Scala analysis: xen10-wilson-purvi-09c-03
Purvi modulation 3 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: 256/135 1107.821284 octave - major chroma 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 135/128 92.1787 major chroma, major limma 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: 32/27 294.1350 Pythagorean minor third 7: 135/128 92.1787 major chroma, major limma
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 1107.8 1200.0 111.7 : 203.9 386.3 590.2 702.0 996.1 1088.3 1200.0 315.6 : 182.4 386.3 498.0 792.2 884.4 996.1 1200.0 498.0 : 203.9 315.6 609.8 702.0 813.7 1017.6 1200.0 702.0 : 111.7 405.9 498.0 609.8 813.7 996.1 1200.0 813.7 : 294.1 386.3 498.0 702.0 884.4 1088.3 1200.0 1107.8: 92.2 203.9 407.8 590.2 794.1 905.9 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 : 172.57377 cents, oct.: 1208.01640 cents Scale is not proper Step pattern alph. order: ABCBADE Step pattern size order : BDCDBEA 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 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 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: 135 Scale harmonicity : 0.038363 Average absolute harmonicity : 0.259129 Specific harmonicity : 0.212107 Fundamental : 1/270, -8.0768 octaves, 0.9690 Hz. Guide tone : 768, 9.5850 octaves, 200928.434 Hz. Exponens Consonantiae : 2.073600E+05, 17.66178 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 230.5, average 32.92857 Mersenne's string divisions : 181996815 Sum of van Prooijen's expressibility: 5.65861, average 0.80837 Sum of Tenney's harmonic distance : 12.15633, average 1.73662 Vogel's harmonic complexity : 13.42857 Wille's k value : 202 Wilson's harmonic complexity : 17 Rectangular lattice diameter : 5 Triangular lattice diameter : 5 Lattice compactness : 104.59080, average 3.73539 Lattice compactness (without 2's) : 48.64115, average 1.73718 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 8 2.57143 20 1 3: -3 .. 1 -0.42857 7 2 5: -1 .. 0 -0.57143 4 4 Average exponent except 2's :-7 / 7 =-1.00000 Average absolute exponent except 2's: 11 / 7 = 1.57143
FIT/MODE
7: 1 1 1 1 1 2 0 N T3 SD: 46.6252 c. M:-92.1787 c. 8: 1 1 1 2 0 2 1 P D3 S SD: 44.2800 c. M: 63.6863 c. 9: 1 1 2 1 1 2 1 P M ME S SD: 32.1530 c. M: 48.9746 c. 10: 1 2 1 2 1 2 1 P M ME I SD: 24.3596 c. M:-44.3587 c. 12: 1 2 2 2 1 3 1 N T3 SD: 9.5499 c. M: 15.6413 c. Neapolitan Minor, Mela Dhenuka, Raga Bhinnasadjam, Dhunibinnashadjam, Kirvanti, Takka, Maqam Shahnaz Kurdi, Hungarian Gipsy 22: 2 4 3 4 2 5 2 N SD: 8.8668 c. M: 16.9122 c. 29: 3 5 4 5 3 7 2 N SD: 9.8364 c. M:-15.3932 c. 31: 3 5 5 5 3 8 2 N SD: 6.8352 c. M:-14.7594 c. 34: 3 6 5 6 3 8 3 N SD: 6.1011 c. M: 13.7036 c. 39: 4 6 6 7 3 10 3 N SD: 7.9738 c. M: 13.6863 c. 41: 4 7 6 7 4 10 3 N SD: 4.1729 c. M:-6.3099 c. 53: 5 9 8 9 5 13 4 N SD: 1.1063 c. M:-1.6127 c. 65: 6 11 10 11 6 16 5 N SD: 0.9571 c. M: 1.7951 c. 118: 11 20 18 20 11 29 9 N SD: 0.3264 c. M:-0.6533 c. 289: 27 49 44 49 27 71 22 N SD: 0.3706 c. M:-0.8292 c. 323: 30 55 49 55 30 79 25 N SD: 0.3124 c. M: 0.7005 c. 376: 35 64 57 64 35 92 29 N SD: 0.2142 c. M: 0.3745 c. 429: 40 73 65 73 40 105 33 N SD: 0.2292 c. M:-0.4426 c. 441: 41 75 67 75 41 108 34 N SD: 0.1528 c. M: 0.3383 c. 494: 46 84 75 84 46 121 38 N SD: 0.0882 c. M:-0.1482 c. 559: 52 95 85 95 52 137 43 N SD: 0.0774 c. M: 0.1290 c. 612: 57 104 93 104 57 150 47 N SD: 0.0273 c. M:-0.0450 c. 1171: 109 199 178 199 109 287 90 N SD: 0.0251 c. M: 0.0501 c. 1289: 120 219 196 219 120 316 99 N SD: 0.0248 c. M: 0.0478 c. 1783: 166 303 271 303 166 437 137 N SD: 0.0114 c. M: 0.0254 c. 1901: 177 323 289 323 177 466 146 N SD: 0.0109 c. M: 0.0179 c. 2395: 223 407 364 407 223 587 184 N SD: 0.0095 c. M:-0.0163 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: 23.5575 cents 4 x 5 x 6 x x 8 S SD: 23.5575 cents 5 x 6:7 x 8:9:10 S SD: 24.7186 cents 6 x 7:8:9:10:11:12 S SD: 17.3129 cents 7 x 8:9 x 11:13:14 SD: 23.1313 cents 8:9:10:11:12:13:15:16 SD: 18.8616 cents 9:10:11:12 x 14:17:18 SD: 15.3008 cents 10:11:12:13:15:16:19:20 SD: 9.8671 cents 12:13:14:16:18:19:23:24 SD: 8.7713 cents 14:15:17:19:21:22:27:28 SD: 8.1378 cents 15:16:18:20:23:24:28:30 SD: 6.6872 cents 18:19:22:24:27:29:34:36 SD: 5.5828 cents 20:21:24:27:30:32:38:40 SD: 4.9842 cents 26:28:31:35:39:42:49:52 SD: 4.6550 cents 28:30:34:37:42:45:53:56 SD: 4.0144 cents 30:32:36:40:45:48:57:60 SD: 0.4826 cents 150:160:180:200:225:240:284:300 SD: 0.3867 cents 180:192:216:240:270:288:341:360 SD: 0.2416 cents 210:224:252:280:315:336:398:420 SD: 0.1381 cents 240:256:288:320:360:384:455:480 SD: 0.0604 cents 270:288:324:360:405:432:512:540 SD: 0.0000 cents