Scala analysis: xen10-wilson-purvi-09c-01
Purvi modulation 1 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: 81/64 407.820003 Pythagorean major third 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: 135/128 92.1787 major chroma, major limma 4: 32/27 294.1350 Pythagorean minor third 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: 1 9/8 203.910 cents major whole tone 2: 1 1215/1024 296.089 cents wide augmented second 2: 1 6/5 315.641 cents minor third 2: 2 5/4 386.314 cents major third 2: 2 512/405 405.866 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: 2 405/256 794.134 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: 1 2048/1215 903.911 cents narrow diminished seventh 5: 1 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 : 111.7 315.6 407.8 702.0 813.7 905.9 1200.0 111.7 : 203.9 296.1 590.2 702.0 794.1 1088.3 1200.0 315.6 : 92.2 386.3 498.0 590.2 884.4 996.1 1200.0 407.8 : 294.1 405.9 498.0 792.2 903.9 1107.8 1200.0 702.0 : 111.7 203.9 498.0 609.8 813.7 905.9 1200.0 813.7 : 92.2 386.3 498.0 702.0 794.1 1088.3 1200.0 905.9 : 294.1 405.9 609.8 702.0 996.1 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 : 16/15, 111.7313 cents, amount: 2 Least squares average step : 161.98511 cents, oct.: 1133.89577 cents Scale is not proper Step pattern alph. order: ABCDACD Step pattern size order : BCADBAD Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 1.390463 Lumma stability : 0.156887 Lumma impropriety factor : 0.166669 Rothenberg efficiency : 0.448980 redundancy: 0.551020 Efficiency x scale size : 3.142857 Number of different interval sizes : 22 = 3.66667 / 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: 4 Number of recognisable fifths : 4, average 701.9550 cents Scale is Hypophrygian octave species of abstract tetrachord Best fifths form a closed circle Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions with margin 201.9563 cents: 3 -- Rational properties -- Prime limit : 5 Odd number limit : 1215 (O: 1215 U: 1215) Highest odd numerator or denominator: 81 Scale harmonicity : 0.033632 Average absolute harmonicity : 0.242616 Specific harmonicity : 0.181818 Fundamental : 1/960, -9.9069 octaves, 0.2725 Hz. Guide tone : 1296, 10.3399 octaves, 339066.733 Hz. Exponens Consonantiae : 1.244160E+06, 20.24674 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 125.5, average 17.92857 Mersenne's string divisions : 82919265 Sum of van Prooijen's expressibility: 6.39100, average 0.91300 Sum of Tenney's harmonic distance : 12.88872, average 1.84125 Vogel's harmonic complexity : 15.00000 Wille's k value : 607 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 6 Triangular lattice diameter : 6 Lattice compactness : 128.70679, average 4.59667 Lattice compactness (without 2's) : 60.21299, average 2.15046 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -6 .. 4 -0.28571 20 1 3: -1 .. 4 1.14286 10 3 5: -1 .. 0 -0.42857 3 3 Average exponent except 2's : 5 / 7 = 0.71429 Average absolute exponent except 2's: 13 / 7 = 1.85714
