Scala analysis: xen10-wilson-purvi-02a-04
Purvi modulation 4 from Figure 2a, Helmholtz (75/64 16/15 16/15), (16/15 16/15 75/64)
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: 5/4 386.313714 major third 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: 75/64 274.5824 classic augmented second 3: 16/15 111.7313 minor diatonic semitone 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: 3 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 75/64 274.582 cents classic augmented second 2: 1 32/27 294.135 cents Pythagorean minor third 2: 3 6/5 315.641 cents minor third 2: 3 5/4 386.314 cents major third 3: 1 32/25 427.373 cents classic diminished fourth 3: 4 4/3 498.045 cents perfect fourth 3: 2 45/32 590.224 cents diatonic tritone 4: 2 64/45 609.776 cents 2nd tritone 4: 4 3/2 701.955 cents perfect fifth 4: 1 25/16 772.627 cents classic augmented fifth 5: 3 8/5 813.686 cents minor sixth 5: 3 5/3 884.359 cents major sixth, BP sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 6: 1 128/75 925.418 cents diminished seventh 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 3 15/8 1088.269 cents classic major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.33333 = 10/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 111.7 386.3 498.0 702.0 813.7 996.1 1200.0 111.7 : 274.6 386.3 590.2 702.0 884.4 1088.3 1200.0 386.3 : 111.7 315.6 427.4 609.8 813.7 925.4 1200.0 498.0 : 203.9 315.6 498.0 702.0 813.7 1088.3 1200.0 702.0 : 111.7 294.1 498.0 609.8 884.4 996.1 1200.0 813.7 : 182.4 386.3 498.0 772.6 884.4 1088.3 1200.0 996.1 : 203.9 315.6 590.2 702.0 905.9 1017.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 274.5824 cents 1125/1024, 162.8511 cents 16/15, 111.7313 cents 2: 294.1350 .. 386.3137 cents 135/128, 92.1787 cents 2048/2025, 19.5526 cents 3: 427.3726 .. 590.2237 cents 1125/1024, 162.8511 cents 128/125, 41.0589 cents 4: 609.7763 .. 772.6274 cents 1125/1024, 162.8511 cents 2048/2025, 19.5526 cents 5: 813.6863 .. 905.8650 cents 135/128, 92.1787 cents 128/125, 41.0589 cents 6: 925.4176 .. 1088.2687 cents 1125/1024, 162.8511 cents 2048/2025, 19.5526 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 75/64, 274.5824 cents Average / Smallest step : 1.534293 Largest / Average step : 1.601731 Largest / Smallest step : 2.457525 Median interval of one step : 10/9, 182.4037 cents, amount: 1 Most common interval of one step : 16/15, 111.7313 cents, amount: 3 Least squares average step : 168.79489 cents, oct.: 1181.56426 cents Scale is strictly proper Step pattern alph. order: ABACADC Step pattern size order : ADACABC Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.434704 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.303532 Rothenberg efficiency : 0.466667 redundancy: 0.533333 Efficiency x scale size : 3.266667 Number of different interval sizes : 20 = 3.33333 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.33333 = 10/3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 2048/2025, 19.5526 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Number of recognisable fifths : 4, average 701.9550 cents Best fifths form a closed circle Scale is fully connected 5-limit major-minor triadic Scale contains a complete diamond : 1 3 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 n-1 differentially