Scala analysis: xen10-wilson-purvi-09b-01
Purvi modulation 1 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: 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: 135/128 92.1787 major chroma, major limma 3: 9/8 203.9100 major whole tone 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: 2 9/8 203.910 cents major whole tone 2: 1 1215/1024 296.089 cents wide augmented second 2: 1 5/4 386.314 cents major third 2: 2 512/405 405.866 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: 2 405/256 794.134 cents wide augmented fifth 5: 1 8/5 813.686 cents minor sixth 5: 1 2048/1215 903.911 cents narrow diminished seventh 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 : 111.7 203.9 407.8 702.0 813.7 905.9 1200.0 111.7 : 92.2 296.1 590.2 702.0 794.1 1088.3 1200.0 203.9 : 203.9 498.0 609.8 702.0 996.1 1107.8 1200.0 407.8 : 294.1 405.9 498.0 792.2 903.9 996.1 1200.0 702.0 : 111.7 203.9 498.0 609.8 702.0 905.9 1200.0 813.7 : 92.2 386.3 498.0 590.2 794.1 1088.3 1200.0 905.9 : 294.1 405.9 498.0 702.0 996.1 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 .. 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 : 160.38895 cents, oct.: 1122.72264 cents Scale is not proper Step pattern alph. order: ABCDABD Step pattern size order : BACDBAD Scale is not a Constant Structure Scale diversity : 1.361761 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 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 n-1 differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined -- 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 : 0.245567 Specific harmonicity : 0.184544 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 : 128.5, average 18.35714 Mersenne's string divisions : 128147955 Sum of van Prooijen's expressibility: 6.64627, average 0.94947 Sum of Tenney's harmonic distance : 13.26893, average 1.89556 Vogel's harmonic complexity : 15.57143 Wille's k value : 607 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 6 Triangular lattice diameter : 6 Lattice compactness : 133.74226, average 4.77651 Lattice compactness (without 2's) : 61.38456, average 2.19231 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -6 .. 4 -0.85714 22 1 3: -1 .. 4 1.28571 11 4 5: -1 .. 0 -0.28571 2 2 Average exponent except 2's : 7 / 7 = 1.00000 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is weakly epimorphic with val: <7 10 17| Scale is weakly epimorphic with val: <7 11 18|
FIT/MODE
7: 1 0 1 2 1 0 2 N T3 SD: 43.6955 c. M: 64.9629 c. 8: 1 0 2 2 0 1 2 N S SD: 42.3398 c. M: 63.6863 c. 9: 1 1 1 2 1 1 2 P M ME S SD: 30.8297 c. M:-62.7567 c. 11: 1 1 2 2 1 1 3 N D3 S SD: 31.3418 c. M: 50.0499 c. 12: 1 1 2 3 1 1 3 N SD: 7.9246 c. M: 13.6863 c. Chromatic Phrygian inverse 29: 3 2 5 7 3 2 7 N SD: 7.6907 c. M:-13.8999 c. 40: 4 3 7 9 4 3 10 N SD: 7.9707 c. M:-12.1800 c. 41: 4 3 7 10 4 3 10 N SD: 3.1511 c. M:-5.8259 c. 53: 5 4 9 13 5 4 13 N SD: 0.7839 c. M:-1.4763 c. 118: 11 9 20 29 11 9 29 N SD: 0.5429 c. M: 1.0403 c. 171: 16 13 29 42 16 13 42 N SD: 0.4827 c. M: 0.8025 c. 224: 21 17 38 55 21 17 55 N SD: 0.5085 c. M:-0.7687 c. 289: 27 22 49 71 27 22 71 N SD: 0.4907 c. M: 0.8996 c. 323: 30 25 55 79 30 25 79 N SD: 0.4521 c. M:-0.8487 c. 335: 31 26 57 82 31 26 82 N SD: 0.4341 c. M: 0.6865 c. 376: 35 29 64 92 35 29 92 N SD: 0.3617 c. M:-0.6906 c. 388: 36 30 66 95 36 30 95 N SD: 0.2869 c. M:-0.4274 c. 429: 40 33 73 105 40 33 105 N SD: 0.3223 c. M:-0.5716 c. 441: 41 34 75 108 41 34 108 N SD: 0.1910 c. M:-0.3433 c. 494: 46 38 84 121 46 38 121 N SD: 0.1466 c. M:-0.2772 c. 506: 47 39 86 124 47 39 124 N SD: 0.1450 c. M: 0.2688 c. 547: 51 42 93 134 51 42 134 N SD: 0.1512 c. M:-0.2239 c. 559: 52 43 95 137 52 43 137 N SD: 0.0583 c. M: 0.1034 c. 612: 57 47 104 150 57 47 150 N SD: 0.0229 c. M:-0.0392 c. 1171: 109 90 199 287 109 90 287 N SD: 0.0240 c. M:-0.0365 c. 1783: 166 137 303 437 166 137 437 N SD: 0.0169 c. M:-0.0319 c. 1901: 177 146 323 466 177 146 466 N SD: 0.0183 c. M: 0.0346 c. 2395: 223 184 407 587 223 184 587 N SD: 0.0157 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 x 6 x 8 x 10 S SD: 30.7262 cents 6 x 7:8:9 x 10:12 S SD: 22.4207 cents 7 x 8:9 x 11:12:14 SD: 11.3191 cents 8 x 9:10:12:13:14:16 S SD: 11.9572 cents 9 x 10:11 x 14:15:18 SD: 16.6772 cents 10 x 11:13:15:16:17:20 SD: 10.3136 cents 11:12 x 14:17:18:19:22 SD: 14.3554 cents 12:13:14:15:18:19:20:24 S SD: 11.0085 cents 14:15:16:18:21:22:24:28 S SD: 8.1598 cents 15:16:17:19:23:24:25:30 SD: 6.5085 cents 16:17:18:20:24:26:27:32 SD: 5.0079 cents 26:28:29:33:39:42:44:52 SD: 4.0865 cents 30:32:34:38:45:48:51:60 SD: 2.5893 cents 42:45:47:53:63:67:71:84 SD: 2.0490 cents 48:51:54:61:72:77:81:96 SD: 1.5435 cents 64:68:72:81:96:102:108:128 SD: 1.3689 cents 72:77:81:91:108:115:122:144 SD: 1.3211 cents 80:85:90:101:120:128:135:160 SD: 1.1449 cents 90:96:101:114:135:144:152:180 SD: 0.6757 cents 120:128:135:152:180:192:203:240 SD: 0.6430 cents 150:160:169:190:225:240:253:300 SD: 0.4363 cents 192:205:216:243:288:307:324:384 SD: 0.2902 cents 240:256:270:304:360:384:405:480 SD: 0.2035 cents 422:450:475:534:633:675:712:844 SD: 0.1774 cents 432:461:486:547:648:691:729:864 SD: 0.1715 cents 448:478:504:567:672:717:756:896 SD: 0.0976 cents 512:546:576:648:768:819:864:1024 SD: 0.0854 cents