Scala analysis: xen10-wilson-purvi-09a-05
Purvi modulation 5 from Figure 9a, Hawkins (135/128 16/15 32/27), (32/27 135/128 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: 16/9 996.089998 Pythagorean minor seventh 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: 32/27 294.1350 Pythagorean minor third 6: 135/128 92.1787 major chroma, major limma 7: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 135/128 92.179 cents major chroma, major limma 1: 2 16/15 111.731 cents minor diatonic semitone 1: 1 10/9 182.404 cents minor whole tone 1: 2 9/8 203.910 cents major whole tone 1: 1 32/27 294.135 cents Pythagorean minor third 2: 1 9/8 203.910 cents major whole tone 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 4/3 498.045 cents perfect fourth 3: 1 81/64 407.820 cents Pythagorean major third 3: 4 4/3 498.045 cents perfect fourth 3: 1 45/32 590.224 cents diatonic tritone 3: 1 64/45 609.776 cents 2nd tritone 4: 1 45/32 590.224 cents diatonic tritone 4: 1 64/45 609.776 cents 2nd tritone 4: 4 3/2 701.955 cents perfect fifth 4: 1 128/81 792.180 cents Pythagorean minor sixth 5: 1 3/2 701.955 cents perfect fifth 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 16/9 996.090 cents Pythagorean minor seventh 6: 1 27/16 905.865 cents Pythagorean major sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 2 15/8 1088.269 cents classic major seventh 6: 1 256/135 1107.821 cents octave - major chroma 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 : 203.9 386.3 498.0 702.0 996.1 1088.3 1200.0 203.9 : 182.4 294.1 498.0 792.2 884.4 996.1 1200.0 386.3 : 111.7 315.6 609.8 702.0 813.7 1017.6 1200.0 498.0 : 203.9 498.0 590.2 702.0 905.9 1088.3 1200.0 702.0 : 294.1 386.3 498.0 702.0 884.4 996.1 1200.0 996.1 : 92.2 203.9 407.8 590.2 702.0 905.9 1200.0 1088.3: 111.7 315.6 498.0 609.8 813.7 1107.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 92.1787 .. 294.1350 cents 4096/3645, 201.9563 cents 135/128, 92.1787 cents 2: 203.9100 .. 498.0450 cents 32/27, 294.1350 cents 243/256,-90.2250 cents 3: 407.8200 .. 609.7763 cents 4096/3645, 201.9563 cents 243/256,-90.2250 cents 4: 590.2237 .. 792.1800 cents 4096/3645, 201.9563 cents 2025/2048,-19.5526 cents 5: 701.9550 .. 996.0900 cents 32/27, 294.1350 cents 243/256,-90.2250 cents 6: 905.8650 .. 1107.8213 cents 4096/3645, 201.9563 cents 243/256,-90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 135/128, 92.1787 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 32/27, 294.1350 cents Average / Smallest step : 1.859741 Largest / Average step : 1.715787 Largest / Smallest step : 3.190921 Median interval of one step : 10/9, 182.4037 cents, amount: 1 Least squares average step : 179.91825 cents, oct.: 1259.42774 cents Scale is not proper Step pattern alph. order: ABCADEC Step pattern size order : DCBDEAB Scale is not a Constant Structure Scale diversity : 1.422264 Lumma stability : 0.153631 Lumma impropriety factor : 0.317044 Rothenberg efficiency : 0.540136 redundancy: 0.459864 Efficiency x scale size : 3.780952 Number of different interval sizes : 20 = 3.33333 / 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 : 2048/2025, 19.5526 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 5, average 701.9550 cents Scale