Scala analysis: xen10-wilson-purvi-10a-06
Purvi modulation 6 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: 3/2 701.955001 perfect fifth 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: 9/8 203.9100 major whole tone 5: 6/5 315.6413 minor third 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 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 : 315.6 427.4 498.0 702.0 1017.6 1129.3 1200.0 315.6 : 111.7 182.4 386.3 702.0 813.7 884.4 1200.0 427.4 : 70.7 274.6 590.2 702.0 772.6 1088.3 1200.0 498.0 : 203.9 519.6 631.3 702.0 1017.6 1129.3 1200.0 702.0 : 315.6 427.4 498.0 813.7 925.4 996.1 1200.0 1017.6: 111.7 182.4 498.0 609.8 680.4 884.4 1200.0 1129.3: 70.7 386.3 498.0 568.7 772.6 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 : 183.83063 cents, oct.: 1286.81442 cents Scale is not proper Step pattern alph. order: ABCDABC Step pattern size order : DBACDBA 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 : 0.254161 Specific harmonicity : 0.195599 Fundamental : 1/150, -7.2288 octaves, 1.7442 Hz. Guide tone : 288, 8.1699 octaves, 75348.163 Hz. Exponens Consonantiae : 4.320000E+04, 15.39874 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 85.0, average 12.14286 Mersenne's string divisions : 3203970 Sum of van Prooijen's expressibility: 5.40334, average 0.77191 Sum of Tenney's harmonic distance : 11.27097, average 1.61014 Vogel's harmonic complexity : 13.14286 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: -1 .. 5 1.71429 14 1 3: -1 .. 2 0.57143 6 2 5: -2 .. 0 -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: 2 1 0 1 2 1 0 N T3 SD: 44.6209 c. M:-86.9131 c. 8: 2 1 0 2 2 1 0 N SD: 40.3872 c. M:-70.6724 c. 9: 2 1 1 1 3 0 1 N SD: 41.3566 c. M: 62.6609 c. 10: 2 1 1 2 2 1 1 P D3 S SD: 48.7888 c. M: 75.6413 c. Pseudo Rast 11: 3 1 0 2 3 1 1 N G SD: 35.9055 c. M: 61.6814 c. 12: 3 1 1 2 3 1 1 N SD: 17.6120 c. M: 29.3276 c. Mela Calanata, Raga None, Chromatic Dorian inverse 14: 4 1 1 2 4 1 1 N SD: 15.1957 c. M:-27.2159 c. 19: 5 2 1 3 5 2 1 N SD: 7.8169 c. M:-14.7327 c. 31: 8 3 2 5 8 3 2 N SD: 6.1112 c. M: 11.1447 c. 34: 9 3 2 6 9 3 2 N SD: 3.4816 c. M:-5.9331 c. 53: 14 5 3 9 14 5 3 N SD: 1.6433 c. M:-2.8161 c. 99: 26 9 6 17 26 9 6 N SD: 1.5545 c. M: 3.1301 c. 118: 31 11 7 20 31 11 7 N SD: 0.3841 c. M: 0.6471 c. 171: 45 16 10 29 45 16 10 N SD: 0.3462 c. M:-0.6976 c. 289: 76 27 17 49 76 27 17 N SD: 0.2056 c. M:-0.3091 c. 323: 85 30 19 55 85 30 19 N SD: 0.1947 c. M:-0.3604 c. 441: 116 41 26 75 116 41 26 N SD: 0.0886 c. M: 0.1617 c. 559: 147 52 33 95 147 52 33 N SD: 0.1013 c. M: 0.1812 c. 612: 161 57 36 104 161 57 36 N SD: 0.0506 c. M:-0.0842 c. 730: 192 68 43 124 192 68 43 N SD: 0.0338 c. M: 0.0620 c. 1171: 308 109 69 199 308 109 69 N SD: 0.0232 c. M: 0.0455 c. 1783: 469 166 105 303 469 166 105 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 5 x 6 S SD: 44.4125 cents 4 x 5 x 6:7 x 8 S SD: 15.9381 cents 5:6 x 7:8:9 x 10 S SD: 28.0133 cents 6:7 x 8:9:11 x 12 SD: 11.6407 cents 7:8:9 x 11:13 x 14 SD: 25.7742 cents 8 x 10:11:12:14:15:16 S SD: 15.4454 cents 9:11 x 12:14:16:17:18 SD: 13.1610 cents 10:12:13 x 15:18:19:20 SD: 5.3983 cents 13:16 x 17:20:23:25:26 SD: 12.7705 cents 14:17:18:19:21:25:27:28 SD: 5.8343 cents 20:24:26:27:30:36:38:40 S SD: 5.5542 cents 21:25:27:28:32:38:40:42 SD: 5.0847 cents 24:29:31:32:36:43:46:48 SD: 3.0768 cents 36:43:46:48:54:65:69:72 SD: 1.5058 cents 50:60:64:67:75:90:96:100 SD: 1.2335 cents 60:72:77:80:90:108:115:120 SD: 0.7736 cents 90:108:115:120:135:162:173:180 SD: 0.5163 cents 114:137:146:152:171:205:219:228 SD: 0.4748 cents 150:180:192:200:225:270:288:300 S SD: 0.0000 cents