Scala analysis: xen10-wilson-purvi-07a-04
Purvi modulation 4 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: 5/4 386.313714 major third 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: 10/9 182.4037 minor whole tone 3: 16/15 111.7313 minor diatonic semitone 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: 2 16/15 111.731 cents minor diatonic semitone 1: 1 13/12 138.573 cents tridecimal 2/3-tone 1: 1 10/9 182.404 cents minor whole tone 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: 2 6/5 315.641 cents minor third 2: 1 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 2: 1 16/13 359.472 cents tridecimal neutral third 2: 2 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: 2 8/5 813.686 cents minor sixth 5: 1 13/8 840.528 cents tridecimal neutral sixth 5: 1 64/39 857.517 cents 39th subharmonic 5: 2 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 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 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: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 386.3 498.0 702.0 840.5 1088.3 1200.0 203.9 : 182.4 294.1 498.0 636.6 884.4 996.1 1200.0 386.3 : 111.7 315.6 454.2 702.0 813.7 1017.6 1200.0 498.0 : 203.9 342.5 590.2 702.0 905.9 1088.3 1200.0 702.0 : 138.6 386.3 498.0 702.0 884.4 996.1 1200.0 840.5 : 247.7 359.5 563.4 745.8 857.5 1061.4 1200.0 1088.3: 111.7 315.6 498.0 609.8 813.7 952.3 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 : 10/9, 182.4037 cents, amount: 1 Least squares average step : 174.36245 cents, oct.: 1220.53715 cents Scale is strictly proper Step pattern alph. order: ABCADEC Step pattern size order : DCADBEA Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.575480 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 : 2 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% Scale is 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 Scale is n-1 differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 13 Odd number limit : 45 (O: 45 U: 45) Highest odd numerator or denominator: 15 Scale harmonicity : 0.024065 Average absolute harmonicity : 0.264098 Specific harmonicity : 0.171026 Fundamental : 1/24, -4.5850 octaves, 10.9011 Hz. Guide tone : 2340, 11.1923 octaves, 612203.823 Hz. Exponens Consonantiae : 5.616000E+04, 15.77726 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 42.5, average 6.07143 Mersenne's string divisions : 123165 Sum of van Prooijen's expressibility: 4.89749, average 0.69964 Sum of Tenney's harmonic distance : 9.41294, average 1.34471 Vogel's harmonic complexity : 9.28571 Wille's k value : 22 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 80.60553, average 2.87877 Lattice compactness (without 2's) : 39.75396, average 1.41978 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -1.28571 15 1 3: -1 .. 2 0.42857 5 3 5: 0 .. 1 0.28571 2 2 13: 0 .. 1 0.14286 1 1 Average exponent except 2's : 6 / 7 = 0.85714 Average absolute exponent except 2's: 8 / 7 = 1.14286 Scale is weakly epimorphic with val: <7 10 16 29| Scale is JI-epimorphic with val: <7 11 16 26| = patent Scale is weakly epimorphic with val: <7 12 15 25|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 32.3173 c. M: 59.6973 c. Lebeng 10: 2 1 1 2 1 2 1 P M ME S SD: 19.6933 c. M:-36.0900 c. Sethares Neutral, Beatles-7, Dichotic-7 12: 2 2 1 2 1 3 1 P D3 SD: 16.8623 c. M: 40.5277 c. Harmonic Major, Mischung 2, Mela Sarasangi, Raga Anand Leela, Haripriya, Nat Bhairav, Simhavahini, Ethiopian, Tabahaniotikos: Greece 17: 3 2 2 3 2 3 2 SP M ME S SD: 17.3861 c. M: 33.3725 c. Beatles-7, Dichotic-7 19: 3 3 2 3 2 4 2 SP D3 SD: 11.7038 c. M: 19.4750 c. Nineteen-tone Harmonic Major 22: 4 3 2 4 2 5 2 P SD: 10.9025 c. M: 22.3458 c. Twenty-two tone Harmonic Major 24: 4 4 2 4 3 5 2 P SD: 7.9066 c. M:-13.6863 c. 31: 5 5 3 5 4 6 3 SP SD: 6.5887 c. M:-11.0852 c. 34: 6 5 3 6 4 7 3 P SD: 4.9728 c. M:-7.8547 c. 41: 7 6 4 7 5 8 4 SP SD: 4.3423 c. M:-8.2528 c. 46: 8 7 4 8 5 10 4 P SD: 4.5792 c. M:-7.3835 c. 53: 9 8 5 9 6 11 5 SP SD: 1.3084 c. M: 2.7918 c. 130: 22 20 12 22 15 27 12 SP SD: 0.7696 c. M:-1.3786 c. 171: 29 26 16 29 20 35 16 SP SD: 0.6712 c. M:-1.5776 c. 183: 31 28 17 31 21 38 17 SP SD: 0.5844 c. M: 1.1834 c. 217: 37 33 20 37 25 45 20 SP SD: 0.6126 c. M:-1.1322 c. 224: 38 34 21 38 26 46 21 SP SD: 0.4501 c. M: 0.7687 c. 270: 46 41 25 46 31 56 25 SP SD: 0.4168 c. M:-0.6202 c. 277: 47 42 26 47 32 57 26 SP SD: 0.4675 c. M: 0.9041 c. 301: 51 46 28 51 35 62 28 SP SD: 0.4024 c. M:-0.6684 c. 354: 60 54 33 60 41 73 33 SP SD: 0.2570 c. M: 0.5202 c. 407: 69 62 38 69 47 84 38 SP SD: 0.2635 c. M: 0.4702 c. 441: 75 67 41 75 51 91 41 SP SD: 0.1520 c. M:-0.2887 c. 494: 84 75 46 84 57 102 46 SP SD: 0.0726 c. M:-0.1386 c. 848: 144 129 79 144 98 175 79 SP SD: 0.0688 c. M: 0.1364 c. 1118: 190 170 104 190 129 231 104 SP SD: 0.0650 c. M:-0.1034 c. 1289: 219 196 120 219 149 266 120 SP SD: 0.0509 c. M:-0.1240 c. 1342: 228 204 125 228 155 277 125 SP SD: 0.0248 c. M: 0.0422 c. 1836: 312 279 171 312 212 379 171 SP SD: 0.0203 c. M: 0.0392 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: 0.0000 cents 5 x 6:7 x 8:9:10 S SD: 26.7165 cents 6:7 x 8:9:10:11:12 S SD: 14.3361 cents 7:8:9 x x 11:13:14 SD: 16.4493 cents 8:9:10:11:12:13:15:16 SD: 7.6104 cents 10:11 x 13:15:16:19:20 SD: 11.4031 cents 14:16:18:19:21:23:26:28 SD: 9.7868 cents 15:17:19:20:23:24:28:30 SD: 7.7154 cents 16:18:20:21:24:26:30:32 SD: 3.8949 cents 24:27:30:32:36:39:45:48 SD: 0.0000 cents