattice compactness (without 2's) : 48.47887, average 1.73139 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 4 0.85714 16 1 3: -1 .. 3 0.42857 7 3 5: -1 .. 0 -0.42857 3 3 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 10 / 7 = 1.42857
FIT/MODE
7: 1 1 1 1 1 0 2 N T3 SD: 36.0442 c. M:-59.6973 c. 9: 1 1 2 1 1 1 2 P M ME S SD: 29.9941 c. M: 48.9746 c. Pseudo Pelog, Pelogic-7, Antiionian 10: 1 2 1 2 1 1 2 P M ME S SD: 30.0246 c. M:-54.1350 c. 12: 1 2 2 2 1 1 3 N T3 SD: 9.3475 c. M: 15.6413 c. Mela Senavati, Raga Senagrani, Malini 29: 3 5 4 5 3 2 7 N SD: 9.3244 c. M:-15.3932 c. 31: 3 5 5 5 3 2 8 N SD: 7.0788 c. M: 15.5424 c. 33: 3 6 5 5 3 3 8 N SD: 9.1340 c. M: 13.6863 c. 34: 3 6 5 6 3 3 8 N SD: 5.4979 c. M:-11.7821 c. 41: 4 7 6 7 4 3 10 N SD: 3.8706 c. M:-6.3099 c. 53: 5 9 8 9 5 4 13 N SD: 0.9265 c. M:-1.4763 c. 118: 11 20 18 20 11 9 29 N SD: 0.3641 c. M: 0.7803 c. 171: 16 29 26 29 16 13 42 N SD: 0.3562 c. M: 0.6018 c. 289: 27 49 44 49 27 22 71 N SD: 0.3228 c. M: 0.6747 c. 323: 30 55 49 55 30 25 79 N SD: 0.2922 c. M:-0.6365 c. 376: 35 64 57 64 35 29 92 N SD: 0.2534 c. M:-0.5180 c. 388: 36 66 59 66 36 30 95 N SD: 0.2363 c. M: 0.3911 c. 429: 40 73 65 73 40 33 105 N SD: 0.2765 c. M:-0.4426 c. 441: 41 75 67 75 41 34 108 N SD: 0.1284 c. M:-0.2574 c. 494: 46 84 75 84 46 38 121 N SD: 0.1076 c. M:-0.2079 c. 559: 52 95 85 95 52 43 137 N SD: 0.0618 c. M: 0.1034 c. 612: 57 104 93 104 57 47 150 N SD: 0.0268 c. M:-0.0450 c. 1171: 109 199 178 199 109 90 287 N SD: 0.0194 c. M: 0.0319 c. 1783: 166 303 271 303 166 137 437 N SD: 0.0109 c. M:-0.0239 c. 2395: 223 407 364 407 223 184 587 N SD: 0.0117 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 5 x 6 x 7:8 S SD: 23.6626 cents 5 x 6:7 x 8 x 10 S SD: 21.1168 cents 6 x 7:8:9 x 10:12 S SD: 10.6603 cents 7 x 8:9 x 11:12:14 SD: 22.6408 cents 8:9:10:11:12:13:14:16 S SD: 20.7089 cents 9:10:11:12 x 14:15:18 S SD: 15.6745 cents 10:11:12:13:15:16:17:20 SD: 10.0228 cents 12:13:14:16:18:19:20:24 S SD: 8.9102 cents 14:15:17:19:21:22:24:28 SD: 7.9982 cents 15:16:18:20:23:24:25:30 SD: 6.2440 cents 16:17:19:21:24:26:27:32 SD: 6.1251 cents 20:21:24:27:30:32:34:40 SD: 5.2859 cents 25:27:30:33:38:40:42:50 SD: 5.2500 cents 26:28:31:35:39:42:44:52 SD: 4.4529 cents 28:30:34:37:42:45:47:56 SD: 4.1995 cents 30:32:36:40:45:48:51:60 SD: 1.8252 cents 60:64:72:80:90:96:101:120 SD: 0.6114 cents 90:96:108:120:135:144:152:180 SD: 0.2035 cents 150:160:180:200:225:240:253:300 SD: 0.1222 cents 240:256:288:320:360:384:405:480 SD: 0.0000 cents