Scala analysis: xen10-wilson-purvi-07c-03
Purvi modulation 3 from Figure 7c, Kathleen Schlesinger (16/15 15/13 13/12), (13/12 15/13 16/15)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 13/12 138.572661 tridecimal 2/3-tone 2: 39/32 342.482663 39th harmonic, Zalzal wosta of Ibn Sina 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 13/8 840.527662 tridecimal neutral sixth 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: 13/12 138.5727 tridecimal 2/3-tone 2: 9/8 203.9100 major whole tone 3: 128/117 155.5623 4: 9/8 203.9100 major whole tone 5: 13/12 138.5727 tridecimal 2/3-tone 6: 15/13 247.7411 tridecimal 5/4-tone 7: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 16/15 111.731 cents minor diatonic semitone 1: 2 13/12 138.573 cents tridecimal 2/3-tone 1: 1 128/117 155.562 cents 1: 2 9/8 203.910 cents major whole tone 1: 1 15/13 247.741 cents tridecimal 5/4-tone 2: 1 52/45 250.304 cents 2: 2 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 2: 3 16/13 359.472 cents tridecimal neutral third 2: 1 5/4 386.314 cents major third 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 8/5 813.686 cents minor sixth 5: 3 13/8 840.528 cents tridecimal neutral sixth 5: 2 64/39 857.517 cents 39th subharmonic 5: 1 45/26 949.696 cents 6: 1 26/15 952.259 cents tridecimal semi-augmented sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 117/64 1044.438 cents 6: 2 24/13 1061.427 cents tridecimal neutral seventh 6: 1 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 : 138.6 342.5 498.0 702.0 840.5 1088.3 1200.0 138.6 : 203.9 359.5 563.4 702.0 949.7 1061.4 1200.0 342.5 : 155.6 359.5 498.0 745.8 857.5 996.1 1200.0 498.0 : 203.9 342.5 590.2 702.0 840.5 1044.4 1200.0 702.0 : 138.6 386.3 498.0 636.6 840.5 996.1 1200.0 840.5 : 247.7 359.5 498.0 702.0 857.5 1061.4 1200.0 1088.3: 111.7 250.3 454.2 609.8 813.7 952.3 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 .. 386.3137 cents 225/208, 136.0098 cents 676/675, 2.5629 cents 3: 454.2139 .. 590.2237 cents 225/208, 136.0098 cents 26/25, 67.9002 cents 4: 609.7763 .. 745.7861 cents 225/208, 136.0098 cents 2048/2025, 19.5526 cents 5: 813.6863 .. 949.6961 cents 225/208, 136.0098 cents 26/25, 67.9002 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 : 128/117, 155.5623 cents, amount: 1 Least squares average step : 173.26960 cents, oct.: 1212.88718 cents Scale is strictly proper Step pattern alph. order: ABCBADE Step pattern size order : BDCDBEA Scale is a Constant Structure, by a margin of 2.56289 cents Scale diversity : 1.498679 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.319951 Rothenberg efficiency : 0.423129 redundancy: 0.576871 Efficiency x scale size : 2.961905 Number of different interval sizes : 26 = 4.33333 / 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 : 676/675, 2.5629 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 Best minor thirds form a closed circle 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 classes 3 and 4 combined -- Rational properties -- Prime limit : 13 Odd number limit : 117 (O: 117 U: 117) Highest odd numerator or denominator: 39 Scale harmonicity : 0.024458 Average absolute harmonicity : 0.240065 Specific harmonicity : 