Scala analysis: xen10-wilson-purvi-10a-02
Purvi modulation 2 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: 9/8 203.910002 major whole tone 2: 6/5 315.641287 minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 8/5 813.686286 minor sixth 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: 9/8 203.9100 major whole tone 2: 16/15 111.7313 minor diatonic semitone 3: 10/9 182.4037 minor whole tone 4: 9/8 203.9100 major whole tone 5: 16/15 111.7313 minor diatonic semitone 6: 25/24 70.6724 classic chromatic semitone, minor chroma 7: 6/5 315.6413 minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 2 16/15 111.731 cents minor diatonic semitone 1: 1 10/9 182.404 cents minor whole tone 1: 2 9/8 203.910 cents major whole tone 1: 1 6/5 315.641 cents minor third 2: 1 10/9 182.404 cents minor whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 2 6/5 315.641 cents minor third 2: 2 5/4 386.314 cents major third 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: 2 8/5 813.686 cents minor sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 5/3 884.359 cents major sixth, BP sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 2 15/8 1088.269 cents classic major seventh 6: 1 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: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 315.6 498.0 702.0 813.7 884.4 1200.0 203.9 : 111.7 294.1 498.0 609.8 680.4 996.1 1200.0 315.6 : 182.4 386.3 498.0 568.7 884.4 1088.3 1200.0 498.0 : 203.9 315.6 386.3 702.0 905.9 1017.6 1200.0 702.0 : 111.7 182.4 498.0 702.0 813.7 996.1 1200.0 813.7 : 70.7 386.3 590.2 702.0 884.4 1088.3 1200.0 884.4 : 315.6 519.6 631.3 813.7 1017.6 1129.3 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 : 10/9, 182.4037 cents, amount: 1 Least squares average step : 163.65522 cents, oct.: 1145.58656 cents Scale is not proper Step pattern alph. order: ABCABDE Step pattern size order : DBCDBAE Scale is not a Constant Structure Scale diversity : 1.463320 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 : 5 Highest interval variety : 5 Mean interval variety : 4.66667 = 14/3 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 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 2 Formal octave complements present : 5 = 71.4286% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 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: 9 Scale harmonicity : 0.037313 Average absolute harmonicity : 0.274718 Specific harmonicity : 0.234203 Fundamental : 1/120, -6.9069 octaves, 2.1802 Hz. Guide tone : 360, 8.4919 octaves, 94185.204 Hz. Exponens Consonantiae : 4.320000E+04, 15.39874 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 32.0, average 4.57143 Mersenne's string divisions : 2042040 Sum of van Prooijen's expressibility: 4.00540, average 0.57220 Sum of Tenney's harmonic distance : 8.27097, average 1.18157 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 : 79.06989, average 2.82392 Lattice compactness (without 2's) : 43.83447, average 1.56552 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 0.42857 11 1 3: -1 .. 2 0.28571 6 3 5: -1 .. 1 -0.14286 3 3 Average exponent except 2's : 1 / 7 = 0.14286 Average absolute exponent except 2's: 9 / 7 = 1.28571
FIT/MODE
7: 1 1 1 1 1 0 2 N T3 SD: 26.5987 c. M:-43.4566 c. 12: 2 1 2 2 1 1 3 N SD: 9.9968 c. M: 15.6413 c. Mela Jhankaradhvani, Raga Jhankara Bhramavi 19: 3 2 3 3 2 1 5 N SD: 7.2399 c. M: 14.4363 c. 22: 4 2 3 4 2 1 6 N SD: 9.2297 c. M:-14.2718 c. 31: 5 3 5 5 3 2 8 N SD: 5.7668 c. M: 10.3616 c. 34: 6 3 5 6 3 2 9 N SD: 3.8597 c. M:-7.8547 c. 41: 7 4 6 7 4 2 11 N SD: 4.0528 c. M:-6.3099 c. 46: 8 4 7 8 4 3 12 N SD: 3.2240 c. M: 4.9906 c. 53: 9 5 8 9 5 3 14 N SD: 0.8945 c. M:-1.4081 c. 118: 20 11 18 20 11 7 31 N SD: 0.3211 c. M: 0.5202 c. 171: 29 16 26 29 16 10 45 N SD: 0.2411 c. M: 0.4012 c. 289: 49 27 44 49 27 17 76 N SD: 0.2195 c. M: 0.4498 c. 323: 55 30 49 55 30 19 85 N SD: 0.2132 c. M:-0.4244 c. 376: 64 35 57 64 35 22 99 N SD: 0.2389 c. M:-0.3453 c. 388: 66 36 59 66 36 23 102 N SD: 0.1741 c. M: 0.2842 c. 441: 75 41 67 75 41 26 116 N SD: 0.0852 c. M:-0.1716 c. 494: 84 46 75 84 46 29 130 N SD: 0.1062 c. M: 0.1482 c. 559: 95 52 85 95 52 33 147 N SD: 0.0551 c. M: 0.0906 c. 612: 104 57 93 104 57 36 161 N SD: 0.0287 c. M:-0.0450 c. 1171: 199 109 178 199 109 69 308 N SD: 0.0141 c. M: 0.0228 c. 1783: 303 166 271 303 166 105 469 N SD: 0.0082 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: 0.0000 cents 3 x x 4 x x 5:6 S SD: 0.0000 cents 4 x 5 x 6 x 7:8 S SD: 27.5333 cents 5 x 6:7 x 8 x 10 S SD: 21.1168 cents 6 x 7:8:9 x 10:12 S SD: 9.7541 cents 7:8 x 9 x 11:12:14 SD: 17.9544 cents 8:9:10:11:12:13 x 16 SD: 15.4138 cents 9:10:11:12 x 14:15:18 S SD: 10.3417 cents 10:11:12:13:15:16:17:20 SD: 9.6997 cents 11:12:13:15:17 x 18:22 SD: 15.5728 cents 12 x 14:16:18:19:20:24 S SD: 8.6718 cents 15:17:18:20:23:24:25:30 SD: 5.7341 cents 24:27:29:32:36:38:40:48 SD: 3.1042 cents 30:34:36:40:45:48:50:60 SD: 1.8252 cents 54:61:65:72:81:86:90:108 SD: 1.7116 cents 64:72:77:85:96:102:107:128 SD: 1.6980 cents 66:74:79:88:99:106:110:132 SD: 1.4004 cents 70:79:84:93:105:112:117:140 SD: 1.3767 cents 72:81:86:96:108:115:120:144 SD: 1.2255 cents 80:90:96:107:120:128:133:160 SD: 0.9893 cents 90:101:108:120:135:144:150:180 SD: 0.6114 cents 120:135:144:160:180:192:200:240 S SD: 0.0000 cents