Scala analysis: xen10-wilson-purvi-03a-05
Purvi modulation 5 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: 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: 9/8 203.9100 major whole tone 2: 28/27 62.9609 Archytas' 1/3-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: 1 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 2 9/8 203.910 cents major whole tone 1: 3 8/7 231.174 cents septimal whole tone 2: 1 147/128 239.607 cents 2: 2 7/6 266.871 cents septimal minor third 2: 1 32/27 294.135 cents Pythagorean 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: 1 27/16 905.865 cents Pythagorean major sixth 5: 2 12/7 933.129 cents septimal major sixth 5: 1 256/147 960.393 cents 6: 3 7/4 968.826 cents harmonic seventh 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 27/14 1137.039 cents septimal major seventh 6: 1 96/49 1164.303 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 266.9 498.0 702.0 737.7 968.8 1200.0 203.9 : 63.0 294.1 498.0 533.7 764.9 996.1 1200.0 266.9 : 231.2 435.1 470.8 702.0 933.1 1137.0 1200.0 498.0 : 203.9 239.6 470.8 702.0 905.9 968.8 1200.0 702.0 : 35.7 266.9 498.0 702.0 764.9 996.1 1200.0 737.7 : 231.2 462.3 666.3 729.2 960.4 1164.3 1200.0 968.8 : 231.2 435.1 498.0 729.2 933.1 968.8 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 : 9/8, 203.9100 cents, amount: 2 Most common interval of one step : 8/7, 231.1741 cents, amount: 3 Least squares average step : 163.86301 cents, oct.: 1147.04107 cents Scale is not proper Step pattern alph. order: ABCADCC Step pattern size order : CBDCADD Scale is a Constant Structure, by a margin of 8.43272 cents Scale diversity : 1.315534 Lumma stability : 0.087604 Lumma impropriety factor : 0.110430 Rothenberg efficiency : 0.436735 redundancy: 0.563265 Efficiency x scale size : 3.057143 Number of different interval sizes : 24 = 4.00000 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.00000 = 4 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 1029/1024, 8.4327 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Most common triad is 0.0 498.045 701.955 cents, amount: 2 Number of recognisable fifths : 4, average 701.9550 cents 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 n-1 differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions with margin 222.7414 cents: 6 -- Rational properties -- Prime limit : 7 Odd number limit : 147 (O: 147 U: 147) Highest odd numerator or denominator: 49 Scale harmonicity : 0.028112 Average absolute harmonicity : 0.257026 Specific harmonicity : 0.166687 Fundamental : 1/96, -6.5850 octaves, 2.7253 Hz. Guide tone : 1764, 10.7846 octaves, 461507.497 Hz. Exponens Consonantiae : 1.693440E+05, 17.36960 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 68.5, average 9.78571 Mersenne's string divisions : 6891885 Sum of van Prooijen's expressibility: 5.28888, average 0.75555 Sum of Tenney's harmonic distance : 10.28145, average 1.46878 Vogel's harmonic complexity : 11.14286 Wille's k value : 73 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 91.11889, average 3.25425 Lattice compactness (without 2's) : 45.00604, average 1.60736 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 2 -1.28571 15 1 3: -1 .. 