Scala analysis: xen10-wilson-purvi-03a-06
Purvi modulation 6 from Figure 3a, Al-Farabi (8/7 8/7 49/48), (49/48 8/7 8/7)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 49/48 35.696812 slendro diesis, septimal 1/6-tone 2: 7/6 266.870906 septimal minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 49/32 737.651813 6: 7/4 968.825906 harmonic seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 49/48 35.6968 slendro diesis, septimal 1/6-tone 2: 8/7 231.1741 septimal whole tone 3: 8/7 231.1741 septimal whole tone 4: 9/8 203.9100 major whole tone 5: 49/48 35.6968 slendro diesis, septimal 1/6-tone 6: 8/7 231.1741 septimal whole 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: 1 147/128 239.607 cents 2: 3 7/6 266.871 cents septimal minor third 2: 1 9/7 435.084 cents septimal major third, BP third 2: 2 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: 2 49/32 737.652 cents 5: 1 14/9 764.916 cents septimal minor sixth 5: 3 12/7 933.129 cents septimal major sixth 5: 1 256/147 960.393 cents 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: 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 : 35.7 266.9 498.0 702.0 737.7 968.8 1200.0 35.7 : 231.2 462.3 666.3 702.0 933.1 1164.3 1200.0 266.9 : 231.2 435.1 470.8 702.0 933.1 968.8 1200.0 498.0 : 203.9 239.6 470.8 702.0 737.7 968.8 1200.0 702.0 : 35.7 266.9 498.0 533.7 764.9 996.1 1200.0 737.7 : 231.2 462.3 498.0 729.2 960.4 1164.3 1200.0 968.8 : 231.2 266.9 498.0 729.2 933.1 968.8 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: 239.6068 .. 462.3482 cents 8192/7203, 222.7414 cents 1029/1024, 8.4327 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 .. 960.3932 cents 8192/7203, 222.7414 cents 1029/1024, 8.4327 cents 6: 968.8259 .. 1164.3032 cents 384/343, 195.4773 cents 1029/1024, 8.4327 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 : 162.66149 cents, oct.: 1138.63041 cents Scale is not proper Step pattern alph. order: ABBCABB Step pattern size order : SLLMSLL Scale is a Constant Structure, by a margin of 8.43272 cents Scale diversity : 1.190224 Lumma stability : 0.087604 Lumma impropriety factor : 0.110430 Rothenberg efficiency : 0.478912 redundancy: 0.521088 Efficiency x scale size : 3.352381 Number of different interval sizes : 20 = 3.33333 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.33333 = 10/3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 1029/1024, 8.4327 cents Most common triad is 0.0 701.955 968.826 cents, amount: 3 Number of recognisable fifths : 4, average 701.9550 cents Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 2 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions with margin 222.7414 cents: 5 -- Rational properties -- Prime limit : 7 Odd number limit : 147 (O: 147 U: 147) Highest odd numerator or denominator: 49 Scale harmonicity : 0.030391 Average absolute harmonicity : 0.245128 Specific harmonicity : 0.150000 Fundamental : 1/96, -6.5850 octaves, 2.7253 Hz. Guide tone : 588, 9.1997 octaves, 153835.832 Hz. Exponens Consonantiae : 5.644800E+04, 15.78463 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 108.5, average 15.50000 Mersenne's string divisions : 39324285 Sum of van Prooijen's expressibility: 6.02483, average 0.86069 Sum of Tenney's harmonic distance : 11.79555, average 1.68508 Vogel's harmonic complexity : 11.71429 Wille's k value : 73 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 92.85238, average 3.31616 Lattice compactness (without 2's) : 41.49405, average 1.48193 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 2 -1.42857 16 1 3: -1 .. 