Scala analysis: xen10-wilson-purvi-10b-05
Purvi modulation 5 from Figure 10b, Didymus (6/5 25/24 16/15), (25/24 16/15 6/5)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 25/24 70.672427 classic chromatic semitone, minor chroma 2: 5/4 386.313714 major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 5/3 884.358713 major sixth, BP 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: 25/24 70.6724 classic chromatic semitone, minor chroma 2: 6/5 315.6413 minor third 3: 16/15 111.7313 minor diatonic semitone 4: 9/8 203.9100 major whole tone 5: 10/9 182.4037 minor whole tone 6: 16/15 111.7313 minor diatonic semitone 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 25/24 70.672 cents classic chromatic semitone, minor chroma 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 6/5 315.641 cents minor third 2: 1 75/64 274.582 cents classic augmented second 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 32/25 427.373 cents classic diminished fourth 3: 1 5/4 386.314 cents major third 3: 4 4/3 498.045 cents perfect fourth 3: 1 45/32 590.224 cents diatonic tritone 3: 1 36/25 631.283 cents classic diminished fifth 4: 1 25/18 568.717 cents classic augmented fourth 4: 1 64/45 609.776 cents 2nd tritone 4: 4 3/2 701.955 cents perfect fifth 4: 1 8/5 813.686 cents minor sixth 5: 1 25/16 772.627 cents classic augmented 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: 1 128/75 925.418 cents diminished seventh 6: 1 5/3 884.359 cents major sixth, BP 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 48/25 1129.328 cents classic diminished octave 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 : 70.7 386.3 498.0 702.0 884.4 996.1 1200.0 70.7 : 315.6 427.4 631.3 813.7 925.4 1129.3 1200.0 386.3 : 111.7 315.6 498.0 609.8 813.7 884.4 1200.0 498.0 : 203.9 386.3 498.0 702.0 772.6 1088.3 1200.0 702.0 : 182.4 294.1 498.0 568.7 884.4 996.1 1200.0 884.4 : 111.7 315.6 386.3 702.0 813.7 1017.6 1200.0 996.1 : 203.9 274.6 590.2 702.0 905.9 1088.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 315.6413 cents 144/125, 244.9689 cents 25/24, 70.6724 cents 2: 274.5824 .. 427.3726 cents 2048/1875, 152.7901 cents 125/128,-41.0589 cents 3: 386.3137 .. 631.2826 cents 144/125, 244.9689 cents 125/128,-41.0589 cents 4: 568.7174 .. 813.6863 cents 144/125, 244.9689 cents 625/648,-62.5651 cents 5: 772.6274 .. 925.4176 cents 2048/1875, 152.7901 cents 125/128,-41.0589 cents 6: 884.3587 .. 1129.3276 cents 144/125, 244.9689 cents 125/128,-41.0589 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 25/24, 70.6724 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 2.425678 Largest / Average step : 1.841241 Largest / Smallest step : 4.466258 Median interval of one step : 10/9, 182.4037 cents, amount: 1 Least squares average step : 171.02563 cents, oct.: 1197.17942 cents Scale is not proper Step pattern alph. order: ABCDECD Step pattern size order : AEBDCBD Scale is not a Constant Structure Scale diversity : 1.549589 Lumma stability : 0.117787 Lumma impropriety factor : 0.189000 Rothenberg efficiency : 0.425850 redundancy: 0.574150 Efficiency x scale size : 2.980952 Number of different interval sizes : 24 = 4.00000 / 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: 