Scala analysis: xen10-wilson-purvi-11c-01
Purvi modulation 1 from Figure 11c, Archytas (28/27 5/4 36/35), (36/35 5/4 28/27)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 36/35 48.770381 septimal diesis, 1/4-tone 2: 81/70 252.680383 Al-Hwarizmi's lute middle finger 3: 6/5 315.641287 minor third 4: 3/2 701.955001 perfect fifth 5: 54/35 750.725382 septimal semi-augmented fifth 6: 8/5 813.686286 minor sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 5/4 386.3137 major third 1: 36/35 48.7704 septimal diesis, 1/4-tone 2: 9/8 203.9100 major whole tone 3: 28/27 62.9609 Archytas' 1/3-tone 4: 5/4 386.3137 major third 5: 36/35 48.7704 septimal diesis, 1/4-tone 6: 28/27 62.9609 Archytas' 1/3-tone 7: 5/4 386.3137 major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 5/4 386.314 cents major third 2: 1 16/15 111.731 cents minor diatonic semitone 2: 1 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 1 7/6 266.871 cents septimal minor third 2: 2 9/7 435.084 cents septimal major third, BP third 2: 2 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 3: 1 6/5 315.641 cents minor third 3: 4 4/3 498.045 cents perfect fourth 3: 1 81/56 638.994 cents 3: 1 35/24 653.185 cents septimal semi-diminished fifth 4: 1 48/35 546.815 cents septimal semi-augmented fourth 4: 1 112/81 561.006 cents 4: 4 3/2 701.955 cents perfect fifth 4: 1 5/3 884.359 cents major sixth, BP sixth 5: 2 54/35 750.725 cents septimal semi-augmented fifth 5: 2 14/9 764.916 cents septimal minor sixth 5: 1 12/7 933.129 cents septimal major sixth 5: 1 140/81 947.320 cents 5: 1 15/8 1088.269 cents classic major seventh 6: 2 8/5 813.686 cents minor sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 27/14 1137.039 cents septimal major seventh 6: 2 35/18 1151.230 cents septimal semi-diminished octave Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 48.8 252.7 315.6 702.0 750.7 813.7 1200.0 48.8 : 203.9 266.9 653.2 702.0 764.9 1151.2 1200.0 252.7 : 63.0 449.3 498.0 561.0 947.3 996.1 1200.0 315.6 : 386.3 435.1 498.0 884.4 933.1 1137.0 1200.0 702.0 : 48.8 111.7 498.0 546.8 750.7 813.7 1200.0 750.7 : 63.0 449.3 498.0 702.0 764.9 1151.2 1200.0 813.7 : 386.3 435.1 639.0 702.0 1088.3 1137.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 386.3137 cents 175/144, 337.5433 cents 36/35, 48.7704 cents 2: 111.7313 .. 449.2746 cents 175/144, 337.5433 cents 64/75,-274.5824 cents 3: 315.6413 .. 653.1846 cents 175/144, 337.5433 cents 162/175,-133.6333 cents 4: 546.8154 .. 884.3587 cents 175/144, 337.5433 cents 1152/1225,-106.3692 cents 5: 750.7254 .. 1088.2687 cents 175/144, 337.5433 cents 162/175,-133.6333 cents 6: 813.6863 .. 1151.2296 cents 175/144, 337.5433 cents 64/75,-274.5824 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 5/4, 386.3137 cents Average / Smallest step : 3.515014 Largest / Average step : 2.253497 Largest / Smallest step : 7.921072 Median interval of one step : 28/27, 62.9609 cents, amount: 2 Least squares average step : 152.46157 cents, oct.: 1067.23098 cents Scale is not proper Step pattern alph. order: ABCDACD Step pattern size order : ACBDABD Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 48.77038 cents Scale diversity : 1.569058 Lumma stability : 0.081284 Lumma impropriety factor : 0.651213 Rothenberg efficiency : 0.421769 redundancy: 0.578231 Efficiency x scale size : 2.952381 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 245/243, 14.1905 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Number of recognisable fifths : 4, average 701.9550 cents Scale is Hypophrygian octave species of abstract tetrachord All steps are superparticular (epimoric) 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 differentially coherent in interval class 1 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 337.5433 cents: 3 -- Rational properties -- Prime limit : 7 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 81 Scale harmonicity : 0.031896 Average absolute harmonicity : 0.227754 Specific harmonicity : 0.149899 Fundamental : 1/70, -6.1293 octaves, 3.7375 Hz. Guide tone : 648, 9.3399 octaves, 169533.366 Hz. Exponens Consonantiae : 4.536000E+04, 15.46913 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 171.5, average 24.50000 Mersenne's string divisions : 2046692505 Sum of van Prooijen's expressibility: 6.87168, average 0.98167 Sum of Tenney's harmonic distance : 14.28878, average 2.04125 Vogel's harmonic complexity : 12.00000 Wille's k value : 52 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 80.39206, average 2.87115 Lattice compactness (without 2's) : 58.09233, average 2.07473 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 0.85714 10 1 3: 0 .. 