Scala analysis: xen10-wilson-purvi-10b-07
Purvi modulation 7 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: 6/5 315.641287 minor third 2: 5/4 386.313714 major third 3: 4/3 498.044999 perfect fourth 4: 8/5 813.686286 minor sixth 5: 5/3 884.358713 major sixth, BP 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: 6/5 315.6413 minor third 2: 25/24 70.6724 classic chromatic semitone, minor chroma 3: 16/15 111.7313 minor diatonic semitone 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: 9/8 203.9100 major whole tone
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 : 315.6 386.3 498.0 813.7 884.4 996.1 1200.0 315.6 : 70.7 182.4 498.0 568.7 680.4 884.4 1200.0 386.3 : 111.7 427.4 498.0 609.8 813.7 1129.3 1200.0 498.0 : 315.6 386.3 498.0 702.0 1017.6 1088.3 1200.0 813.7 : 70.7 182.4 386.3 702.0 772.6 884.4 1200.0 884.4 : 111.7 315.6 631.3 702.0 813.7 1129.3 1200.0 996.1 : 203.9 519.6 590.2 702.0 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 : 175.96773 cents, oct.: 1231.77412 cents Scale is not proper Step pattern alph. order: ABCABCD Step pattern size order : DABDABC 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 Mixolydian octave species of abstract tetrachord Scale contains two identical conjunct tetrachords Scale contains a complete diamond : 1 5 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 : 5 = 71.4286% 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: 9 Scale harmonicity : 0.037313 Average absolute harmonicity : 0.250927 Specific harmonicity : 0.217736 Fundamental : 1/180, -7.4919 octaves, 1.4535 Hz. Guide tone : 240, 7.9069 octaves, 62790.136 Hz. Exponens Consonantiae : 4.320000E+04, 15.39874 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 38.0, average 5.42857 Mersenne's string divisions : 1801800 Sum of van Prooijen's expressibility: 4.22724, average 0.60389 Sum of Tenney's harmonic distance : 9.09488, average 1.29927 Vogel's harmonic complexity : 13.00000 Wille's k value : 112 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 80.50828, average 2.87530 Lattice compactness (without 2's) : 43.07054, average 1.53823 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 4 1.28571 13 1 3: -2 .. 1 -0.42857 5 2 5: -1 .. 1 0.00000 4 4 Average exponent except 2's :-3 / 7 =-0.42857 Average absolute exponent except 2's: 9 / 7 = 1.28571
FIT/MODE
7: 2 0 1 2 0 1 1 N T3 SD: 30.6528 c. M: 43.4566 c. 12: 3 1 1 3 1 1 2 N SD: 11.2316 c. M: 15.6413 c. Chromatic Hypodorian inverse 19: 5 1 2 5 1 2 3 N SD: 7.2612 c. M:-14.4363 c. 22: 6 1 2 6 1 2 4 N SD: 8.9889 c. M: 14.2718 c. 31: 8 2 3 8 2 3 5 N SD: 5.4323 c. M:-10.3616 c. 34: 9 2 3 9 2 3 6 N SD: 3.6362 c. M: 7.8547 c. 41: 11 2 4 11 2 4 7 N SD: 4.6088 c. M:-6.3099 c. 46: 12 3 4 12 3 4 8 N SD: 3.6241 c. M: 4.9906 c. 53: 14 3 5 14 3 5 9 N SD: 1.0405 c. M: 1.4081 c. 118: 31 7 11 31 7 11 20 N SD: 0.3094 c. M:-0.5202 c. 171: 45 10 16 45 10 16 29 N SD: 0.2642 c. M:-0.4012 c. 289: 76 17 27 76 17 27 49 N SD: 0.2106 c. M:-0.4498 c. 323: 85 19 30 85 19 30 55 N SD: 0.1990 c. M: 0.4244 c. 376: 99 22 35 99 22 35 64 N SD: 0.2361 c. M: 0.3453 c. 388: 102 23 36 102 23 36 66 N SD: 0.2006 c. M:-0.2842 c. 441: 116 26 41 116 26 41 75 N SD: 0.0845 c. M: 0.1716 c. 494: 130 29 46 130 29 46 84 N SD: 0.1072 c. M: 0.1482 c. 559: 147 33 52 147 33 52 95 N SD: 0.0647 c. M: 0.0906 c. 612: 161 36 57 161 36 57 104 N SD: 0.0323 c. M:-0.0450 c. 730: 192 43 68 192 43 68 124 N SD: 0.0348 c. M:-0.0744 c. 1171: 308 69 109 308 69 109 199 N SD: 0.0161 c. M:-0.0228 c. 1783: 469 105 166 469 105 166 303 N SD: 0.0076 c. M: 0.0160 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 x 5 x 6 S SD: 0.0000 cents 4 x 5 x 6 x 7:8 S SD: 28.7524 cents 5:6 x 7:8 x 9:10 S SD: 17.4324 cents 6:7 x 8 x 10:11:12 S SD: 14.4451 cents 7:8:9 x 11:12 x 14 SD: 22.6847 cents 8 x 10:11:13 x 14:16 SD: 13.1176 cents 9:11 x 12:14:15:16:18 SD: 9.7006 cents 10:12 x 13:16:17:18:20 SD: 9.9429 cents 11:13:14:15 x 18:20:22 SD: 12.5920 cents 12:14:15:16:19:20:21:24 SD: 8.3916 cents 13 x 16:17:21:22:23:26 SD: 8.9649 cents 15:18:19:20:24:25:27:30 SD: 4.4911 cents 24:29:30:32:38:40:43:48 SD: 3.6525 cents 30:36:38:40:48:50:53:60 SD: 3.6243 cents 33:40:41:44:53:55:59:66 SD: 3.3581 cents 35:42:44:47:56:58:62:70 SD: 2.8065 cents 36:43:45:48:58:60:64:72 SD: 2.0607 cents 40:48:50:53:64:67:71:80 SD: 2.0188 cents 45:54:56:60:72:75:80:90 S SD: 1.1016 cents 60:72:75:80:96:100:107:120 SD: 0.7717 cents 105:126:131:140:168:175:187:210 SD: 0.6458 cents 120:144:150:160:192:200:213:240 SD: 0.3867 cents 135:162:169:180:216:225:240:270 SD: 0.3661 cents 180:216:225:240:288:300:320:360 S SD: 0.0000 cents