Scala analysis: xen10-wilson-purvi-11a-01
Purvi modulation 1 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: 6/5 315.641287 minor third 4: 3/2 701.955001 perfect fifth 5: 14/9 764.915905 septimal minor sixth 6: 8/5 813.686286 minor sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 5/4 386.3137 major third 1: 9/8 203.9100 major whole tone 2: 28/27 62.9609 Archytas' 1/3-tone 3: 36/35 48.7704 septimal diesis, 1/4-tone 4: 5/4 386.3137 major third 5: 28/27 62.9609 Archytas' 1/3-tone 6: 36/35 48.7704 septimal diesis, 1/4-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: 2 16/15 111.731 cents minor diatonic semitone 2: 1 7/6 266.871 cents septimal 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 2: 1 45/32 590.224 cents diatonic tritone 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 64/45 609.776 cents 2nd tritone 5: 1 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: 2 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 : 203.9 266.9 315.6 702.0 764.9 813.7 1200.0 203.9 : 63.0 111.7 498.0 561.0 609.8 996.1 1200.0 266.9 : 48.8 435.1 498.0 546.8 933.1 1137.0 1200.0 315.6 : 386.3 449.3 498.0 884.4 1088.3 1151.2 1200.0 702.0 : 63.0 111.7 498.0 702.0 764.9 813.7 1200.0 764.9 : 48.8 435.1 639.0 702.0 750.7 1137.0 1200.0 813.7 : 386.3 590.2 653.2 702.0 1088.3 1151.2 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 .. 590.2237 cents 675/512, 478.4924 cents 64/75,-274.5824 cents 3: 315.6413 .. 653.1846 cents 175/144, 337.5433 cents 64/75,-274.5824 cents 4: 546.8154 .. 884.3587 cents 175/144, 337.5433 cents 1152/1225,-106.3692 cents 5: 609.7763 .. 1088.2687 cents 675/512, 478.4924 cents 64/75,-274.5824 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 : 154.27924 cents, oct.: 1079.95465 cents Scale is not proper Step pattern alph. order: ABCDBCD Step pattern size order : CBADBAD Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.578397 Lumma stability : 0.081284 Lumma impropriety factor : 0.813781 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 Hypodorian 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 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: 9 Scale harmonicity : 0.029983 Average absolute harmonicity : 0.247184 Specific harmonicity : 0.173647 Fundamental : 1/360, -8.4919 octaves, 0.7267 Hz. Guide tone : 504, 8.9773 octaves, 131859.285 Hz. Exponens Consonantiae : 1.814400E+05, 17.46913 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 42.5, average 6.07143 Mersenne's string divisions : 838695 Sum of van Prooijen's expressibility: 4.62864, average 0.66123 Sum of Tenney's harmonic distance : 9.73931, average 1.39133 Vogel's harmonic complexity : 15.14286 Wille's k value : 202 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 83.43638, average 2.97987 Lattice compactness (without 2's) : 49.82487, average 1.77946 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 0.14286 11 1 3: -2 .. 2 0.14286 7 2 5: -1 .. 0 -0.28571 2 2 7: 0 .. 1 0.28571 2 2 Average exponent except 2's : 1 / 7 = 0.14286 Average absolute exponent except 2's: 11 / 7 = 1.57143 Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 11 16 21| Scale is weakly epimorphic with val: <7 12 17 18|
FIT/MODE
