Scala analysis: xen10-wilson-purvi-09a-04
Purvi modulation 4 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: 9/8 203.910002 major whole tone 2: 5/4 386.313714 major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 405/256 794.133717 wide augmented fifth 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: 9/8 203.9100 major whole tone 2: 10/9 182.4037 minor whole tone 3: 16/15 111.7313 minor diatonic semitone 4: 9/8 203.9100 major whole tone 5: 135/128 92.1787 major chroma, major limma 6: 32/27 294.1350 Pythagorean minor third 7: 16/15 111.7313 minor diatonic semitone
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 32/27 294.135 cents Pythagorean minor third 2: 1 1215/1024 296.089 cents wide augmented second 2: 2 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 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: 2 8/5 813.686 cents minor sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 1 2048/1215 903.911 cents narrow diminished seventh 5: 1 27/16 905.865 cents Pythagorean major sixth 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: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 386.3 498.0 702.0 794.1 1088.3 1200.0 203.9 : 182.4 294.1 498.0 590.2 884.4 996.1 1200.0 386.3 : 111.7 315.6 407.8 702.0 813.7 1017.6 1200.0 498.0 : 203.9 296.1 590.2 702.0 905.9 1088.3 1200.0 702.0 : 92.2 386.3 498.0 702.0 884.4 996.1 1200.0 794.1 : 294.1 405.9 609.8 792.2 903.9 1107.8 1200.0 1088.3: 111.7 315.6 498.0 609.8 813.7 905.9 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: 294.1350 .. 405.8663 cents 16/15, 111.7313 cents 1/1, 0.0000 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 .. 905.8650 cents 16/15, 111.7313 cents 32805/32768, 1.9537 cents 6: 905.8650 .. 1107.8213 cents 4096/3645, 201.9563 cents 1/1, 0.0000 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 : 172.70552 cents, oct.: 1208.93867 cents Scale is not proper Step pattern alph. order: ABCADEC Step pattern size order : DCBDAEB Scale is not a Constant Structure Scale diversity : 1.424003 Lumma stability : 0.156887 Lumma impropriety factor : 0.016294 Rothenberg efficiency : 0.435374 redundancy: 0.564626 Efficiency x scale size : 3.047619 Number of different interval sizes : 24 = 4.00000 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.66667 = 14/3 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 0 Length of longest subharmonic part : 1 at degree 0 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 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 : 1215 (O: 1215 U: 1215) Highest odd numerator or denominator: 405 Scale harmonicity : 0.033632 Average absolute harmonicity : 0.264118 Specific harmonicity : 0.195918 Fundamental : 1/768, -9.5850 octaves, 0.3407 Hz. Guide tone : 1620, 10.6618 octaves, 423833.416 Hz. Exponens Consonantiae : 1.244160E+06, 20.24674 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 362.5, average 51.78571 Mersenne's string divisions : 81412065 Sum of van Prooijen's expressibility: 6.39100, average 0.91300 Sum of Tenney's harmonic distance : 12.41160, average 1.77309 Vogel's harmonic complexity : 14.14286 Wille's k value : 607 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 6 Triangular lattice diameter : 6 Lattice compactness : 116.29923, average 4.15354 Lattice compactness (without 2's) : 55.28678, average 1.97453 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -8 .. 2 -2.00000 20 1 3: -1 .. 4 1.00000 9 3 5: 0 .. 1 0.42857 3 3 Average exponent except 2's : 10 / 7 = 1.42857 Average absolute exponent except 2's: 12 / 7 = 1.71429
