Scala analysis: xen10-wilson-purvi-06b-07
Purvi modulation 7 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: 27/25 133.237575 large limma, BP small semitone, Zarlino semitone 2: 6/5 315.641287 minor third 3: 4/3 498.044999 perfect fourth 4: 36/25 631.282574 classic diminished fifth 5: 8/5 813.686286 minor 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: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 2: 10/9 182.4037 minor whole tone 3: 10/9 182.4037 minor whole tone 4: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 5: 10/9 182.4037 minor whole tone 6: 9/8 203.9100 major whole tone 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 : 133.2 315.6 498.0 631.3 813.7 1017.6 1200.0 133.2 : 182.4 364.8 498.0 680.4 884.4 1066.8 1200.0 315.6 : 182.4 315.6 498.0 702.0 884.4 1017.6 1200.0 498.0 : 133.2 315.6 519.6 702.0 835.2 1017.6 1200.0 631.3 : 182.4 386.3 568.7 702.0 884.4 1066.8 1200.0 813.7 : 203.9 386.3 519.6 702.0 884.4 1017.6 1200.0 1017.6: 182.4 315.6 498.0 680.4 813.7 996.1 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 : 166.84139 cents, oct.: 1167.88973 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABBABCB Step pattern size order : SMMSMLM 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 Lydian octave species of abstract tetrachord 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 Length of longest harmonic part : 2 at degree 5 Length of longest subharmonic part : 2 at degree 4 Formal octave complements present : 1 = 14.2857% 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 Limited inverse transpositions : 4 Inversional symmetry on degrees : 2 Inversional symmetry on intervals : 5-6 -- Rational properties -- Prime limit : 5 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 27 Scale harmonicity : 0.037783 Average absolute harmonicity : 0.228997 Specific harmonicity : 0.194057 Fundamental : 1/75, -6.2288 octaves, 3.4883 Hz. Guide tone : 216, 7.7549 octaves, 56511.122 Hz. Exponens Consonantiae : 1.620000E+04, 13.98371 octaves Euler's gradus suavitatis : 20 Sum of Mann's harmonic distance : 80.5, average 11.50000 Mersenne's string divisions : 732732 Sum of van Prooijen's expressibility: 5.65861, average 0.80837 Sum of Tenney's harmonic distance : 11.89615, average 1.69945 Vogel's harmonic complexity : 12.28571 Wille's k value : 67 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 72.25160, average 2.58041 Lattice compactness (without 2's) : 55.52161, average 1.98291 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 0 .. 3 1.28571 9 1 3: -1 .. 3 1.00000 9 1 5: -2 .. 0 -1.00000 7 5 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 16 / 7 = 2.28571 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: 32.5900 c. M:-54.4317 c. Lebeng 9: 1 1 2 1 1 2 1 P M ME S SD: 32.7131 c. M:-49.0704 c. 12: 1 2 2 1 2 2 2 P M ME S SD: 20.1024 c. M: 33.2376 c. G.Mixolydian, G.Hyperdorian, M.Hypophrygian, M.Locrian, G.M.Hyperaeolian, Rut biscale descending, Pien chih: China, Makam Lami, Yishtabach: Jewish 15: 2 2 2 2 2 3 2 SP M ME S SD: 16.1514 c. M:-26.7624 c. 19: 2 3 3 2 3 3 3 SP M ME S SD: 5.4033 c. M:-7.3663 c. Nineteen-tone Locrian 34: 4 5 5 4 5 6 5 SP T3 S SD: 4.4314 c. M:-7.9389 c. 46: 5 7 7 5 7 8 7 SP T3 S SD: 3.2132 c. M: 5.1956 c. 53: 6 8 8 6 8 9 8 SP T3 S SD: 1.6648 c. M:-2.6797 c. 72: 8 11 11 8 11 12 11 SP T3 S SD: 1.6403 c. M:-2.9804 c. 99: 11 15 15 11 15 17 15 SP T3 S SD: 0.8583 c. M: 1.5651 c. 118: 13 18 18 13 18 20 18 SP T3 S SD: 0.5758 c. M: 1.0342 c. 152: 17 23 23 17 23 26 23 SP T3 S SD: 0.5945 c. M:-0.9730 c. 171: 19 26 26 19 26 29 26 SP T3 S SD: 0.2013 c. M:-0.3488 c. 270: 30 41 41 30 41 46 41 SP T3 S SD: 0.1981 c. M: 0.3530 c. 388: 43 59 59 43 59 66 59 SP T3 S SD: 0.2124 c. M: 0.3547 c. 441: 49 67 67 49 67 75 67 SP T3 S SD: 0.0670 c. M:-0.0958 c. 612: 68 93 93 68 93 104 93 SP T3 S SD: 0.0579 c. M:-0.0958 c. 730: 81 111 111 81 111 124 111 SP T3 S SD: 0.0478 c. M: 0.0869 c. 901: 100 137 137 100 137 153 137 SP T3 S SD: 0.0495 c. M:-0.0762 c. 1000: 111 152 152 111 152 170 152 SP T3 S SD: 0.0527 c. M: 0.0863 c. 1053: 117 160 160 117 160 179 160 SP T3 S SD: 0.0526 c. M:-0.0958 c. 1171: 130 178 178 130 178 199 178 SP T3 S SD: 0.0164 c. M: 0.0272 c. 1342: 149 204 204 149 204 228 204 SP T3 S SD: 0.0135 c. M:-0.0246 c. 1783: 198 271 271 198 271 303 271 SP T3 S SD: 0.0115 c. M:-0.0210 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: 35.3362 cents 3 x x 4 x 5 x 6 S SD: 23.5575 cents 4 x 5 x 6 x 7:8 S SD: 27.8026 cents 5 x 6 x 7:8:9:10 S SD: 9.7541 cents 6 x 7:8:9:10:11:12 S SD: 19.2764 cents 7 x 8:9:10:11:13:14 SD: 20.5410 cents 9:10:11:12:13:14:16:18 S SD: 11.3353 cents 10:11:12:13:14:16:18:20 S SD: 10.4088 cents 11:12:13:15:16:18:20:22 SD: 9.7250 cents 12:13:14:16:17:19:22:24 SD: 9.6306 cents 14:15:17:19:20:22:25:28 SD: 7.6966 cents 15:16:18:20:22:24:27:30 S SD: 5.4803 cents 24:26:29:32:35:38:43:48 SD: 4.6178 cents 25:27:30:33:36:40:45:50 SD: 2.4856 cents 36:39:43:48:52:58:65:72 SD: 2.4473 cents 39:42:47:52:56:62:70:78 SD: 2.2662 cents 45:49:54:60:65:72:81:90 SD: 2.1658 cents 50:54:60:67:72:80:90:100 SD: 1.2335 cents 75:81:90:100:108:120:135:150 SD: 0.0000 cents