Scala analysis: xen10-wilson-purvi-07b-03
Purvi modulation 3 from Figure 7b, Kathleen Schlesinger (15/13 16/15 13/12), (16/15 13/12 15/13)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 16/15 111.731285 minor diatonic semitone 2: 52/45 250.303946 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 8/5 813.686286 minor sixth 6: 16/9 996.089998 Pythagorean minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 16/15 111.7313 minor diatonic semitone 2: 13/12 138.5727 tridecimal 2/3-tone 3: 15/13 247.7411 tridecimal 5/4-tone 4: 9/8 203.9100 major whole tone 5: 16/15 111.7313 minor diatonic semitone 6: 10/9 182.4037 minor whole tone 7: 9/8 203.9100 major whole tone
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: 1 32/27 294.135 cents Pythagorean minor third 2: 2 6/5 315.641 cents minor third 2: 2 5/4 386.314 cents major third 2: 1 135/104 451.651 cents 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: 1 208/135 748.349 cents 5: 2 8/5 813.686 cents minor sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 1 27/16 905.865 cents Pythagorean major 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: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 111.7 250.3 498.0 702.0 813.7 996.1 1200.0 111.7 : 138.6 386.3 590.2 702.0 884.4 1088.3 1200.0 250.3 : 247.7 451.7 563.4 745.8 949.7 1061.4 1200.0 498.0 : 203.9 315.6 498.0 702.0 813.7 952.3 1200.0 702.0 : 111.7 294.1 498.0 609.8 748.3 996.1 1200.0 813.7 : 182.4 386.3 498.0 636.6 884.4 1088.3 1200.0 996.1 : 203.9 315.6 454.2 702.0 905.9 1017.6 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 .. 451.6511 cents 6075/5408, 201.3471 cents 676/675, 2.5629 cents 3: 454.2139 .. 590.2237 cents 225/208, 136.0098 cents 676/675, 2.5629 cents 4: 609.7763 .. 745.7861 cents 225/208, 136.0098 cents 2048/2025, 19.5526 cents 5: 748.3489 .. 949.6961 cents 6075/5408, 201.3471 cents 676/675, 2.5629 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 : 166.85190 cents, oct.: 1167.96328 cents Scale is strictly proper Step pattern alph. order: ABCDAED Step pattern size order : ABEDACD Scale is a Constant Structure, by a margin of 2.56289 cents Scale diversity : 1.535644 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.211056 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 : 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 Scale contains a complete diamond : 1 3 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 5 Formal octave complements present : 3 = 42.8571% Scale is n-1 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 : 135 (O: 135 U: 135) Highest odd numerator or denominator: 45 Scale harmonicity : 0.024065 Average absolute harmonicity : 0.257847 Specific harmonicity : 0.157864 Fundamental : 1/90, -6.4919 octaves, 2.9070 Hz. Guide tone : 624, 9.2854 octaves, 163254.353 Hz. Exponens Consonantiae : 5.616000E+04, 15.77726 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 90.5, average 12.92857 Mersenne's string divisions : 20522775 Sum of van Prooijen's expressibility: 5.43676, average 0.77668 Sum of Tenney's harmonic distance : 11.66821, average 1.66689 Vogel's harmonic complexity : 11.71429 Wille's k value : 67 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 79.33502, average 2.83339 Lattice compactness (without 2's) : 44.55535, average 1.59126 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 2.14286 17 1 3: -2 .. 