Scala analysis: xen10-wilson-purvi-11b-06
Purvi modulation 6 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: 3/2 701.955001 perfect fifth 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: 9/8 203.9100 major whole tone 5: 8/7 231.1741 septimal whole 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: 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 16/15 111.731 cents minor diatonic semitone 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 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: 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 15/8 1088.269 cents classic major seventh 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 : 386.3 435.1 498.0 702.0 933.1 996.1 1200.0 386.3 : 48.8 111.7 315.6 546.8 609.8 813.7 1200.0 435.1 : 63.0 266.9 498.0 561.0 764.9 1151.2 1200.0 498.0 : 203.9 435.1 498.0 702.0 1088.3 1137.0 1200.0 702.0 : 231.2 294.1 498.0 884.4 933.1 996.1 1200.0 933.1 : 63.0 266.9 653.2 702.0 764.9 968.8 1200.0 996.1 : 203.9 590.2 639.0 702.0 905.9 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 : 9/8, 203.9100 cents, amount: 2 Least squares average step : 175.71873 cents, oct.: 1230.03112 cents Scale is not proper Step pattern alph. order: ABCDECD Step pattern size order : EABCDBC Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.605831 Lumma stability : 0.081284 Lumma impropriety factor : 0.813781 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 : 1 at degree 0 Length of longest subharmonic part : 2 at degree 3 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: 9 Scale harmonicity : 0.029983 Average absolute harmonicity : 0.263443 Specific harmonicity : 0.187374 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 : 42.0, average 6.00000 Mersenne's string divisions : 478800 Sum of van Prooijen's expressibility: 4.40680, average 0.62954 Sum of Tenney's harmonic distance : 9.34137, average 1.33448 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 : 84.80960, average 3.02891 Lattice compactness (without 2's) : 48.64454, average 1.73731 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 4 0.85714 12 1 3: -2 .. 2 0.14286 7 3 5: 0 .. 1 0.14286 1 1 7: -1 .. 0 -0.28571 2 2 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 10 / 7 = 1.42857 Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 12 17 18|
FIT/MODE
7: 2 1 0 1 1 1 1 N T3 SD: 47.0833 c. M:-79.2016 c. 8: 3 0 0 2 1 1 1 N SD: 42.9267 c. M:-63.6863 c. 9: 3 0 1 1 2 0 2 N SD: 33.4817 c. M: 62.7567 c. 10: 3 1 0 2 2 0 2 N SD: 27.7376 c. M:-44.9159 c. 12: 4 0 1 2 2 1 2 N SD: 19.0438 c. M: 35.0841 c. 17: 5 1 1 3 3 1 3 N SD: 15.0213 c. M: 33.3725 c. 19: 6 1 1 3 4 1 3 N SD: 9.4031 c. M:-14.4363 c. 22: 7 1 1 4 4 1 4 N SD: 7.1880 c. M: 14.2718 c. 31: 10 1 2 5 6 2 5 N SD: 6.1472 c. M:-10.3616 c. 36: 12 1 2 6 7 2 6 N SD: 5.5208 c. M:-13.6863 c. 41: 13 2 2 7 8 2 7 N SD: 2.9957 c. M: 5.8259 c. 53: 17 2 3 9 10 3 9 N SD: 2.6532 c. M: 4.8954 c. 72: 23 3 4 12 14 4 12 N SD: 2.2336 c. M:-3.9100 c. 77: 25 3 4 13 15 4 13 N SD: 1.6404 c. M:-3.2967 c. 94: 30 4 5 16 18 5 16 N SD: 1.4071 c. M: 3.3350 c. 99: 32 4 5 17 19 5 17 N SD: 1.2573 c. M: 2.1506 c. 118: 38 5 6 20 23 6 20 N SD: 1.2734 c. M:-2.4641 c. 130: 42 5 7 22 25 7 22 N SD: 0.8576 c. M:-1.3786 c. 152: 49 6 8 26 29 8 26 N SD: 0.9405 c. M: 1.5501 c. 171: 55 7 9 29 33 9 29 N SD: 0.2405 c. M:-0.4012 c. 441: 142 18 23 75 85 23 75 N SD: 0.1588 c. M:-0.2901 c. 494: 159 20 26 84 95 26 84 N SD: 0.1767 c. M: 0.3356 c. 571: 184 23 30 97 110 30 97 N SD: 0.1467 c. M:-0.3763 c. 612: 197 25 32 104 118 32 104 N SD: 0.1118 c. M:-0.2100 c. 665: 214 27 35 113 128 35 113 N SD: 0.1192 c. M: 0.1969 c. 742: 239 30 39 126 143 39 126 N SD: 0.1029 c. M:-0.2092 c. 836: 269 34 44 142 161 44 142 N SD: 0.1092 c. M: 0.1893 c. 913: 294 37 48 155 176 48 155 N SD: 0.0982 c. M:-0.1860 c. 935: 301 38 49 159 180 49 159 N SD: 0.0777 c. M: 0.1542 c. 1106: 356 45 58 188 213 58 188 N SD: 0.0407 c. M: 0.0683 c. 1277: 411 52 67 217 246 67 217 N SD: 0.0364 c. M: 0.0960 c. 1848: 595 75 97 314 356 97 314 N SD: 0.0217 c. M:-0.0499 c. 2019: 650 82 106 343 389 106 343 N SD: 0.0235 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 5 x 6 S SD: 16.2568 cents 4:5 x x 6 x 7:8 S SD: 6.8160 cents 5:6 x 7:8 x 9:10 S SD: 31.6706 cents 6 x x 8:9:10:11:12 S SD: 14.4451 cents 7 x 9 x 11:12 x 14 SD: 20.1343 cents 8:10 x 11:12 x 14:16 S SD: 11.9689 cents 9:11 x 12:14:15:16:18 SD: 14.7726 cents 10 x 13 x 15:17:18:20 SD: 6.4447 cents 11 x 14:15:17:19:20:22 SD: 13.1001 cents 12:15 x 16:18 x 21:24 S SD: 5.4528 cents 13:16:17 x 20:22:23:26 SD: 10.6345 cents 14 x 18:19:21:24:25:28 SD: 5.2663 cents 15:19 x 20:23:26:27:30 SD: 8.8225 cents 16:20 x 21:24:27:28:32 S SD: 7.8705 cents 17:21:22:23:26:29:30:34 SD: 7.2160 cents 18 x 23:24:27:31:32:36 SD: 2.2290 cents 19:24 x 25:29:33:34:38 SD: 8.1684 cents 20:25:26:27:30:34:36:40 SD: 5.5345 cents 21:26:27:28:32:36:37:42 SD: 5.0687 cents 22 x 28:29:33:38:39:44 SD: 4.9871 cents 24:30:31:32:36:41:43:48 SD: 2.3978 cents 26 x 33:35:39:45:46:52 SD: 5.5717 cents 27:34:35:36:41:46:48:54 SD: 4.3584 cents 28:35:36:37:42:48:50:56 SD: 2.4766 cents 32:40:41:43:48:55:57:64 SD: 2.2563 cents 36:45:46:48:54:62:64:72 SD: 1.9105 cents 48:60:62:64:72:82:85:96 SD: 1.7268 cents 56:70:72:75:84:96:100:112 SD: 1.5580 cents 60:75:77:80:90:103:107:120 SD: 0.9610 cents 84:105:108:112:126:144:149:168 SD: 0.5527 cents 108:135:139:144:162:185:192:216 SD: 0.3180 cents 144:180:185:192:216:247:256:288 SD: 0.2386 cents 252:315:324:336:378:432:448:504 S SD: 0.0000 cents