Scala analysis: xen10-wilson-purvi-10a-04
Purvi modulation 4 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: 32/25 427.372572 classic diminished fourth 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 8/5 813.686286 minor sixth 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: 9/8 203.9100 major whole tone 2: 256/225 223.4626 Neapolitan diminished third 3: 25/24 70.6724 classic chromatic semitone, minor chroma 4: 9/8 203.9100 major whole tone 5: 16/15 111.7313 minor diatonic semitone 6: 6/5 315.6413 minor third 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: 1 16/15 111.731 cents minor diatonic semitone 1: 2 9/8 203.910 cents major whole tone 1: 1 256/225 223.463 cents Neapolitan diminished third 1: 1 6/5 315.641 cents minor third 2: 2 75/64 274.582 cents classic augmented second 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 6/5 315.641 cents minor third 2: 1 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: 1 8/5 813.686 cents minor sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 2 128/75 925.418 cents diminished seventh 6: 1 5/3 884.359 cents major sixth, BP sixth 6: 1 225/128 976.537 cents augmented sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 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: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 427.4 498.0 702.0 813.7 1129.3 1200.0 203.9 : 223.5 294.1 498.0 609.8 925.4 996.1 1200.0 427.4 : 70.7 274.6 386.3 702.0 772.6 976.5 1200.0 498.0 : 203.9 315.6 631.3 702.0 905.9 1129.3 1200.0 702.0 : 111.7 427.4 498.0 702.0 925.4 996.1 1200.0 813.7 : 315.6 386.3 590.2 813.7 884.4 1088.3 1200.0 1129.3: 70.7 274.6 498.0 568.7 772.6 884.4 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: 274.5824 .. 427.3726 cents 2048/1875, 152.7901 cents 125/128,-41.0589 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 .. 925.4176 cents 2048/1875, 152.7901 cents 125/128,-41.0589 cents 6: 884.3587 .. 1129.3276 cents 144/125, 244.9689 cents 125/128,-41.0589 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 : 9/8, 203.9100 cents, amount: 2 Least squares average step : 175.75005 cents, oct.: 1230.25035 cents Scale is not proper Step pattern alph. order: ABCADEC Step pattern size order : CDACBEA Scale is not a Constant Structure Scale diversity : 1.534657 Lumma stability : 0.117787 Lumma impropriety factor : 0.189000 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 : 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 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 n-1 differentially coherent in interval class 1 Scale is differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 5 Odd number limit : 225 (O: 225 U: 225) Highest odd numerator or denominator: 25 Scale harmonicity : 0.034722 Average absolute harmonicity : 0.260135 Specific harmonicity : 0.187609 Fundamental : 1/600, -9.2288 octaves, 0.4360 Hz. Guide tone : 288, 8.1699 octaves, 75348.163 Hz. Exponens Consonantiae : 1.728000E+05, 17.39874 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 87.5, average 12.50000 Mersenne's string divisions : 32185335 Sum of van Prooijen's expressibility: 5.40334, average 0.77191 Sum of Tenney's harmonic distance : 11.60003, average 1.65715 Vogel's harmonic complexity : 15.28571 Wille's k value : 337 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 104.21865, average 3.72209 Lattice compactness (without 2's) : 47.31590, average 1.68985 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 5 1.57143 19 1 3: -1 .. 