1 -0.71429 7 3 5: -1 .. 0 -0.42857 3 2 13: 0 .. 1 0.14286 1 1 Average exponent except 2's :-7 / 7 =-1.00000 Average absolute exponent except 2's: 11 / 7 = 1.57143 Scale is weakly epimorphic with val: <7 10 16 28| Scale is JI-epimorphic with val: <7 11 16 26| = patent Scale is weakly epimorphic with val: <7 12 15 28|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 47.2091 c. M:-92.5532 c. Lebeng 9: 1 1 2 1 1 1 2 P M ME S SD: 32.4051 c. M: 62.7567 c. Pseudo Pelog, Pelogic-7, Antiionian 10: 1 1 2 2 1 1 2 P D3 S SD: 20.0737 c. M: 36.0900 c. 12: 1 2 2 2 1 2 2 P M ME S SD: 20.0626 c. M:-49.6961 c. G.Dorian, M.Phrygian, G.M.Hypoaeolian, Bhairavi That, Mela Hanumatodi, Raga Asavari (Asaveri), Bilashkhani Todi, Ghanta, Makam Kurd, Gregorian nr.3, In, Zokuso: Japan, Ousak: Greece, Major inverse 15: 1 2 3 3 1 2 3 N SD: 21.5609 c. M: 36.0900 c. 17: 2 2 3 3 2 2 3 SP D3 S SD: 21.0456 c. M:-33.3725 c. 19: 2 2 4 3 2 3 3 P SD: 9.1417 c. M:-14.5845 c. 24: 2 3 5 4 2 4 4 P SD: 7.0505 c. M: 13.6863 c. 34: 3 4 7 6 3 5 6 P SD: 4.4877 c. M: 7.8547 c. 43: 4 5 9 7 4 7 7 P SD: 4.3079 c. M:-8.5612 c. 53: 5 6 11 9 5 8 9 P SD: 0.9060 c. M:-1.4763 c. 130: 12 15 27 22 12 20 22 P SD: 0.8467 c. M: 1.3786 c. 183: 17 21 38 31 17 28 31 P SD: 0.5673 c. M: 1.1236 c. 236: 22 27 49 40 22 36 40 P SD: 0.5022 c. M: 1.1514 c. 258: 24 30 53 44 24 39 44 SP SD: 0.4846 c. M:-0.8588 c. 301: 28 35 62 51 28 46 51 SP SD: 0.4511 c. M:-0.8588 c. 311: 29 36 64 53 29 47 53 SP SD: 0.3809 c. M: 0.5916 c. 335: 31 39 69 57 31 51 57 SP SD: 0.3928 c. M: 0.6865 c. 354: 33 41 73 60 33 54 60 SP SD: 0.3241 c. M:-0.5435 c. 388: 36 45 80 66 36 59 66 SP SD: 0.2226 c. M: 0.3911 c. 441: 41 51 91 75 41 67 75 SP SD: 0.1068 c. M: 0.1716 c. 494: 46 57 102 84 46 75 84 SP SD: 0.0806 c. M: 0.1386 c. 848: 79 98 175 144 79 129 144 SP SD: 0.0925 c. M:-0.1678 c. 901: 84 104 186 153 84 137 153 SP SD: 0.0939 c. M:-0.1444 c. 935: 87 108 193 159 87 142 159 SP SD: 0.0778 c. M: 0.1542 c. 1289: 120 149 266 219 120 196 219 SP SD: 0.0505 c. M:-0.1227 c. 1342: 125 155 277 228 125 204 228 SP SD: 0.0358 c. M:-0.0686 c. 1783: 166 206 368 303 166 271 303 SP SD: 0.0243 c. M:-0.0606 c. 1836: 171 212 379 312 171 279 312 SP SD: 0.0220 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: 23.5575 cents 4 x x 5:6 x 7:8 S SD: 28.7524 cents 5 x 6:7 x 8:9:10 S SD: 21.7864 cents 6 x 7:8:9:10:11:12 S SD: 15.0065 cents 7 x 8:9 x 11:12:14 SD: 19.2532 cents 8 x 9:11:12:13:14:16 SD: 13.3897 cents 9 x 10:12 x 14:16:18 S SD: 16.7200 cents 10:11:12:13:15:16:18:20 SD: 13.9171 cents 12:13:14:16:18:19:21:24 SD: 6.4947 cents 18:19:21:24:27:29:32:36 SD: 3.9035 cents 30:32:35:40:45:48:53:60 SD: 2.8294 cents 32:34:37:43:48:51:57:64 SD: 2.4152 cents 44:47:51:59:66:70:78:88 SD: 2.2668 cents 45:48:52:60:68:72:80:90 SD: 1.8252 cents 58:62:67:77:87:93:103:116 SD: 1.3365 cents 72:77:83:96:108:115:128:144 SD: 0.9761 cents 90:96:104:120:135:144:160:180 SD: 0.0000 cents