0.121187 Fundamental : 1/96, -6.5850 octaves, 2.7253 Hz. Guide tone : 780, 9.6073 octaves, 204067.941 Hz. Exponens Consonantiae : 7.488000E+04, 16.19229 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 77.5, average 11.07143 Mersenne's string divisions : 857325 Sum of van Prooijen's expressibility: 5.94929, average 0.84990 Sum of Tenney's harmonic distance : 11.54392, average 1.64913 Vogel's harmonic complexity : 13.14286 Wille's k value : 58 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 91.36367, average 3.26299 Lattice compactness (without 2's) : 38.61767, average 1.37920 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 2 -1.57143 17 1 3: -1 .. 1 0.14286 5 2 5: 0 .. 1 0.14286 1 1 13: 0 .. 1 0.42857 3 3 Average exponent except 2's : 5 / 7 = 0.71429 Average absolute exponent except 2's: 9 / 7 = 1.28571 Scale is weakly epimorphic with val: <7 10 17 26| 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: 27.8952 c. M: 59.6973 c. Lebeng 8: 1 1 1 2 1 1 1 P M ME I SD: 40.6263 c. M:-59.4723 c. 9: 1 2 1 1 1 2 1 P M ME I SD: 33.6693 c. M:-57.5173 c. 10: 1 2 1 2 1 2 1 P M ME I SD: 13.9984 c. M: 18.5727 c. 17: 2 3 2 3 2 3 2 SP M ME I SD: 12.2864 c. M: 29.4452 c. Neutral Dorian, Maqamic-7 24: 3 4 3 4 3 5 2 P SD: 7.7652 c. M:-11.7313 c. 34: 4 6 4 6 4 7 3 P SD: 5.6553 c. M:-10.4585 c. 41: 5 7 5 7 5 8 4 SP SD: 5.7793 c. M:-8.7368 c. 43: 5 7 6 7 5 9 4 P SD: 3.8976 c. M: 7.5989 c. 53: 6 9 7 9 6 11 5 P SD: 1.9116 c. M: 2.8600 c. 77: 9 13 10 13 9 16 7 P SD: 1.3029 c. M:-2.6404 c. 87: 10 15 11 15 10 18 8 P SD: 1.3637 c. M:-2.3449 c. 130: 15 22 17 22 15 27 12 P SD: 0.5922 c. M:-0.9621 c. 217: 25 37 28 37 25 45 20 P SD: 0.5031 c. M:-1.1322 c. 224: 26 38 29 38 26 46 21 SP SD: 0.4770 c. M: 0.7687 c. 270: 31 46 35 46 31 56 25 P SD: 0.4638 c. M: 0.7949 c. 277: 32 47 36 47 32 57 26 SP SD: 0.3653 c. M: 0.9041 c. 354: 41 60 46 60 41 73 33 SP SD: 0.2255 c. M:-0.4104 c. 364: 42 62 47 62 42 75 34 SP SD: 0.2435 c. M:-0.3745 c. 407: 47 69 53 69 47 84 38 SP SD: 0.2615 c. M: 0.4679 c. 441: 51 75 57 75 51 91 41 SP SD: 0.2095 c. M:-0.3745 c. 484: 56 82 63 82 56 100 45 SP SD: 0.2373 c. M: 0.3339 c. 494: 57 84 64 84 57 102 46 SP SD: 0.0592 c. M: 0.1111 c. 848: 98 144 110 144 98 175 79 SP SD: 0.0618 c. M:-0.1066 c. 1342: 155 228 174 228 155 277 125 SP SD: 0.0216 c. M: 0.0422 c. 1836: 212 312 238 312 212 379 171 SP SD: 0.0137 c. M: 0.0334 c. 2330: 269 396 302 396 269 481 217 SP SD: 0.0199 c. M: 0.0319 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: 14.6104 cents 4 x 5 x 6 x x 8 S SD: 14.6104 cents 5 x 6:7 x 8:9:10 S SD: 23.2983 cents 6 x 7:8:9:10:11:12 S SD: 15.9443 cents 7:8 x 9 x 11:13:14 SD: 25.4415 cents 8:9:10:11:12:13:15:16 SD: 13.5738 cents 9:10:11:12:14:15:17:18 SD: 12.7727 cents 10:11:12:13:15:16:19:20 SD: 9.6748 cents 13:14:16:17:20:21:24:26 SD: 9.3367 cents 14:15:17:19:21:23:26:28 SD: 6.3531 cents 22:24:27:29:33:36:41:44 SD: 4.3773 cents 24:26:29:32:36:39:45:48 SD: 2.1229 cents 46:50:56:61:69:75:86:92 SD: 1.9421 cents 50:54:61:67:75:81:94:100 SD: 1.7836 cents 60:65:73:80:90:98:113:120 SD: 1.7269 cents 64:69:78:85:96:104:120:128 SD: 1.5355 cents 72:78:88:96:108:117:135:144 SD: 0.7036 cents 96:104:117:128:144:156:180:192 SD: 0.0000 cents