Scala analysis: xen10-wilson-purvi-10b-01
Purvi modulation 1 from Figure 10b, Didymus (6/5 25/24 16/15), (25/24 16/15 6/5)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 25/24 70.672427 classic chromatic semitone, minor chroma 2: 10/9 182.403712 minor whole tone 3: 5/4 386.313714 major third 4: 3/2 701.955001 perfect fifth 5: 25/16 772.627428 classic augmented fifth 6: 5/3 884.358713 major sixth, BP sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 6/5 315.6413 minor third 1: 25/24 70.6724 classic chromatic semitone, minor chroma 2: 16/15 111.7313 minor diatonic semitone 3: 9/8 203.9100 major whole tone 4: 6/5 315.6413 minor third 5: 25/24 70.6724 classic chromatic semitone, minor chroma 6: 16/15 111.7313 minor diatonic semitone 7: 6/5 315.6413 minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 2 16/15 111.731 cents minor diatonic semitone 1: 1 9/8 203.910 cents major whole tone 1: 2 6/5 315.641 cents minor third 2: 2 10/9 182.404 cents minor whole tone 2: 1 6/5 315.641 cents minor third 2: 2 5/4 386.314 cents major third 2: 1 32/25 427.373 cents classic diminished fourth 2: 1 27/20 519.551 cents acute fourth 3: 1 5/4 386.314 cents major third 3: 4 4/3 498.045 cents perfect fourth 3: 1 45/32 590.224 cents diatonic tritone 3: 1 36/25 631.283 cents classic diminished fifth 4: 1 25/18 568.717 cents classic augmented fourth 4: 1 64/45 609.776 cents 2nd tritone 4: 4 3/2 701.955 cents perfect fifth 4: 1 8/5 813.686 cents minor sixth 5: 1 40/27 680.449 cents grave fifth 5: 1 25/16 772.627 cents classic augmented fifth 5: 2 8/5 813.686 cents minor sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 2 9/5 1017.596 cents just minor seventh, BP seventh 6: 2 5/3 884.359 cents major sixth, BP sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 15/8 1088.269 cents classic major seventh 6: 2 48/25 1129.328 cents classic 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 : 70.7 182.4 386.3 702.0 772.6 884.4 1200.0 70.7 : 111.7 315.6 631.3 702.0 813.7 1129.3 1200.0 182.4 : 203.9 519.6 590.2 702.0 1017.6 1088.3 1200.0 386.3 : 315.6 386.3 498.0 813.7 884.4 996.1 1200.0 702.0 : 70.7 182.4 498.0 568.7 680.4 884.4 1200.0 772.6 : 111.7 427.4 498.0 609.8 813.7 1129.3 1200.0 884.4 : 315.6 386.3 498.0 702.0 1017.6 1088.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 315.6413 cents 144/125, 244.9689 cents 25/24, 70.6724 cents 2: 182.4037 .. 519.5513 cents 243/200, 337.1476 cents 25/27,-133.2376 cents 3: 386.3137 .. 631.2826 cents 144/125, 244.9689 cents 25/27,-133.2376 cents 4: 568.7174 .. 813.6863 cents 144/125, 244.9689 cents 625/648,-62.5651 cents 5: 680.4487 .. 1017.5963 cents 243/200, 337.1476 cents 25/27,-133.2376 cents 6: 884.3587 .. 1129.3276 cents 144/125, 244.9689 cents 25/27,-133.2376 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 25/24, 70.6724 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 2.425678 Largest / Average step : 1.841241 Largest / Smallest step : 4.466258 Median interval of one step : 16/15, 111.7313 cents, amount: 2 Least squares average step : 156.93950 cents, oct.: 1098.57652 cents Scale is not proper Step pattern alph. order: ABCDABD Step pattern size order : ABCDABD Scale is not a Constant Structure Scale diversity : 1.487547 Lumma stability : 0.117787 Lumma impropriety factor : 0.496263 Rothenberg efficiency : 0.451701 redundancy: 0.548299 Efficiency x scale size : 3.161905 Number of different interval sizes : 22 = 3.66667 / 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 : 2048/2025, 19.5526 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Number of recognisable fifths : 4, average 701.9550 cents Scale is Hypolydian 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 -- Rational properties -- Prime limit : 5 Odd number limit : 45 (O: 45 U: 45) Highest odd numerator or denominator: 25 Scale harmonicity : 0.038760 Average absolute harmonicity : 0.242039 Specific harmonicity : 0.205040 Fundamental : 1/144, -7.1699 octaves, 1.8168 Hz. Guide tone : 150, 7.2288 octaves, 39243.835 Hz. Exponens Consonantiae : 2.160000E+04, 14.39874 octaves Euler's gradus suavitatis : 20 Sum of Mann's harmonic distance : 67.0, average 9.57143 Mersenne's string divisions : 13741560 Sum of van Prooijen's expressibility: 5.62518, average 0.80360 Sum of Tenney's harmonic distance : 10.89076, average 1.55582 Vogel's harmonic complexity : 12.57143 Wille's k value : 112 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 80.95389, average 2.89121 Lattice compactness (without 2's) : 45.12846, average 1.61173 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 1 -1.14286 12 1 3: -2 .. 1 -0.42857 5 1 5: 0 .. 2 1.00000 7 5 Average exponent except 2's : 4 / 7 = 0.57143 Average absolute exponent except 2's: 12 / 7 = 1.71429
FIT/MODE
7: 0 1 1 2 0 1 2 N T3 SD: 47.1500 c. M: 86.9131 c. 8: 0 1 2 2 0 1 2 N SD: 43.3680 c. M: 70.6724 c. 11: 0 1 2 3 1 1 3 N SD: 48.2834 c. M: 73.3128 c. 12: 1 1 2 3 1 1 3 N SD: 18.3411 c. M:-29.3276 c. Chromatic Phrygian inverse 15: 1 1 3 4 1 1 4 N SD: 16.3450 c. M:-27.3726 c. 19: 1 2 3 5 1 2 5 N SD: 7.8367 c. M: 14.7327 c. 31: 2 3 5 8 2 3 8 N SD: 5.7965 c. M:-11.1447 c. 34: 2 3 6 9 2 3 9 N SD: 3.2320 c. M: 5.9331 c. 53: 3 5 9 14 3 5 14 N SD: 1.7271 c. M: 2.8161 c. 84: 5 8 14 22 5 8 22 N SD: 1.6470 c. M:-3.3106 c. 87: 5 8 15 23 5 8 23 N SD: 1.5734 c. M: 3.0934 c. 118: 7 11 20 31 7 11 31 N SD: 0.3744 c. M:-0.6471 c. 171: 10 16 29 45 10 16 45 N SD: 0.3626 c. M: 0.6976 c. 289: 17 27 49 76 17 27 76 N SD: 0.1961 c. M: 0.3091 c. 323: 19 30 55 85 19 30 85 N SD: 0.1790 c. M: 0.3604 c. 441: 26 41 75 116 26 41 116 N SD: 0.0879 c. M:-0.1617 c. 612: 36 57 104 161 36 57 161 N SD: 0.0527 c. M: 0.0842 c. 730: 43 68 124 192 43 68 192 N SD: 0.0311 c. M:-0.0620 c. 1171: 69 109 199 308 69 109 308 N SD: 0.0245 c. M:-0.0455 c. 1783: 105 166 303 469 105 166 469 N SD: 0.0071 c. M: 0.0145 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: 37.2438 cents 4 x x 5:6 x 7:8 S SD: 21.1168 cents 5 x x 6 x 8 x 10 S SD: 27.2446 cents 6 x 7:8:9 x 10:12 S SD: 28.0133 cents 7 x 8:9 x 11:12:14 SD: 17.0094 cents 8 x 9:10:12 x 13:16 SD: 9.7646 cents 9 x 10:11 x 14:15:18 SD: 7.9325 cents 10 x 11:13:15:16:17:20 SD: 14.6954 cents 11 x 12:14 x 17:18:22 SD: 11.5792 cents 12 x 13:15:18:19:20:24 SD: 8.2445 cents 13 x 14:16 x 20:22:26 SD: 14.2365 cents 14:15:16:18:21:22:23:28 SD: 12.6600 cents 15:16:17:19 x 23:25:30 SD: 11.1195 cents 16:17:18:20:24:25:27:32 SD: 6.5471 cents 18:19:20:23:27:28:30:36 SD: 6.4415 cents 20:21:22:25:30:31:33:40 SD: 4.4930 cents 24:25:27:30:36:38:40:48 SD: 4.4911 cents 27:28:30:34:41:42:45:54 SD: 3.8688 cents 28:29:31:35:42:44:47:56 SD: 2.8065 cents 44:46:49:55:66:69:73:88 SD: 1.7879 cents 48:50:53:60:72:75:80:96 SD: 1.5506 cents 64:67:71:80:96:100:107:128 SD: 1.5055 cents 72:75:80:90:108:113:120:144 SD: 1.0968 cents 92:96:102:115:138:144:153:184 SD: 0.9740 cents 96:100:107:120:144:150:160:192 SD: 0.7717 cents 116:121:129:145:174:181:193:232 SD: 0.6785 cents 144:150:160:180:216:225:240:288 S SD: 0.0000 cents