Scala analysis: xen10-wilson-purvi-07b-01
Purvi modulation 1 from Figure 7b, Kathleen Schlesinger (15/13 16/15 13/12), (16/15 13/12 15/13)
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: 52/45 250.303946 3: 13/10 454.213948 tridecimal semi-diminished fourth 4: 3/2 701.955001 perfect fifth 5: 8/5 813.686286 minor sixth 6: 26/15 952.258947 tridecimal semi-augmented sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 15/13 247.7411 tridecimal 5/4-tone 1: 16/15 111.7313 minor diatonic semitone 2: 13/12 138.5727 tridecimal 2/3-tone 3: 9/8 203.9100 major whole tone 4: 15/13 247.7411 tridecimal 5/4-tone 5: 16/15 111.7313 minor diatonic semitone 6: 13/12 138.5727 tridecimal 2/3-tone 7: 15/13 247.7411 tridecimal 5/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 16/15 111.731 cents minor diatonic semitone 1: 2 13/12 138.573 cents tridecimal 2/3-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 15/13 247.741 cents tridecimal 5/4-tone 2: 2 52/45 250.304 cents 2: 1 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 2: 2 16/13 359.472 cents tridecimal neutral third 2: 1 5/4 386.314 cents major third 2: 1 135/104 451.651 cents 3: 1 13/10 454.214 cents tridecimal semi-diminished fourth 3: 4 4/3 498.045 cents perfect fourth 3: 1 18/13 563.382 cents tridecimal augmented fourth 3: 1 45/32 590.224 cents diatonic tritone 4: 1 64/45 609.776 cents 2nd tritone 4: 1 13/9 636.618 cents tridecimal diminished fifth 4: 4 3/2 701.955 cents perfect fifth 4: 1 20/13 745.786 cents tridecimal semi-augmented fifth 5: 1 208/135 748.349 cents 5: 1 8/5 813.686 cents minor sixth 5: 2 13/8 840.528 cents tridecimal neutral sixth 5: 1 64/39 857.517 cents 39th subharmonic 5: 2 45/26 949.696 cents 6: 2 26/15 952.259 cents tridecimal semi-augmented sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 24/13 1061.427 cents tridecimal neutral seventh 6: 2 15/8 1088.269 cents classic major seventh 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 : 111.7 250.3 454.2 702.0 813.7 952.3 1200.0 111.7 : 138.6 342.5 590.2 702.0 840.5 1088.3 1200.0 250.3 : 203.9 451.7 563.4 702.0 949.7 1061.4 1200.0 454.2 : 247.7 359.5 498.0 745.8 857.5 996.1 1200.0 702.0 : 111.7 250.3 498.0 609.8 748.3 952.3 1200.0 813.7 : 138.6 386.3 498.0 636.6 840.5 1088.3 1200.0 952.3 : 247.7 359.5 498.0 702.0 949.7 1061.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 247.7411 cents 225/208, 136.0098 cents 16/15, 111.7313 cents 2: 250.3039 .. 451.6511 cents 6075/5408, 201.3471 cents 676/675, 2.5629 cents 3: 454.2139 .. 590.2237 cents 225/208, 136.0098 cents 676/675, 2.5629 cents 4: 609.7763 .. 745.7861 cents 225/208, 136.0098 cents 2048/2025, 19.5526 cents 5: 748.3489 .. 949.6961 cents 6075/5408, 201.3471 cents 676/675, 2.5629 cents 6: 952.2589 .. 1088.2687 cents 225/208, 136.0098 cents 676/675, 2.5629 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 15/13, 247.7411 cents Average / Smallest step : 1.534293 Largest / Average step : 1.445156 Largest / Smallest step : 2.217294 Median interval of one step : 13/12, 138.5727 cents, amount: 2 Least squares average step : 164.03419 cents, oct.: 1148.23931 cents Scale is strictly proper Step pattern alph. order: ABCDABD Step pattern size order : ABCDABD Scale is a Constant Structure, by a margin of 2.56289 cents Scale diversity : 1.481717 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.211056 Rothenberg efficiency : 0.421769 redundancy: 0.578231 Efficiency x scale size : 2.952381 Number of different interval sizes : 26 = 4.33333 / 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 : 676/675, 2.5629 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Number of recognisable fifths : 4, 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 differentially coherent in