2 0.42857 5 3 5: -2 .. 0 -0.71429 5 3 Average exponent except 2's :-2 / 7 =-0.28571 Average absolute exponent except 2's: 10 / 7 = 1.42857 Scale is weakly epimorphic with val: <7 11 15| Scale is weakly epimorphic with val: <7 12 17|
FIT/MODE
7: 1 1 1 1 1 2 0 N T3 SD: 47.2206 c. M: 84.5154 c. 8: 1 2 0 2 0 3 0 N SD: 49.4043 c. M:-70.6724 c. 9: 1 2 0 2 1 2 1 N D3 SD: 54.3824 c. M: 98.0450 c. 10: 2 2 0 2 1 2 1 N T3 SD: 33.4856 c. M:-52.6274 c. 11: 2 2 0 2 1 3 1 N SD: 38.3923 c. M: 61.6814 c. 12: 2 2 1 2 1 3 1 P D3 SD: 16.1228 c. M: 29.3276 c. Harmonic Major, Mischung 2, Mela Sarasangi, Raga Anand Leela, Haripriya, Nat Bhairav, Simhavahini, Ethiopian, Tabahaniotikos: Greece 16: 3 3 1 2 2 4 1 N SD: 19.1112 c. M:-26.9550 c. 17: 3 3 1 3 2 4 1 N SD: 13.2074 c. M:-33.3725 c. 19: 3 4 1 3 2 5 1 N SD: 9.5648 c. M:-14.7327 c. 22: 4 4 1 4 2 6 1 N SD: 9.7589 c. M:-16.1270 c. 29: 5 5 2 5 3 7 2 N SD: 8.7592 c. M:-13.8999 c. 31: 5 6 2 5 3 8 2 N SD: 5.4724 c. M: 10.3616 c. 34: 6 6 2 6 3 9 2 N SD: 3.9824 c. M:-7.8547 c. 53: 9 10 3 9 5 14 3 N SD: 1.5808 c. M:-2.8161 c. 87: 15 16 5 15 8 23 5 N SD: 1.5283 c. M:-2.9865 c. 118: 20 22 7 20 11 31 7 N SD: 0.3275 c. M: 0.5202 c. 289: 49 54 17 49 27 76 17 N SD: 0.2478 c. M: 0.4498 c. 323: 55 60 19 55 30 85 19 N SD: 0.2062 c. M:-0.4244 c. 441: 75 82 26 75 41 116 26 N SD: 0.1086 c. M:-0.1716 c. 494: 84 92 29 84 46 130 29 N SD: 0.1262 c. M:-0.2271 c. 559: 95 104 33 95 52 147 33 N SD: 0.1003 c. M: 0.1812 c. 612: 104 114 36 104 57 161 36 N SD: 0.0463 c. M:-0.0842 c. 730: 124 136 43 124 68 192 43 N SD: 0.0363 c. M: 0.0744 c. 1171: 199 218 69 199 109 308 69 N SD: 0.0251 c. M: 0.0455 c. 1783: 303 332 105 303 166 469 105 N SD: 0.0077 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 5 x 6 S SD: 23.5575 cents 4 x 5 x 6 x x 8 S SD: 13.6863 cents 5:6 x 7 x 8 x 10 S SD: 35.0166 cents 6:7 x 8:9:10 x 12 S SD: 18.9300 cents 7:8:9 x x 11:13:14 SD: 14.2781 cents 8:9:10:11:12:13:15:16 SD: 11.8925 cents 9:10 x 12 x 14:17:18 SD: 12.0681 cents 10:11:13 x 15:16:19:20 SD: 8.4373 cents 13:15 x 17:20:21:25:26 SD: 12.0814 cents 14:16:18:19:21:22:27:28 SD: 7.5245 cents 15:17:19:20:23:24:29:30 SD: 6.5204 cents 18:20:23:24:27:29:35:36 SD: 4.7268 cents 22:25:28:29:33:35:42:44 SD: 4.4861 cents 24:27:31:32:36:38:46:48 SD: 3.4536 cents 32:36:41:43:48:51:61:64 SD: 2.8034 cents 39:44:50:52:59:62:75:78 SD: 2.7873 cents 40:45:51:53:60:64:77:80 SD: 1.9378 cents 50:56:64:67:75:80:96:100 SD: 1.6538 cents 64:72:82:85:96:102:123:128 SD: 1.4109 cents 72:81:92:96:108:115:138:144 SD: 0.7443 cents 128:144:164:171:192:205:246:256 SD: 0.6385 cents 150:169:192:200:225:240:288:300 SD: 0.3661 cents 200:225:256:267:300:320:384:400 SD: 0.3090 cents 240:270:307:320:360:384:461:480 SD: 0.1935 cents 360:405:461:480:540:576:691:720 SD: 0.1290 cents 450:506:576:600:675:720:864:900 SD: 0.1222 cents 528:594:676:704:792:845:1014:1056 SD: 0.1014 cents 600:675:768:800:900:960:1152:1200 SD: 0.0000 cents