coherent in interval class 1 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 : 75 (O: 75 U: 75) Highest odd numerator or denominator: 15 Scale harmonicity : 0.037313 Average absolute harmonicity : 0.270873 Specific harmonicity : 0.231940 Fundamental : 1/180, -7.4919 octaves, 1.4535 Hz. Guide tone : 240, 7.9069 octaves, 62790.136 Hz. Exponens Consonantiae : 4.320000E+04, 15.39874 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 46.5, average 6.64286 Mersenne's string divisions : 634725 Sum of van Prooijen's expressibility: 4.48252, average 0.64036 Sum of Tenney's harmonic distance : 9.60003, average 1.37143 Vogel's harmonic complexity : 12.57143 Wille's k value : 112 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 89.53878, average 3.19781 Lattice compactness (without 2's) : 40.84377, average 1.45871 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 4 1.57143 17 1 3: -2 .. 1 -0.42857 5 3 5: -1 .. 1 -0.14286 3 3 Average exponent except 2's :-4 / 7 =-0.57143 Average absolute exponent except 2's: 8 / 7 = 1.14286 Scale is JI-epimorphic with val: <7 11 16| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 35.7037 c. M:-59.6973 c. Lebeng 9: 1 2 1 1 1 1 2 N D3 S SD: 32.2273 c. M: 62.7567 c. 10: 1 2 1 2 1 1 2 P M ME S SD: 22.0614 c. M: 36.0900 c. 12: 1 3 1 2 1 2 2 P D3 SD: 8.7438 c. M: 13.6863 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 19: 2 4 2 3 2 3 3 SP D3 SD: 9.5157 c. M:-14.5845 c. 22: 2 5 2 4 2 3 4 P SD: 7.1005 c. M: 14.2718 c. 31: 3 7 3 5 3 5 5 SP D3 SD: 5.0936 c. M:-10.3616 c. 34: 3 8 3 6 3 5 6 P SD: 4.3775 c. M: 7.8547 c. 41: 4 9 4 7 4 6 7 SP SD: 3.7383 c. M: 5.8259 c. 53: 5 12 5 9 5 8 9 SP SD: 0.9390 c. M:-1.4763 c. 65: 6 15 6 11 6 10 11 SP SD: 0.9077 c. M:-1.3786 c. 118: 11 27 11 20 11 18 20 SP SD: 0.2552 c. M:-0.5202 c. 289: 27 66 27 49 27 44 49 SP SD: 0.2660 c. M:-0.4498 c. 323: 30 74 30 55 30 49 55 SP SD: 0.2251 c. M: 0.4244 c. 376: 35 86 35 64 35 57 64 SP SD: 0.1776 c. M: 0.3453 c. 429: 40 98 40 73 40 65 73 SP SD: 0.2161 c. M: 0.2997 c. 441: 41 101 41 75 41 67 75 SP SD: 0.1102 c. M: 0.1716 c. 494: 46 113 46 84 46 75 84 SP SD: 0.0769 c. M: 0.1386 c. 559: 52 128 52 95 52 85 95 SP SD: 0.0633 c. M: 0.1034 c. 612: 57 140 57 104 57 93 104 SP SD: 0.0250 c. M: 0.0392 c. 1171: 109 268 109 199 109 178 199 SP SD: 0.0191 c. M: 0.0319 c. 1783: 166 408 166 303 166 271 303 SP SD: 0.0082 c. M: 0.0160 c. 2395: 223 548 223 407 223 364 407 SP SD: 0.0084 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 5 x 6 x 7:8 S SD: 6.8160 cents 5 x 6:7 x 8:9:10 S SD: 22.4427 cents 6 x x 8:9:10:11:12 S SD: 17.7004 cents 7:8:9 x x 11:12:14 SD: 29.3818 cents 8:9:10:11:12:13:14:16 S SD: 16.1616 cents 9:10:11:12 x 14:16:18 S SD: 15.7116 cents 10:11 x 13:15:16:18:20 SD: 12.0435 cents 12:13:15:16:18:19:21:24 SD: 6.0481 cents 20:21:25:27:30:32:36:40 SD: 5.8351 cents 24:26:30:32:36:38:43:48 SD: 5.0114 cents 27:29:34:36:41:43:48:54 SD: 4.0972 cents 28:30:35:37:42:45:50:56 SD: 2.9259 cents 32:34:40:43:48:51:57:64 SD: 2.4106 cents 44:47:55:59:66:70:78:88 SD: 2.1372 cents 45:48:56:60:68:72:80:90 SD: 2.1319 cents 48:51:60:64:72:77:85:96 SD: 1.5125 cents 60:64:75:80:90:96:107:120 SD: 0.7717 cents 108:115:135:144:162:173:192:216 SD: 0.5163 cents 120:128:150:160:180:192:213:240 SD: 0.3867 cents 180:192:225:240:270:288:320:360 SD: 0.0000 cents