Scala analysis: xen10-wilson-purvi-04-01
Purvi modulation 1 from Figure 4, Archytas (8/7 9/8 28/27) all 6 permutations
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: 9/7 435.084095 septimal major third, BP third 3: 81/56 638.994097 4: 3/2 701.955001 perfect fifth 5: 12/7 933.129094 septimal major sixth 6: 27/14 1137.039096 septimal major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 28/27 62.9609 Archytas' 1/3-tone 1: 9/8 203.9100 major whole tone 2: 8/7 231.1741 septimal whole tone 3: 9/8 203.9100 major whole tone 4: 28/27 62.9609 Archytas' 1/3-tone 5: 8/7 231.1741 septimal whole tone 6: 9/8 203.9100 major whole tone 7: 28/27 62.9609 Archytas' 1/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 3 9/8 203.910 cents major whole tone 1: 2 8/7 231.174 cents septimal whole tone 2: 3 7/6 266.871 cents septimal minor third 2: 1 32/27 294.135 cents Pythagorean minor third 2: 3 9/7 435.084 cents septimal major third, BP third 3: 1 21/16 470.781 cents narrow fourth 3: 5 4/3 498.045 cents perfect fourth 3: 1 81/56 638.994 cents 4: 1 112/81 561.006 cents 4: 5 3/2 701.955 cents perfect fifth 4: 1 32/21 729.219 cents wide fifth 5: 3 14/9 764.916 cents septimal minor sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 3 12/7 933.129 cents septimal major sixth 6: 2 7/4 968.826 cents harmonic seventh 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 2 27/14 1137.039 cents septimal 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 : 203.9 435.1 639.0 702.0 933.1 1137.0 1200.0 203.9 : 231.2 435.1 498.0 729.2 933.1 996.1 1200.0 435.1 : 203.9 266.9 498.0 702.0 764.9 968.8 1200.0 639.0 : 63.0 294.1 498.0 561.0 764.9 996.1 1200.0 702.0 : 231.2 435.1 498.0 702.0 933.1 1137.0 1200.0 933.1 : 203.9 266.9 470.8 702.0 905.9 968.8 1200.0 1137.0: 63.0 266.9 498.0 702.0 764.9 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 231.1741 cents 54/49, 168.2132 cents 28/27, 62.9609 cents 2: 266.8709 .. 435.0841 cents 54/49, 168.2132 cents 49/48, 35.6968 cents 3: 470.7809 .. 638.9941 cents 54/49, 168.2132 cents 49/48, 35.6968 cents 4: 561.0059 .. 729.2191 cents 54/49, 168.2132 cents 6272/6561,-77.9882 cents 5: 764.9159 .. 933.1291 cents 54/49, 168.2132 cents 49/48, 35.6968 cents 6: 968.8259 .. 1137.0391 cents 54/49, 168.2132 cents 49/48, 35.6968 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 2.722778 Largest / Average step : 1.348516 Largest / Smallest step : 3.671709 Median interval of one step : 9/8, 203.9100 cents, amount: 3 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 183.47686 cents, oct.: 1284.33803 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1277-tone equal temperament with octave 2/1 degrees: 217 463 680 747 993 1210 1277 Least number of segments generator : 639 of 600.470 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 747 of 701.958 cents and inv. generated superset size: 72 = 65 more = 1028.571% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABACBAC Step pattern size order : MLMSLMS Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 1.317229 Lumma stability : 0.223924 Lumma impropriety factor : 0.064990 Rothenberg efficiency : 0.544218 redundancy: 0.455782 Efficiency x scale size : 3.809524 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 : 64/63, 27.2641 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 266.871 701.955 cents 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 All steps are superparticular (epimoric) 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 