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 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 3 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% Scale is differentially coherent in interval class 1 Scale is 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 : 75 (O: 75 U: 75) Highest odd numerator or denominator: 25 Scale harmonicity : 0.035971 Average absolute harmonicity : 0.268235 Specific harmonicity : 0.216362 Fundamental : 1/72, -6.1699 octaves, 3.6337 Hz. Guide tone : 1200, 10.2288 octaves, 313950.678 Hz. Exponens Consonantiae : 8.640000E+04, 16.39874 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 53.0, average 7.57143 Mersenne's string divisions : 88200 Sum of van Prooijen's expressibility: 4.70437, average 0.67205 Sum of Tenney's harmonic distance : 9.57200, average 1.36743 Vogel's harmonic complexity : 10.28571 Wille's k value : 37 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 89.55381, average 3.19835 Lattice compactness (without 2's) : 43.49405, average 1.55336 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 4 0.14286 13 1 3: -2 .. 1 -0.57143 6 3 5: 0 .. 2 0.57143 4 3 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 10 / 7 = 1.42857
FIT/MODE
7: 0 2 1 1 1 1 1 N T3 SD: 36.2656 c. M: 70.6724 c. 10: 0 3 1 2 1 1 2 N SD: 37.0491 c. M: 70.6724 c. 12: 1 3 1 2 2 1 2 P D3 SD: 13.7061 c. M:-29.3276 c. Harmonic Minor inverse, Mixolydian flat 2, Mela Cakravaka, Raga Ahir Bhairav, Bindumalini, Hevitri, Vegavahini, Makam Hicaz, Zanjaran 16: 1 4 2 2 3 1 3 N SD: 18.0844 c. M:-26.9550 c. 19: 1 5 2 3 3 2 3 N SD: 7.7769 c. M:-14.4363 c. 31: 2 8 3 5 5 3 5 N SD: 5.8888 c. M:-10.3616 c. 34: 2 9 3 6 5 3 6 N SD: 3.7847 c. M: 7.8547 c. 46: 3 12 4 8 7 4 8 N SD: 4.2019 c. M:-7.5884 c. 53: 3 14 5 9 8 5 9 N SD: 1.2737 c. M: 2.7479 c. 99: 6 26 9 17 15 9 17 N SD: 1.4066 c. M: 2.1506 c. 118: 7 31 11 20 18 11 20 N SD: 0.3456 c. M:-0.5202 c. 171: 10 45 16 29 26 16 29 N SD: 0.3005 c. M: 0.4970 c. 289: 17 76 27 49 44 27 49 N SD: 0.2202 c. M:-0.4498 c. 323: 19 85 30 55 49 30 55 N SD: 0.2081 c. M: 0.4244 c. 441: 26 116 41 75 67 41 75 N SD: 0.0898 c. M: 0.1716 c. 559: 33 147 52 95 85 52 95 N SD: 0.0789 c. M:-0.1684 c. 612: 36 161 57 104 93 57 104 N SD: 0.0394 c. M: 0.0842 c. 730: 43 192 68 124 111 68 124 N SD: 0.0363 c. M:-0.0744 c. 1171: 69 308 109 199 178 109 199 N SD: 0.0190 c. M:-0.0364 c. 1342: 79 353 125 228 204 125 228 N SD: 0.0224 c. M:-0.0352 c. 1783: 105 469 166 303 271 166 303 N SD: 0.0080 c. M: 0.0160 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: 0.0000 cents 4 x 5 x 6 x 7:8 S SD: 6.8160 cents 5 x 6:7 x 8:9:10 S SD: 26.5228 cents 6 x x 8:9:10:11:12 S SD: 10.6546 cents 7 x 9 x 11:12 x 14 SD: 26.5086 cents 8:9:10:11:12:13:14:16 S SD: 21.7850 cents 9:10:11:12:14:15:16:18 S SD: 19.1458 cents 10:11 x 13:15:17:18:20 SD: 18.6022 cents 11:12:14:15:17:18:20:22 SD: 16.9483 cents 12:13:15:16:18:20:21:24 SD: 10.4528 cents 15:16:19:20:23:25:27:30 SD: 9.1718 cents 16:17:20:21:24:27:28:32 SD: 7.9853 cents 18:19:23:24:27:30:32:36 SD: 6.3466 cents 20:21:25:27:30:33:36:40 SD: 5.3796 cents 21:22:26:28:32:35:37:42 SD: 5.2609 cents 24:25:30:32:36:40:43:48 SD: 1.9247 cents 48:50:60:64:72:80:85:96 SD: 0.9680 cents 72:75:90:96:108:120:128:144 S SD: 0.0000 cents