Scala analysis: xen10-wilson-purvi-01-01
Purvi modulation 1 from Figure 1, Pythagoras (9/8 9/8 256/243) all 3 permutations
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: 81/64 407.820003 Pythagorean major third 3: 729/512 611.730005 Pythagorean tritone 4: 3/2 701.955001 perfect fifth 5: 27/16 905.865003 Pythagorean major sixth 6: 243/128 1109.775004 Pythagorean major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 256/243 90.2250 limma, Pythagorean minor second 1: 9/8 203.9100 major whole tone 2: 9/8 203.9100 major whole tone 3: 9/8 203.9100 major whole tone 4: 256/243 90.2250 limma, Pythagorean minor second 5: 9/8 203.9100 major whole tone 6: 9/8 203.9100 major whole tone 7: 256/243 90.2250 limma, Pythagorean minor second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 256/243 90.225 cents limma, Pythagorean minor second 1: 5 9/8 203.910 cents major whole tone 2: 4 32/27 294.135 cents Pythagorean minor third 2: 3 81/64 407.820 cents Pythagorean major third 3: 6 4/3 498.045 cents perfect fourth 3: 1 729/512 611.730 cents Pythagorean tritone 4: 1 1024/729 588.270 cents Pythagorean diminished fifth 4: 6 3/2 701.955 cents perfect fifth 5: 3 128/81 792.180 cents Pythagorean minor sixth 5: 4 27/16 905.865 cents Pythagorean major sixth 6: 5 16/9 996.090 cents Pythagorean minor seventh 6: 2 243/128 1109.775 cents Pythagorean major seventh Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 407.8 611.7 702.0 905.9 1109.8 1200.0 203.9 : 203.9 407.8 498.0 702.0 905.9 996.1 1200.0 407.8 : 203.9 294.1 498.0 702.0 792.2 996.1 1200.0 611.7 : 90.2 294.1 498.0 588.3 792.2 996.1 1200.0 702.0 : 203.9 407.8 498.0 702.0 905.9 1109.8 1200.0 905.9 : 203.9 294.1 498.0 702.0 905.9 996.1 1200.0 1109.8: 90.2 294.1 498.0 702.0 792.2 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 203.9100 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 2: 294.1350 .. 407.8200 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 3: 498.0450 .. 611.7300 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 4: 588.2700 .. 701.9550 cents 2187/2048, 113.6850 cents 524288/531441,-23.4600 cents 5: 792.1800 .. 905.8650 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 6: 996.0900 .. 1109.7750 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 256/243, 90.2250 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.900012 Largest / Average step : 1.189475 Largest / Smallest step : 2.260017 Median interval of one step : 9/8, 203.9100 cents, amount: 5 Most common interval of one step : 9/8, 203.9100 cents, amount: 5 Least squares average step : 180.36096 cents, oct.: 1262.52675 cents Scale is not proper Scale has Myhill's property chromas: 2187/2048, 113.6850 cents and 531441/524288, 23.4600 cents, ratio: 4.845906 generators: 498.04500 cents and 4 of 701.95500 cents ET pair of linear temperament : 12&41 Scale is distributional even Scale is a mode of a 665-tone equal temperament with octave 2/1 degrees: 113 226 339 389 502 615 665 generators: 276 and 389 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAABAAB Step pattern size order : LLLSLLS Scale is a Constant Structure, by a margin of 23.46001 cents Ratio Whole / Half tone : 2.260017 Scale diversity : 1.288369 Lumma stability : 0.451125 Lumma impropriety factor : 0.019550 Rothenberg efficiency : 0.761905 redundancy: 0.238095 Efficiency x scale size : 5.333333 Number of different interval sizes : 12 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 531441/524288, 23.4600 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 6 Scale is a chain of 3 triads 0.0 498.045 996.090 cents Most common triad is 0.0 498.045 701.955 cents, amount: 5 Number of recognisable fifths : 6, average 701.9550 cents Scale is Hypolydian octave species of abstract tetrachord Scale