Scala analysis: xen10-wilson-purvi-07b-02
Purvi modulation 2 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: 4/3 498.044999 perfect 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: 15/13 247.7411 tridecimal 5/4-tone 4: 9/8 203.9100 major whole 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 6/5 315.641 cents minor third 2: 1 16/13 359.472 cents tridecimal neutral third 2: 2 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: 2 8/5 813.686 cents minor sixth 5: 1 13/8 840.528 cents tridecimal neutral sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 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 : 111.7 250.3 498.0 702.0 813.7 952.3 1200.0 111.7 : 138.6 386.3 590.2 702.0 840.5 1088.3 1200.0 250.3 : 247.7 451.7 563.4 702.0 949.7 1061.4 1200.0 498.0 : 203.9 315.6 454.2 702.0 813.7 952.3 1200.0 702.0 : 111.7 250.3 498.0 609.8 748.3 996.1 1200.0 813.7 : 138.6 386.3 498.0 636.6 884.4 1088.3 1200.0 952.3 : 247.7 359.5 498.0 745.8 949.7 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 : 164.97342 cents, oct.: 1154.81396 cents Scale is strictly proper Step pattern alph. order: ABCDABC Step pattern size order : ABDCABD Scale is a Constant Structure, by a margin of 2.56289 cents Scale diversity : 1.515941 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 Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Scale contains a complete diamond : 1 3 Length of longest harmonic part : 1 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 class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval class 3 -- 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 : 0.246975 Specific harmonicity : 0.127427 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 : 98.5, average 14.07143 Mersenne's string divisions : 168286755 Sum of van Prooijen's expressibility: 5.65861, average 0.80837 Sum of Tenney's harmonic distance : 12.10091, average 1.72870 Vogel's harmonic complexity : 12.85714 Wille's k value : 67 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 72.52948, average 2.59034 Lattice compactness (without 2's) : 42.23288, average 1.50832 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 1.71429 14 1 3: -2 .. 1 -0.57143 6 2 5: -1 .. 0 -0.57143 4 2 13: 0 .. 1 0.28571 2 2 Average exponent except 2's :-6 / 7 =-0.85714 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is weakly epimorphic with val: <7 11 15 24| Scale is JI-epimorphic with val: <7 11 16 26| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 53.9437 c. M:-92.5532 c. Lebeng 8: 1 1 1 2 0 1 2 N D3 SD: 46.8093 c. M: 63.6863 c. 9: 1 1 2 1 1 1 2 P M ME S SD: 23.2084 c. M:-35.2883 c. Pseudo Pelog, Pelogic-7, Antiionian 10: 1 1 2 2 1 1 2 P D3 S SD: 15.0149 c. M:-26.3137 c. 19: 2 2 4 3 2 2 4 P SD: 7.5641 c. M:-14.5845 c. 24: 2 3 5 4 2 3 5 P SD: 6.9465 c. M: 13.6863 c. Soft Diatonic Dorian 33: 3 4 7 5 3 4 7 P SD: 8.4735 c. M: 13.6863 c. 34: 3 4 7 6 3 4 7 P SD: 3.3753 c. M: 5.8489 c. 43: 4 5 9 7 4 5 9 P SD: 3.1242 c. M: 4.3840 c. 53: 5 6 11 9 5 6 11 P SD: 1.0322 c. M:-1.4763 c. 130: 12 15 27 22 12 15 27 P SD: 0.9669 c. M: 1.4897 c. 140: 13 16 29 24 13 16 29 P SD: 0.9079 c. M: 1.7325 c. 183: 17 21 38 31 17 21 38 P SD: 0.7488 c. M: 1.4393 c. 236: 22 27 49 40 22 27 49 P SD: 0.7058 c. M: 1.4115 c. 248: 23 29 51 42 23 29 51 SP SD: 0.7260 c. M:-1.3090 c. 258: 24 30 53 44 24 30 53 SP SD: 0.6101 c. M:-1.2294 c. 277: 26 32 57 47 26 32 57 SP SD: 0.6555 c. M:-0.9596 c. 301: 28 35 62 51 28 35 62 SP SD: 0.4469 c. M:-0.8588 c. 311: 29 36 64 53 29 36 64 SP SD: 0.4307 c. M:-0.7957 c. 335: 31 39 69 57 31 39 69 SP SD: 0.4376 c. M: 0.6865 c. 354: 33 41 73 60 33 41 73 SP SD: 0.2790 c. M:-0.5435 c. 388: 36 45 80 66 36 45 80 SP SD: 0.2398 c. M: 0.3911 c. 407: 38 47 84 69 38 47 84 SP SD: 0.2114 c. M:-0.3103 c. 441: 41 51 91 75 41 51 91 SP SD: 0.0965 c. M: 0.1667 c. 494: 46 57 102 84 46 57 102 SP SD: 0.0624 c. M: 0.1015 c. 935: 87 108 193 159 87 108 193 SP SD: 0.0538 c. M:-0.0771 c. 1342: 125 155 277 228 125 155 277 SP SD: 0.0384 c. M:-0.0686 c. 1783: 166 206 368 303 166 206 368 SP SD: 0.0350 c. M:-0.0686 c. 1836: 171 212 379 312 171 212 379 SP SD: 0.0241 c. M:-0.0392 c. 2277: 212 263 470 387 212 263 470 SP SD: 0.0240 c. M:-0.0467 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: 22.6334 cents 4 x x 5:6 x 7:8 S SD: 28.2382 cents 5 x 6:7 x 8:9:10 S SD: 25.0381 cents 6 x 7:8:9 x 10:12 S SD: 13.9784 cents 7 x 8:9 x 11:12:14 SD: 15.0586 cents 8 x 9:11:12:13:14:16 SD: 12.8942 cents 9 x 10:12 x 14:16:18 S SD: 18.8787 cents 10:11:12:13:15:16:17:20 SD: 14.3983 cents 11:12:13:15:17:18:19:22 SD: 13.3726 cents 12:13:14:16:18:19:21:24 SD: 5.7108 cents 18:19:21:24:27:29:31:36 SD: 4.2151 cents 26:28:30:35:39:42:45:52 SD: 4.1318 cents 30:32:35:40:45:48:52:60 SD: 2.3667 cents 44:47:51:59:66:70:76:88 SD: 2.3225 cents 45:48:52:60:68:72:78:90 SD: 1.8252 cents 58:62:67:77:87:93:101:116 SD: 1.7398 cents 60:64:69:80:90:96:104:120 SD: 1.1919 cents 72:77:83:96:108:115:125:144 SD: 1.0534 cents 78:83:90:104:117:125:135:156 SD: 0.8827 cents 90:96:104:120:135:144:156:180 SD: 0.0000 cents