Scala analysis: xen10-wilson-purvi-06b-01
Purvi modulation 1 from Figure 6b, Al-Farabi (10/9 27/25 10/9)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 10/9 182.403712 minor whole tone 2: 5/4 386.313714 major third 3: 25/18 568.717426 classic augmented fourth 4: 3/2 701.955001 perfect fifth 5: 5/3 884.358713 major sixth, BP sixth 6: 50/27 1066.762425 grave major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 1: 10/9 182.4037 minor whole tone 2: 9/8 203.9100 major whole tone 3: 10/9 182.4037 minor whole tone 4: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 5: 10/9 182.4037 minor whole tone 6: 10/9 182.4037 minor whole tone 7: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 4 10/9 182.404 cents minor whole tone 1: 1 9/8 203.910 cents major whole tone 2: 4 6/5 315.641 cents minor third 2: 1 100/81 364.807 cents grave major third 2: 2 5/4 386.314 cents major third 3: 4 4/3 498.045 cents perfect fourth 3: 2 27/20 519.551 cents acute fourth 3: 1 25/18 568.717 cents classic augmented fourth 4: 1 36/25 631.283 cents classic diminished fifth 4: 2 40/27 680.449 cents grave fifth 4: 4 3/2 701.955 cents perfect fifth 5: 2 8/5 813.686 cents minor sixth 5: 1 81/50 835.193 cents acute minor sixth 5: 4 5/3 884.359 cents major sixth, BP sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 4 9/5 1017.596 cents just minor seventh, BP seventh 6: 2 50/27 1066.762 cents grave major seventh Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 182.4 386.3 568.7 702.0 884.4 1066.8 1200.0 182.4 : 203.9 386.3 519.6 702.0 884.4 1017.6 1200.0 386.3 : 182.4 315.6 498.0 680.4 813.7 996.1 1200.0 568.7 : 133.2 315.6 498.0 631.3 813.7 1017.6 1200.0 702.0 : 182.4 364.8 498.0 680.4 884.4 1066.8 1200.0 884.4 : 182.4 315.6 498.0 702.0 884.4 1017.6 1200.0 1066.8: 133.2 315.6 519.6 702.0 835.2 1017.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 133.2376 .. 203.9100 cents 25/24, 70.6724 cents 27/25, 133.2376 cents 2: 315.6413 .. 386.3137 cents 25/24, 70.6724 cents 16/15, 111.7313 cents 3: 498.0450 .. 568.7174 cents 25/24, 70.6724 cents 16/15, 111.7313 cents 4: 631.2826 .. 701.9550 cents 25/24, 70.6724 cents 648/625, 62.5651 cents 5: 813.6863 .. 884.3587 cents 25/24, 70.6724 cents 16/15, 111.7313 cents 6: 996.0900 .. 1066.7624 cents 25/24, 70.6724 cents 16/15, 111.7313 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 27/25, 133.2376 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.286638 Largest / Average step : 1.189475 Largest / Smallest step : 1.530424 Median interval of one step : 10/9, 182.4037 cents, amount: 4 Most common interval of one step : 10/9, 182.4037 cents, amount: 4 Least squares average step : 176.36694 cents, oct.: 1234.56858 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABACAAC Step pattern size order : MLMSMMS Scale is a Constant Structure, by a margin of 62.56515 cents Scale diversity : 1.337678 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.646638 Rothenberg efficiency : 0.506122 redundancy: 0.493878 Efficiency x scale size : 3.542857 Number of different interval sizes : 18 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 81/80, 21.5063 cents Number of recognisable fifths : 4, average 701.9550 cents Scale is Hypophrygian octave species of abstract tetrachord Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Scale is fully connected 5-limit major-minor triadic Length of longest harmonic part : 2 at degree 1 Length of longest subharmonic part : 2 at degree 0 Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval class 2 Scale is differentially coherent in interval classes 3 and 4 combined Scale is differentially coherent in