Scala analysis: xen10-wilson-purvi-11b-07
Purvi modulation 7 from Figure 11b, Archytas (5/4 36/35 28/27), (36/35 28/27 5/4)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 5/4 386.313714 major third 2: 9/7 435.084095 septimal major third, BP third 3: 4/3 498.044999 perfect fourth 4: 5/3 884.358713 major sixth, BP sixth 5: 12/7 933.129094 septimal 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: 5/4 386.3137 major third 2: 36/35 48.7704 septimal diesis, 1/4-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: 9/8 203.9100 major whole tone
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 : 386.3 435.1 498.0 884.4 933.1 996.1 1200.0 386.3 : 48.8 111.7 498.0 546.8 609.8 813.7 1200.0 435.1 : 63.0 449.3 498.0 561.0 764.9 1151.2 1200.0 498.0 : 386.3 435.1 498.0 702.0 1088.3 1137.0 1200.0 884.4 : 48.8 111.7 315.6 702.0 750.7 813.7 1200.0 933.1 : 63.0 266.9 653.2 702.0 764.9 1151.2 1200.0 996.1 : 203.9 590.2 639.0 702.0 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 .. 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 : 180.93027 cents, oct.: 1266.51186 cents Scale is not proper Step pattern alph. order: ABCABCD Step pattern size order : DABDABC 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 Mixolydian octave species of abstract tetrachord Scale contains two identical conjunct tetrachords 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 -- 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 : 0.240239 Specific harmonicity : 0.173647 Fundamental : 1/252, -7.9773 octaves, 1.0382 Hz. Guide tone : 720, 9.4919 octaves, 188370.407 Hz. Exponens Consonantiae : 1.814400E+05, 17.46913 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 43.5, average 6.21429 Mersenne's string divisions : 478800 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 : 15.00000 Wille's k value : 157 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: -2 .. 4 1.00000 11 1 3: -2 .. 2 -0.14286 7 2 5: 0 .. 1 0.28571 2 2 7: -1 .. 0 -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: 2 1 0 2 0 1 1 N T3 SD: 47.8014 c. M:-79.2016 c. 8: 3 0 0 3 0 1 1 N SD: 39.3432 c. M:-63.6863 c. 9: 3 0 1 3 0 0 2 N SD: 35.8577 c. M: 62.7567 c. 10: 3 0 1 3 1 0 2 N SD: 39.0016 c. M: 75.0841 c. 11: 3 1 0 4 0 1 2 N G SD: 40.1416 c. M: 61.6814 c. 12: 4 0 1 4 0 1 2 N SD: 19.9267 c. M: 35.0841 c. 16: 5 1 1 5 0 1 3 N SD: 20.2274 c. M: 33.1291 c. 17: 5 1 1 5 1 1 3 N SD: 20.5473 c. M: 37.2999 c. 18: 6 1 0 6 1 1 3 N SD: 18.8896 c. M:-31.5826 c. 19: 6 1 1 6 1 1 3 N SD: 8.9988 c. M:-14.4363 c. 22: 7 1 1 7 1 1 4 N SD: 7.9825 c. M: 14.2718 c. 31: 10 1 2 10 1 2 5 N SD: 6.2478 c. M:-10.3616 c. 41: 13 2 2 13 2 2 7 N SD: 3.8247 c. M: 6.3099 