is Hypophrygian octave species of abstract tetrachord Scale is Hypodorian octave species of abstract tetrachord Scale contains two identical disjunct "tetrachords" of 3 notes Best major thirds form a closed circle Best minor thirds form a closed circle Scale is a complete genus musicum : 2^m 3^6 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 14.2857% Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval class 3 Scale is n-1 differentially coherent in interval class 4 Limited inverse transpositions : 3 Inversional symmetry on degrees : 5 Inversional symmetry on intervals : 1-2 -- Rational properties -- Prime limit : 3 Odd number limit : 729 (O: 729 U: 729) Highest odd numerator or denominator: 729 Scale harmonicity : 0.038462 Average absolute harmonicity : 0.232177 Specific harmonicity : 0.196118 Fundamental : 1/512, -9.0000 octaves, 0.5110 Hz. Guide tone : 1458, 10.5098 octaves, 381450.074 Hz. Exponens Consonantiae : 7.464960E+05, 19.50978 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 912.5, average 130.35714 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.01955, average 1.43136 Sum of Tenney's harmonic distance : 19.35148, average 2.76450 Vogel's harmonic complexity : 13.85714 Wille's k value : 364 Wilson's harmonic complexity : 18 Rectangular lattice diameter : 6 Triangular lattice diameter : 6 Lattice compactness : 143.82407, average 5.13657 Lattice compactness (without 2's) : 77.00000, average 2.75000 Number of different primes : 2 Prime exponents' range, average, count, tones@limit: 2: -9 .. 1 -4.14286 31 1 3: 0 .. 6 3.00000 21 6 Average exponent except 2's : 21 / 7 = 3.00000 Average absolute exponent except 2's: 21 / 7 = 3.00000 Scale is weakly epimorphic with val: <7 10| Scale is JI-epimorphic with val: <7 11| = patent Scale is weakly epimorphic with val: <7 12|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 58.5567 c. M: 97.4443 c. Lebeng 8: 1 2 1 1 1 1 1 P M ME S SD: 39.1678 c. M: 59.7750 c. 10: 2 1 2 1 2 1 1 P M ME S SD: 33.5295 c. M:-54.1350 c. 11: 2 2 2 0 2 2 1 N T3 SD: 30.5971 c. M: 47.4095 c. 12: 2 2 2 1 2 2 1 P M ME S SD: 7.0489 c. M: 11.7300 c. G.Hypolydian, M.Lydian, G.M.Hypolocrian, Rut biscale ascending, Kalyan That (Yaman), Mela Mecakalyani, Raga Chandrakant, Malarani, Shuddh Kalyan, Ping, Kung, Gu: China 29: 5 5 5 2 5 5 2 N M DE S SD: 5.3841 c. M:-8.9596 c. 41: 7 7 7 3 7 7 3 N M DE S SD: 1.7452 c. M:-2.9041 c. 53: 9 9 9 4 9 9 4 N M DE S SD: 0.2459 c. M: 0.4093 c. 200: 34 34 34 15 34 34 15 N M DE S SD: 0.1622 c. M:-0.2700 c. 253: 43 43 43 19 43 43 19 N M DE S SD: 0.0767 c. M:-0.1277 c. 306: 52 52 52 23 52 52 23 N M DE S SD: 0.0209 c. M:-0.0347 c. 359: 61 61 61 27 61 61 27 N M DE S SD: 0.0185 c. M: 0.0308 c. 665: 113 113 113 50 113 113 50 N M DE S SD: 0.0004 c. M: 0.0007 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 4 x x 5 x 6 S SD: 30.9176 cents 4 x 5 x 6:7 x 8 S SD: 16.6332 cents 5 x 6:7 x 8 x 10 S SD: 33.3986 cents 6:7:8 x 9:10:11:12 S SD: 21.2242 cents 7:8:9:10:11:12:13:14 H SD: 14.4271 cents 8:9:10:11:12:14:15:16 S SD: 13.2008 cents 10:11:13:14:15:17:19:20 SD: 9.7782 cents 13:15:16 x 20:22:25:26 SD: 13.6448 cents 14:16:18:20:21:24:27:28 S SD: 7.8330 cents 16:18:20:23:24:27:30:32 SD: 4.9462 cents 22:25:28:31:33:37:42:44 SD: 4.1625 cents 26:29:33:37:39:44:49:52 SD: 2.9631 cents 38:43:48:54:57:64:72:76 SD: 1.7353 cents 48:54:61:68:72:81:91:96 SD: 1.6438 cents 64:72:81:91:96:108:122:128 SD: 1.0709 cents 80:90:101:114:120:135:152:160 SD: 0.6757 cents 128:144:162:182:192:216:243:256 SD: 0.3395 cents 208:234:263:296:312:351:395:416 SD: 0.2800 cents 304:342:385:433:456:513:577:608 SD: 0.1914 cents 368:414:466:524:552:621:699:736 SD: 0.1883 cents 384:432:486:547:576:648:729:768 SD: 0.1131 cents 512:576:648:729:768:864:972:1024 SD: 0.0000 cents