Scala analysis: xen10-wilson-purvi-03a-01
Purvi modulation 1 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: 9/8 203.910002 major 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: 9/8 203.9100 major whole tone 2: 8/7 231.1741 septimal 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: 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 : 203.9 435.1 666.3 702.0 933.1 1164.3 1200.0 203.9 : 231.2 462.3 498.0 729.2 960.4 996.1 1200.0 435.1 : 231.2 266.9 498.0 729.2 764.9 968.8 1200.0 666.3 : 35.7 266.9 498.0 533.7 737.7 968.8 1200.0 702.0 : 231.2 462.3 498.0 702.0 933.1 1164.3 1200.0 933.1 : 231.2 266.9 470.8 702.0 933.1 968.8 1200.0 1164.3: 35.7 239.6 470.8 702.0 737.7 968.8 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: 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 : 185.22955 cents, oct.: 1296.60687 cents Scale is not proper Step pattern alph. order: ABBCBBC Step pattern size order : MLLSLLS Scale is sum-free (all different intervals) 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 0.0 231.174 498.045 cents, amount: 3 Number of recognisable fifths : 4, average 701.9550 cents Scale is Hypodorian octave species of abstract tetrachord All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 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 differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions with margin 195.4773 cents: 3 -- Rational properties -- Prime limit : 7 Odd number limit : 147 (O: 147 U: 147) Highest odd numerator or denominator: 49 Scale harmonicity : 0.029494 Average absolute harmonicity : 0.227662 Specific harmonicity : 0.144469 Fundamental : 1/392, -8.6147 octaves, 0.6674 Hz. Guide tone : 288, 8.1699 octaves, 75348.163 Hz. Exponens Consonantiae : 1.128960E+05, 16.78463 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 163.0, average 23.28571 Mersenne's string divisions : 272017680 Sum of van Prooijen's expressibility: 6.61110, average 0.94444 Sum of Tenney's harmonic distance : 13.88013, average 1.98288 Vogel's harmonic complexity : 15.85714 Wille's k value : 220 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 97.99411, average 3.49979 Lattice compactness (without 2's) : 44.55854, average 1.59138 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 5 1.00000 15 1 3: 0 .. 2 1.28571 9 2 7: -2 .. 0 -0.85714 6 4 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 15 / 7 = 2.14286 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 2 1 0 1 2 0 N T3 SD: 46.3194 c. M:-79.2016 c. 8: 1 2 1 1 1 2 0 N D3 SD: 41.7459 c. M: 66.2582 c. 9: 2 1 2 0 2 2 0 N T3 S SD: 33.1426 c. M:-62.7567 c. 11: 2 2 2 0 3 2 0 N SD: 29.8450 c. M:-48.6891 c. 12: 2 2 3 0 2 3 0 N SD: 26.0777 c. M:-35.6968 c. 13: 2 3 2 1 2 3 0 N SD: 24.4492 c. M:-36.5065 c. 14: 2 3 3 0 3 3 0 N SD: 21.0735 c. M:-35.6968 c. 17: 3 3 3 1 3 3 1 N M DE S SD: 19.3705 c. M: 34.8914 c. 19: 3 4 4 0 4 3 1 N SD: 17.2283 c. M:-28.4787 c. 22: 4 4 4 1 4 4 1 N M DE S SD: 10.5763 c. M: 18.8486 c. Raga Yaman 24: 4 5 4 1 5 4 1 N T3 SD: 11.9232 c. M:-16.8709 c. 27: 5 5 5 1 5 5 1 N M DE S SD: 9.1302 c. M:-18.3122 c. 31: 5 6 6 1 6 6 1 N SD: 6.6898 c. M: 10.3616 c. 36: 6 7 7 1 7 7 1 N SD: 1.9989 c. M: 3.9100 c. 94: 16 18 18 3 18 18 3 N SD: 1.4818 c. M: 2.6011 c. 99: 17 19 19 3 19 19 3 N SD: 1.0738 c. M:-2.1506 c. 130: 22 25 25 4 25 25 4 N SD: 1.0196 c. M: 1.6428 c. 135: 23 26 26 4 26 26 4 N SD: 0.3397 c. M:-0.5344 c. 171: 29 33 33 5 33 33 5 N SD: 0.3340 c. M:-0.6091 c. 306: 52 59 59 9 59 59 9 N SD: 0.2435 c. M:-0.4085 c. 400: 68 77 77 12 77 77 12 N SD: 0.1658 c. M: 0.3032 c. 436: 74 84 84 13 84 84 13 N SD: 0.1603 c. M: 0.2403 c. 535: 91 103 103 16 103 103 16 N SD: 0.1200 c. M:-0.2021 c. 571: 97 110 110 17 110 110 17 N SD: 0.0424 c. M: 0.0585 c. 706: 120 136 136 21 136 136 21 N SD: 0.0316 c. M:-0.0560 c. 1277: 217 246 246 38 246 246 38 N SD: 0.0064 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: 39.5555 cents 6:7:8 x 9:10 x 12 S SD: 20.3044 cents 7:8:9:10:11:12 x 14 S SD: 16.3368 cents 8:9:10 x 12:14 x 16 S SD: 12.0877 cents 9:10:12:13:14:15 x 18 S SD: 17.9875 cents 10:11:13 x 15:17 x 20 SD: 9.1422 cents 11:12:14:16:17:19 x 22 SD: 13.2263 cents 12:14:15 x 18:21 x 24 S SD: 17.4550 cents 13:15:17:19:20:22:25:26 SD: 11.3618 cents 14:16:18 x 21:24:27:28 S SD: 6.4262 cents 16:18:21 x 24:27:31:32 SD: 8.1460 cents 17:19:22:25:26:29:33:34 SD: 5.9180 cents 18:20:23:26:27:31:35:36 SD: 5.8743 cents 21:24:27:31:32:36:41:42 SD: 5.6908 cents 22:25:28:32:33:38:43:44 SD: 4.7555 cents 24:27:31:35:36:41:47:48 SD: 2.3547 cents 32:36:41:47:48:55:63:64 SD: 1.6176 cents 56:63:72:82:84:96:110:112 SD: 1.0741 cents 70:79:90:103:105:120:137:140 SD: 0.8937 cents 94:106:121:138:141:161:184:188 SD: 0.7555 cents 98:110:126:144:147:168:192:196 SD: 0.5615 cents 126:142:162:185:189:216:247:252 SD: 0.4968 cents 168:189:216:247:252:288:329:336 SD: 0.1789 cents 224:252:288:329:336:384:439:448 SD: 0.1342 cents 392:441:504:576:588:672:768:784 S SD: 0.0000 cents