4 1.57143 11 1 5: -1 .. 0 -0.71429 5 2 7: -1 .. 0 -0.42857 3 3 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 19 / 7 = 2.71429 Scale is weakly epimorphic with val: <7 10 15 21| Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 12 17 18| Scale is weakly epimorphic with val: <7 12 18 21|
FIT/MODE
7: 0 1 1 2 0 1 2 N T3 SD: 47.9580 c. M: 81.2518 c. 8: 0 2 0 3 0 0 3 N T3 S SD: 40.0484 c. M: 63.6863 c. 9: 0 2 0 3 0 1 3 N SD: 43.8685 c. M: 84.0587 c. 10: 0 2 1 3 0 1 3 N SD: 30.4000 c. M: 48.7704 c. 11: 0 2 1 3 1 0 4 N SD: 35.0985 c. M: 50.0499 c. 12: 0 2 1 4 0 1 4 N SD: 34.1480 c. M: 52.6804 c. 14: 1 2 1 4 1 1 4 N T3 S SD: 25.9294 c. M:-43.4566 c. 15: 1 2 1 5 0 1 5 N SD: 19.3171 c. M:-31.2296 c. 16: 1 2 1 5 1 1 5 N T3 S SD: 19.1010 c. M: 27.6804 c. 18: 1 3 1 6 0 1 6 N SD: 18.1395 c. M:-31.3783 c. 19: 1 3 1 6 1 1 6 N T3 S SD: 7.2189 c. M:-14.3875 c. 27: 1 5 1 9 1 1 9 N T3 S SD: 8.6959 c. M:-13.9863 c. 34: 1 6 2 11 1 2 11 N SD: 6.8404 c. M: 13.4763 c. 41: 2 7 2 13 2 2 13 N T3 S SD: 7.4610 c. M:-10.7343 c. 43: 2 7 2 14 2 2 14 N T3 S SD: 4.9593 c. M: 8.6645 c. 46: 2 8 2 15 2 2 15 N T3 S SD: 4.6233 c. M:-8.1892 c. 53: 2 9 3 17 2 3 17 N SD: 2.4413 c. M: 3.6238 c. 72: 3 12 4 23 3 4 23 N SD: 1.8118 c. M:-2.9804 c. 99: 4 17 5 32 4 5 32 N SD: 1.0710 c. M:-1.8651 c. 118: 5 20 6 38 5 6 38 N SD: 1.2114 c. M:-2.0771 c. 152: 6 26 8 49 6 8 49 N SD: 0.6817 c. M: 1.4020 c. 171: 7 29 9 55 7 9 55 N SD: 0.2183 c. M:-0.3524 c. 441: 18 75 23 142 18 23 142 N SD: 0.2035 c. M:-0.3808 c. 494: 20 84 26 159 20 26 159 N SD: 0.1098 c. M: 0.1874 c. 665: 27 113 35 214 27 35 214 N SD: 0.0854 c. M:-0.1483 c. 935: 38 159 49 301 38 49 301 N SD: 0.0775 c. M:-0.1538 c. 1106: 45 188 58 356 45 58 356 N SD: 0.0741 c. M:-0.1225 c. 1258: 51 214 66 405 51 66 405 N SD: 0.0824 c. M: 0.1217 c. 1277: 52 217 67 411 52 67 411 N SD: 0.0821 c. M:-0.0996 c. 1354: 55 230 71 436 55 71 436 N SD: 0.0769 c. M: 0.1317 c. 1429: 58 243 75 460 58 75 460 N SD: 0.0639 c. M:-0.1040 c. 1525: 62 259 80 491 62 80 491 N SD: 0.0596 c. M: 0.1003 c. 1600: 65 272 84 515 65 84 515 N SD: 0.0583 c. M:-0.1087 c. 1696: 69 288 89 546 69 89 546 N SD: 0.0543 c. M: 0.0860 c. 1795: 73 305 94 578 73 94 578 N SD: 0.0541 c. M: 0.0981 c. 1848: 75 314 97 595 75 97 595 N SD: 0.0576 c. M: 0.0830 c. 1867: 76 317 98 601 76 98 601 N SD: 0.0574 c. M: 0.0826 c. 1966: 80 334 103 633 80 103 633 N SD: 0.0456 c. M: 0.0767 c. 2019: 82 343 106 650 82 106 650 N SD: 0.0433 c. M: 0.0801 c. 2190: 89 372 115 705 89 115 705 N SD: 0.0375 c. M: 0.0776 c. 2289: 93 389 120 737 93 120 737 N SD: 0.0282 c. M: 0.0559 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 x 5:6 S SD: 65.2054 cents 4 x x 5:6 x x 8 S SD: 23.5575 cents 5 x x 6 x x 8:10 S SD: 0.0000 cents 6 x 7 x 9 x 10:12 SD: 18.0208 cents 7 x 8 x x x 11:14 SD: 12.6298 cents 8 x 9:10:12 x 13:16 SD: 17.9929 cents 9 x 10:11 x 14 x 18 SD: 19.6044 cents 10 x x 12:15 x 16:20 S SD: 0.0000 cents 11:12 x 13 x 17:18:22 SD: 22.4478 cents 12:13:14 x 18 x 19:24 SD: 18.5413 cents 13:14:15:16 x 20:21:26 SD: 15.4282 cents 14:15:16:17:21 x 22:28 SD: 13.7941 cents 15:16:17:18 x 23:24:30 SD: 12.2185 cents 16:17 x 19:24:25:26:32 SD: 11.4085 cents 17:18:20 x x 26:27:34 SD: 12.2209 cents 18:19:21:22:27:28:29:36 SD: 8.5301 cents 19:20:22:23 x 29:30:38 SD: 8.6704 cents 20:21:23:24:30:31:32:40 SD: 5.4457 cents 21:22:24:25 x 32:34:42 SD: 8.4067 cents 22:23:25:26:33:34:35:44 SD: 7.2605 cents 23:24:27:28 x 35:37:46 SD: 8.3648 cents 24:25:28:29:36:37:38:48 SD: 4.8551 cents 26:27:30:31:39:40:42:52 SD: 3.8377 cents 30:31:35:36:45:46:48:60 SD: 2.7856 cents 40:41:46:48:60:62:64:80 SD: 2.0953 cents 62:64:72:74:93:96:99:124 SD: 2.0918 cents 64:66:74:77:96:99:102:128 SD: 1.4882 cents 70:72:81:84:105:108:112:140 S SD: 0.0000 cents