Scala analysis: xen10-wilson-purvi-07a-03
Purvi modulation 3 from Figure 7a, Kathleen Schlesinger (13/12 16/15 15/13), (15/13 13/12 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: 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: 9/8 203.9100 major whole tone 2: 13/12 138.5727 tridecimal 2/3-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 32/27 294.135 cents Pythagorean minor third 2: 1 6/5 315.641 cents minor third 2: 2 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 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: 2 13/8 840.528 cents tridecimal neutral sixth 5: 2 64/39 857.517 cents 39th subharmonic 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 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: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 342.5 498.0 702.0 840.5 1088.3 1200.0 203.9 : 138.6 294.1 498.0 636.6 884.4 996.1 1200.0 342.5 : 155.6 359.5 498.0 745.8 857.5 1061.4 1200.0 498.0 : 203.9 342.5 590.2 702.0 905.9 1044.4 1200.0 702.0 : 138.6 386.3 498.0 702.0 840.5 996.1 1200.0 840.5 : 247.7 359.5 563.4 702.0 857.5 1061.4 1200.0 1088.3: 111.7 315.6 454.2 609.8 813.7 952.3 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: 294.1350 .. 386.3137 cents 135/128, 92.1787 cents 416/405, 46.3939 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 .. 905.8650 cents 135/128, 92.1787 cents 26/25, 67.9002 cents 6: 952.2589 .. 1088.2687 cents 225/208, 136.0098 cents 416/405, 46.3939 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 : 173.73629 cents, oct.: 1216.15405 cents Scale is strictly proper Step pattern alph. order: ABCABDE Step pattern size order : DBCDBEA Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.571781 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.393003 Rothenberg efficiency : 0.408163 redundancy: 0.591837 Efficiency x scale size : 2.857143 Number of different interval sizes : 28 = 4.66667 / 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 : 512/507, 16.9897 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 differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined Limited inverse transpositions with margin 136.0098 cents: 4 -- Rational properties -- Prime limit : 13 Odd number limit : 117 (O: 117 U: 117) Highest odd numerator or denominator: 39 Scale harmonicity : 0.022960 Average absolute harmonicity : 0.251882 Specific harmonicity : 0.135983 Fundamental : 1/96, -6.5850 octaves, 2.7253 Hz. Guide tone : 2340, 11.1923 octaves, 612203.823 Hz. Exponens Consonantiae : 2.246400E+05, 17.77726 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 73.5, average 10.50000 Mersenne's string divisions : 2914905 Sum of van Prooijen's expressibility: 5.78958, average 0.82708 Sum of Tenney's harmonic distance : 11.20812, average 1.60116 Vogel's harmonic complexity : 12.42857 Wille's k value : 58 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 93.60393, average 3.34300 Lattice compactness (without 2's) : 40.16818, average 1.43458 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 2 -1.71429 18 1 3: -1 .. 2 0.57143 6 3 5: 0 .. 1 0.14286 1 1 13: 0 .. 1 0.28571 2 2 Average exponent except 2's : 7 / 7 = 1.00000 Average absolute exponent except 2's: 9 / 7 = 1.28571 Scale is JI-epimorphic with val: <7 11 16 26| = patent Scale is weakly epimorphic with val: <7 12 17 27|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 27.8325 c. M: 59.6973 c. Lebeng 10: 2 1 1 2 1 2 1 P M ME S SD: 18.2414 c. M:-36.0900 c. Sethares Neutral, Beatles-7, Dichotic-7 14: 2 2 2 2 2 3 1 P T3 SD: 19.0325 c. M: 32.4814 c. 17: 3 2 2 3 2 3 2 SP M ME S SD: 12.6016 c. M: 29.4452 c. Beatles-7, Dichotic-7 19: 3 2 3 3 2 4 2 SP D3 SD: 15.1993 c. M: 26.6932 c. Nineteen-tone Harmonic Minor 20: 3 3 2 4 2 4 2 P D3 S SD: 15.1112 c. M: 23.9100 c. 21: 4 2 3 3 3 4 2 SP T3 SD: 14.2350 c. M:-24.6614 c. 22: 4 2 3 4 2 5 2 P SD: 12.2076 c. M: 22.3458 c. Twenty-two tone Harmonic Minor 24: 4 3 3 4 3 5 2 P SD: 6.6202 c. M:-11.7313 c. 31: 5 4 4 5 4 6 3 SP SD: 6.9501 c. M:-11.0852 c. 34: 6 4 4 6 4 7 3 P SD: 6.3109 c. M:-10.4585 c. 41: 7 5 5 7 5 8 4 SP SD: 4.9912 c. M:-8.7368 c. 43: 7 5 6 7 5 9 4 SP SD: 5.0527 c. M: 8.5612 c. 46: 8 5 6 8 5 10 4 P SD: 4.3607 c. M:-7.3835 c. 53: 9 6 7 9 6 11 5 SP SD: 1.6116 c. M: 2.8600 c. 77: 13 9 10 13 9 16 7 SP SD: 1.2397 c. M:-2.6404 c. 130: 22 15 17 22 15 27 12 SP SD: 0.6694 c. M:-0.9621 c. 217: 37 25 28 37 25 45 20 SP SD: 0.5547 c. M:-1.1322 c. 224: 38 26 29 38 26 46 21 SP SD: 0.4138 c. M: 0.7687 c. 270: 46 31 35 46 31 56 25 SP SD: 0.4070 c. M:-0.6202 c. 277: 47 32 36 47 32 57 26 SP SD: 0.3819 c. M: 0.9041 c. 354: 60 41 46 60 41 73 33 SP SD: 0.2559 c. M: 0.5202 c. 364: 62 42 47 62 42 75 34 SP SD: 0.3020 c. M:-0.4856 c. 407: 69 47 53 69 47 84 38 SP SD: 0.3162 c. M: 0.4702 c. 417: 71 48 54 71 48 86 39 SP SD: 0.2818 c. M: 0.4989 c. 441: 75 51 57 75 51 91 41 SP SD: 0.2055 c. M:-0.3745 c. 494: 84 57 64 84 57 102 46 SP SD: 0.0670 c. M:-0.1386 c. 848: 144 98 110 144 98 175 79 SP SD: 0.0697 c. M: 0.1364 c. 1065: 181 123 138 181 123 220 99 SP SD: 0.0745 c. M:-0.1820 c. 1118: 190 129 145 190 129 231 104 SP SD: 0.0640 c. M:-0.1034 c. 1289: 219 149 167 219 149 266 120 SP SD: 0.0642 c. M:-0.1240 c. 1342: 228 155 174 228 155 277 125 SP SD: 0.0233 c. M: 0.0422 c. 1836: 312 212 238 312 212 379 171 SP SD: 0.0138 c. M: 0.0334 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 6:7 x 8:9:10:11:12 S SD: 14.3361 cents 7:8 x 9 x 11:13:14 SD: 18.2757 cents 8:9:10:11:12:13:15:16 SD: 9.8552 cents 14:16:17:19:21:23:26:28 SD: 6.9328 cents 18:20:22:24:27:29:34:36 SD: 4.2158 cents 24:27:29:32:36:39:45:48 SD: 2.1229 cents 32:36:39:43:48:52:60:64 SD: 1.9247 cents 54:61:66:72:81:88:101:108 SD: 1.5478 cents 56:63:68:75:84:91:105:112 SD: 1.4274 cents 64:72:78:85:96:104:120:128 SD: 0.9680 cents 72:81:88:96:108:117:135:144 SD: 0.7036 cents 96:108:117:128:144:156:180:192 SD: 0.0000 cents