Scala analysis: xen10-wilson-purvi-10b-02
Purvi modulation 2 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: 4/3 498.044999 perfect fourth 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: 6/5 315.6413 minor third 4: 9/8 203.9100 major whole tone 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 75/64 274.582 cents classic augmented second 2: 1 5/4 386.314 cents major third 2: 2 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: 2 25/16 772.627 cents classic augmented fifth 5: 1 8/5 813.686 cents minor sixth 5: 1 128/75 925.418 cents diminished seventh 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 : 70.7 182.4 498.0 702.0 772.6 884.4 1200.0 70.7 : 111.7 427.4 631.3 702.0 813.7 1129.3 1200.0 182.4 : 315.6 519.6 590.2 702.0 1017.6 1088.3 1200.0 498.0 : 203.9 274.6 386.3 702.0 772.6 884.4 1200.0 702.0 : 70.7 182.4 498.0 568.7 680.4 996.1 1200.0 772.6 : 111.7 427.4 498.0 609.8 925.4 1129.3 1200.0 884.4 : 315.6 386.3 498.0 813.7 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 : 159.33374 cents, oct.: 1115.33621 cents Scale is not proper Step pattern alph. order: ABCDABC Step pattern size order : ABDCABD Scale is not a Constant Structure Scale diversity : 1.568476 Lumma stability : 0.117787 Lumma impropriety factor : 0.496263 Rothenberg efficiency : 0.435374 redundancy: 0.564626 Efficiency x scale size : 3.047619 Number of different interval sizes : 24 = 4.00000 / 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 Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords 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 : 1 at degree 0 Formal octave complements present : 3 = 42.8571% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 5 Odd number limit : 75 (O: 75 U: 75) Highest odd numerator or denominator: 25 Scale harmonicity : 0.037313 Average absolute harmonicity : 0.255645 Specific harmonicity : 0.195599 Fundamental : 1/144, -7.1699 octaves, 1.8168 Hz. Guide tone : 300, 8.2288 octaves, 78487.670 Hz. Exponens Consonantiae : 4.320000E+04, 15.39874 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 66.0, average 9.42857 Mersenne's string divisions : 4580520 Sum of van Prooijen's expressibility: 5.40334, average 0.77191 Sum of Tenney's harmonic distance : 10.66891, average 1.52413 Vogel's harmonic complexity : 12.00000 Wille's k value : 112 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 87.02600, average 3.10807 Lattice compactness (without 2's) : 46.95032, average 1.67680 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -0.57143 12 1 3: -2 .. 1 -0.57143 6 2 5: 0 .. 2 0.85714 6 4 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 12 / 7 = 1.71429
FIT/MODE
7: 0 1 2 1 0 1 2 N T3 SD: 44.6209 c. M: 86.9131 c. 11: 0 1 3 2 1 1 3 N G SD: 48.7526 c. M: 73.3128 c. 12: 1 1 3 2 1 1 3 N SD: 17.6120 c. M:-29.3276 c. Chromatic Dorian, Mela Kanakangi, Raga Kanakambari 14: 1 1 4 2 1 1 4 N SD: 15.1957 c. M: 27.2159 c. 19: 1 2 5 3 1 2 5 N SD: 7.8169 c. M: 14.7327 c. Ratio 1:2 Chromatic Dorian 31: 2 3 8 5 2 3 8 N SD: 6.1112 c. M:-11.1447 c. Ratio 2:3 Chromatic Dorian 34: 2 3 9 6 2 3 9 N SD: 3.4816 c. M: 5.9331 c. 53: 3 5 14 9 3 5 14 N SD: 1.6433 c. M: 2.8161 c. 99: 6 9 26 17 6 9 26 N SD: 1.5545 c. M:-3.1301 c. 118: 7 11 31 20 7 11 31 N SD: 0.3841 c. M:-0.6471 c. 171: 10 16 45 29 10 16 45 N SD: 0.3462 c. M: 0.6976 c. 289: 17 27 76 49 17 27 76 N SD: 0.2056 c. M: 0.3091 c. 323: 19 30 85 55 19 30 85 N SD: 0.1947 c. M: 0.3604 c. 441: 26 41 116 75 26 41 116 N SD: 0.0886 c. M:-0.1617 c. 559: 33 52 147 95 33 52 147 N SD: 0.1013 c. M:-0.1812 c. 612: 36 57 161 104 36 57 161 N SD: 0.0506 c. M: 0.0842 c. 730: 43 68 192 124 43 68 192 N SD: 0.0338 c. M:-0.0620 c. 1171: 69 109 308 199 69 109 308 N SD: 0.0232 c. M:-0.0455 c. 1783: 105 166 469 303 105 166 469 N SD: 0.0077 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: 0.0000 cents 4 x x 5:6 x 7:8 S SD: 35.0166 cents 5 x 6:7 x 8 x 10 S SD: 40.7529 cents 6 x 7:8:9 x 10:12 S SD: 16.8934 cents 7 x 8:9 x 11:12:14 SD: 18.7814 cents 8 x 9:11:12 x 13:16 SD: 14.4522 cents 9 x 10:12 x 14:15:18 S SD: 1.5423 cents 10 x 11:13:15:16:17:20 SD: 11.8849 cents 11 x 12:15 x 17:18:22 SD: 12.4780 cents 12 x 13:16:18:19:20:24 SD: 8.2445 cents 13 x 14:17 x 20:22:26 SD: 14.8008 cents 14:15:16:19:21:22:23:28 SD: 11.4409 cents 15:16:17:20 x 23:25:30 SD: 10.4421 cents 16:17:18:21:24:25:27:32 SD: 7.6180 cents 18:19:20:24:27:28:30:36 S SD: 3.4561 cents 27:28:30:36:41:42:45:54 SD: 3.4112 cents 30:31:33:40:45:47:50:60 SD: 3.2494 cents 42:44:47:56:63:66:70:84 SD: 2.6590 cents 44:46:49:59:66:69:73:88 SD: 2.2716 cents 45:47:50:60:68:70:75:90 SD: 2.2314 cents 46:48:51:61:69:72:77:92 SD: 1.9044 cents 48:50:53:64:72:75:80:96 SD: 1.5506 cents 66:69:73:88:99:103:110:132 SD: 1.4715 cents 72:75:80:96:108:113:120:144 SD: 1.0968 cents 90:94:100:120:135:141:150:180 SD: 0.9315 cents 96:100:107:128:144:150:160:192 SD: 0.7717 cents 126:131:140:168:189:197:210:252 SD: 0.4970 cents 144:150:160:192:216:225:240:288 S SD: 0.0000 cents