Scala analysis: xen10-wilson-purvi-01-03
Purvi modulation 3 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: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 27/16 905.865003 Pythagorean major sixth 6: 16/9 996.089998 Pythagorean minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 9/8 203.9100 major whole tone 2: 9/8 203.9100 major whole tone 3: 256/243 90.2250 limma, Pythagorean minor second 4: 9/8 203.9100 major whole tone 5: 9/8 203.9100 major whole tone 6: 256/243 90.2250 limma, Pythagorean minor second 7: 9/8 203.9100 major whole tone
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 : 203.9 407.8 498.0 702.0 905.9 996.1 1200.0 203.9 : 203.9 294.1 498.0 702.0 792.2 996.1 1200.0 407.8 : 90.2 294.1 498.0 588.3 792.2 996.1 1200.0 498.0 : 203.9 407.8 498.0 702.0 905.9 1109.8 1200.0 702.0 : 203.9 294.1 498.0 702.0 905.9 996.1 1200.0 905.9 : 90.2 294.1 498.0 702.0 792.2 996.1 1200.0 996.1 : 203.9 407.8 611.7 702.0 905.9 1109.8 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 : 173.05264 cents, oct.: 1211.36850 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: 3 of 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: 113 226 276 389 502 552 665 generators: 276 and 389 Number of contiguous 1-step segments: 0 Step pattern alph. order: AABAABA Step pattern size order : LLSLLSL 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 Mixolydian 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 conjunct tetrachords Best major thirds form a closed circle Best minor thirds form a closed circle Scale is a complete genus musicum : 2^m 3^6 Scale contains a complete diamond : 1 3 9 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 5 = 71.4286% 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 : 1 Inversional symmetry on degrees : 4 Inversional symmetry on intervals : 0-1 -- Rational properties -- Prime limit : 3 Odd number limit : 729 (O: 729 U: 729) Highest odd numerator or denominator: 81 Scale harmonicity : 0.038462 Average absolute harmonicity : 0.265355 Specific harmonicity : 0.215488 Fundamental : 1/576, -9.1699 octaves, 0.4542 Hz. Guide tone : 1296, 10.3399 octaves, 339066.733 Hz. Exponens Consonantiae : 7.464960E+05, 19.50978 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 122.5, average 17.50000 Mersenne's string divisions : 11129475 Sum of van Prooijen's expressibility: 6.20258, average 0.88608 Sum of Tenney's harmonic distance : 12.52421, average 1.78917 Vogel's harmonic complexity : 14.00000 Wille's k value : 364 Wilson's harmonic complexity : 18 Rectangular lattice diameter : 6 Triangular lattice diameter : 6 Lattice compactness : 132.79540, average 4.74269 Lattice compactness (without 2's) : 69.00000, average 2.46429 Number of different primes : 2 Prime exponents' range, average, count, tones@limit: 2: -6 .. 4 -1.00000 21 1 3: -2 .. 4 1.00000 13 6 Average exponent except 2's : 7 / 7 = 1.00000 Average absolute exponent except 2's: 13 / 7 = 1.85714 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: 36.3153 c. M: 64.9629 c. Lebeng 8: 1 2 0 2 1 1 1 P D3 S SD: 41.8207 c. M:-53.9100 c. 11: 2 2 1 1 2 1 2 N D3 SD: 31.2034 c. M:-47.4095 c. 12: 2 2 1 2 2 1 2 P M ME S SD: 4.3715 c. M: 7.8200 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 29: 5 5 2 5 5 2 5 N M DE S SD: 3.3391 c. M:-5.9731 c. 41: 7 7 3 7 7 3 7 N M DE S SD: 1.0823 c. M:-1.9361 c. 53: 9 9 4 9 9 4 9 N M DE S SD: 0.1525 c. M: 0.2728 c. 200: 34 34 15 34 34 15 34 N M DE S SD: 0.1006 c. M:-0.1800 c. 253: 43 43 19 43 43 19 43 N M DE S SD: 0.0476 c. M:-0.0851 c. 306: 52 52 23 52 52 23 52 N M DE S SD: 0.0129 c. M:-0.0231 c. 359: 61 61 27 61 61 27 61 N M DE S SD: 0.0115 c. M: 0.0206 c. 665: 113 113 50 113 113 50 113 N M DE S SD: 0.0003 c. M: 0.0005 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: 7.1688 cents 4 x 5 x 6 x 7:8 S SD: 8.6813 cents 5 x 6:7 x 8:9:10 S SD: 31.3631 cents 6:7 x 8:9:10:11:12 S SD: 14.2054 cents 7:8:9 x 11:12 x 14 SD: 18.6721 cents 8:9:10:11:12 x 14:16 S SD: 10.5986 cents 10:11 x 13:15:17:18:20 SD: 10.6205 cents 14:16:18:19:21:24:25:28 SD: 8.1170 cents 15:17:19:20:23:25:27:30 SD: 7.1972 cents 16:18:20:21:24:27:28:32 S SD: 6.3071 cents 18:20:23:24:27:30:32:36 SD: 4.9462 cents 22:25:28:29:33:37:39:44 SD: 4.1562 cents 26:29:33:35:39:44:46:52 SD: 3.5382 cents 30:34:38:40:45:51:53:60 SD: 3.0181 cents 38:43:48:51:57:64:68:76 SD: 2.7939 cents 41:46:52:55:62:69:73:82 SD: 2.7540 cents 42:47:53:56:63:71:75:84 SD: 1.9118 cents 48:54:61:64:72:81:85:96 SD: 1.4031 cents 64:72:81:85:96:108:114:128 SD: 1.0816 cents 72:81:91:96:108:122:128:144 SD: 1.0709 cents 80:90:101:107:120:135:142:160 SD: 1.0578 cents 90:101:114:120:135:152:160:180 SD: 0.6757 cents 144:162:182:192:216:243:256:288 SD: 0.3395 cents 192:216:243:256:288:324:341:384 SD: 0.2416 cents 320:360:405:427:480:540:569:640 SD: 0.1991 cents 342:385:433:456:513:577:608:684 SD: 0.1914 cents 384:432:486:512:576:648:683:768 SD: 0.1207 cents 432:486:547:576:648:729:768:864 SD: 0.1131 cents 576:648:729:768:864:972:1024:1152 SD: 0.0000 cents