Scala analysis: xen10-wilson-purvi-07c-05
Purvi modulation 5 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: 5/4 386.313714 major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 5/3 884.358713 major sixth, BP 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: 15/13 247.7411 tridecimal 5/4-tone 3: 16/15 111.7313 minor diatonic semitone 4: 9/8 203.9100 major whole tone 5: 10/9 182.4037 minor whole tone 6: 9/8 203.9100 major whole 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 52/45 250.304 cents 2: 2 6/5 315.641 cents minor third 2: 1 16/13 359.472 cents tridecimal neutral third 2: 3 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: 3 8/5 813.686 cents minor sixth 5: 1 13/8 840.528 cents tridecimal neutral sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 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 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: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 138.6 386.3 498.0 702.0 884.4 1088.3 1200.0 138.6 : 247.7 359.5 563.4 745.8 949.7 1061.4 1200.0 386.3 : 111.7 315.6 498.0 702.0 813.7 952.3 1200.0 498.0 : 203.9 386.3 590.2 702.0 840.5 1088.3 1200.0 702.0 : 182.4 386.3 498.0 636.6 884.4 996.1 1200.0 884.4 : 203.9 315.6 454.2 702.0 813.7 1017.6 1200.0 1088.3: 111.7 250.3 498.0 609.8 813.7 996.1 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 : 10/9, 182.4037 cents, amount: 1 Least squares average step : 175.46115 cents, oct.: 1228.22805 cents Scale is strictly proper Step pattern alph. order: ABCDEDC Step pattern size order : BEADCDA Scale is a Constant Structure, by a margin of 2.56289 cents Scale diversity : 1.537528 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 : 2 at degree 3 Length of longest subharmonic part : 2 at degree 4 Formal octave complements present : 3 = 42.8571% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 Scale is differentially coherent in interval class 3 -- Rational properties -- Prime limit : 13 Odd number limit : 45 (O: 45 U: 45) Highest odd numerator or denominator: 15 Scale harmonicity : 0.025715 Average absolute harmonicity : 0.262358 Specific harmonicity : 0.168387 Fundamental : 1/24, -4.5850 octaves, 10.9011 Hz. Guide tone : 780, 9.6073 octaves, 204067.941 Hz. Exponens Consonantiae : 1.872000E+04, 14.19229 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 40.0, average 5.71429 Mersenne's string divisions : 289800 Sum of van Prooijen's expressibility: 4.64222, average 0.66317 Sum of Tenney's harmonic distance : 8.90779, average 1.27254 Vogel's harmonic complexity : 8.85714 Wille's k value : 22 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 72.80537, average 2.60019 Lattice compactness (without 2's) : 38.61767, average 1.37920 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.71429 11 1 3: -1 .. 1 -0.14286 5 2 5: 0 .. 1 0.42857 3 3 13: 0 .. 1 0.14286 1 1 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 9 / 7 = 1.28571 Scale is weakly epimorphic with val: <7 10 16 25| 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: 33.3809 c. M: 59.6973 c. Lebeng 9: 1 2 1 1 2 1 1 P M ME S SD: 28.2096 c. M:-48.9746 c. Pelog Saptanada: Sunda 10: 1 2 1 2 1 2 1 P M ME I SD: 23.0672 c. M: 44.3587 c. 12: 1 3 1 2 2 2 1 N T3 SD: 17.1759 c. M: 38.5727 c. Mela Suryakanta, Bhairubahar That, Raga Supradhipam, Sowrashtram (Sourashtra), Jaganmohini, Major-Melodic Phrygian, Hungarian Gipsy inverse 15: 2 3 1 3 2 3 1 N T3 SD: 18.2192 c. M:-31.7313 c. 19: 2 4 2 3 3 3 2 P T3 SD: 8.6307 c. M: 14.5845 c. 24: 3 5 2 4 4 4 2 P SD: 10.0557 c. M:-15.6413 c. 31: 4 6 3 5 5 5 3 SP SD: 7.3074 c. M:-16.2660 c. 33: 4 7 3 5 5 6 3 P SD: 9.4185 c. M:-13.6863 c. 34: 4 7 3 6 5 6 3 P SD: 3.3712 c. M:-5.8489 c. 53: 6 11 5 9 8 9 5 P SD: 1.3828 c. M: 2.7236 c. 87: 10 18 8 15 13 15 8 P SD: 1.1567 c. M: 1.6001 c. 130: 15 27 12 22 20 22 12 P SD: 0.9568 c. M:-1.7951 c. 140: 16 29 13 24 21 24 13 P SD: 0.9545 c. M: 1.5016 c. 171: 20 35 16 29 26 29 16 SP SD: 0.7259 c. M:-1.7782 c. 183: 21 38 17 31 28 31 17 P SD: 0.5518 c. M:-0.8872 c. 217: 25 45 20 37 33 37 20 P SD: 0.5894 c. M:-1.1322 c. 224: 26 46 21 38 34 38 21 SP SD: 0.4930 c. M: 0.7687 c. 258: 30 53 24 44 39 44 24 SP SD: 0.4913 c. M:-0.9622 c. 270: 31 56 25 46 41 46 25 P SD: 0.4295 c. M: 0.7949 c. 277: 32 57 26 47 42 47 26 SP SD: 0.5070 c. M: 0.9041 c. 301: 35 62 28 51 46 51 28 SP SD: 0.4992 c. M:-0.9622 c. 311: 36 64 29 53 47 53 29 SP SD: 0.3966 c. M: 0.7574 c. 354: 41 73 33 60 54 60 33 SP SD: 0.2639 c. M:-0.4104 c. 388: 45 80 36 66 59 66 36 SP SD: 0.3050 c. M:-0.6026 c. 407: 47 84 38 69 62 69 38 SP SD: 0.1840 c. M: 0.3080 c. 441: 51 91 41 75 67 75 41 SP SD: 0.1135 c. M:-0.2028 c. 494: 57 102 46 84 75 84 46 SP SD: 0.0847 c. M: 0.1482 c. 848: 98 175 79 144 129 144 79 SP SD: 0.0656 c. M:-0.1066 c. 901: 104 186 84 153 137 153 84 SP SD: 0.0752 c. M: 0.1444 c. 935: 108 193 87 159 142 159 87 SP SD: 0.0600 c. M: 0.0806 c. 1289: 149 266 120 219 196 219 120 SP SD: 0.0580 c. M:-0.1395 c. 1342: 155 277 125 228 204 228 125 SP SD: 0.0232 c. M: 0.0422 c. 1836: 212 379 171 312 279 312 171 SP SD: 0.0263 c. M: 0.0450 c. 2277: 263 470 212 387 346 387 212 SP SD: 0.0224 c. M: 0.0372 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: 0.0000 cents 4 x 5 x 6:7 x 8 S SD: 21.1168 cents 5 x 6:7 x 8:9:10 S SD: 29.7446 cents 6 x x 8:9:10:11:12 S SD: 7.7812 cents 7:8:9 x 11:12:13:14 SD: 23.6248 cents 8:9:10:11:12:13:15:16 SD: 13.5738 cents 9:10:11:12:14:15:17:18 SD: 12.4229 cents 10:11 x 13:15:17:19:20 SD: 10.9556 cents 12:13:15:16:18:20:23:24 SD: 5.4358 cents 24:26:30:32:36:40:45:48 SD: 0.0000 cents