Scala analysis: xen10-wilson-purvi-07c-04
Purvi modulation 4 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: 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: 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: 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: 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: 1 52/45 250.304 cents 2: 1 6/5 315.641 cents minor third 2: 1 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 2: 2 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: 2 13/8 840.528 cents tridecimal neutral sixth 5: 1 64/39 857.517 cents 39th subharmonic 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 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 : 138.6 386.3 498.0 702.0 840.5 1088.3 1200.0 138.6 : 247.7 359.5 563.4 702.0 949.7 1061.4 1200.0 386.3 : 111.7 315.6 454.2 702.0 813.7 952.3 1200.0 498.0 : 203.9 342.5 590.2 702.0 840.5 1088.3 1200.0 702.0 : 138.6 386.3 498.0 636.6 884.4 996.1 1200.0 840.5 : 247.7 359.5 498.0 745.8 857.5 1061.4 1200.0 1088.3: 111.7 250.3 498.0 609.8 813.7 952.3 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: 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 : 13/12, 138.5727 cents, amount: 2 Least squares average step : 173.89575 cents, oct.: 1217.27028 cents Scale is strictly proper Step pattern alph. order: ABCDABC Step pattern size order : BDACBDA Scale is a Constant Structure, by a margin of 2.56289 cents Scale diversity : 1.523872 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.319951 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 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 differentially coherent in interval class 1 Scale is 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 : 45 (O: 45 U: 45) Highest odd numerator or denominator: 15 Scale harmonicity : 0.025715 Average absolute harmonicity : 0.252282 Specific harmonicity : 0.136563 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 : 46.5, average 6.64286 Mersenne's string divisions : 36225 Sum of van Prooijen's expressibility: 5.05719, average 0.72246 Sum of Tenney's harmonic distance : 9.74873, average 1.39268 Vogel's harmonic complexity : 10.00000 Wille's k value : 22 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 76.49178, average 2.73185 Lattice compactness (without 2's) : 37.11365, average 1.32549 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -1.14286 14 1 3: -1 .. 1 0.00000 4 2 5: 0 .. 1 0.28571 2 2 13: 0 .. 1 0.28571 2 2 Average exponent except 2's : 4 / 7 = 0.57143 Average absolute exponent except 2's: 8 / 7 = 1.14286 Scale is weakly epimorphic with val: <7 11 15 27| Scale is JI-epimorphic with val: <7 11 16 26| = patent Scale is weakly epimorphic with val: <7 12 17 25|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 32.3714 c. M: 59.6973 c. Lebeng 9: 1 2 1 1 1 2 1 P M ME I SD: 26.2255 c. M: 40.5277 c. 10: 1 2 1 2 1 2 1 P M ME I SD: 15.8441 c. M: 26.3137 c. 19: 2 4 2 3 2 4 2 P T3 I SD: 11.3432 c. M: 19.4750 c. 24: 3 5 2 4 3 5 2 P SD: 8.8873 c. M:-13.6863 c. Athanasopoulos' Byzantine Liturgical Chromatic, Dastgah-e Chahargah 31: 4 6 3 5 4 6 3 SP SD: 8.1161 c. M:-16.2660 c. 34: 4 7 3 6 4 7 3 P SD: 4.1090 c. M:-6.5312 c. 43: 5 9 4 7 5 9 4 P SD: 3.1125 c. M:-4.3840 c. 53: 6 11 5 9 6 11 5 P SD: 1.6641 c. M: 2.7918 c. 87: 10 18 8 15 10 18 8 P SD: 1.0372 c. M: 1.4933 c. 130: 15 27 12 22 15 27 12 P SD: 0.7034 c. M:-1.3786 c. 183: 21 38 17 31 21 38 17 P SD: 0.6262 c. M: 1.1834 c. 217: 25 45 20 37 25 45 20 P SD: 0.5662 c. M:-1.1322 c. 224: 26 46 21 38 26 46 21 SP SD: 0.5087 c. M: 0.7687 c. 270: 31 56 25 46 31 56 25 P SD: 0.4724 c. M: 0.7949 c. 277: 32 57 26 47 32 57 26 SP SD: 0.4540 c. M: 0.9041 c. 311: 36 64 29 53 36 64 29 SP SD: 0.3633 c. M:-0.6299 c. 354: 41 73 33 60 41 73 33 SP SD: 0.2268 c. M:-0.4104 c. 407: 47 84 38 69 47 84 38 SP SD: 0.1946 c. M: 0.3080 c. 441: 51 91 41 75 51 91 41 SP SD: 0.1574 c. M:-0.2887 c. 494: 57 102 46 84 57 102 46 SP SD: 0.0655 c. M: 0.1111 c. 848: 98 175 79 144 98 175 79 SP SD: 0.0609 c. M:-0.1066 c. 1342: 155 277 125 228 155 277 125 SP SD: 0.0232 c. M: 0.0422 c. 1836: 212 379 171 312 212 379 171 SP SD: 0.0202 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 x x 8:9:10:11:12 S SD: 11.7215 cents 7:8:9 x x 11:13:14 SD: 24.1629 cents 8:9:10:11:12:13:15:16 SD: 12.0433 cents 10:11 x 13:15:16:19:20 SD: 10.3629 cents 12:13:15:16:18:20:23:24 SD: 8.2919 cents 16:17:20:21:24:26:30:32 SD: 6.1833 cents 21:23:26:28:32:34:39:42 SD: 5.8739 cents 23:25:29:31:35:37:43:46 SD: 5.6405 cents 24:26:30:32:36:39:45:48 SD: 0.0000 cents