Scala analysis: xen10-wilson-purvi-10c-07
Purvi modulation 7 from Figure 10c, Didymus (25/24 6/5 16/15), (16/15 6/5 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: 128/75 925.417571 diminished 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: 16/15 111.7313 minor diatonic semitone 6: 9/8 203.9100 major whole tone 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: 1 10/9 182.404 cents minor whole tone 2: 1 75/64 274.582 cents classic augmented second 2: 1 6/5 315.641 cents minor third 2: 2 5/4 386.314 cents major third 2: 2 32/25 427.373 cents classic diminished 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: 2 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: 1 128/75 925.418 cents diminished seventh 5: 1 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 : 315.6 427.4 498.0 813.7 925.4 1129.3 1200.0 315.6 : 111.7 182.4 498.0 609.8 813.7 884.4 1200.0 427.4 : 70.7 386.3 498.0 702.0 772.6 1088.3 1200.0 498.0 : 315.6 427.4 631.3 702.0 1017.6 1129.3 1200.0 813.7 : 111.7 315.6 386.3 702.0 813.7 884.4 1200.0 925.4 : 203.9 274.6 590.2 702.0 772.6 1088.3 1200.0 1129.3: 70.7 386.3 498.0 568.7 884.4 996.1 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 .. 427.3726 cents 144/125, 244.9689 cents 25/27,-133.2376 cents 3: 386.3137 .. 631.2826 cents 144/125, 244.9689 cents 125/128,-41.0589 cents 4: 568.7174 .. 813.6863 cents 144/125, 244.9689 cents 625/648,-62.5651 cents 5: 772.6274 .. 1017.5963 cents 144/125, 244.9689 cents 125/128,-41.0589 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 : 183.73086 cents, oct.: 1286.11599 cents Scale is not proper Step pattern alph. order: ABCABDC Step pattern size order : DBADBCA Scale is not a Constant Structure Scale diversity : 1.537490 Lumma stability : 0.117787 Lumma impropriety factor : 0.342632 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 Lydian octave species of abstract tetrachord Best fifths form a closed circle 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 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 : 75 (O: 75 U: 75) Highest odd numerator or denominator: 75 Scale harmonicity : 0.039788 Average absolute harmonicity : 0.224580 Specific harmonicity : 0.191044 Fundamental : 1/75, -6.2288 octaves, 3.4883 Hz. Guide tone : 384, 8.5850 octaves, 100464.217 Hz. Exponens Consonantiae : 2.880000E+04, 14.81378 octaves Euler's gradus suavitatis : 20 Sum of Mann's harmonic distance : 183.5, average 26.21429 Mersenne's string divisions : 120789669 Sum of van Prooijen's expressibility: 6.54600, average 0.93514 Sum of Tenney's harmonic distance : 14.42393, average 2.06056 Vogel's harmonic complexity : 10.57143 Wille's k value : 37 Wilson's harmonic complexity : 16 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 93.41119, average 3.33611 Lattice compactness (without 2's) : 43.96618, average 1.57022 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 1 .. 7 3.28571 23 1 3: -1 .. 1 0.00000 4 1 5: -2 .. 0 -1.14286 8 5 Average exponent except 2's :-8 / 7 =-1.14286 Average absolute exponent except 2's: 12 / 7 = 1.71429
FIT/MODE
7: 1 1 0 2 1 1 1 N T3 SD: 109.0305 c. M: 155.1879 c. 8: 2 1 0 2 1 1 1 N D3 SD: 44.8168 c. M: 79.3276 c. 9: 2 1 1 2 1 1 1 P M ME S SD: 34.9886 c. M: 62.6609 c. 11: 3 1 0 3 1 2 1 N SD: 39.2391 c. M: 61.6814 c. 12: 3 1 1 3 1 2 1 N T3 S SD: 19.6076 c. M: 29.3276 c. 16: 4 2 1 4 1 3 1 N SD: 18.0317 c. M:-26.9550 c. 19: 5 2 1 5 2 3 1 N SD: 11.0953 c. M:-21.9508 c. 22: 6 2 1 6 2 4 1 N SD: 8.8703 c. M:-16.1270 c. 31: 8 3 2 8 3 5 2 N SD: 4.2099 c. M: 6.7469 c. 34: 9 3 2 9 3 6 2 N SD: 3.7473 c. M: 7.7705 c. 53: 14 5 3 14 5 9 3 N SD: 1.9851 c. M:-2.8843 c. 84: 22 8 5 22 8 14 5 N SD: 1.6024 c. M:-3.1539 c. 87: 23 8 5 23 8 15 5 N SD: 1.1587 c. M:-1.7069 c. 118: 31 11 7 31 11 20 7 N SD: 0.2834 c. M: 0.5140 c. 289: 76 27 17 76 27 49 17 N SD: 0.2583 c. M:-0.5340 c. 323: 85 30 19 85 30 55 19 N SD: 0.1733 c. M: 0.3402 c. 441: 116 41 26 116 41 75 26 N SD: 0.1237 c. M: 0.2475 c. 494: 130 46 29 130 46 84 29 N SD: 0.1294 c. M:-0.2271 c. 559: 147 52 33 147 52 95 33 N SD: 0.1272 c. M: 0.1940 c. 612: 161 57 36 161 57 104 36 N SD: 0.0562 c. M:-0.0842 c. 730: 192 68 43 192 68 124 43 N SD: 0.0310 c. M:-0.0619 c. 1053: 277 98 62 277 98 179 62 N SD: 0.0317 c. M: 0.0614 c. 1171: 308 109 69 308 109 199 69 N SD: 0.0320 c. M: 0.0546 c. 1665: 438 155 98 438 155 283 98 N SD: 0.0241 c. M:-0.0418 c. 1783: 469 166 105 469 166 303 105 N SD: 0.0061 c. M: 0.0110 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: 13.6863 cents 4 x 5 x 6:7 x 8 S SD: 31.6761 cents 5:6 x 7:8:9 x 10 S SD: 25.0053 cents 6:7 x 8 x 10 x 12 S SD: 15.9381 cents 7:8:9 x 11:12:13:14 SD: 17.9098 cents 8 x 10:11:13:14:15:16 SD: 15.6475 cents 9:11 x 12:14:15:17:18 SD: 12.7730 cents 10:12:13 x 16:17:19:20 SD: 5.5151 cents 13:16 x 17:21:22:25:26 SD: 9.9267 cents 14:17:18:19:22:24:27:28 SD: 7.1574 cents 15:18:19:20:24:26:29:30 SD: 4.9335 cents 21:25:27:28:34:36:40:42 SD: 4.3314 cents 24:29:31:32:38:41:46:48 SD: 3.8620 cents 25:30:32:33:40:43:48:50 SD: 3.1437 cents 35:42:45:47:56:60:67:70 SD: 2.4636 cents 40:48:51:53:64:68:77:80 SD: 2.1661 cents 45:54:58:60:72:77:86:90 SD: 2.1588 cents 50:60:64:67:80:85:96:100 SD: 1.5680 cents 60:72:77:80:96:102:115:120 SD: 1.2391 cents 65:78:83:87:104:111:125:130 SD: 1.1977 cents 75:90:96:100:120:128:144:150 S SD: 0.0000 cents