Scala analysis: xen10-wilson-purvi-06a-01
Purvi modulation 1 from Figure 6a, Al-Farabi (10/9 10/9 27/25), (27/25 10/9 10/9)
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: 5/4 386.313714 major third 3: 25/18 568.717426 classic augmented fourth 4: 3/2 701.955001 perfect fifth 5: 5/3 884.358713 major sixth, BP sixth 6: 50/27 1066.762425 grave major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 1: 9/8 203.9100 major whole tone 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: 10/9 182.4037 minor whole tone 7: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone
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: 3 6/5 315.641 cents minor third 2: 1 243/200 337.148 cents acute minor third 2: 2 100/81 364.807 cents grave major third 2: 1 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: 1 8/5 813.686 cents minor sixth 5: 2 81/50 835.193 cents acute minor sixth 5: 1 400/243 862.852 cents grave major sixth 5: 3 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: 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 : 203.9 386.3 568.7 702.0 884.4 1066.8 1200.0 203.9 : 182.4 364.8 498.0 680.4 862.9 996.1 1200.0 386.3 : 182.4 315.6 498.0 680.4 813.7 1017.6 1200.0 568.7 : 133.2 315.6 498.0 631.3 835.2 1017.6 1200.0 702.0 : 182.4 364.8 498.0 702.0 884.4 1066.8 1200.0 884.4 : 182.4 315.6 519.6 702.0 884.4 1017.6 1200.0 1066.8: 133.2 337.1 519.6 702.0 835.2 1017.6 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 : 176.52056 cents, oct.: 1235.64389 cents Scale is strictly proper Step pattern alph. order: ABBCBBC Step pattern size order : LMMSMMS Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 62.56515 cents Scale diversity : 1.349275 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.646638 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 : 3 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 0.0 182.404 498.045 cents, amount: 3 Number of recognisable fifths : 4, average 701.9550 cents Scale is Hypodorian 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 Length of longest harmonic part : 2 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 1 and 2 combined Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions with margin 70.6724 cents: 3 -- Rational properties -- Prime limit : 5 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 27 Scale harmonicity : 0.033186 Average absolute harmonicity : 0.245743 Specific harmonicity : 0.174133 Fundamental : 1/216, -7.7549 octaves, 1.2112 Hz. Guide tone : 450, 8.8138 octaves, 117731.504 Hz. Exponens Consonantiae : 9.720000E+04, 16.56867 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 81.0, average 11.57143 Mersenne's string divisions : 20263320 Sum of van Prooijen's expressibility: 5.65861, average 0.80837 Sum of Tenney's harmonic distance : 11.19718, average 1.59960 Vogel's harmonic complexity : 14.28571 Wille's k value : 121 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 83.88367, average 2.99585 Lattice compactness (without 2's) : 62.72863, average 2.24031 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -0.71429 9 1 3: -3 .. 2 -0.42857 9 2 5: 0 .. 2 0.85714 6 4 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 15 / 7 = 2.14286 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: 34.5777 c. M: 54.4317 c. Lebeng 10: 2 1 2 1 1 2 1 P M ME S SD: 27.8825 c. M: 44.3587 c. 12: 2 2 2 1 2 2 1 P M ME S SD: 19.0278 c. M:-33.2376 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 16: 3 2 3 1 3 2 2 P D3 SD: 20.0128 c. M:-31.2826 c. 17: 3 2 3 2 2 3 2 SP M ME S SD: 19.4982 c. M: 37.2999 c. 18: 3 3 3 2 2 3 2 P D3 SD: 18.8180 c. M:-31.3783 c. 19: 3 3 3 2 3 3 2 SP M ME S SD: 7.1991 c. M: 14.4363 c. Nineteen-tone Lydian 34: 6 5 5 4 5 5 4 SP T3 SD: 4.8396 c. M: 7.9389 c. 46: 8 7 7 5 7 7 5 SP SD: 3.6865 c. M:-5.1956 c. 53: 9 8 8 6 8 8 6 SP SD: 1.5947 c. M: 2.6797 c. 99: 17 15 15 11 15 15 11 SP SD: 1.1612 c. M:-2.1506 c. 118: 20 18 18 13 18 18 13 SP SD: 0.5572 c. M:-1.0342 c. 171: 29 26 26 19 26 26 19 SP SD: 0.2512 c. M: 0.4012 c. 289: 49 44 44 32 44 44 32 SP SD: 0.2493 c. M: 0.4498 c. 388: 66 59 59 43 59 59 43 SP SD: 0.2257 c. M:-0.3547 c. 441: 75 67 67 49 67 67 49 SP SD: 0.0867 c. M:-0.1716 c. 559: 95 85 85 62 85 85 62 SP SD: 0.0923 c. M:-0.1556 c. 612: 104 93 93 68 93 93 68 SP SD: 0.0548 c. M: 0.0958 c. 730: 124 111 111 81 111 111 81 SP SD: 0.0503 c. M:-0.0869 c. 1171: 199 178 178 130 178 178 130 SP SD: 0.0177 c. M:-0.0272 c. 1783: 303 271 271 198 271 271 198 SP SD: 0.0118 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: 0.0000 cents 3 x x 4 x 5 x 6 S SD: 23.5575 cents 4 x 5 x 6:7 x 8 S SD: 21.1168 cents 5 x 6:7 x 8:9:10 S SD: 22.4471 cents 6:7 x 8:9:10:11:12 S SD: 16.0394 cents 8:9:10:11:12:13:15:16 SD: 7.4044 cents 9:10:11 x 14:15:17:18 SD: 14.0590 cents 10:11:13:14:15:17:19:20 SD: 13.8978 cents 12:14:15:17:18:20:22:24 SD: 10.5387 cents 13:15:16:18:20:22:24:26 SD: 10.4181 cents 15:17:19:21:23:25:28:30 SD: 7.1678 cents 16:18:20:22:24:27:30:32 S SD: 5.0057 cents 24:27:30:33:36:40:44:48 S SD: 3.5152 cents 32:36:40:44:48:53:59:64 SD: 3.1239 cents 39:44:49:54:59:65:72:78 SD: 2.7727 cents 40:45:50:56:60:67:74:80 SD: 2.3380 cents 48:54:60:67:72:80:89:96 SD: 1.2716 cents 72:81:90:100:108:120:133:144 SD: 0.6191 cents 120:135:150:167:180:200:222:240 SD: 0.5526 cents 128:144:160:178:192:213:237:256 SD: 0.4965 cents 136:153:170:189:204:227:252:272 SD: 0.4176 cents 144:162:180:200:216:240:267:288 SD: 0.3090 cents 208:234:260:289:312:347:385:416 SD: 0.2823 cents 216:243:270:300:324:360:400:432 SD: 0.0000 cents