FIT/MODE
7: 1 1 1 1 0 2 1 N T3 SD: 51.8095 c. M: 108.4194 c. 8: 1 1 1 1 1 2 1 P M ME S SD: 61.4954 c. M: 101.9550 c. 9: 2 1 1 1 1 2 1 N D3 S SD: 31.8866 c. M:-62.7567 c. 10: 2 1 1 2 1 2 1 P M ME S SD: 26.2358 c. M:-45.8663 c. Sethares Neutral, Beatles-7, Dichotic-7 12: 2 2 1 2 1 3 1 P D3 SD: 7.3900 c. M:-13.6863 c. Harmonic Major, Mischung 2, Mela Sarasangi, Raga Anand Leela, Haripriya, Nat Bhairav, Simhavahini, Ethiopian, Tabahaniotikos: Greece 41: 7 6 4 7 3 10 4 N SD: 3.3597 c. M: 5.8259 c. 53: 9 8 5 9 4 13 5 N SD: 1.0011 c. M: 1.6809 c. 65: 11 10 6 11 5 16 6 N SD: 0.7512 c. M:-1.3786 c. 118: 20 18 11 20 9 29 11 N SD: 0.4266 c. M: 0.9134 c. 183: 31 28 17 31 14 45 17 N SD: 0.4579 c. M: 0.6911 c. 301: 51 46 28 51 23 74 28 N SD: 0.4297 c. M: 0.7782 c. 311: 53 47 29 53 24 76 29 N SD: 0.4287 c. M:-0.7216 c. 323: 55 49 30 55 25 79 30 N SD: 0.4112 c. M:-0.9127 c. 364: 62 55 34 62 28 89 34 N SD: 0.3739 c. M: 0.5994 c. 376: 64 57 35 64 29 92 35 N SD: 0.2672 c. M:-0.5471 c. 429: 73 65 40 73 33 105 40 N SD: 0.2107 c. M: 0.2997 c. 441: 75 67 41 75 34 108 41 N SD: 0.1921 c. M:-0.4241 c. 494: 84 75 46 84 38 121 46 N SD: 0.1031 c. M:-0.1983 c. 559: 95 85 52 95 43 137 52 N SD: 0.0756 c. M:-0.1418 c. 612: 104 93 57 104 47 150 57 N SD: 0.0211 c. M: 0.0392 c. 1289: 219 196 120 219 99 316 120 N SD: 0.0228 c. M:-0.0323 c. 1783: 303 271 166 303 137 437 166 N SD: 0.0151 c. M:-0.0334 c. 1901: 323 289 177 323 146 466 177 N SD: 0.0130 c. M: 0.0254 c. 2395: 407 364 223 407 184 587 223 N SD: 0.0110 c. M:-0.0208 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: 30.0750 cents 4 x 5 x 6 x x 8 S SD: 0.0000 cents 5 x 6:7 x 8:9:10 S SD: 26.4622 cents 6:7 x 8:9:10:11:12 S SD: 19.4496 cents 7:8:9 x x 11:13:14 SD: 11.8859 cents 8:9:10:11:12:13:15:16 SD: 10.0918 cents 9:10:11:12 x 14:17:18 SD: 9.1182 cents 10:11 x 13:15:16:19:20 SD: 10.9835 cents 11:12:14:15 x 17:21:22 SD: 14.8490 cents 12:14:15:16:18:19:23:24 SD: 10.5114 cents 14:16:18:19:21:22:26:28 SD: 9.5520 cents 15:17:19:20:23:24:28:30 SD: 7.2544 cents 16:18:20:21:24:25:30:32 S SD: 4.9608 cents 24:27:30:32:36:38:45:48 SD: 0.2035 cents 328:369:410:437:492:519:615:656 SD: 0.1938 cents 352:396:440:469:528:557:660:704 SD: 0.1843 cents 376:423:470:501:564:595:705:752 SD: 0.1769 cents 392:441:490:523:588:620:735:784 SD: 0.1695 cents 416:468:520:555:624:658:780:832 SD: 0.1558 cents 440:495:550:587:660:696:825:880 SD: 0.1444 cents 456:513:570:608:684:721:855:912 SD: 0.1393 cents 464:522:580:619:696:734:870:928 SD: 0.1349 cents 480:540:600:640:720:759:900:960 SD: 0.1222 cents 504:567:630:672:756:797:945:1008 SD: 0.1066 cents 528:594:660:704:792:835:990:1056 SD: 0.0925 cents 552:621:690:736:828:873:1035:1104 SD: 0.0797 cents 576:648:720:768:864:911:1080:1152 SD: 0.0679 cents 600:675:750:800:900:949:1125:1200 SD: 0.0570 cents