Scala analysis: xen10-wilson-purvi-10c-02
Purvi modulation 2 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: 16/15 111.731285 minor diatonic semitone 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: 16/15 111.7313 minor diatonic semitone 2: 9/8 203.9100 major whole tone 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: 2 6/5 315.641 cents minor third 2: 3 5/4 386.314 cents major third 2: 1 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: 1 25/16 772.627 cents classic augmented fifth 5: 3 8/5 813.686 cents minor sixth 5: 2 5/3 884.359 cents major sixth, BP 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: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 111.7 315.6 498.0 702.0 813.7 884.4 1200.0 111.7 : 203.9 386.3 590.2 702.0 772.6 1088.3 1200.0 315.6 : 182.4 386.3 498.0 568.7 884.4 996.1 1200.0 498.0 : 203.9 315.6 386.3 702.0 813.7 1017.6 1200.0 702.0 : 111.7 182.4 498.0 609.8 813.7 996.1 1200.0 813.7 : 70.7 386.3 498.0 702.0 884.4 1088.3 1200.0 884.4 : 315.6 427.4 631.3 813.7 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 .. 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 : 10/9, 182.4037 cents, amount: 1 Least squares average step : 162.99680 cents, oct.: 1140.97763 cents Scale is not proper Step pattern alph. order: ABCBADE Step pattern size order : BDCDBAE Scale is not a Constant Structure Scale diversity : 1.460961 Lumma stability : 0.117787 Lumma impropriety factor : 0.342632 Rothenberg efficiency : 0.478912 redundancy: 0.521088 Efficiency x scale size : 3.352381 Number of different interval sizes : 20 = 3.33333 / class Number of one step interval sizes : 5 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 triad is 0.0 386.314 701.955 cents, amount: 3 Number of recognisable fifths : 4, average 701.9550 cents Scale is fully connected 5-limit major-minor triadic Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 1 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 Scale is n-1 differentially coherent in interval class 5 -- Rational properties -- Prime limit : 5 Odd number limit : 45 (O: 45 U: 45) Highest odd numerator or denominator: 15 Scale harmonicity : 0.043228 Average absolute harmonicity : 0.268508 Specific harmonicity : 0.238095 Fundamental : 1/30, -4.9069 octaves, 8.7209 Hz. Guide tone : 240, 7.9069 octaves, 62790.136 Hz. Exponens Consonantiae : 7.200000E+03, 12.81378 octaves Euler's gradus suavitatis : 18 Sum of Mann's harmonic distance : 39.0, average 5.57143 Mersenne's string divisions : 3723720 Sum of van Prooijen's expressibility: 4.22724, average 0.60389 Sum of Tenney's harmonic distance : 8.79385, average 1.25626 Vogel's harmonic complexity : 8.57143 Wille's k value : 22 Wilson's harmonic complexity : 16 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 72.68498, average 2.59589 Lattice compactness (without 2's) : 40.08641, average 1.43166 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 1.42857 12 1 3: -1 .. 1 -0.14286 5 2 5: -1 .. 1 -0.28571 4 4 Average exponent except 2's :-3 / 7 =-0.42857 Average absolute exponent except 2's: 9 / 7 = 1.28571 Scale is weakly epimorphic with val: <7 10 16| Scale is weakly epimorphic with val: <7 12 15|
FIT/MODE
7: 1 1 1 1 1 0 2 N T3 SD: 32.6478 c. M:-59.6973 c. 9: 1 1 2 1 1 1 2 P M ME S SD: 33.6824 c. M: 48.9746 c. Pseudo Pelog, Pelogic-7, Antiionian 10: 1 2 1 2 1 0 3 N SD: 27.6390 c. M:-44.3587 c. 12: 1 2 2 2 1 1 3 N T3 SD: 10.8357 c. M: 15.6413 c. Mela Senavati, Raga Senagrani, Malini 19: 2 3 3 3 2 1 5 N SD: 7.2823 c. M:-14.5845 c. 22: 2 4 3 4 2 1 6 N SD: 7.5556 c. M:-11.6314 c. 31: 3 5 5 5 3 2 8 N SD: 4.5477 c. M: 5.9639 c. 34: 3 6 5 6 3 2 9 N SD: 3.3122 c. M: 5.8489 c. 53: 5 9 8 9 5 3 14 N SD: 1.0530 c. M:-1.4763 c. 118: 11 20 18 20 11 7 31 N SD: 0.2588 c. M:-0.3870 c. 171: 16 29 26 29 16 10 45 N SD: 0.2798 c. M:-0.5494 c. 289: 27 49 44 49 27 17 76 N SD: 0.1996 c. M:-0.3794 c. 323: 30 55 49 55 30 19 85 N SD: 0.1750 c. M: 0.2762 c. 441: 41 75 67 75 41 26 116 N SD: 0.0837 c. M: 0.1667 c. 494: 46 84 75 84 46 29 130 N SD: 0.0925 c. M: 0.1482 c. 559: 52 95 85 95 52 33 147 N SD: 0.0669 c. M: 0.1034 c. 612: 57 104 93 104 57 36 161 N SD: 0.0311 c. M:-0.0450 c. 730: 68 124 111 124 68 43 192 N SD: 0.0307 c. M:-0.0495 c. 1171: 109 199 178 199 109 69 308 N SD: 0.0172 c. M: 0.0319 c. 1783: 166 303 271 303 166 105 469 N SD: 0.0066 c. M: 0.0095 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 x 8:9 x 11:12:14 SD: 24.0420 cents 8:9:10:11:12:13 x 16 SD: 21.7626 cents 9:10:11:12 x 14:15:18 S SD: 15.2591 cents 10:11:12:13:15:16:17:20 SD: 11.0051 cents 11:12:13:15:17 x 18:22 SD: 14.3432 cents 12:13:14:16:18:19:20:24 S SD: 8.3637 cents 14:15:17:19:21:22:23:28 SD: 7.8400 cents 15:16:18:20:23:24:25:30 SD: 5.4358 cents 24:26:29:32:36:38:40:48 SD: 4.9335 cents 26:28:31:35:39:42:43:52 SD: 4.7938 cents 27:29:32:36:41:43:45:54 SD: 4.7848 cents 28:30:34:37:42:45:47:56 SD: 4.3603 cents 30:32:36:40:45:48:50:60 S SD: 0.0000 cents