Scala analysis: xen10-wilson-purvi-10b-04
Purvi modulation 4 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: 25/16 772.627428 classic augmented fifth 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: 25/24 70.6724 classic chromatic semitone, minor chroma 6: 256/225 223.4626 Neapolitan diminished third 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 1 16/15 111.731 cents minor diatonic semitone 1: 2 9/8 203.910 cents major whole tone 1: 1 256/225 223.463 cents Neapolitan diminished third 1: 1 6/5 315.641 cents minor third 2: 2 75/64 274.582 cents classic augmented second 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 6/5 315.641 cents minor third 2: 1 5/4 386.314 cents major third 2: 2 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: 2 25/16 772.627 cents classic augmented fifth 5: 1 8/5 813.686 cents minor sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 2 128/75 925.418 cents diminished seventh 6: 1 5/3 884.359 cents major sixth, BP sixth 6: 1 225/128 976.537 cents augmented sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 15/8 1088.269 cents classic major seventh 6: 2 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 : 70.7 386.3 498.0 702.0 772.6 996.1 1200.0 70.7 : 315.6 427.4 631.3 702.0 925.4 1129.3 1200.0 386.3 : 111.7 315.6 386.3 609.8 813.7 884.4 1200.0 498.0 : 203.9 274.6 498.0 702.0 772.6 1088.3 1200.0 702.0 : 70.7 294.1 498.0 568.7 884.4 996.1 1200.0 772.6 : 223.5 427.4 498.0 813.7 925.4 1129.3 1200.0 996.1 : 203.9 274.6 590.2 702.0 905.9 976.5 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 : 9/8, 203.9100 cents, amount: 2 Least squares average step : 167.03523 cents, oct.: 1169.24660 cents Scale is not proper Step pattern alph. order: ABCDAED Step pattern size order : AEBCADC Scale is not a Constant Structure Scale diversity : 1.534657 Lumma stability : 0.117787 Lumma impropriety factor : 0.189000 Rothenberg efficiency : 0.435374 redundancy: 0.564626 Efficiency x scale size : 3.047619 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 Best fifths form a closed circle Scale contains a complete diamond : 1 3 Length of longest harmonic part : 1 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 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 : 225 (O: 225 U: 225) Highest odd numerator or denominator: 25 Scale harmonicity : 0.034722 Average absolute harmonicity : 0.260982 Specific harmonicity : 0.187609 Fundamental : 1/144, -7.1699 octaves, 1.8168 Hz. Guide tone : 1200, 10.2288 octaves, 313950.678 Hz. Exponens Consonantiae : 1.728000E+05, 17.39874 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 69.5, average 9.92857 Mersenne's string divisions : 452025 Sum of van Prooijen's expressibility: 5.40334, average 0.77191 Sum of Tenney's harmonic distance : 10.99797, average 1.57114 Vogel's harmonic complexity : 11.85714 Wille's k value : 112 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 104.21865, average 3.72209 Lattice compactness (without 2's) : 47.31590, average 1.68985 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 4 -0.42857 17 1 3: -2 .. 1 -0.42857 5 3 5: 0 .. 2 0.71429 5 3 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 10 / 7 = 1.42857 Scale is weakly epimorphic with val: <7 11 15| Scale is weakly epimorphic with val: <7 12 17|
FIT/MODE
7: 0 2 1 1 1 1 1 N T3 SD: 47.2206 c. M:-84.5154 c. 10: 0 3 1 2 0 2 2 N SD: 38.5642 c. M: 70.6724 c. 11: 0 3 1 2 1 2 2 N SD: 46.0081 c. M: 70.6724 c. 12: 1 3 1 2 1 2 2 P D3 SD: 16.1228 c. M:-29.3276 c. Phrygian Dominant, Phrygian Major, Mela Vakulabharanam, Raga Ahiri, Basant Mukhari, Jogiya, Vativasantabhairavi, Zilof, Ahava Rabba, Freygish: Jewish, Maqam Hijaz-Nahawand, Humayun, Spanish Gipsy, Dorico Flamenco: Spain, Hitzaz: Greece, Harmonic Major inverse, Mixolydian flat 2 flat 6 17: 1 4 2 3 1 3 3 N SD: 13.2074 c. M: 33.3725 c. 19: 1 5 2 3 1 4 3 N SD: 9.5648 c. M: 14.7327 c. 22: 1 6 2 4 1 4 4 N SD: 9.7589 c. M: 16.1270 c. 29: 2 7 3 5 2 5 5 N SD: 8.7592 c. M: 13.8999 c. 31: 2 8 3 5 2 6 5 N SD: 5.4724 c. M:-10.3616 c. 34: 2 9 3 6 2 6 6 N SD: 3.9824 c. M: 7.8547 c. 53: 3 14 5 9 3 10 9 N SD: 1.5808 c. M: 2.8161 c. 87: 5 23 8 15 5 16 15 N SD: 1.5283 c. M: 2.9865 c. 118: 7 31 11 20 7 22 20 N SD: 0.3275 c. M:-0.5202 c. 289: 17 76 27 49 17 54 49 N SD: 0.2478 c. M:-0.4498 c. 323: 19 85 30 55 19 60 55 N SD: 0.2062 c. M: 0.4244 c. 441: 26 116 41 75 26 82 75 N SD: 0.1086 c. M: 0.1716 c. 494: 29 130 46 84 29 92 84 N SD: 0.1262 c. M: 0.2271 c. 559: 33 147 52 95 33 104 95 N SD: 0.1003 c. M:-0.1812 c. 612: 36 161 57 104 36 114 104 N SD: 0.0463 c. M: 0.0842 c. 730: 43 192 68 124 43 136 124 N SD: 0.0363 c. M:-0.0744 c. 1171: 69 308 109 199 69 218 199 N SD: 0.0251 c. M:-0.0455 c. 1783: 105 469 166 303 105 332 303 N SD: 0.0077 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 x 5:6 S SD: 37.2438 cents 4 x 5 x 6 x 7:8 S SD: 6.8160 cents 5 x 6:7 x 8:9:10 S SD: 23.8978 cents 6 x x 8:9 x 11:12 SD: 13.3182 cents 7 x 9 x x 11:12:14 SD: 20.0623 cents 9:10:11:12 x 14:16:18 S SD: 19.7604 cents 10:11 x 13:15:16:18:20 SD: 18.9795 cents 11:12:14:15 x 17:20:22 SD: 17.2847 cents 12:13:15:16:18:19:21:24 SD: 10.9541 cents 13:14:16:17 x 20:23:26 SD: 12.8683 cents 14:15:18:19:21:22:25:28 SD: 10.9291 cents 15:16:19:20 x 23:27:30 SD: 10.1903 cents 16:17:20:21:24:25:28:32 SD: 7.3706 cents 18:19:23:24:27:28:32:36 SD: 6.4415 cents 20:21:25:27:30:31:36:40 SD: 5.1680 cents 23:24:29:31:35:36:41:46 SD: 5.0217 cents 24:25:30:32:36:38:43:48 SD: 3.7994 cents 28:29:35:37:42:44:50:56 SD: 3.1825 cents 32:33:40:43:48:50:57:64 SD: 3.1805 cents 44:46:55:59:66:69:78:88 SD: 2.0175 cents 48:50:60:64:72:75:85:96 SD: 0.9680 cents 96:100:120:128:144:150:171:192 SD: 0.4826 cents 144:150:180:192:216:225:256:288 SD: 0.0000 cents