Scala analysis: xen10-wilson-purvi-09a-01
Purvi modulation 1 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: 1215/1024 296.088718 wide augmented second 3: 81/64 407.820003 Pythagorean major third 4: 3/2 701.955001 perfect fifth 5: 405/256 794.133717 wide augmented fifth 6: 27/16 905.865003 Pythagorean major sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 32/27 294.1350 Pythagorean minor third 1: 9/8 203.9100 major whole tone 2: 135/128 92.1787 major chroma, major limma 3: 16/15 111.7313 minor diatonic semitone 4: 32/27 294.1350 Pythagorean minor third 5: 135/128 92.1787 major chroma, major limma 6: 16/15 111.7313 minor diatonic semitone 7: 32/27 294.1350 Pythagorean minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 135/128 92.179 cents major chroma, major limma 1: 2 16/15 111.731 cents minor diatonic semitone 1: 1 9/8 203.910 cents major whole tone 1: 2 32/27 294.135 cents Pythagorean minor third 2: 2 9/8 203.910 cents major whole tone 2: 1 1215/1024 296.089 cents wide augmented second 2: 1 5/4 386.314 cents major third 2: 2 512/405 405.866 cents narrow diminished fourth 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: 2 405/256 794.134 cents wide augmented fifth 5: 1 8/5 813.686 cents minor sixth 5: 1 2048/1215 903.911 cents narrow diminished seventh 5: 2 16/9 996.090 cents Pythagorean minor seventh 6: 2 27/16 905.865 cents Pythagorean major sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 15/8 1088.269 cents classic major seventh 6: 2 256/135 1107.821 cents octave - major chroma Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 296.1 407.8 702.0 794.1 905.9 1200.0 203.9 : 92.2 203.9 498.0 590.2 702.0 996.1 1200.0 296.1 : 111.7 405.9 498.0 609.8 903.9 1107.8 1200.0 407.8 : 294.1 386.3 498.0 792.2 996.1 1088.3 1200.0 702.0 : 92.2 203.9 498.0 702.0 794.1 905.9 1200.0 794.1 : 111.7 405.9 609.8 702.0 813.7 1107.8 1200.0 905.9 : 294.1 498.0 590.2 702.0 996.1 1088.3 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 : 16/15, 111.7313 cents, amount: 2 Least squares average step : 161.66590 cents, oct.: 1131.66130 cents Scale is not proper Step pattern alph. order: ABCDBCD Step pattern size order : CABDABD Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 1.361761 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 : 4 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 32805/32768, 1.9537 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 is Hypodorian octave species of abstract tetrachord Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval classes 1 and 2 combined Scale is differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 5 Odd number limit : 1215 (O: 1215 U: 1215) Highest odd numerator or denominator: 1215 Scale harmonicity : 0.032538 Average absolute harmonicity : 0.229940 Specific harmonicity : 0.167043 Fundamental : 1/1024, -10.0000 octaves, 0.2555 Hz. Guide tone : 2430, 11.2467 octaves, 635750.124 Hz. Exponens Consonantiae : 2.488320E+06, 21.24674 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 1556.5, average 222.35714 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.46324, average 1.49475 Sum of Tenney's harmonic distance : 20.39723, average 2.91389 Vogel's harmonic complexity : 15.14286 Wille's k value : 607 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 6 Triangular lattice diameter : 6 Lattice compactness : 150.10906, average 5.36104 Lattice compactness (without 2's) : 68.19247, average 2.43545 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -10 .. 