7: 1 1 0 2 0 1 2 N T3 SD: 47.8014 c. M: 79.2016 c. 8: 1 1 0 3 0 0 3 N SD: 39.3432 c. M: 63.6863 c. 9: 1 1 0 3 1 0 3 N SD: 37.8778 c. M: 70.5767 c. 10: 2 0 1 3 0 1 3 N SD: 31.6853 c. M: 44.9159 c. 11: 2 0 1 3 1 0 4 N G SD: 32.6538 c. M: 50.0499 c. 12: 2 1 0 4 1 0 4 N SD: 19.9267 c. M:-35.0841 c. 16: 3 1 0 5 1 1 5 N SD: 20.2274 c. M:-33.1291 c. 17: 3 1 1 5 1 1 5 N SD: 20.5473 c. M:-37.2999 c. 19: 3 1 1 6 1 1 6 N SD: 8.9988 c. M: 14.4363 c. 22: 4 1 1 7 1 1 7 N SD: 7.9825 c. M:-14.2718 c. 31: 5 2 1 10 2 1 10 N SD: 6.2478 c. M: 10.3616 c. 41: 7 2 2 13 2 2 13 N SD: 3.8247 c. M:-6.3099 c. 53: 9 3 2 17 3 2 17 N SD: 2.7010 c. M:-4.8954 c. 72: 12 4 3 23 4 3 23 N SD: 2.1431 c. M: 3.9100 c. 77: 13 4 3 25 4 3 25 N SD: 2.2049 c. M: 3.9530 c. 94: 16 5 4 30 5 4 30 N SD: 1.9322 c. M:-3.5076 c. 99: 17 5 4 32 5 4 32 N SD: 1.2041 c. M:-2.1506 c. 118: 20 6 5 38 6 5 38 N SD: 1.2780 c. M: 2.4641 c. 130: 22 7 5 42 7 5 42 N SD: 1.0822 c. M: 1.7951 c. 152: 26 8 6 49 8 6 49 N SD: 0.9068 c. M:-1.5501 c. 171: 29 9 7 55 9 7 55 N SD: 0.2350 c. M: 0.4012 c. 441: 75 23 18 142 23 18 142 N SD: 0.1555 c. M: 0.2901 c. 494: 84 26 20 159 26 20 159 N SD: 0.1835 c. M:-0.3356 c. 612: 104 32 25 197 32 25 197 N SD: 0.1131 c. M: 0.2100 c. 665: 113 35 27 214 35 27 214 N SD: 0.1317 c. M:-0.1969 c. 783: 133 41 32 252 41 32 252 N SD: 0.1150 c. M: 0.2042 c. 836: 142 44 34 269 44 34 269 N SD: 0.1217 c. M:-0.1893 c. 913: 155 48 37 294 48 37 294 N SD: 0.1183 c. M: 0.1977 c. 935: 159 49 38 301 49 38 301 N SD: 0.0782 c. M:-0.1542 c. 1106: 188 58 45 356 58 45 356 N SD: 0.0517 c. M:-0.0911 c. 1677: 285 88 68 540 88 68 540 N SD: 0.0489 c. M: 0.0906 c. 1718: 292 90 70 553 90 70 553 N SD: 0.0518 c. M:-0.0747 c. 1848: 314 97 75 595 97 75 595 N SD: 0.0304 c. M: 0.0569 c. 2019: 343 106 82 650 106 82 650 N SD: 0.0264 c. M: 0.0467 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: 17.6681 cents 7:8 x x x 11 x 14 SD: 10.8128 cents 8:9 x 10:12 x 13:16 SD: 15.1196 cents 9:10 x 11 x 14 x 18 SD: 9.5905 cents 10:11 x 12:15 x 16:20 S SD: 7.7812 cents 11:12:13 x x 17:18:22 SD: 14.1108 cents 12 x 14 x 18 x 19:24 SD: 4.5321 cents 13 x 15:16 x 20:21:26 SD: 10.8213 cents 14:16 x 17:21:22 x 28 SD: 7.6734 cents 15:17 x 18 x 23:24:30 SD: 5.5992 cents 16:18 x 19:24:25:26:32 SD: 5.5492 cents 17:19:20 x x 26:27:34 SD: 7.3839 cents 18:20:21:22:27:28:29:36 SD: 5.7413 cents 19:21:22:23:29 x 30:38 SD: 8.7728 cents 20 x 23:24:30:31:32:40 SD: 4.2781 cents 21:24 x 25:32:33:34:42 SD: 8.1746 cents 22:25:26 x 33:34:35:44 SD: 5.3393 cents 24:27:28:29:36:37:38:48 SD: 3.8153 cents 25:28:29:30:38:39:40:50 SD: 3.8015 cents 27:30 x 32:41:42:43:54 SD: 6.3264 cents 28:32:33:34:42:44:45:56 SD: 6.1286 cents 29:33:34:35:44:45:46:58 SD: 4.9418 cents 30:34:35:36:45:47:48:60 SD: 2.5358 cents 40:45:47:48:60:62:64:80 SD: 1.9702 cents 50:56:58:60:75:78:80:100 SD: 1.9288 cents 54:61:63:65:81:84:86:108 SD: 1.7116 cents 65:73:76:78:98:101:104:130 SD: 1.4657 cents 70:79:82:84:105:109:112:140 SD: 1.3012 cents 72:81:84:86:108:112:115:144 SD: 1.2255 cents 90:101:105:108:135:140:144:180 SD: 0.6114 cents 120:135:140:144:180:187:192:240 SD: 0.4412 cents 200:225:233:240:300:311:320:400 SD: 0.3644 cents 210:236:245:252:315:327:336:420 SD: 0.3636 cents 216:243:252:259:324:336:346:432 SD: 0.3439 cents 240:270:280:288:360:373:384:480 SD: 0.2209 cents 270:304:315:324:405:420:432:540 SD: 0.2035 cents 360:405:420:432:540:560:576:720 S SD: 0.0000 cents