Scala analysis: xen10-wilson-purvi-03a-07
Purvi modulation 7 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: 49/36 533.741811 Arabic lute acute fourth 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: 49/48 35.6968 slendro diesis, septimal 1/6-tone 5: 9/8 203.9100 major whole 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 : 35.7 266.9 498.0 533.7 737.7 968.8 1200.0 35.7 : 231.2 462.3 498.0 702.0 933.1 1164.3 1200.0 266.9 : 231.2 266.9 470.8 702.0 933.1 968.8 1200.0 498.0 : 35.7 239.6 470.8 702.0 737.7 968.8 1200.0 533.7 : 203.9 435.1 666.3 702.0 933.1 1164.3 1200.0 737.7 : 231.2 462.3 498.0 729.2 960.4 996.1 1200.0 968.8 : 231.2 266.9 498.0 729.2 764.9 968.8 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 : 157.85540 cents, oct.: 1104.98777 cents Scale is not proper Step pattern alph. order: ABBACBB Step pattern size order : SLLSMLL 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 Phrygian 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 4 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 222.7414 cents: 4 -- 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 : 0.211287 Specific harmonicity : 0.141936 Fundamental : 1/288, -8.1699 octaves, 0.9084 Hz. Guide tone : 196, 7.6147 octaves, 51278.611 Hz. Exponens Consonantiae : 5.644800E+04, 15.78463 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 148.5, average 21.21429 Mersenne's string divisions : 668512845 Sum of van Prooijen's expressibility: 7.23791, average 1.03399 Sum of Tenney's harmonic distance : 14.26390, average 2.03770 Vogel's harmonic complexity : 15.28571 Wille's k value : 220 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 94.90227, average 3.38937 Lattice compactness (without 2's) : 43.32248, average 1.54723 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 2 -1.57143 17 1 3: -2 .. 0 -0.71429 5 1 7: 0 .. 2 1.14286 8 5 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 13 / 7 = 1.85714 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 0 1 2 1 N T3 SD: 44.6534 c. M:-75.9862 c. 8: 0 2 1 0 2 1 2 N T3 SD: 48.6713 c. M: 83.7418 c. 9: 0 2 2 0 2 1 2 N T3 S SD: 33.0946 c. M:-62.3482 c. 10: 0 2 2 0 2 2 2 N M DE S SD: 28.2832 c. M: 53.7418 c. 11: 0 2 3 0 2 2 2 N SD: 31.3363 c. M: 48.6891 c. 13: 0 3 2 1 2 2 3 N SD: 27.2707 c. M: 45.7490 c. 15: 0 3 3 0 3 3 3 N M DE S SD: 28.2832 c. M: 53.7418 c. 16: 1 3 3 0 3 3 3 N T3 SD: 22.7906 c. M:-39.3032 c. 18: 0 4 3 1 3 3 4 N SD: 22.4800 c. M: 35.6968 c. 19: 1 3 4 0 4 3 4 N SD: 19.6040 c. M: 28.4787 c. 20: 0 4 4 1 3 4 4 N SD: 19.8227 c. M: 35.6968 c. 21: 1 4 4 0 4 4 4 N T3 SD: 14.5954 c. M:-21.4460 c. 22: 1 4 4 1 4 4 4 N M DE S SD: 14.2512 c. M:-25.9846 c. 