Scala analysis: xen10-wilson-purvi-11a-03
Purvi modulation 3 from Figure 11a, Archytas (28/27 36/35 5/4), (5/4 28/27 36/35)
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: 7/6 266.870906 septimal minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 14/9 764.915905 septimal minor sixth 6: 35/18 1151.229619 septimal semi-diminished octave 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 36/35 48.7704 septimal diesis, 1/4-tone 1: 9/8 203.9100 major whole tone 2: 28/27 62.9609 Archytas' 1/3-tone 3: 8/7 231.1741 septimal whole tone 4: 9/8 203.9100 major whole tone 5: 28/27 62.9609 Archytas' 1/3-tone 6: 5/4 386.3137 major third 7: 36/35 48.7704 septimal diesis, 1/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 2 9/8 203.910 cents major whole tone 1: 1 8/7 231.174 cents septimal whole tone 1: 1 5/4 386.314 cents major third 2: 1 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 2 7/6 266.871 cents septimal minor third 2: 1 32/27 294.135 cents Pythagorean minor third 2: 2 9/7 435.084 cents septimal major third, BP third 2: 1 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: 1 54/35 750.725 cents septimal semi-augmented fifth 5: 2 14/9 764.916 cents septimal minor sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 2 12/7 933.129 cents septimal major sixth 5: 1 140/81 947.320 cents 6: 1 8/5 813.686 cents minor sixth 6: 1 7/4 968.826 cents harmonic seventh 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 2 27/14 1137.039 cents septimal major seventh 6: 1 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: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 266.9 498.0 702.0 764.9 1151.2 1200.0 203.9 : 63.0 294.1 498.0 561.0 947.3 996.1 1200.0 266.9 : 231.2 435.1 498.0 884.4 933.1 1137.0 1200.0 498.0 : 203.9 266.9 653.2 702.0 905.9 968.8 1200.0 702.0 : 63.0 449.3 498.0 702.0 764.9 996.1 1200.0 764.9 : 386.3 435.1 639.0 702.0 933.1 1137.0 1200.0 1151.2: 48.8 252.7 315.6 546.8 750.7 813.7 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: 252.6804 .. 449.2746 cents 2450/2187, 196.5942 cents 162/175,-133.6333 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 .. 947.3196 cents 2450/2187, 196.5942 cents 162/175,-133.6333 cents 6: 813.6863 .. 1151.2296 cents 175/144, 337.5433 cents 162/175,-133.6333 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 : 9/8, 203.9100 cents, amount: 2 Least squares average step : 172.65403 cents, oct.: 1208.57820 cents Scale is not proper Step pattern alph. order: ABCABDE Step pattern size order : CBDCBEA Scale is a Constant Structure, by a margin of 21.50629 cents Scale diversity : 1.477280 Lumma stability : 0.081284 Lumma impropriety factor : 0.416298 Rothenberg efficiency : 0.408163 redundancy: 0.591837 Efficiency x scale size : 2.857143 Number of different interval sizes : 28 = 4.66667 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.66667 = 14/3 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 Most common triad is 0.0 498.045 701.955 cents, amount: 2 Number of recognisable fifths : 4, average 701.9550 cents Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 2 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% 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 -- Rational properties -- Prime limit : 7 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 35 Scale harmonicity : 0.030910 Average absolute harmonicity : 0.254614 Specific harmonicity : 0.170023 Fundamental : 1/72, -6.1699 octaves, 3.6337 Hz. Guide tone : 1260, 10.2992 octaves, 329648.212 Hz. Exponens Consonantiae : 9.072000E+04, 16.46913 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 60.5, average 8.64286 Mersenne's string divisions : 28286895 Sum of van Prooijen's expressibility: 5.25189, average 0.75027 Sum of Tenney's harmonic distance : 10.53866, average 1.50552 Vogel's harmonic complexity : 11.14286 Wille's k value : 40 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 80.44171, average 2.87292 Lattice compactness (without 2's) : 54.00301, average 1.92868 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.28571 10 1 3: -2 .. 