Scala analysis: xen10-wilson-purvi-03b-01
Purvi modulation 1 from Figure 3b, Al-Farabi (8/7 49/48 8/7)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 8/7 231.174094 septimal whole tone 2: 9/7 435.084095 septimal major third, BP third 3: 72/49 666.258189 Arabic lute grave fifth 4: 3/2 701.955001 perfect fifth 5: 12/7 933.129094 septimal major sixth 6: 96/49 1164.303188 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 49/48 35.6968 slendro diesis, septimal 1/6-tone 1: 8/7 231.1741 septimal whole tone 2: 9/8 203.9100 major whole tone 3: 8/7 231.1741 septimal whole tone 4: 49/48 35.6968 slendro diesis, septimal 1/6-tone 5: 8/7 231.1741 septimal whole tone 6: 8/7 231.1741 septimal whole tone 7: 49/48 35.6968 slendro diesis, septimal 1/6-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 1 9/8 203.910 cents major whole tone 1: 4 8/7 231.174 cents septimal whole tone 2: 4 7/6 266.871 cents septimal minor third 2: 2 9/7 435.084 cents septimal major third, BP third 2: 1 64/49 462.348 cents 2 septatones or septatonic major third 3: 2 21/16 470.781 cents narrow fourth 3: 4 4/3 498.045 cents perfect fourth 3: 1 72/49 666.258 cents Arabic lute grave fifth 4: 1 49/36 533.742 cents Arabic lute acute fourth 4: 4 3/2 701.955 cents perfect fifth 4: 2 32/21 729.219 cents wide fifth 5: 1 49/32 737.652 cents 5: 2 14/9 764.916 cents septimal minor sixth 5: 4 12/7 933.129 cents septimal major sixth 6: 4 7/4 968.826 cents harmonic seventh 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 96/49 1164.303 cents 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 : 231.2 435.1 666.3 702.0 933.1 1164.3 1200.0 231.2 : 203.9 435.1 470.8 702.0 933.1 968.8 1200.0 435.1 : 231.2 266.9 498.0 729.2 764.9 996.1 1200.0 666.3 : 35.7 266.9 498.0 533.7 764.9 968.8 1200.0 702.0 : 231.2 462.3 498.0 729.2 933.1 1164.3 1200.0 933.1 : 231.2 266.9 498.0 702.0 933.1 968.8 1200.0 1164.3: 35.7 266.9 470.8 702.0 737.7 968.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 35.6968 .. 231.1741 cents 384/343, 195.4773 cents 49/48, 35.6968 cents 2: 266.8709 .. 462.3482 cents 384/343, 195.4773 cents 49/48, 35.6968 cents 3: 470.7809 .. 666.2582 cents 384/343, 195.4773 cents 1029/1024, 8.4327 cents 4: 533.7418 .. 729.2191 cents 384/343, 195.4773 cents 2401/2592,-132.5164 cents 5: 737.6518 .. 933.1291 cents 384/343, 195.4773 cents 1029/1024, 8.4327 cents 6: 968.8259 .. 1164.3032 cents 384/343, 195.4773 cents 49/48, 35.6968 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 49/48, 35.6968 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 4.802350 Largest / Average step : 1.348516 Largest / Smallest step : 6.476043 Median interval of one step : 8/7, 231.1741 cents, amount: 4 Most common interval of one step : 8/7, 231.1741 cents, amount: 4 Least squares average step : 185.42430 cents, oct.: 1297.97007 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABACAAC Step pattern size order : LMLSLLS Scale is a Constant Structure, by a margin of 8.43272 cents Scale diversity : 1.186908 Lumma stability : 0.133044 Lumma impropriety factor : 0.110430 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 : 1029/1024, 8.4327 cents Number of recognisable fifths : 4, average 701.9550 cents Scale is Hypophrygian octave species of abstract tetrachord All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 0 Length of longest subharmonic part : 2 at degree 1 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 : 3 