Scala analysis: xen10-wilson-purvi-06b-04
Purvi modulation 4 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: 6/5 315.641287 minor 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: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 3: 10/9 182.4037 minor whole tone 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: 2 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 4 10/9 182.404 cents minor whole tone 1: 1 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: 1 16/9 996.090 cents Pythagorean minor seventh 6: 4 9/5 1017.596 cents just minor seventh, BP seventh 6: 2 50/27 1066.762 cents grave major seventh Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 182.4 315.6 498.0 702.0 884.4 1017.6 1200.0 182.4 : 133.2 315.6 519.6 702.0 835.2 1017.6 1200.0 315.6 : 182.4 386.3 568.7 702.0 884.4 1066.8 1200.0 498.0 : 203.9 386.3 519.6 702.0 884.4 1017.6 1200.0 702.0 : 182.4 315.6 498.0 680.4 813.7 996.1 1200.0 884.4 : 133.2 315.6 498.0 631.3 813.7 1017.6 1200.0 1017.6: 182.4 364.8 498.0 680.4 884.4 1066.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 133.2376 .. 203.9100 cents 25/24, 70.6724 cents 27/25, 133.2376 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 .. 1066.7624 cents 25/24, 70.6724 cents 16/15, 111.7313 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 27/25, 133.2376 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.286638 Largest / Average step : 1.189475 Largest / Smallest step : 1.530424 Median interval of one step : 10/9, 182.4037 cents, amount: 4 Most common interval of one step : 10/9, 182.4037 cents, amount: 4 Least squares average step : 171.73580 cents, oct.: 1202.15063 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABACABA Step pattern size order : MSMLMSM Scale is a Constant Structure, by a margin of 62.56515 cents Scale diversity : 1.337678 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.646638 Rothenberg efficiency : 0.506122 redundancy: 0.493878 Efficiency x scale size : 3.542857 Number of different interval sizes : 18 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 81/80, 21.5063 cents Number of recognisable fifths : 4, average 701.9550 cents Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Scale is fully connected 5-limit major-minor triadic Scale is a complete diamond : 3 5 9 Length of longest harmonic part : 2 at degree 3 Length of longest subharmonic part : 2 at degree 2 Formal octave complements present : 7 = 100.0000% Scale is differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval class 2 Scale is differentially coherent in interval classes 3 and 4 combined Scale is differentially coherent in interval classes 4 and 5 combined Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 3-4 -- Rational properties -- Prime limit : 5 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 9 Scale harmonicity : 0.037783 Average absolute harmonicity : 0.265772 Specific harmonicity : 0.212671 Fundamental : 1/90, -6.4919 octaves, 2.9070 Hz. Guide tone : 180, 7.4919 octaves, 47092.602 Hz. Exponens Consonantiae : 1.620000E+04, 13.98371 octaves Euler's gradus suavitatis : 20 Sum of Mann's harmonic distance : 33.5, average 4.78571 Mersenne's string divisions : 175560 Sum of van Prooijen's expressibility: 4.26067, average 0.60867 Sum of Tenney's harmonic distance : 8.41903, average 1.20272 Vogel's harmonic complexity : 12.57143 Wille's k value : 67 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 65.51040, average 2.33966 Lattice compactness (without 2's) : 52.73791, average 1.88350 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.57143 6 1 3: -2 .. 2 0.00000 8 2 5: -1 .. 1 0.00000 4 4 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is weakly epimorphic with val: <7 10 18| Scale is JI-epimorphic with val: <7 11 16| = patent Scale is weakly epimorphic with val: <7 11 17| Scale is weakly epimorphic with val: <7 12 16|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 17.9278 c. M: 27.2159 c. Lebeng 12: 2 1 2 2 2 1 2 P M ME I SD: 12.6276 c. M: 17.5963 c. G.Phrygian, M.Dorian, M.Hypomixolydian, Kafi That, Mela Kharaharapriya, Raga Bageshri, Bhimpalasi, Huseni, Kanara, Kapi, Nayaki Kanada, Ritigaula, Sriraga, Mischung 5, Gregorian nr.8, Eskimo Heptatonic, Yu: China, Hyojo, Oshikicho, Banshikicho: Japan, Nam: Vietnam 19: 3 2 3 3 3 2 3 SP M ME I SD: 5.4013 c. M:-7.2182 c. Nineteen-tone Dorian 34: 5 4 5 6 5 4 5 SP T3 I SD: 3.9515 c. M: 5.9331 c. 46: 7 5 7 8 7 5 7 SP T3 I SD: 1.8910 c. M: 2.5978 c. 53: 8 6 8 9 8 6 8 SP T3 I SD: 0.9881 c. M: 1.3398 c. 99: 15 11 15 17 15 11 15 SP T3 I SD: 0.7049 c. M:-1.0753 c. 118: 18 13 18 20 18 13 18 SP T3 I SD: 0.4264 c. M: 0.6471 c. 171: 26 19 26 29 26 19 26 SP T3 I SD: 0.1362 c. M:-0.2006 c. 388: 59 43 59 66 59 43 59 SP T3 I SD: 0.1169 c. M: 0.1774 c. 441: 67 49 67 75 67 49 67 SP T3 I SD: 0.0668 c. M: 0.0908 c. 559: 85 62 85 95 85 62 85 SP T3 I SD: 0.0546 c. M:-0.0778 c. 612: 93 68 93 104 93 68 93 SP T3 I SD: 0.0364 c. M: 0.0508 c. 1000: 152 111 152 170 152 111 152 SP T3 I SD: 0.0327 c. M:-0.0450 c. 1171: 178 130 178 199 178 130 178 SP T3 I SD: 0.0091 c. M: 0.0136 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: 21.4668 cents 5 x 6:7 x 8:9:10 S SD: 22.0266 cents 6 x 7:8:9:10:11:12 S SD: 9.7006 cents 7:8 x 9:11:12:13:14 SD: 22.4442 cents 8:9:10:11:12:13:14:16 S SD: 16.0324 cents 9:10:11:12:14:15:16:18 S SD: 10.5325 cents 10:11:12:13:15:17:18:20 SD: 8.3290 cents 15:17:18:20:23:25:27:30 SD: 7.3167 cents 16:18:19:21:24:27:29:32 SD: 6.6094 cents 18:20:22:24:27:30:32:36 S SD: 5.4803 cents 20:22:24:27:30:33:36:40 S SD: 4.6686 cents 24:27:29:32:36:40:43:48 SD: 3.6994 cents 30:33:36:40:45:50:54:60 SD: 2.4856 cents 36:40:43:48:54:60:65:72 SD: 1.3777 cents 54:60:65:72:81:90:97:108 SD: 0.9167 cents 90:100:108:120:135:150:162:180 SD: 0.0000 cents