contains a complete diamond : 1 3 9 Length of longest harmonic part : 2 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 5 = 71.4286% Scale is differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval classes 3 and 4 combined Scale is differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 5 Odd number limit : 135 (O: 135 U: 135) Highest odd numerator or denominator: 15 Scale harmonicity : 0.041551 Average absolute harmonicity : 0.273725 Specific harmonicity : 0.236920 Fundamental : 1/72, -6.1699 octaves, 3.6337 Hz. Guide tone : 720, 9.4919 octaves, 188370.407 Hz. Exponens Consonantiae : 5.184000E+04, 15.66178 octaves Euler's gradus suavitatis : 20 Sum of Mann's harmonic distance : 44.5, average 6.35714 Mersenne's string divisions : 615825 Sum of van Prooijen's expressibility: 4.73779, average 0.67683 Sum of Tenney's harmonic distance : 9.55427, average 1.36490 Vogel's harmonic complexity : 10.57143 Wille's k value : 67 Wilson's harmonic complexity : 17 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 98.26557, average 3.50948 Lattice compactness (without 2's) : 46.94155, average 1.67648 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 4 -0.28571 16 1 3: -2 .. 2 0.14286 7 4 5: 0 .. 1 0.28571 2 2 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| Scale is weakly epimorphic with val: <7 12 15|
FIT/MODE
7: 1 1 1 1 2 0 1 N T3 SD: 33.9955 c. M: 59.6973 c. 10: 2 1 1 2 2 1 1 P D3 S SD: 23.9553 c. M:-36.0900 c. Pseudo Rast 12: 2 2 1 2 3 1 1 N SD: 7.2028 c. M:-13.6863 c. Mela Naganandini, Raga Nagabharanam, Nupur, Samanta 29: 5 4 3 5 7 2 3 N SD: 7.2647 c. M: 13.8999 c. 31: 5 5 3 5 8 2 3 N SD: 6.4183 c. M:-10.3616 c. 34: 6 5 3 6 8 3 3 N SD: 5.2392 c. M:-7.8547 c. 41: 7 6 4 7 10 3 4 N SD: 3.0430 c. M: 5.8259 c. 53: 9 8 5 9 13 4 5 N SD: 0.7754 c. M: 1.4763 c. 65: 11 10 6 11 16 5 6 N SD: 0.8072 c. M:-1.3786 c. 118: 20 18 11 20 29 9 11 N SD: 0.3185 c. M:-0.5202 c. 289: 49 44 27 49 71 22 27 N SD: 0.3102 c. M:-0.4498 c. 323: 55 49 30 55 79 25 30 N SD: 0.2753 c. M:-0.4244 c. 376: 64 57 35 64 92 29 35 N SD: 0.2137 c. M:-0.3453 c. 388: 66 59 36 66 95 30 36 N SD: 0.2229 c. M:-0.3911 c. 429: 73 65 40 73 105 33 40 N SD: 0.2134 c. M: 0.2997 c. 441: 75 67 41 75 108 34 41 N SD: 0.1242 c. M:-0.1716 c. 494: 84 75 46 84 121 38 46 N SD: 0.0881 c. M:-0.1386 c. 559: 95 85 52 95 137 43 52 N SD: 0.0542 c. M:-0.1034 c. 612: 104 93 57 104 150 47 57 N SD: 0.0207 c. M: 0.0392 c. 1171: 199 178 109 199 287 90 109 N SD: 0.0184 c. M:-0.0319 c. 1783: 303 271 166 303 437 137 166 N SD: 0.0102 c. M:-0.0160 c. 2395: 407 364 223 407 587 184 223 N SD: 0.0095 c. M:-0.0148 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: 37.2438 cents 4 x 5 x 6:7 x 8 S SD: 6.8160 cents 5 x 6:7:8:9 x 10 S SD: 31.6706 cents 6:7 x 8:9 x 11:12 SD: 14.8023 cents 7:8:9 x 11:12:13:14 SD: 19.6120 cents 8:9:10:11:12:14:15:16 S SD: 8.5492 cents 10:11 x 13:15:18:19:20 SD: 11.0845 cents 14:16:18:19:21:25:26:28 SD: 9.4704 cents 15:17:19:20:23:27:28:30 SD: 7.3664 cents 16:18:20:21:24:28:30:32 S SD: 5.5082 cents 23:26:29:31:35:41:43:46 SD: 5.1754 cents 24:27:30:32:36:43:45:48 SD: 1.9247 cents 40:45:50:53:60:71:75:80 SD: 1.5981 cents 48:54:60:64:72:85:90:96 SD: 0.9680 cents 72:81:90:96:108:128:135:144 SD: 0.0000 cents