Scala analysis: xen10-wilson-purvi-03b-04
Purvi modulation 4 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: 7/6 266.870906 septimal minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 12/7 933.129094 septimal major sixth 6: 7/4 968.825906 harmonic seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 8/7 231.1741 septimal whole tone 2: 49/48 35.6968 slendro diesis, septimal 1/6-tone 3: 8/7 231.1741 septimal whole tone 4: 9/8 203.9100 major whole tone 5: 8/7 231.1741 septimal whole tone 6: 49/48 35.6968 slendro diesis, septimal 1/6-tone 7: 8/7 231.1741 septimal whole 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 : 231.2 266.9 498.0 702.0 933.1 968.8 1200.0 231.2 : 35.7 266.9 470.8 702.0 737.7 968.8 1200.0 266.9 : 231.2 435.1 666.3 702.0 933.1 1164.3 1200.0 498.0 : 203.9 435.1 470.8 702.0 933.1 968.8 1200.0 702.0 : 231.2 266.9 498.0 729.2 764.9 996.1 1200.0 933.1 : 35.7 266.9 498.0 533.7 764.9 968.8 1200.0 968.8 : 231.2 462.3 498.0 729.2 933.1 1164.3 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 : 171.03908 cents, oct.: 1197.27359 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABACABA Step pattern size order : LSLMLSL 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 Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Scale is a complete diamond : 1 3 7 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 2 Length of longest subharmonic part : 2 at degree 3 Formal octave complements present : 7 = 100.0000% 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 Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 3-4 -- Rational properties -- Prime limit : 7 Odd number limit : 49 (O: 49 U: 49) Highest odd numerator or denominator: 7 Scale harmonicity : 0.032357 Average absolute harmonicity : 0.254604 Specific harmonicity : 0.172573 Fundamental : 1/84, -6.3923 octaves, 3.1146 Hz. Guide tone : 168, 7.3923 octaves, 43953.095 Hz. Exponens Consonantiae : 1.411200E+04, 13.78463 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 36.5, average 5.21429 Mersenne's string divisions : 285285 Sum of van Prooijen's expressibility: 4.33463, average 0.61923 Sum of Tenney's harmonic distance : 8.90124, average 1.27161 Vogel's harmonic complexity : 12.57143 Wille's k value : 73 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 75.31381, average 2.68978 Lattice compactness (without 2's) : 39.08641, average 1.39594 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 0.57143 12 1 3: -1 .. 1 0.00000 4 2 7: -1 .. 1 0.00000 4 4 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 8 / 7 = 1.14286 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 1 1 1 1 1 SP B ME I SD: 52.3919 c. M: 75.9862 c. Lebeng 9: 2 0 2 1 2 0 2 N T3 I SD: 26.7530 c. M:-35.4926 c. 10: 2 0 2 2 2 0 2 N M DE I SD: 17.9329 c. M:-26.8709 c. 14: 3 0 3 2 3 0 3 N T3 I SD: 17.1778 c. M:-25.9688 c. 17: 3 1 3 3 3 1 3 N M DE I SD: 13.4360 c. M:-19.4094 c. Supra-7 21: 4 1 4 3 4 1 4 N T3 I SD: 13.3696 c. M: 18.8434 c. 22: 4 1 4 4 4 1 4 N M DE I SD: 8.5192 c. M:-12.9923 c. Supra-7 26: 5 1 5 4 5 1 5 N T3 I SD: 7.4504 c. M:-10.0522 c. 27: 5 1 5 5 5 1 5 N M DE I SD: 6.8455 c. M: 9.1561 c. Supra-7 31: 6 1 6 5 6 1 6 N T3 I SD: 3.5777 c. M: 5.1808 c. 36: 7 1 7 6 7 1 7 N T3 I SD: 1.5608 c. M:-2.1592 c. 94: 18 3 18 16 18 3 18 N T3 I SD: 0.9896 c. M:-1.3869 c. 99: 19 3 19 17 19 3 19 N T3 I SD: 0.7477 c. M:-1.0753 c. 130: 25 4 25 22 25 4 25 N T3 I SD: 0.5378 c. M:-0.8214 c. 135: 26 4 26 23 26 4 26 N T3 I SD: 0.1829 c. M:-0.2672 c. 306: 59 9 59 52 59 9 59 N T3 I SD: 0.1523 c. M: 0.2042 c. 400: 77 12 77 68 77 12 77 N T3 I SD: 0.1183 c. M:-0.1741 c. 436: 84 13 84 74 84 13 84 N T3 I SD: 0.0847 c. M:-0.1201 c. 571: 110 17 110 97 110 17 110 N T3 I SD: 0.0219 c. M: 0.0293 c. 706: 136 21 136 120 136 21 136 N T3 I SD: 0.0184 c. M:-0.0280 c. 1277: 246 38 246 217 246 38 246 N T3 I SD: 0.0048 c. M:-0.0073 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: 16.2568 cents 4 x x 5:6 x 7:8 S SD: 27.9328 cents 5 x 6:7:8 x 9:10 S SD: 31.2254 cents 6 x 7:8:9:10:11:12 S SD: 15.6921 cents 7:8 x 9:11:12 x 14 SD: 20.4453 cents 8:9 x 11:12 x 14:16 SD: 11.9689 cents 11 x 13:15:17:19 x 22 SD: 13.9348 cents 12 x 14:16:18 x 21:24 S SD: 0.0000 cents 13:15 x 17:20:22:23:26 SD: 10.7790 cents 14:16 x 19:21:24:25:28 SD: 7.7500 cents 15:17:18:20:23 x 26:30 SD: 10.9427 cents 16:18:19:21:24:27:28:32 SD: 8.0419 cents 18 x 21:24:27:31:32:36 SD: 4.7354 cents 19 x 22:25:29 x 33:38 SD: 8.4233 cents 20:23 x 27:30:34:35:40 SD: 4.6808 cents 24:27:28:32:36:41:42:48 SD: 3.9887 cents 25 x 29:33:38:43:44:50 SD: 5.4198 cents 26:30 x 35:39:45:46:52 SD: 5.7286 cents 27:31:32:36:41:46:47:54 SD: 5.4544 cents 28:32:33:37:42:48:49:56 SD: 3.3503 cents 32 x 37:43:48:55:56:64 SD: 3.5074 cents 35:40:41:47:53:60:61:70 SD: 3.2607 cents 36:41:42:48:54:62:63:72 SD: 1.4300 cents 48:55:56:64:72:82:84:96 SD: 1.0741 cents 84:96:98:112:126:144:147:168 S SD: 0.0000 cents