1 -0.28571 4 2 7: 0 .. 2 0.85714 6 4 Average exponent except 2's : 4 / 7 = 0.57143 Average absolute exponent except 2's: 10 / 7 = 1.42857 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: 0 2 1 1 0 2 1 N T3 SD: 44.4695 c. M:-75.9862 c. 8: 0 2 1 2 0 1 2 N T3 SD: 41.1928 c. M: 68.8259 c. 10: 0 2 2 2 0 2 2 N M DE S SD: 20.8294 c. M: 35.6968 c. 15: 0 3 3 3 0 3 3 N M DE S SD: 20.8294 c. M: 35.6968 c. 17: 1 3 3 3 1 3 3 N M DE S SD: 21.9466 c. M:-38.8188 c. 19: 1 3 4 3 1 3 4 N T3 SD: 16.6101 c. M:-27.4611 c. 21: 1 4 4 3 1 4 4 N SD: 14.0224 c. M:-21.4460 c. Gorgo-Pelog 22: 1 4 4 4 1 4 4 N M DE S SD: 13.8120 c. M:-25.9846 c. Raga Bilashkhani Todi 24: 1 4 5 4 1 4 5 N T3 SD: 11.9746 c. M: 18.8259 c. 26: 1 5 5 4 1 5 5 N SD: 7.5343 c. M:-10.4570 c. 31: 1 6 6 5 1 6 6 N SD: 3.4932 c. M: 5.1808 c. 36: 1 7 7 6 1 7 7 N SD: 2.2861 c. M: 4.3185 c. 67: 2 13 13 11 2 13 13 N SD: 2.4137 c. M:-3.4475 c. 94: 3 18 18 16 3 18 18 N SD: 1.5998 c. M:-2.7737 c. 99: 3 19 19 17 3 19 19 N SD: 0.9705 c. M:-1.7421 c. 130: 4 25 25 22 4 25 25 N SD: 0.6913 c. M:-1.2263 c. 135: 4 26 26 23 4 26 26 N SD: 0.1790 c. M:-0.2672 c. 400: 12 77 77 68 12 77 77 N SD: 0.1943 c. M:-0.3482 c. 436: 13 84 84 74 13 84 84 N SD: 0.0826 c. M:-0.1201 c. 571: 17 110 110 97 17 110 110 N SD: 0.0220 c. M:-0.0300 c. 706: 21 136 136 120 21 136 136 N SD: 0.0193 c. M:-0.0280 c. 1277: 38 246 246 217 38 246 246 N SD: 0.0080 c. M:-0.0146 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 x 5:6 S SD: 28.1557 cents 4 x x 5:6 x 7:8 S SD: 27.9328 cents 5 x 6:7 x 8:9:10 S SD: 26.5880 cents 6 x 7:8:9 x 11:12 SD: 16.1074 cents 7 x 8:9 x 11:12:14 SD: 18.4643 cents 8 x 9:11:12 x 14:16 SD: 16.4949 cents 9 x 11:12 x 14:16:18 SD: 17.8582 cents 10 x 12:13:15 x 18:20 SD: 16.3441 cents 11:12:13:15 x 17:19:22 SD: 21.0763 cents 12:13:14:16:18 x 21:24 S SD: 17.1460 cents 13:14:15:17 x 20:23:26 SD: 17.0744 cents 14:15:16:19:21 x 25:28 SD: 17.0374 cents 15:16:18:20 x 23:26:30 SD: 15.3114 cents 16:17:19:21:24:25:28:32 SD: 12.5375 cents 17:18:20:23 x 26:30:34 SD: 11.8608 cents 18:19:21:24:27:28:32:36 SD: 9.9384 cents 19:20:22:25 x 29:33:38 SD: 10.1632 cents 20:21:23:27:30:31:35:40 SD: 8.9278 cents 21:22:25:28 x 32:37:42 SD: 9.7792 cents 22:23:26:29:33:34:39:44 SD: 8.2653 cents 23:24:27:31 x 35:40:46 SD: 7.7112 cents 24:25:28:32:36:37:42:48 SD: 5.2704 cents 25:26:29:33 x 38:44:50 SD: 6.8688 cents 26:27:30:35:39:40:46:52 SD: 6.2973 cents 27:28:32:36 x 41:47:54 SD: 7.0316 cents 28:29:33:37:42:43:49:56 SD: 4.9552 cents 29:30:34:39 x 44:51:58 SD: 5.6458 cents 30:31:35:40:45:46:53:60 SD: 3.8300 cents 31:32:36:41 x 47:54:62 SD: 5.2462 cents 32:33:37:43:48:49:56:64 SD: 3.8638 cents 36:37:42:48:54:55:63:72 SD: 1.7682 cents 48:49:56:64:72:74:84:96 SD: 1.6767 cents 60:61:70:80:90:92:105:120 SD: 1.0660 cents 84:86:98:112:126:129:147:168 SD: 1.0182 cents 90:92:105:120:135:138:158:180 SD: 0.9169 cents 96:98:112:128:144:147:168:192 S SD: 0.0000 cents