2 0.14286 5 3 7: 0 .. 2 0.57143 4 3 Average exponent except 2's : 5 / 7 = 0.71429 Average absolute exponent except 2's: 9 / 7 = 1.28571 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 1 1 1 0 2 1 N T3 SD: 44.1159 c. M:-75.9862 c. 8: 1 1 1 2 0 1 2 N D3 SD: 43.9317 c. M: 68.8259 c. 10: 2 0 2 2 0 2 2 N M DE S SD: 20.9259 c. M:-36.0900 c. 15: 2 1 3 3 0 3 3 N SD: 22.9623 c. M: 43.9100 c. 16: 3 1 3 2 1 3 3 N SD: 21.3343 c. M:-33.1291 c. 17: 3 1 3 3 0 4 3 N SD: 15.6673 c. M: 31.7695 c. 19: 3 1 4 3 1 3 4 N T3 SD: 14.0691 c. M: 21.4575 c. 22: 4 1 4 4 1 4 4 N M DE S SD: 13.0045 c. M:-25.9846 c. Twenty-two tone Minor, Superpyth-7 24: 4 1 5 4 1 4 5 N T3 SD: 10.7866 c. M: 18.8259 c. 26: 4 2 5 4 1 5 5 N SD: 9.7122 c. M: 19.2946 c. 27: 5 1 5 5 1 5 5 N M DE S SD: 11.3624 c. M:-18.3122 c. 29: 5 1 6 5 1 5 6 N T3 SD: 10.0222 c. M: 18.5950 c. 31: 5 2 6 5 1 6 6 N SD: 5.1228 c. M: 10.3616 c. 36: 6 2 7 6 1 7 7 N SD: 2.5714 c. M: 4.3185 c. 77: 13 4 15 13 2 15 15 N SD: 2.3883 c. M: 5.1843 c. 89: 15 5 17 15 3 17 17 N SD: 2.1099 c. M:-3.9212 c. 94: 16 5 18 16 3 18 18 N SD: 1.2689 c. M:-2.7737 c. 99: 17 5 19 17 3 19 19 N SD: 1.2406 c. M:-2.1506 c. 130: 22 7 25 22 4 25 25 N SD: 0.6018 c. M: 0.8331 c. 135: 23 7 26 23 4 26 26 N SD: 0.2646 c. M:-0.5344 c. 265: 45 14 51 45 8 51 51 N SD: 0.2340 c. M:-0.4614 c. 306: 52 16 59 52 9 59 59 N SD: 0.1847 c. M: 0.3969 c. 400: 68 21 77 68 12 77 77 N SD: 0.1605 c. M:-0.3482 c. 436: 74 23 84 74 13 84 84 N SD: 0.1187 c. M: 0.2403 c. 441: 75 23 85 75 13 85 85 N SD: 0.1493 c. M: 0.2368 c. 571: 97 30 110 97 17 110 110 N SD: 0.0287 c. M: 0.0571 c. 706: 120 37 136 120 21 136 136 N SD: 0.0286 c. M:-0.0560 c. 1277: 217 67 246 217 38 246 246 N SD: 0.0069 c. M:-0.0146 c. 1848: 314 97 356 314 55 356 356 N SD: 0.0091 c. M: 0.0139 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 7:8 x 9 x 11:12:14 SD: 17.8799 cents 8:9 x 11:12 x 14:16 SD: 10.6546 cents 9:10:11:12 x 14:16:18 S SD: 15.3074 cents 10:11:12:13:15 x 18:20 SD: 15.0849 cents 11:12:13:15 x 17:19:22 SD: 12.4926 cents 12 x 14:16:18 x 21:24 S SD: 0.0000 cents 13 x 15:17 x 20:23:26 SD: 8.7641 cents 14:16 x 19:21 x 25:28 SD: 10.7807 cents 15:17:18:20 x 23:26:30 SD: 8.8534 cents 16:18:19:21:24:25:28:32 SD: 7.7005 cents 17:19:20:23 x 26:30:34 SD: 5.7536 cents 19:21:22:25 x 29:33:38 SD: 7.1442 cents 20 x 23:27:30:31:35:40 SD: 6.5128 cents 21:24:25:28 x 32:37:42 SD: 7.7737 cents 22:25:26:29:33:34:39:44 SD: 6.3048 cents 23:26:27:31 x 35:40:46 SD: 4.6174 cents 24:27:28:32:36:37:42:48 SD: 1.6767 cents 25:28:29:33 x 38:44:50 SD: 4.4750 cents 27:30:32:36 x 41:47:54 SD: 6.4531 cents 28:32:33:37:42:43:49:56 SD: 5.1878 cents 29:33:34:39 x 44:51:58 SD: 5.2973 cents 30:34:35:40:45:46:53:60 SD: 2.9900 cents 31:35:36:41 x 47:54:62 SD: 4.2751 cents 32:36:37:43:48:49:56:64 SD: 2.9367 cents 40:45:47:53:60:61:70:80 SD: 2.5546 cents 42:47:49:56:63:64:74:84 SD: 2.4463 cents 48:54:56:64:72:74:84:96 SD: 1.6767 cents 64:72:75:85:96:98:112:128 SD: 1.4665 cents 66:74:77:88:99:101:116:132 SD: 1.3640 cents 72:81:84:96:108:110:126:144 SD: 0.5615 cents 96:108:112:128:144:147:168:192 S SD: 0.0000 cents