Scala analysis: xen10-wilson-purvi-07a-05
Purvi modulation 5 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: 45/26 949.696054 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: 15/13 247.7411 tridecimal 5/4-tone 6: 13/12 138.5727 tridecimal 2/3-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: 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 : 203.9 386.3 498.0 702.0 949.7 1088.3 1200.0 203.9 : 182.4 294.1 498.0 745.8 884.4 996.1 1200.0 386.3 : 111.7 315.6 563.4 702.0 813.7 1017.6 1200.0 498.0 : 203.9 451.7 590.2 702.0 905.9 1088.3 1200.0 702.0 : 247.7 386.3 498.0 702.0 884.4 996.1 1200.0 949.7 : 138.6 250.3 454.2 636.6 748.3 952.3 1200.0 1088.3: 111.7 315.6 498.0 609.8 813.7 1061.4 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 : 178.26132 cents, oct.: 1247.82925 cents Scale is strictly proper Step pattern alph. order: ABCADEC Step pattern size order : DCADEBA 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 : 2 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 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined -- 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 : 0.262513 Specific harmonicity : 0.157864 Fundamental : 1/312, -8.2854 octaves, 0.8385 Hz. Guide tone : 180, 7.4919 octaves, 47092.602 Hz. Exponens Consonantiae : 5.616000E+04, 15.77726 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 67.5, average 9.64286 Mersenne's string divisions : 8744715 Sum of van Prooijen's expressibility: 5.43676, average 0.77668 Sum of Tenney's harmonic distance : 10.46409, average 1.49487 Vogel's harmonic complexity : 20.42857 Wille's k value : 292 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: -3 .. 2 -1.00000 13 1 3: -1 .. 2 0.71429 7 3 5: 0 .. 1 0.42857 3 2 13: -1 .. 0 -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: 2 1 1 1 2 1 1 P M ME S SD: 32.4051 c. M:-62.7567 c. 10: 2 1 1 2 2 1 1 P D3 S SD: 20.0737 c. M:-36.0900 c. Pseudo Rast 12: 2 2 1 2 2 2 1 P M ME S SD: 20.0626 c. M: 49.6961 c. G.Lydian, M.Ionian, M.Hypolydian, Major, Bilaval That, Mela Shankarabharanam, Raga Atana, Ghana Heptatonic, Peruvian Major, Matzore, Rast ascending: Greece, 4th plagal Byzantine, Ararai: Ethiopia, Makam Cargah, Ajam Ashiran, Dastgah-e Mahur, Dastgah-e Rast Panjgah, Xin: China, DS2, Heptatonia prima 15: 3 2 1 3 3 2 1 N SD: 21.5609 c. M:-36.0900 c. 17: 3 2 2 3 3 2 2 SP D3 S SD: 21.0456 c. M: 33.3725 c. Pseudo Rast 18: 3 3 1 3 4 2 2 P SD: 21.2699 c. M: 35.2883 c. 19: 3 3 2 3 4 2 2 P SD: 9.1417 c. M: 14.5845 c. 24: 4 4 2 4 5 3 2 P SD: 7.0505 c. M:-13.6863 c. 34: 6 5 3 6 7 4 3 P SD: 4.4877 c. M:-7.8547 c. 43: 7 7 4 7 9 5 4 P SD: 4.3079 c. M: 8.5612 c. 53: 9 8 5 9 11 6 5 P SD: 0.9060 c. M: 1.4763 c. 130: 22 20 12 22 27 15 12 P SD: 0.8467 c. M:-1.3786 c. 183: 31 28 17 31 38 21 17 P SD: 0.5673 c. M:-1.1236 c. 236: 40 36 22 40 49 27 22 P SD: 0.5022 c. M:-1.1514 c. 258: 44 39 24 44 53 30 24 SP SD: 0.4846 c. M: 0.8588 c. 301: 51 46 28 51 62 35 28 SP SD: 0.4511 c. M: 0.8588 c. 311: 53 47 29 53 64 36 29 SP SD: 0.3809 c. M:-0.5916 c. 335: 57 51 31 57 69 39 31 SP SD: 0.3928 c. M:-0.6865 c. 354: 60 54 33 60 73 41 33 SP SD: 0.3241 c. M: 0.5435 c. 388: 66 59 36 66 80 45 36 SP SD: 0.2226 c. M:-0.3911 c. 441: 75 67 41 75 91 51 41 SP SD: 0.1068 c. M:-0.1716 c. 494: 84 75 46 84 102 57 46 SP SD: 0.0806 c. M:-0.1386 c. 848: 144 129 79 144 175 98 79 SP SD: 0.0925 c. M: 0.1678 c. 901: 153 137 84 153 186 104 84 SP SD: 0.0939 c. M: 0.1444 c. 935: 159 142 87 159 193 108 87 SP SD: 0.0778 c. M:-0.1542 c. 1289: 219 196 120 219 266 149 120 SP SD: 0.0505 c. M: 0.1227 c. 1342: 228 204 125 228 277 155 125 SP SD: 0.0358 c. M: 0.0686 c. 1783: 303 271 166 303 368 206 166 SP SD: 0.0243 c. M: 0.0606 c. 1836: 312 279 171 312 379 212 171 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: 21.7791 cents 4 x 5 x 6:7 x 8 S SD: 4.7825 cents 5 x 6:7:8:9 x 10 S SD: 34.1898 cents 6:7 x 8:9:10:11:12 S SD: 16.4542 cents 7:8:9 x 11:12:13:14 SD: 16.7970 cents 8:9:10:11:12:14:15:16 S SD: 8.0862 cents 10:11 x 13:15:17:19:20 SD: 11.6964 cents 12:14:15:16:18:21:23:24 SD: 10.8589 cents 14:16:18:19:21:24:26:28 SD: 9.6993 cents 15:17:19:20:23:26:28:30 SD: 6.7051 cents 16:18:20:21:24:28:30:32 S SD: 4.7580 cents 24:27:30:32:36:42:45:48 S SD: 2.7328 cents 32:36:40:43:48:55:60:64 SD: 2.5836 cents 40:45:50:53:60:69:75:80 SD: 1.7568 cents 48:54:60:64:72:83:90:96 SD: 0.2291 cents 168:189:210:224:252:291:315:336 SD: 0.1962 cents 216:243:270:288:324:374:405:432 SD: 0.1018 cents 264:297:330:352:396:457:495:528 SD: 0.0416 cents 312:351:390:416:468:540:585:624 SD: 0.0000 cents