1 -4.42857 33 1 3: 0 .. 5 2.71429 19 4 5: 0 .. 1 0.28571 2 2 Average exponent except 2's : 21 / 7 = 3.00000 Average absolute exponent except 2's: 21 / 7 = 3.00000 Scale is weakly epimorphic with val: <7 10 17| Scale is weakly epimorphic with val: <7 11 18|
FIT/MODE
7: 1 0 1 2 0 1 2 N T3 SD: 70.9202 c. M: 124.6601 c. 8: 1 1 1 2 0 1 2 N D3 SD: 35.8394 c. M: 53.9100 c. 9: 2 0 1 2 1 1 2 N SD: 31.3947 c. M:-62.7567 c. 11: 2 1 1 2 1 1 3 N SD: 29.9207 c. M: 47.4095 c. 12: 2 1 1 3 1 1 3 N SD: 4.8458 c. M: 7.8200 c. Chromatic Hypodorian, Relative Blues scale, Raga Dvigandharabushini 41: 7 3 4 10 3 4 10 N SD: 2.1960 c. M: 3.8898 c. 53: 9 4 5 13 4 5 13 N SD: 0.9277 c. M: 1.7491 c. 65: 11 5 6 16 5 6 16 N SD: 0.9090 c. M: 1.6662 c. 118: 20 9 11 29 9 11 29 N SD: 0.7783 c. M: 1.1735 c. 301: 51 23 28 74 23 28 74 N SD: 0.7879 c. M: 1.1755 c. 311: 53 24 29 76 24 29 76 N SD: 0.7728 c. M:-1.1832 c. 323: 55 25 30 79 25 30 79 N SD: 0.7019 c. M:-1.1249 c. 335: 57 26 31 82 26 31 82 N SD: 0.6794 c. M:-1.2247 c. 364: 62 28 34 89 28 34 89 N SD: 0.5713 c. M:-0.9712 c. 376: 64 29 35 92 29 35 92 N SD: 0.4945 c. M:-0.7198 c. 388: 66 30 36 95 30 36 95 N SD: 0.4658 c. M:-0.8185 c. 417: 71 32 39 102 32 39 102 N SD: 0.4392 c. M:-0.8131 c. 429: 73 33 40 105 33 40 105 N SD: 0.3502 c. M:-0.5716 c. 441: 75 34 41 108 34 41 108 N SD: 0.3072 c. M:-0.5099 c. 482: 82 37 45 118 37 45 118 N SD: 0.2575 c. M:-0.4788 c. 494: 84 38 46 121 38 46 121 N SD: 0.1908 c. M:-0.2772 c. 506: 86 39 47 124 39 47 124 N SD: 0.1888 c. M:-0.3540 c. 547: 93 42 51 134 42 51 134 N SD: 0.1192 c. M:-0.2239 c. 559: 95 43 52 137 43 52 137 N SD: 0.0836 c. M:-0.1546 c. 612: 104 47 57 150 47 57 150 N SD: 0.0140 c. M:-0.0231 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 x 5:6 S SD: 30.9176 cents 4 x x 5:6 x 7:8 S SD: 16.6332 cents 5 x 6 x x 8 x 10 S SD: 9.2172 cents 6 x 7:8:9 x 10:12 S SD: 19.4492 cents 7:8 x 9 x 11:12:14 SD: 9.7273 cents 8:9 x 10:12:13:14:16 S SD: 13.5185 cents 9:10:11 x x 14:15:18 SD: 13.2852 cents 10:11:12:13:15:16:17:20 SD: 9.6826 cents 11:12:13:14 x 17:19:22 SD: 13.1716 cents 12 x 14:15:18:19:20:24 S SD: 7.0332 cents 13:15 x 16:20:21:22:26 SD: 14.4421 cents 14:16:17:18:21:22:24:28 S SD: 8.9998 cents 15:17:18:19:23:24:25:30 SD: 7.6134 cents 16:18:19:20:24:25:27:32 SD: 4.3497 cents 22:25:26:28:33:35:37:44 SD: 3.4163 cents 26:29:31:33:39:41:44:52 SD: 2.7538 cents 38:43:45:48:57:60:64:76 SD: 1.7353 cents 48:54:57:61:72:76:81:96 SD: 1.0557 cents 64:72:76:81:96:101:108:128 SD: 0.6444 cents 112:126:133:142:168:177:189:224 SD: 0.5476 cents 144:162:171:182:216:228:243:288 SD: 0.4450 cents 192:216:228:243:288:304:324:384 SD: 0.2878 cents 256:288:304:324:384:405:432:512 SD: 0.2035 cents 440:495:522:557:660:696:743:880 SD: 0.1817 cents 520:585:617:658:780:823:878:1040 SD: 0.1809 cents 538:605:638:681:807:851:908:1076 SD: 0.1806 cents 546:614:648:691:819:864:921:1092 SD: 0.1664 cents 584:657:693:739:876:924:986:1168 SD: 0.1369 cents