24: 1 4 5 1 4 4 5 N SD: 13.4390 c. M: 18.8259 c. 26: 1 5 5 1 4 5 5 N SD: 10.0603 c. M:-20.1043 c. 27: 1 5 5 1 5 5 5 N M DE S SD: 8.9542 c. M:-17.9037 c. 31: 1 6 6 1 5 6 6 N SD: 4.2378 c. M:-8.1937 c. 36: 1 7 7 1 6 7 7 N SD: 2.1689 c. M: 4.3185 c. 67: 2 13 13 2 11 13 13 N SD: 2.4394 c. M:-3.5716 c. 94: 3 18 18 3 16 18 18 N SD: 1.8433 c. M:-2.7737 c. 99: 3 19 19 3 17 19 19 N SD: 0.8947 c. M:-1.7421 c. 130: 4 25 25 4 22 25 25 N SD: 0.9158 c. M:-1.6428 c. 135: 4 26 26 4 23 26 26 N SD: 0.2137 c. M: 0.4085 c. 400: 12 77 77 12 68 77 77 N SD: 0.2167 c. M:-0.3482 c. 436: 13 84 84 13 74 84 84 N SD: 0.1033 c. M:-0.2031 c. 571: 17 110 110 17 97 110 110 N SD: 0.0293 c. M:-0.0585 c. 706: 21 136 136 21 120 136 136 N SD: 0.0199 c. M: 0.0308 c. 1277: 38 246 246 38 217 246 246 N SD: 0.0086 c. M:-0.0146 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x 4 S SD: 17.8484 cents 3 x x 4 x x 5:6 S SD: 28.1557 cents 4 x x 5 x 6:7:8 S SD: 29.3238 cents 5 x 6 x 7:8:9:10 S SD: 22.7305 cents 6 x 7:8 x 9:11:12 SD: 17.6187 cents 7 x 8:9:10:11:12:14 S SD: 20.7743 cents 8 x 9 x 11:12:14:16 SD: 14.8960 cents 9 x 11:12 x 14:16:18 SD: 17.8582 cents 10 x 12:13:14:15:18:20 S SD: 16.9403 cents 11:12:13 x 15:17:19:22 SD: 20.0612 cents 12:13:14:16 x 18:21:24 S SD: 18.1488 cents 13:14:15:17:18:20:23:26 SD: 15.2354 cents 14:15:16 x 19:21:25:28 SD: 17.3291 cents 15:16:18:20 x 23:26:30 SD: 15.3114 cents 16:17:19:21:22:25:28:32 SD: 12.7865 cents 17:18:20 x 23:26:30:34 SD: 11.2228 cents 18:19:21:24:25:28:32:36 SD: 11.1237 cents 19:20:22:25:26:29:33:38 SD: 8.8115 cents 20:21:23 x 27:31:35:40 SD: 10.0615 cents 21:22:25:28:29:32:37:42 SD: 9.1144 cents 22:23:26:29:30:34:39:44 SD: 8.2780 cents 23:24:27 x 31:35:40:46 SD: 7.5988 cents 24:25:28:32:33:37:42:48 SD: 5.8379 cents 26:27:30:35 x 40:46:52 SD: 7.3468 cents 27:28:32:36:37:41:47:54 SD: 6.2559 cents 28:29:33:37:38:43:49:56 SD: 5.0075 cents 29:30:34:39 x 44:51:58 SD: 5.6458 cents 30:31:35:40:41:46:53:60 SD: 3.9603 cents 35:36:41:47:48:54:61:70 SD: 3.9498 cents 36:37:42:48:49:55:63:72 SD: 1.7682 cents 47:48:55:63:64:72:82:94 SD: 1.6989 cents 60:61:70:80:82:92:105:120 SD: 1.4667 cents 83:85:97:111:113:127:145:166 SD: 1.2552 cents 84:86:98:112:114:129:147:168 SD: 1.2483 cents 89:91:104:119:121:136:156:178 SD: 1.1379 cents 91:93:106:121:124:139:159:182 SD: 1.1365 cents 96:98:112:128:131:147:168:192 SD: 0.6301 cents 144:147:168:192:196:221:252:288 SD: 0.5602 cents 180:184:210:240:245:276:315:360 SD: 0.4755 cents 186:190:217:248:253:285:326:372 SD: 0.4729 cents 192:196:224:256:261:294:336:384 SD: 0.3157 cents 252:257:294:336:343:386:441:504 SD: 0.2535 cents 288:294:336:384:392:441:504:576 S SD: 0.0000 cents