interval classes 4 and 5 combined Limited inverse transpositions : 3 Inversional symmetry on degrees : 5 Inversional symmetry on intervals : 1-2 -- Rational properties -- Prime limit : 5 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 27 Scale harmonicity : 0.037783 Average absolute harmonicity : 0.239819 Specific harmonicity : 0.194057 Fundamental : 1/108, -6.7549 octaves, 2.4225 Hz. Guide tone : 150, 7.2288 octaves, 39243.835 Hz. Exponens Consonantiae : 1.620000E+04, 13.98371 octaves Euler's gradus suavitatis : 20 Sum of Mann's harmonic distance : 82.0, average 11.71429 Mersenne's string divisions : 22647240 Sum of van Prooijen's expressibility: 5.65861, average 0.80837 Sum of Tenney's harmonic distance : 11.29409, average 1.61344 Vogel's harmonic complexity : 12.85714 Wille's k value : 67 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 72.25160, average 2.58041 Lattice compactness (without 2's) : 55.52161, average 1.98291 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 1 -0.14286 7 1 3: -3 .. 1 -1.00000 9 1 5: 0 .. 2 1.00000 7 5 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 16 / 7 = 2.28571 Scale is weakly epimorphic with val: <7 10 18| Scale is JI-epimorphic with val: <7 11 16| = patent Scale is weakly epimorphic with val: <7 11 17| Scale is weakly epimorphic with val: <7 12 16|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 32.5900 c. M: 54.4317 c. Lebeng 12: 2 2 2 1 2 2 1 P M ME S SD: 20.1024 c. M:-33.2376 c. G.Hypolydian, M.Lydian, G.M.Hypolocrian, Rut biscale ascending, Kalyan That (Yaman), Mela Mecakalyani, Raga Chandrakant, Malarani, Shuddh Kalyan, Ping, Kung, Gu: China 15: 2 3 2 2 2 2 2 SP M ME S SD: 16.1514 c. M: 26.7624 c. Miller's Porcupine-7 Major 19: 3 3 3 2 3 3 2 SP M ME S SD: 5.4033 c. M: 7.3663 c. Nineteen-tone Lydian 34: 5 6 5 4 5 5 4 SP T3 S SD: 4.4314 c. M: 7.9389 c. 46: 7 8 7 5 7 7 5 SP T3 S SD: 3.2132 c. M:-5.1956 c. 53: 8 9 8 6 8 8 6 SP T3 S SD: 1.6648 c. M: 2.6797 c. 72: 11 12 11 8 11 11 8 SP T3 S SD: 1.6403 c. M: 2.9804 c. 99: 15 17 15 11 15 15 11 SP T3 S SD: 0.8583 c. M:-1.5651 c. 118: 18 20 18 13 18 18 13 SP T3 S SD: 0.5758 c. M:-1.0342 c. 152: 23 26 23 17 23 23 17 SP T3 S SD: 0.5945 c. M: 0.9730 c. 171: 26 29 26 19 26 26 19 SP T3 S SD: 0.2013 c. M: 0.3488 c. 270: 41 46 41 30 41 41 30 SP T3 S SD: 0.1981 c. M:-0.3530 c. 388: 59 66 59 43 59 59 43 SP T3 S SD: 0.2124 c. M:-0.3547 c. 441: 67 75 67 49 67 67 49 SP T3 S SD: 0.0670 c. M: 0.0958 c. 612: 93 104 93 68 93 93 68 SP T3 S SD: 0.0579 c. M: 0.0958 c. 730: 111 124 111 81 111 111 81 SP T3 S SD: 0.0478 c. M:-0.0869 c. 901: 137 153 137 100 137 137 100 SP T3 S SD: 0.0495 c. M: 0.0762 c. 1000: 152 170 152 111 152 152 111 SP T3 S SD: 0.0527 c. M:-0.0863 c. 1053: 160 179 160 117 160 160 117 SP T3 S SD: 0.0526 c. M: 0.0958 c. 1171: 178 199 178 130 178 178 130 SP T3 S SD: 0.0164 c. M:-0.0272 c. 1342: 204 228 204 149 204 204 149 SP T3 S SD: 0.0135 c. M: 0.0246 c. 1783: 271 303 271 198 271 271 198 SP T3 S SD: 0.0115 c. M: 0.0210 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 6:7 x 8 S SD: 21.1168 cents 5 x 6:7 x 8:9:10 S SD: 22.4471 cents 6:7 x 8:9:10:11:12 S SD: 18.5832 cents 7:8:9:10:11:12:13:14 H SD: 18.0842 cents 8:9:10:11:12:13:15:16 SD: 8.0165 cents 9:10:11 x 14:15:17:18 SD: 13.5944 cents 10:11:13:14:15:17:19:20 SD: 12.9783 cents 11:12:14:15:17:18:20:22 SD: 12.5199 cents 12:13:15:17:18:20:22:24 SD: 8.3290 cents 16:18:20:22:24:27:30:32 S SD: 5.8733 cents 20:22:25:28:30:33:37:40 SD: 4.0375 cents 28:31:35:39:42:47:52:56 SD: 2.2085 cents 36:40:45:50:54:60:67:72 SD: 1.2335 cents 72:80:90:100:108:120:133:144 SD: 0.6191 cents 108:120:135:150:162:180:200:216 SD: 0.0000 cents