2 -0.42857 9 3 5: 0 .. 1 0.14286 1 7: 0 .. 1 0.42857 3 3 Average exponent except 2's : 1 / 7 = 0.14286 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is weakly epimorphic with val: <7 10 18 18| Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 12 17 18|
FIT/MODE
7: 1 1 1 1 0 3 0 N T3 S SD: 47.8210 c. M: 79.2016 c. 8: 1 1 1 2 0 3 0 N SD: 40.0384 c. M: 53.9100 c. 9: 2 0 2 1 1 3 0 N SD: 37.8690 c. M:-62.7567 c. 10: 2 0 2 2 0 4 0 N D3 SD: 31.7845 c. M:-48.7704 c. 12: 2 1 2 2 1 4 0 N SD: 25.9943 c. M:-48.7704 c. 14: 2 1 3 2 1 4 1 N SD: 20.9914 c. M: 36.9439 c. 17: 3 1 3 3 1 5 1 N D3 SD: 11.5991 c. M: 21.8179 c. Seventeen-tone Harmonic Minor 19: 3 1 4 3 1 6 1 N SD: 10.4994 c. M: 14.4363 c. 22: 4 1 4 4 1 7 1 N D3 SD: 7.3174 c. M:-14.2718 c. 24: 4 1 5 4 1 8 1 N SD: 8.7142 c. M: 16.8709 c. 31: 5 2 6 5 2 10 1 N SD: 7.2222 c. M: 10.3616 c. 36: 6 2 7 6 2 12 1 N SD: 6.1452 c. M:-15.4370 c. 41: 7 2 8 7 2 13 2 N SD: 4.2132 c. M: 9.7662 c. 45: 8 2 9 7 3 14 2 N SD: 6.8575 c. M:-9.4233 c. 46: 8 2 9 8 2 15 2 N SD: 4.6662 c. M: 8.3942 c. 49: 8 3 9 9 2 16 2 N SD: 5.8456 c. M: 8.2491 c. 50: 8 3 10 8 3 16 2 N SD: 5.7460 c. M: 11.9100 c. 53: 9 3 10 9 3 17 2 N SD: 2.9144 c. M:-4.8954 c. 72: 12 4 14 12 4 23 3 N SD: 1.9839 c. M: 3.9100 c. 77: 13 4 15 13 4 25 3 N SD: 1.3114 c. M:-2.0171 c. 94: 16 5 18 16 5 30 4 N SD: 1.0689 c. M: 2.2934 c. 152: 26 8 29 26 8 49 6 N SD: 1.0609 c. M:-1.5501 c. 171: 29 9 33 29 9 55 7 N SD: 0.2412 c. M: 0.4012 c. 441: 75 23 85 75 23 142 18 N SD: 0.1748 c. M: 0.2901 c. 494: 84 26 95 84 26 159 20 N SD: 0.1880 c. M:-0.3356 c. 571: 97 30 110 97 30 184 23 N SD: 0.1680 c. M:-0.4341 c. 612: 104 32 118 104 32 197 25 N SD: 0.1455 c. M: 0.2492 c. 665: 113 35 128 113 35 214 27 N SD: 0.1068 c. M:-0.1969 c. 836: 142 44 161 142 44 269 34 N SD: 0.0834 c. M:-0.1559 c. 935: 159 49 180 159 49 301 38 N SD: 0.0777 c. M:-0.1542 c. 1007: 171 53 194 171 53 324 41 N SD: 0.0893 c. M: 0.1364 c. 1012: 172 53 195 172 53 326 41 N SD: 0.0760 c. M:-0.1538 c. 1106: 188 58 213 188 58 356 45 N SD: 0.0402 c. M:-0.0683 c. 1277: 217 67 246 217 67 411 52 N SD: 0.0357 c. M: 0.0941 c. 1848: 314 97 356 314 97 595 75 N SD: 0.0282 c. M:-0.0691 c. 2019: 343 106 389 343 106 650 82 N SD: 0.0260 c. M: 0.0467 c. 2289: 389 120 441 389 120 737 93 N SD: 0.0222 c. M: 0.0404 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: 39.8143 cents 4 x x 5:6 x x 8 S SD: 37.2438 cents 5 x 6:7 x 8 x 10 S SD: 27.2624 cents 6 x 7:8:9 x x 12 S SD: 0.0000 cents 7:8 x 9 x 11 x 14 SD: 17.7065 cents 8:9 x 11:12 x x 16 SD: 13.3182 cents 9:10:11:12 x 14 x 18 SD: 16.6718 cents 10:11:12:13:15:16:19:20 SD: 14.1381 cents 11:12:13:15 x 17:21:22 SD: 12.8960 cents 12 x 14:16:18:19:23:24 SD: 6.5817 cents 13 x 15:17 x 20:25:26 SD: 9.4403 cents 14:16 x 19:21:22:27:28 SD: 7.8041 cents 15:17:18:20 x 23:29:30 SD: 9.5172 cents 16:18:19:21:24:25:31:32 SD: 6.0273 cents 17:19:20:23 x 26:33:34 SD: 7.1629 cents 18:20:21:24:27:28:35:36 S SD: 3.0723 cents 20 x 23:27:30:31:39:40 SD: 5.6416 cents 22:25:26:29:33:34:43:44 SD: 5.3470 cents 23:26:27:31:35:36:45:46 SD: 5.3168 cents 24:27:28:32:36:37:47:48 SD: 2.8317 cents 40:45:47:53:60:62:78:80 SD: 2.6046 cents 42:47:49:56:63:65:82:84 SD: 2.0825 cents 48:54:56:64:72:75:93:96 SD: 1.4130 cents 54:61:63:72:81:84:105:108 SD: 1.0157 cents 72:81:84:96:108:112:140:144 S SD: 0.0000 cents