Scala analysis: xen10-wilson-purvi-09b-03
Purvi modulation 3 from Figure 9b, Hawkins (32/27 16/15 135/128), (16/15 135/128 32/27)
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: 9/8 203.910002 major whole tone 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: 135/128 92.1787 major chroma, major limma 3: 32/27 294.1350 Pythagorean minor third 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: 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 : 111.7 203.9 498.0 702.0 813.7 996.1 1200.0 111.7 : 92.2 386.3 590.2 702.0 884.4 1088.3 1200.0 203.9 : 294.1 498.0 609.8 792.2 996.1 1107.8 1200.0 498.0 : 203.9 315.6 498.0 702.0 813.7 905.9 1200.0 702.0 : 111.7 294.1 498.0 609.8 702.0 996.1 1200.0 813.7 : 182.4 386.3 498.0 590.2 884.4 1088.3 1200.0 996.1 : 203.9 315.6 407.8 702.0 905.9 1017.6 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 : 166.18913 cents, oct.: 1163.32389 cents Scale is not proper Step pattern alph. order: ABCDAED Step pattern size order : BAEDBCD 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 : 1 at degree 0 Length of longest subharmonic part : 2 at degree 5 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 n-1 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 : 0.271009 Specific harmonicity : 0.236920 Fundamental : 1/360, -8.4919 octaves, 0.7267 Hz. Guide tone : 144, 7.1699 octaves, 37674.081 Hz. Exponens Consonantiae : 5.184000E+04, 15.66178 octaves Euler's gradus suavitatis : 20 Sum of Mann's harmonic distance : 50.5, average 7.21429 Mersenne's string divisions : 3596775 Sum of van Prooijen's expressibility: 4.73779, average 0.67683 Sum of Tenney's harmonic distance : 10.15633, average 1.45090 Vogel's harmonic complexity : 13.57143 Wille's k value : 202 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 1.42857 18 1 3: -2 .. 2 -0.14286 7 4 5: -1 .. 0 -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 0 2 1 1 1 1 N T3 SD: 33.9955 c. M:-59.6973 c. 10: 1 1 2 2 1 1 2 P D3 S SD: 23.9553 c. M:-36.0900 c. 12: 1 1 3 2 1 2 2 N SD: 7.2028 c. M: 13.6863 c. Mela Ratnangi, Raga Phenadyuti 29: 3 2 7 5 3 4 5 N SD: 7.2647 c. M:-13.8999 c. 31: 3 2 8 5 3 5 5 N SD: 6.4183 c. M:-10.3616 c. 34: 3 3 8 6 3 5 6 N SD: 5.2392 c. M:-7.8547 c. 41: 4 3 10 7 4 6 7 N SD: 3.0430 c. M:-5.8259 c. 53: 5 4 13 9 5 8 9 N SD: 0.7754 c. M:-1.4763 c. 65: 6 5 16 11 6 10 11 N SD: 0.8072 c. M: 1.3786 c. 118: 11 9 29 20 11 18 20 N SD: 0.3185 c. M:-0.5202 c. 289: 27 22 71 49 27 44 49 N SD: 0.3102 c. M:-0.4498 c. 323: 30 25 79 55 30 49 55 N SD: 0.2753 c. M:-0.4244 c. 376: 35 29 92 64 35 57 64 N SD: 0.2137 c. M:-0.3453 c. 388: 36 30 95 66 36 59 66 N SD: 0.2229 c. M: 0.3911 c. 429: 40 33 105 73 40 65 73 N SD: 0.2134 c. M:-0.2997 c. 441: 41 34 108 75 41 67 75 N SD: 0.1242 c. M:-0.1716 c. 494: 46 38 121 84 46 75 84 N SD: 0.0881 c. M:-0.1386 c. 559: 52 43 137 95 52 85 95 N SD: 0.0542 c. M: 0.1034 c. 612: 57 47 150 104 57 93 104 N SD: 0.0207 c. M:-0.0392 c. 1171: 109 90 287 199 109 178 199 N SD: 0.0184 c. M: 0.0319 c. 1783: 166 137 437 303 166 271 303 N SD: 0.0102 c. M:-0.0160 c. 2395: 223 184 587 407 223 364 407 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: 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: 28.3416 cents 6 x 7:8:9:10:11:12 S SD: 18.1021 cents 7 x 8:9 x 11:12:14 SD: 19.6413 cents 8 x 9:11:12:13:14:16 SD: 10.9313 cents 9 x 10:12 x 14:16:18 S SD: 10.6603 cents 10 x 11:13:15:16:18:20 SD: 10.4048 cents 11:12 x 15:17:18:20:22 SD: 15.5686 cents 12:13:14:16:18:19:21:24 SD: 10.8388 cents 13:14:15:17:20:21:23:26 SD: 10.6818 cents 14:15:16:19:21:22:25:28 SD: 7.5245 cents 15:16:17:20:23:24:27:30 SD: 6.5053 cents 18:19:20:24:27:29:32:36 SD: 4.3675 cents 30:32:34:40:45:48:53:60 SD: 2.3950 cents 42:45:47:56:63:67:75:84 SD: 2.1661 cents 48:51:54:64:72:77:85:96 SD: 1.5125 cents 72:77:81:96:108:115:128:144 SD: 0.7736 cents 90:96:101:120:135:144:160:180 SD: 0.6114 cents 120:128:135:160:180:192:213:240 SD: 0.3867 cents 192:205:216:256:288:307:341:384 SD: 0.3776 cents 210:224:236:280:315:336:373:420 SD: 0.3426 cents 240:256:270:320:360:384:427:480 SD: 0.1931 cents 360:384:405:480:540:576:640:720 SD: 0.0000 cents