interval class 1 Scale is differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 13 Odd number limit : 135 (O: 135 U: 135) Highest odd numerator or denominator: 45 Scale harmonicity : 0.024065 Average absolute harmonicity : 0.221196 Specific harmonicity : 0.112946 Fundamental : 1/90, -6.4919 octaves, 2.9070 Hz. Guide tone : 624, 9.2854 octaves, 163254.353 Hz. Exponens Consonantiae : 5.616000E+04, 15.77726 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 106.5, average 15.21429 Mersenne's string divisions : 552942195 Sum of van Prooijen's expressibility: 6.29543, average 0.89935 Sum of Tenney's harmonic distance : 13.13568, average 1.87653 Vogel's harmonic complexity : 14.00000 Wille's k value : 67 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 78.91589, average 2.81842 Lattice compactness (without 2's) : 42.64709, average 1.52311 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 1.28571 13 1 3: -2 .. 1 -0.42857 5 1 5: -1 .. 0 -0.71429 5 2 13: 0 .. 1 0.42857 3 3 Average exponent except 2's :-5 / 7 =-0.71429 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is weakly epimorphic with val: <7 10 17 29| Scale is JI-epimorphic with val: <7 11 16 26| = patent Scale is weakly epimorphic with val: <7 11 18 27|
FIT/MODE
7: 0 1 1 2 0 1 2 N T3 SD: 90.0739 c. M: 127.9720 c. 8: 1 1 1 2 0 1 2 N D3 SD: 43.1728 c. M: 63.6863 c. 9: 1 1 1 2 1 1 2 P M ME S SD: 27.9395 c. M: 54.2139 c. 10: 1 1 2 2 1 1 2 P D3 S SD: 16.5504 c. M:-26.3137 c. 19: 2 2 3 4 2 2 4 P SD: 8.4094 c. M:-14.5845 c. 24: 2 3 4 5 2 3 5 P SD: 7.0883 c. M: 13.6863 c. 34: 3 4 6 7 3 4 7 P SD: 3.4963 c. M: 5.8489 c. 43: 4 5 7 9 4 5 9 P SD: 3.9519 c. M: 7.7023 c. 53: 5 6 9 11 5 6 11 P SD: 1.1568 c. M:-1.4763 c. 130: 12 15 22 27 12 15 27 P SD: 1.1955 c. M: 1.9063 c. 140: 13 16 24 29 13 16 29 P SD: 0.8419 c. M: 1.7325 c. 193: 18 22 33 40 18 22 40 P SD: 0.8200 c. M: 1.5993 c. 217: 20 25 37 45 20 25 45 P SD: 0.9209 c. M: 1.4560 c. 224: 21 26 38 46 21 26 46 SP SD: 0.9414 c. M:-1.4818 c. 227: 21 26 39 47 21 26 47 P SD: 0.9296 c. M: 1.8458 c. 246: 23 28 42 51 23 28 51 P SD: 0.8500 c. M: 1.5235 c. 248: 23 29 42 51 23 29 51 SP SD: 0.7524 c. M:-1.3090 c. 267: 25 31 45 55 25 31 55 SP SD: 0.6987 c. M:-1.3814 c. 270: 25 31 46 56 25 31 56 P SD: 0.8173 c. M: 1.4151 c. 277: 26 32 47 57 26 32 57 SP SD: 0.6990 c. M:-0.9596 c. 301: 28 35 51 62 28 35 62 SP SD: 0.4448 c. M:-0.8588 c. 335: 31 39 57 69 31 39 69 SP SD: 0.5111 c. M:-0.7114 c. 354: 33 41 60 73 33 41 73 SP SD: 0.2613 c. M:-0.5435 c. 388: 36 45 66 80 36 45 80 SP SD: 0.2859 c. M:-0.4252 c. 407: 38 47 69 84 38 47 84 SP SD: 0.2011 c. M:-0.3103 c. 441: 41 51 75 91 41 51 91 SP SD: 0.1202 c. M:-0.2078 c. 494: 46 57 84 102 46 57 102 SP SD: 0.0584 c. M: 0.1015 c. 1342: 125 155 228 277 125 155 277 SP SD: 0.0399 c. M:-0.0686 c. 1836: 171 212 312 379 171 212 379 SP SD: 0.0273 c. M:-0.0392 c. 2330: 217 269 396 481 217 269 481 SP SD: 0.0265 c. M:-0.0476 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: 26.9394 cents 4 x x 5:6 x 7:8 S SD: 17.4730 cents 5 x 6 x x 8:9:10 S SD: 23.1002 cents 6 x 7:8:9 x 10:12 S SD: 16.4998 cents 7 x 8:9 x 11:12:14 SD: 9.1015 cents 8 x 9:10:12:13:14:16 S SD: 14.6797 cents 9 x 10:12 x 14:16:18 S SD: 20.8147 cents 10:11:12:13:15:16:17:20 SD: 12.9655 cents 12:13:14:16:18:19:21:24 SD: 8.4747 cents 14:15:16:18:21:22:24:28 S SD: 6.5938 cents 18:19:21:23:27:29:31:36 SD: 5.9959 cents 20:21:23:26:30:32:35:40 SD: 4.7108 cents 26:28:30:34:39:42:45:52 SD: 3.6878 cents 30:32:35:39:45:48:52:60 SD: 2.3667 cents 44:47:51:57:66:70:76:88 SD: 2.0447 cents 46:49:53:60:69:74:80:92 SD: 1.9491 cents 57:61:66:74:86:91:99:114 SD: 1.9094 cents 58:62:67:75:87:93:101:116 SD: 1.9016 cents 60:64:69:78:90:96:104:120 SD: 1.1919 cents 90:96:104:117:135:144:156:180 SD: 0.0000 cents