Scala analysis: xen10-wilson-purvi-06b-03
Purvi modulation 3 from Figure 6b, Al-Farabi (10/9 27/25 10/9)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 10/9 182.403712 minor whole tone 2: 5/4 386.313714 major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 5/3 884.358713 major sixth, BP sixth 6: 9/5 1017.596288 just minor seventh, BP seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 10/9 182.4037 minor whole tone 2: 9/8 203.9100 major whole tone 3: 16/15 111.7313 minor diatonic semitone 4: 9/8 203.9100 major whole tone 5: 10/9 182.4037 minor whole tone 6: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 7: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 3 10/9 182.404 cents minor whole tone 1: 2 9/8 203.910 cents major whole tone 2: 4 6/5 315.641 cents minor third 2: 1 100/81 364.807 cents grave major third 2: 2 5/4 386.314 cents major third 3: 4 4/3 498.045 cents perfect fourth 3: 2 27/20 519.551 cents acute fourth 3: 1 25/18 568.717 cents classic augmented fourth 4: 1 36/25 631.283 cents classic diminished fifth 4: 2 40/27 680.449 cents grave fifth 4: 4 3/2 701.955 cents perfect fifth 5: 2 8/5 813.686 cents minor sixth 5: 1 81/50 835.193 cents acute minor sixth 5: 4 5/3 884.359 cents major sixth, BP sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 3 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 50/27 1066.762 cents grave major seventh 6: 1 15/8 1088.269 cents classic major seventh 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 : 182.4 386.3 498.0 702.0 884.4 1017.6 1200.0 182.4 : 203.9 315.6 519.6 702.0 835.2 1017.6 1200.0 386.3 : 111.7 315.6 498.0 631.3 813.7 996.1 1200.0 498.0 : 203.9 386.3 519.6 702.0 884.4 1088.3 1200.0 702.0 : 182.4 315.6 498.0 680.4 884.4 996.1 1200.0 884.4 : 133.2 315.6 498.0 702.0 813.7 1017.6 1200.0 1017.6: 182.4 364.8 568.7 680.4 884.4 1066.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 203.9100 cents 135/128, 92.1787 cents 16/15, 111.7313 cents 2: 315.6413 .. 386.3137 cents 25/24, 70.6724 cents 16/15, 111.7313 cents 3: 498.0450 .. 568.7174 cents 25/24, 70.6724 cents 16/15, 111.7313 cents 4: 631.2826 .. 701.9550 cents 25/24, 70.6724 cents 648/625, 62.5651 cents 5: 813.6863 .. 884.3587 cents 25/24, 70.6724 cents 16/15, 111.7313 cents 6: 996.0900 .. 1088.2687 cents 135/128, 92.1787 cents 16/15, 111.7313 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.534293 Largest / Average step : 1.189475 Largest / Smallest step : 1.825004 Median interval of one step : 10/9, 182.4037 cents, amount: 3 Most common interval of one step : 10/9, 182.4037 cents, amount: 3 Least squares average step : 172.74541 cents, oct.: 1209.21787 cents Scale is strictly proper Step pattern alph. order: ABCBADA Step pattern size order : CDADCBC Scale is a Constant Structure, by a margin of 62.56515 cents Scale diversity : 1.386222 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.610794 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 : 81/80, 21.5063 cents Most common triad is 0.0 315.641 498.045 cents, amount: 3 Number of recognisable fifths : 4, average 701.9550 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 1 3 Length of longest harmonic part : 2 at degree 3 