Inversional symmetry on degrees : 5 Inversional symmetry on intervals : 1-2 -- Rational properties -- Prime limit : 7 Odd number limit : 49 (O: 49 U: 49) Highest odd numerator or denominator: 49 Scale harmonicity : 0.031343 Average absolute harmonicity : 0.221272 Specific harmonicity : 0.153582 Fundamental : 1/98, -6.6147 octaves, 2.6696 Hz. Guide tone : 288, 8.1699 octaves, 75348.163 Hz. Exponens Consonantiae : 2.822400E+04, 14.78463 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 162.0, average 23.14286 Mersenne's string divisions : 16001040 Sum of van Prooijen's expressibility: 6.50195, average 0.92885 Sum of Tenney's harmonic distance : 13.77098, average 1.96728 Vogel's harmonic complexity : 12.85714 Wille's k value : 73 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 84.03705, average 3.00132 Lattice compactness (without 2's) : 42.97276, average 1.53474 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 5 1.85714 15 1 3: 0 .. 2 1.00000 7 1 7: -2 .. 0 -1.00000 7 5 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 14 / 7 = 2.00000 Scale is weakly epimorphic with val: <7 10 22| Scale is weakly epimorphic with val: <7 11 19| Scale is JI-epimorphic with val: <7 11 20| = patent Scale is weakly epimorphic with val: <7 12 18| Scale is weakly epimorphic with val: <7 12 22|
FIT/MODE
7: 1 1 2 0 1 2 0 N T3 SD: 53.1384 c. M: 92.2270 c. 9: 2 1 2 0 2 2 0 N T3 S SD: 26.7538 c. M:-35.6968 c. 14: 3 2 3 0 3 3 0 N T3 S SD: 19.7411 c. M:-35.6968 c. 17: 3 3 3 1 3 3 1 N M DE S SD: 20.4993 c. M: 34.8914 c. 19: 4 3 4 0 4 4 0 N T3 S SD: 20.1773 c. M:-35.6968 c. 20: 4 3 4 1 4 3 1 N T3 SD: 16.8307 c. M:-26.8709 c. 22: 4 4 4 1 4 4 1 N M DE S SD: 10.3380 c. M: 18.8486 c. Raga Yaman 24: 5 4 4 1 5 4 1 N SD: 13.8061 c. M:-18.8259 c. Diatonic + Enharmonic Diesis Hypolydian 25: 5 4 5 1 4 5 1 N T3 SD: 12.2113 c. M: 21.1291 c. 26: 5 4 5 1 5 5 1 N T3 S SD: 12.5122 c. M: 20.1043 c. 27: 5 5 5 1 5 5 1 N M DE S SD: 6.8485 c. M:-9.3603 c. 31: 6 5 6 1 6 6 1 N T3 S SD: 5.4391 c. M: 9.2776 c. 36: 7 6 7 1 7 7 1 N T3 S SD: 1.5741 c. M:-2.3635 c. 94: 18 16 18 3 18 18 3 N T3 S SD: 1.5664 c. M: 2.6011 c. 99: 19 17 19 3 19 19 3 N T3 S SD: 0.7751 c. M:-1.2795 c. 135: 26 23 26 4 26 26 4 N T3 S SD: 0.2742 c. M:-0.4715 c. 306: 59 52 59 9 59 59 9 N T3 S SD: 0.2547 c. M:-0.4085 c. 400: 77 68 77 12 77 77 12 N T3 S SD: 0.1751 c. M: 0.3032 c. 436: 84 74 84 13 84 84 13 N T3 S SD: 0.1322 c. M: 0.2217 c. 535: 103 91 103 16 103 103 16 N T3 S SD: 0.1078 c. M: 0.1910 c. 571: 110 97 110 17 110 110 17 N T3 S SD: 0.0365 c. M: 0.0585 c. 706: 136 120 136 21 136 136 21 N T3 S SD: 0.0240 c. M:-0.0434 c. 1277: 246 217 246 38 246 246 38 N T3 S SD: 0.0067 c. M: 0.0119 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: 36.7514 cents 6:7:8 x 9:10 x 12 S SD: 17.4550 cents 7:8:9:10:11:12 x 14 S SD: 15.6921 cents 8:9:10 x 12:14 x 16 S SD: 13.2607 cents 9:10:12:13:14:15 x 18 S SD: 19.4106 cents 10:11:13 x 15:17 x 20 SD: 14.0773 cents 11:13:14:16:17:19 x 22 SD: 13.7717 cents 12:14:15 x 18:21 x 24 S SD: 14.0386 cents 13:15:17:19:20:22:25:26 SD: 9.7716 cents 14:16:18 x 21:24:27:28 S SD: 4.5440 cents 16:18:21 x 24:27:31:32 SD: 9.3276 cents 17:19:22:25:26:29:33:34 SD: 7.9263 cents 18:21:23:26:27:31:35:36 SD: 7.1466 cents 20:23:26:29:30:34:39:40 SD: 5.1252 cents 21:24:27:31:32:36:41:42 SD: 4.1491 cents 28:32:36:41:42:48:55:56 SD: 1.0741 cents 70:80:90:103:105:120:137:140 SD: 0.4293 cents 98:112:126:144:147:168:192:196 S SD: 0.0000 cents