FIT/MODE
7: 1 1 0 2 1 0 2 N T3 SD: 43.1786 c. M: 64.9629 c. 8: 1 1 1 2 0 1 2 N D3 SD: 37.5822 c. M: 63.6863 c. 9: 1 1 1 2 1 1 2 P M ME S SD: 27.0275 c. M: 48.9746 c. 12: 1 2 1 3 1 1 3 N T3 S SD: 9.7758 c. M: 15.6413 c. 29: 3 5 2 7 3 2 7 N SD: 9.5772 c. M:-15.3932 c. 32: 3 5 3 8 3 2 8 N SD: 8.7891 c. M: 15.6413 c. 33: 3 6 2 8 3 3 8 N SD: 8.6450 c. M: 13.6863 c. 34: 3 6 3 8 3 3 8 N T3 S SD: 7.9548 c. M:-15.7094 c. 38: 4 6 3 9 4 3 9 N SD: 7.7911 c. M:-14.5845 c. 41: 4 7 3 10 4 3 10 N SD: 3.9349 c. M:-6.3099 c. 53: 5 9 4 13 5 4 13 N SD: 0.9318 c. M:-1.4763 c. 118: 11 20 9 29 11 9 29 N SD: 0.5268 c. M: 1.0403 c. 171: 16 29 13 42 16 13 42 N SD: 0.4617 c. M: 0.8025 c. 224: 21 38 17 55 21 17 55 N SD: 0.5183 c. M:-0.7687 c. 289: 27 49 22 71 27 22 71 N SD: 0.4610 c. M: 0.8996 c. 323: 30 55 25 79 30 25 79 N SD: 0.4264 c. M:-0.8487 c. 335: 31 57 26 82 31 26 82 N SD: 0.4505 c. M: 0.6865 c. 376: 35 64 29 92 35 29 92 N SD: 0.3579 c. M:-0.6906 c. 388: 36 66 30 95 36 30 95 N SD: 0.2834 c. M:-0.4274 c. 441: 41 75 34 108 41 34 108 N SD: 0.1796 c. M:-0.3433 c. 494: 46 84 38 121 46 38 121 N SD: 0.1479 c. M:-0.2772 c. 506: 47 86 39 124 47 39 124 N SD: 0.1676 c. M: 0.2688 c. 547: 51 93 42 134 51 42 134 N SD: 0.1761 c. M:-0.2636 c. 559: 52 95 43 137 52 43 137 N SD: 0.0646 c. M: 0.1034 c. 612: 57 104 47 150 57 47 150 N SD: 0.0282 c. M:-0.0450 c. 1171: 109 199 90 287 109 90 287 N SD: 0.0236 c. M:-0.0365 c. 1783: 166 303 137 437 166 137 437 N SD: 0.0160 c. M:-0.0319 c. 1901: 177 323 146 466 177 146 466 N SD: 0.0183 c. M: 0.0346 c. 2395: 223 407 184 587 223 184 587 N SD: 0.0159 c. M:-0.0297 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: 30.9176 cents 4 x x 5:6 x 7:8 S SD: 16.6332 cents 5 x 6 x x 8 x 10 S SD: 0.0000 cents 6 x 7:8:9 x 10:12 S SD: 20.9586 cents 7 x 8:9 x 11:12:14 SD: 19.5903 cents 8:9 x 10:12:13:14:16 S SD: 19.4679 cents 9:10:11 x x 14:15:18 SD: 18.8093 cents 10:11:12:13:15:16:17:20 SD: 10.2556 cents 12:13:14:15:18:19:20:24 S SD: 9.4250 cents 13:14:16 x 20:21:22:26 SD: 11.0749 cents 14:15:17:18:21:22:24:28 SD: 7.7446 cents 15:16:18:19:23:24:25:30 SD: 6.2473 cents 16:17:19:20:24:26:27:32 SD: 5.6379 cents 20:21:24:25:30:32:34:40 SD: 5.2859 cents 26:28:31:33:39:42:44:52 SD: 3.8370 cents 30:32:36:38:45:48:51:60 SD: 1.8365 cents 60:64:72:76:90:96:101:120 SD: 0.6444 cents 90:96:108:114:135:144:152:180 SD: 0.2878 cents 150:160:180:190:225:240:253:300 SD: 0.2373 cents 240:256:288:304:360:384:405:480 SD: 0.2035 cents 410:437:492:519:615:656:692:820 SD: 0.1989 cents 464:495:557:587:696:742:783:928 SD: 0.1946 cents 470:501:564:595:705:752:793:940 SD: 0.1811 cents 490:523:588:620:735:784:827:980 SD: 0.1736 cents 540:576:648:683:810:864:911:1080 SD: 0.1723 cents 550:587:660:696:825:880:928:1100 SD: 0.1482 cents 570:608:684:721:855:912:962:1140 SD: 0.1430 cents