Scala analysis: xen10-wilson-purvi-10a-07
Purvi modulation 7 from Figure 10a, Didymus (16/15 25/24 6/5), (6/5 16/15 25/24)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 6/5 315.641287 minor third 2: 32/25 427.372572 classic diminished fourth 3: 4/3 498.044999 perfect fourth 4: 8/5 813.686286 minor sixth 5: 9/5 1017.596288 just minor seventh, BP seventh 6: 48/25 1129.327573 classic diminished octave 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 25/24 70.6724 classic chromatic semitone, minor chroma 1: 6/5 315.6413 minor third 2: 16/15 111.7313 minor diatonic semitone 3: 25/24 70.6724 classic chromatic semitone, minor chroma 4: 6/5 315.6413 minor third 5: 9/8 203.9100 major whole tone 6: 16/15 111.7313 minor diatonic semitone 7: 25/24 70.6724 classic chromatic semitone, minor chroma
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 : 315.6 427.4 498.0 813.7 1017.6 1129.3 1200.0 315.6 : 111.7 182.4 498.0 702.0 813.7 884.4 1200.0 427.4 : 70.7 386.3 590.2 702.0 772.6 1088.3 1200.0 498.0 : 315.6 519.6 631.3 702.0 1017.6 1129.3 1200.0 813.7 : 203.9 315.6 386.3 702.0 813.7 884.4 1200.0 1017.6: 111.7 182.4 498.0 609.8 680.4 996.1 1200.0 1129.3: 70.7 386.3 498.0 568.7 884.4 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 : 187.02295 cents, oct.: 1309.16067 cents Scale is not proper Step pattern alph. order: ABCADBC Step pattern size order : DBADCBA Scale is sum-free (all different intervals) 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 Phrygian 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 Scale is n-1 differentially coherent in interval classes 4 and 5 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 : 0.230397 Specific harmonicity : 0.205040 Fundamental : 1/75, -6.2288 octaves, 3.4883 Hz. Guide tone : 288, 8.1699 octaves, 75348.163 Hz. Exponens Consonantiae : 2.160000E+04, 14.39874 octaves Euler's gradus suavitatis : 20 Sum of Mann's harmonic distance : 89.0, average 12.71429 Mersenne's string divisions : 8330322 Sum of van Prooijen's expressibility: 5.62518, average 0.80360 Sum of Tenney's harmonic distance : 12.09488, average 1.72784 Vogel's harmonic complexity : 11.57143 Wille's k value : 67 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: 0 .. 5 2.28571 16 1 3: -1 .. 2 0.42857 5 1 5: -2 .. 0 -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: 2 1 0 2 1 1 0 N T3 SD: 47.1500 c. M:-86.9131 c. 8: 2 1 0 2 2 0 1 N S SD: 45.4561 c. M: 79.3276 c. 11: 3 1 0 3 2 1 1 N SD: 36.4138 c. M: 61.6814 c. 12: 3 1 1 3 2 1 1 N SD: 18.3411 c. M: 29.3276 c. Chromatic Phrygian 15: 4 1 1 4 3 1 1 N SD: 16.3450 c. M: 27.3726 c. 19: 5 2 1 5 3 2 1 N SD: 7.8367 c. M:-14.7327 c. 31: 8 3 2 8 5 3 2 N SD: 5.7965 c. M: 11.1447 c. 34: 9 3 2 9 6 3 2 N SD: 3.2320 c. M:-5.9331 c. 53: 14 5 3 14 9 5 3 N SD: 1.7271 c. M:-2.8161 c. 84: 22 8 5 22 14 8 5 N SD: 1.6470 c. M: 3.3106 c. 87: 23 8 5 23 15 8 5 N SD: 1.5734 c. M:-3.0934 c. 118: 31 11 7 31 20 11 7 N SD: 0.3744 c. M: 0.6471 c. 171: 45 16 10 45 29 16 10 N SD: 0.3626 c. M:-0.6976 c. 289: 76 27 17 76 49 27 17 N SD: 0.1961 c. M:-0.3091 c. 323: 85 30 19 85 55 30 19 N SD: 0.1790 c. M:-0.3604 c. 441: 116 41 26 116 75 41 26 N SD: 0.0879 c. M: 0.1617 c. 612: 161 57 36 161 104 57 36 N SD: 0.0527 c. M:-0.0842 c. 730: 192 68 43 192 124 68 43 N SD: 0.0311 c. M: 0.0620 c. 1171: 308 109 69 308 199 109 69 N SD: 0.0245 c. M: 0.0455 c. 1783: 469 166 105 469 303 166 105 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: 55.8656 cents 3 x x 4:5 x x 6 S SD: 23.5575 cents 4 x 5 x 6:7 x 8 S SD: 32.1600 cents 5:6 x 7:8:9 x 10 S SD: 16.8934 cents 6:7 x 8:10:11 x 12 S SD: 18.3109 cents 7:8:9 x 11:13 x 14 SD: 21.0662 cents 8 x 10:11:13:14:15:16 SD: 16.0802 cents 9:11 x 12:14:16:17:18 SD: 11.3652 cents 10:12:13 x 16:18:19:20 SD: 5.3983 cents 13:16 x 17:21:23:25:26 SD: 10.8326 cents 14:17:18:19:22:25:27:28 SD: 7.3415 cents 15:18:19:20:24:27:29:30 SD: 3.1042 cents 25:30:32:33:40:45:48:50 SD: 2.4856 cents 35:42:45:47:56:63:67:70 SD: 2.2036 cents 39:47:50:52:62:70:75:78 SD: 2.1103 cents 40:48:51:53:64:72:77:80 SD: 1.9378 cents 50:60:64:67:80:90:96:100 SD: 1.2335 cents 60:72:77:80:96:108:115:120 SD: 0.7736 cents 75:90:96:100:120:135:144:150 S SD: 0.0000 cents