c. 53: 17 2 3 17 2 3 9 N SD: 2.7010 c. M: 4.8954 c. 72: 23 3 4 23 3 4 12 N SD: 2.1431 c. M:-3.9100 c. 77: 25 3 4 25 3 4 13 N SD: 2.2049 c. M:-3.9530 c. 94: 30 4 5 30 4 5 16 N SD: 1.9322 c. M: 3.5076 c. 99: 32 4 5 32 4 5 17 N SD: 1.2041 c. M: 2.1506 c. 118: 38 5 6 38 5 6 20 N SD: 1.2780 c. M:-2.4641 c. 130: 42 5 7 42 5 7 22 N SD: 1.0822 c. M:-1.7951 c. 152: 49 6 8 49 6 8 26 N SD: 0.9068 c. M: 1.5501 c. 171: 55 7 9 55 7 9 29 N SD: 0.2350 c. M:-0.4012 c. 441: 142 18 23 142 18 23 75 N SD: 0.1555 c. M:-0.2901 c. 494: 159 20 26 159 20 26 84 N SD: 0.1835 c. M: 0.3356 c. 612: 197 25 32 197 25 32 104 N SD: 0.1131 c. M:-0.2100 c. 665: 214 27 35 214 27 35 113 N SD: 0.1317 c. M: 0.1969 c. 783: 252 32 41 252 32 41 133 N SD: 0.1150 c. M:-0.2042 c. 836: 269 34 44 269 34 44 142 N SD: 0.1217 c. M: 0.1893 c. 913: 294 37 48 294 37 48 155 N SD: 0.1183 c. M:-0.1977 c. 935: 301 38 49 301 38 49 159 N SD: 0.0782 c. M: 0.1542 c. 1106: 356 45 58 356 45 58 188 N SD: 0.0517 c. M: 0.0911 c. 1677: 540 68 88 540 68 88 285 N SD: 0.0489 c. M:-0.0906 c. 1718: 553 70 90 553 70 90 292 N SD: 0.0518 c. M: 0.0747 c. 1848: 595 75 97 595 75 97 314 N SD: 0.0304 c. M:-0.0569 c. 2019: 650 82 106 650 82 106 343 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: 91.2019 cents 3 x x 4:5 x x 6 S SD: 0.0000 cents 4:5 x x x x 7:8 SD: 9.0880 cents 5:6 x 7:8 x 9:10 S SD: 26.5228 cents 6 x x 8:10 x 11:12 S SD: 13.3182 cents 7 x 9 x x 12 x 14 SD: 0.0000 cents 8:10 x 11:13 x 14:16 SD: 14.8358 cents 9:11 x 12:15 x 16:18 SD: 7.7812 cents 10 x 13 x x 17:18:20 SD: 8.0559 cents 11 x 14:15:18:19:20:22 SD: 11.2003 cents 12:15 x 16:20 x 21:24 S SD: 5.4528 cents 13:16:17 x x 22:23:26 SD: 9.2739 cents 14 x 18:19:23:24:25:28 SD: 6.7060 cents 15:19 x 20:25:26:27:30 SD: 6.1334 cents 16:20 x 21:27 x 28:32 SD: 8.8299 cents 17:21:22:23:28:29:30:34 SD: 6.1298 cents 18 x 23:24:30:31:32:36 SD: 2.2290 cents 19:24 x 25:32:33:34:38 SD: 7.1183 cents 20:25:26:27:33:34:36:40 SD: 6.0670 cents 21:26:27:28:35:36:37:42 SD: 3.2437 cents 22 x 28:29:37:38:39:44 SD: 5.6294 cents 24:30:31:32:40:41:43:48 SD: 2.3978 cents 26 x 33:35:43:45:46:52 SD: 6.0007 cents 27:34:35:36:45:46:48:54 SD: 3.1283 cents 28:35:36:37:47:48:50:56 SD: 3.0385 cents 32:40:41:43:53:55:57:64 SD: 2.7378 cents 36:45:46:48:60:62:64:72 S SD: 1.9105 cents 45:56:58:60:75:77:80:90 SD: 1.3401 cents 60:75:77:80:100:103:107:120 SD: 0.9610 cents 63:79:81:84:105:108:112:126 SD: 0.7839 cents 81:101:104:108:135:139:144:162 SD: 0.7442 cents 84:105:108:112:140:144:149:168 SD: 0.5527 cents 108:135:139:144:180:185:192:216 SD: 0.3180 cents 144:180:185:192:240:247:256:288 SD: 0.2386 cents 252:315:324:336:420:432:448:504 S SD: 0.0000 cents