class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions with margin 168.2132 cents: 3 -- Rational properties -- Prime limit : 7 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 81 Scale harmonicity : 0.038532 Average absolute harmonicity : 0.231033 Specific harmonicity : 0.183431 Fundamental : 1/56, -5.8074 octaves, 4.6719 Hz. Guide tone : 324, 8.3399 octaves, 84766.683 Hz. Exponens Consonantiae : 1.814400E+04, 14.14720 octaves Euler's gradus suavitatis : 20 Sum of Mann's harmonic distance : 119.0, average 17.00000 Mersenne's string divisions : 435429840 Sum of van Prooijen's expressibility: 6.57055, average 0.93865 Sum of Tenney's harmonic distance : 12.89430, average 1.84204 Vogel's harmonic complexity : 10.85714 Wille's k value : 40 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 84.57744, average 3.02062 Lattice compactness (without 2's) : 52.74838, average 1.88387 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.71429 11 1 3: 0 .. 4 1.85714 13 2 7: -1 .. 0 -0.57143 4 4 Average exponent except 2's : 9 / 7 = 1.28571 Average absolute exponent except 2's: 17 / 7 = 2.42857 Scale is weakly epimorphic with val: <7 10 22| Scale is JI-epimorphic with val: <7 11 20| = patent Scale is weakly epimorphic with val: <7 12 18|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 78.2997 c. M: 124.7084 c. Lebeng 8: 1 2 1 1 1 2 0 N D3 SD: 41.4371 c. M:-62.9609 c. 11: 2 2 2 0 3 1 1 N G SD: 32.0567 c. M:-48.6891 c. 12: 2 2 2 1 2 2 1 P M ME S SD: 27.3600 c. M: 38.9941 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 13: 2 3 2 1 2 2 1 N G T3 S SD: 22.0984 c. M:-36.5065 c. 14: 2 3 2 1 3 2 1 P T3 SD: 22.3419 c. M: 38.9941 c. 15: 3 2 3 1 3 2 1 N T3 SD: 23.5202 c. M:-36.0900 c. 16: 3 3 3 0 3 3 1 N T3 SD: 23.7028 c. M:-36.0059 c. 17: 3 3 3 1 3 3 1 N M DE S SD: 8.6371 c. M: 15.4820 c. 19: 3 4 3 1 4 3 1 N T3 SD: 9.0047 c. M: 14.4363 c. 22: 4 4 4 1 4 4 1 N M DE S SD: 9.2829 c. M:-15.5514 c. Raga Yaman 31: 5 6 5 2 6 5 2 N T3 SD: 10.9009 c. M: 19.6393 c. 32: 5 7 5 2 6 5 2 N SD: 10.4830 c. M: 16.4100 c. 35: 6 7 6 1 7 6 2 N SD: 9.4195 c. M: 16.2407 c. 36: 6 7 6 2 7 6 2 N T3 SD: 3.1166 c. M: 5.6608 c. 41: 7 8 7 2 8 7 2 N T3 SD: 3.2140 c. M:-4.9083 c. 58: 10 11 10 3 11 10 3 N T3 SD: 1.7882 c. M:-2.9865 c. 77: 13 15 13 4 15 13 4 N T3 SD: 1.0642 c. M:-1.9358 c. 94: 16 18 16 5 18 16 5 N T3 SD: 0.7510 c. M: 1.2142 c. 135: 23 26 23 7 26 23 7 N T3 SD: 0.5579 c. M:-1.0059 c. 171: 29 33 29 9 33 29 9 N T3 SD: 0.2507 c. M: 0.4012 c. 306: 52 59 52 16 59 52 16 N T3 SD: 0.1611 c. M:-0.2216 c. 400: 68 77 68 21 77 68 21 N T3 SD: 0.0711 c. M: 0.1291 c. 571: 97 110 97 30 110 97 30 N T3 SD: 0.0643 c. M: 0.1149 c. 706: 120 136 120 37 136 120 37 N T3 SD: 0.0548 c. M:-0.0994 c. 877: 149 169 149 46 169 149 46 N T3 SD: 0.0286 c. M:-0.0522 c. 1277: 217 246 217 67 246 217 67 N T3 SD: 0.0033 c. M:-0.0054 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 4 x x 5 x 6 S SD: 26.5469 cents 4 x 5 x 6:7 x 8 S SD: 15.1096 cents 5:6 x 7:8:9 x 10 S SD: 37.5727 cents 6:7:8 x 9:10 x 12 S SD: 20.3044 cents 7:8:9:10:11:12 x 14 S SD: 14.6174 cents 8:9:10 x 12:14:15:16 S SD: 12.9436 cents 10:11:13:14:15:17:19:20 SD: 11.0171 cents 13:15:17:19:20:22:25:26 SD: 10.6431 cents 14:16:18:20:21:24:27:28 S SD: 4.9608 cents 18:20:23:26:27:31:35:36 SD: 4.1610 cents 24:27:31:35:36:41:46:48 SD: 2.9154 cents 32:36:41:46:48:55:62:64 SD: 2.1918 cents 38:43:49:55:57:65:73:76 SD: 1.9634 cents 42:47:54:61:63:72:81:84 SD: 1.6592 cents 56:63:72:81:84:96:108:112 S SD: 0.0000 cents