Scala analysis: xen10-wilson-purvi-03b-02
Purvi modulation 2 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: 9/7 435.084095 septimal major third, BP third 3: 4/3 498.044999 perfect fourth 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: 8/7 231.1741 septimal whole tone 2: 9/8 203.9100 major whole tone 3: 28/27 62.9609 Archytas' 1/3-tone 4: 9/8 203.9100 major whole 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: 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: 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: 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: 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 : 231.2 435.1 498.0 702.0 933.1 1164.3 1200.0 231.2 : 203.9 266.9 470.8 702.0 933.1 968.8 1200.0 435.1 : 63.0 266.9 498.0 729.2 764.9 996.1 1200.0 498.0 : 203.9 435.1 666.3 702.0 933.1 1137.0 1200.0 702.0 : 231.2 462.3 498.0 729.2 933.1 996.1 1200.0 933.1 : 231.2 266.9 498.0 702.0 764.9 968.8 1200.0 1164.3: 35.7 266.9 470.8 533.7 737.7 968.8 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: 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 : 9/8, 203.9100 cents, amount: 2 Most common interval of one step : 8/7, 231.1741 cents, amount: 3 Least squares average step : 181.81973 cents, oct.: 1272.73809 cents Scale is not proper Step pattern alph. order: ABCBAAD Step pattern size order : DCBCDDA Scale is a Constant Structure, by a margin of 8.43272 cents Scale diversity : 1.245352 Lumma stability : 0.133044 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 : 4 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 0.0 701.955 933.129 cents, amount: 3 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 0 Length of longest subharmonic part : 2 at degree 3 Formal octave complements present : 3 = 42.8571% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions with margin 195.4773 cents: 2 -- Rational properties -- Prime limit : 7 Odd number limit : 49 (O: 49 U: 49) Highest odd numerator or denominator: 49 Scale harmonicity : 0.028926 Average absolute harmonicity : 0.246942 Specific harmonicity : 0.168168 Fundamental : 1/294, -8.1997 octaves, 0.8899 Hz. Guide tone : 288, 8.1699 octaves, 75348.163 Hz. Exponens Consonantiae : 8.467200E+04, 16.36960 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 105.0, average 15.00000 Mersenne's string divisions : 925680 Sum of van Prooijen's expressibility: 5.28888, average 0.75555 Sum of Tenney's harmonic distance : 11.30264, average 1.61466 Vogel's harmonic complexity : 16.42857 Wille's k value : 220 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 81.58952, average 2.91391 Lattice compactness (without 2's) : 43.07054, average 1.53823 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 5 1.71429 14 1 3: -1 .. 2 0.57143 6 2 7: -2 .. 0 -0.71429 5 4 Average exponent except 2's :-1 / 7 =-0.14286 Average absolute exponent except 2's: 11 / 7 = 1.57143 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 1 2 0 N T3 SD: 52.9839 c. M: 92.2270 c. 8: 2 1 0 2 1 2 0 N T3 SD: 41.3140 c. M:-68.8259 c. 9: 2 1 1 1 2 2 0 N T3 SD: 29.8937 c. M:-35.6968 c. 10: 2 2 0 2 2 2 0 N M DE S SD: 26.0299 c. M:-44.9159 c. 14: 3 2 1 2 3 3 0 N SD: 19.3214 c. M:-35.6968 c. 17: 3 3 1 3 3 3 1 N M DE S SD: 16.8954 c. M: 34.8914 c. Seventeen-tone Major 19: 4 3 1 3 4 3 1 N T3 SD: 14.9800 c. M: 27.4611 c. 20: 4 3 1 4 4 3 1 N SD: 18.0054 c. M:-26.8709 c. 22: 4 4 1 4 4 4 1 N M DE S SD: 9.7237 c. M: 18.8486 c. Twenty-two tone Major 24: 5 4 1 4 5 4 1 N T3 SD: 12.3852 c. M:-18.8259 c. 26: 5 4 2 4 5 5 1 N SD: 10.5882 c. M: 19.6995 c. 27: 5 5 1 5 5 5 1 N M DE S SD: 7.6717 c. M:-9.3603 c. 31: 6 5 2 5 6 6 1 N SD: 4.8813 c. M: 9.2776 c. 36: 7 6 2 6 7 7 1 N SD: 1.7320 c. M:-2.3635 c. 94: 18 16 5 16 18 18 3 N SD: 1.2710 c. M: 2.6011 c. 99: 19 17 5 17 19 19 3 N SD: 0.8615 c. M:-1.2795 c. 130: 25 22 7 22 25 25 4 N SD: 0.7766 c. M: 1.2379 c. 135: 26 23 7 23 26 26 4 N SD: 0.2481 c. M:-0.4715 c. 265: 51 45 14 45 51 51 8 N SD: 0.2846 c. M: 0.5296 c. 301: 58 51 16 51 58 58 9 N SD: 0.2803 c. M: 0.5326 c. 306: 59 52 16 52 59 59 9 N SD: 0.2026 c. M:-0.4027 c. 400: 77 68 21 68 77 77 12 N SD: 0.1464 c. M: 0.3032 c. 436: 84 74 23 74 84 84 13 N SD: 0.1168 c. M: 0.2217 c. 535: 103 91 28 91 103 103 16 N SD: 0.1092 c. M: 0.1910 c. 571: 110 97 30 97 110 110 17 N SD: 0.0310 c. M: 0.0578 c. 706: 136 120 37 120 136 136 21 N SD: 0.0235 c. M:-0.0434 c. 1277: 246 217 67 217 246 246 38 N SD: 0.0058 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 x 4 x 5 x 6 S SD: 16.2568 cents 4 x 5 x 6:7 x 8 S SD: 15.1096 cents 5:6 x 7:8:9 x 10 S SD: 36.8174 cents 6:7 x 8:9:10 x 12 S SD: 12.0877 cents 7:8:9 x 11:12 x 14 SD: 16.1074 cents 8:9:10:11:12:14 x 16 S SD: 14.1756 cents 9:10 x 12:14:15 x 18 S SD: 18.6774 cents 10:11:13 x 15:17 x 20 SD: 14.0773 cents 11:13:14:15:17:19 x 22 SD: 14.9374 cents 12:14:15:16:18:21 x 24 S SD: 11.6989 cents 13:15:17 x 20:22:25:26 SD: 11.2950 cents 14:16:18:19:21:24:27:28 SD: 5.8594 cents 16:18 x 21:24:27:31:32 SD: 8.5004 cents 18:21:23:24:27:31:35:36 SD: 5.7570 cents 20:23:26:27:30:34:39:40 SD: 4.9916 cents 21:24:27:28:32:36:41:42 SD: 3.9887 cents 28:32:36:37:42:48:55:56 SD: 2.3095 cents 42:48:54:56:63:72:82:84 SD: 0.8602 cents 84:96:108:112:126:144:165:168 SD: 0.6432 cents 98:112:126:131:147:168:192:196 SD: 0.6301 cents 126:144:162:168:189:216:247:252 SD: 0.1431 cents 168:192:216:224:252:288:329:336 SD: 0.1074 cents 294:336:378:392:441:504:576:588 S SD: 0.0000 cents