Length of longest subharmonic part : 2 at degree 0 Formal octave complements present : 5 = 71.4286% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined Limited inverse transpositions with margin 70.6724 cents: 1 -- Rational properties -- Prime limit : 5 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 9 Scale harmonicity : 0.036408 Average absolute harmonicity : 0.268588 Specific harmonicity : 0.219830 Fundamental : 1/180, -7.4919 octaves, 1.4535 Hz. Guide tone : 180, 7.4919 octaves, 47092.602 Hz. Exponens Consonantiae : 3.240000E+04, 14.98371 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 32.5, average 4.64286 Mersenne's string divisions : 47880 Sum of van Prooijen's expressibility: 4.26067, average 0.60867 Sum of Tenney's harmonic distance : 8.24294, average 1.17756 Vogel's harmonic complexity : 14.14286 Wille's k value : 112 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 70.33757, average 2.51206 Lattice compactness (without 2's) : 49.89629, average 1.78201 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.14286 7 1 3: -2 .. 2 -0.14286 7 2 5: -1 .. 1 0.28571 4 4 Average exponent except 2's : 1 / 7 = 0.14286 Average absolute exponent except 2's: 11 / 7 = 1.57143 Scale is JI-epimorphic with val: <7 11 16| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 22.0312 c. M: 43.4566 c. Lebeng 12: 2 2 1 2 2 1 2 P M ME S SD: 12.2991 c. M: 17.5963 c. G.Hypophrygian, G.Ionian (Iastian), M.Mixolydian, G.M.Hypoionian, Hypermixolydian, Mischung 3, Khamaj That, Mela Harikambhoji, Raga Balahamsa, Bhim, Devamanohari, Harini, Janjhuti, Kaamaai, Khambhavati, Surati, Gregorian nr.7, Enharmonic Byzantine Liturgical, Rast descending: Greece, Ching, Shang: China 19: 3 3 2 3 3 2 3 SP M ME S SD: 6.0764 c. M: 7.3663 c. Nineteen-tone Mixolydian 34: 5 6 3 6 5 4 5 SP SD: 3.9455 c. M: 5.9331 c. 46: 7 8 4 8 7 5 7 SP SD: 2.4840 c. M:-4.9906 c. 53: 8 9 5 9 8 6 8 SP SD: 1.0015 c. M: 1.4081 c. 99: 15 17 9 17 15 11 15 SP SD: 0.9014 c. M:-1.5651 c. 118: 18 20 11 20 18 13 18 SP SD: 0.4033 c. M: 0.6471 c. 171: 26 29 16 29 26 19 26 SP SD: 0.1811 c. M: 0.3488 c. 289: 44 49 27 49 44 32 44 SP SD: 0.2085 c. M: 0.2952 c. 388: 59 66 36 66 59 43 59 SP SD: 0.1439 c. M:-0.2842 c. 441: 67 75 41 75 67 49 67 SP SD: 0.0735 c. M: 0.0908 c. 559: 85 95 52 95 85 62 85 SP SD: 0.0574 c. M:-0.0906 c. 612: 93 104 57 104 93 68 93 SP SD: 0.0354 c. M: 0.0508 c. 1171: 178 199 109 199 178 130 178 SP SD: 0.0114 c. M:-0.0228 c. 1783: 271 303 166 303 271 198 271 SP SD: 0.0092 c. M: 0.0145 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: 0.0000 cents 4 x 5 x 6 x 7:8 S SD: 12.1926 cents 5 x 6:7 x 8:9:10 S SD: 26.1717 cents 6:7 x 8:9:10:11:12 S SD: 15.0405 cents 7:8:9 x 11:12:13:14 SD: 21.4407 cents 8:9:10:11:12:13:14:16 S SD: 12.4542 cents 9:10:11:12:14:15:16:18 S SD: 11.0104 cents 10:11 x 13:15:17:18:20 SD: 9.7171 cents 12:13:15:16:18:20:22:24 SD: 7.7332 cents 16:18:20:21:24:27:29:32 SD: 6.0809 cents 20:22:25:27:30:33:36:40 SD: 4.6686 cents 24:27:30:32:36:40:43:48 SD: 3.2797 cents 36:40:45:48:54:60:65:72 SD: 0.7622 cents 108:120:135:144:162:180:194:216 SD: 0.5094 cents 144:160:180:192:216:240:259:288 SD: 0.1909 cents 180:200:225:240:270:300:324:360 SD: 0.0000 cents