Scala analysis: xen10-wilson-purvi-10b-03
Purvi modulation 3 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: 16/9 996.089998 Pythagorean minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 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: 256/225 223.4626 Neapolitan diminished third 7: 9/8 203.9100 major whole tone
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: 1 10/9 182.404 cents minor whole tone 2: 2 75/64 274.582 cents classic augmented second 2: 1 32/27 294.135 cents Pythagorean minor 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 27/16 905.865 cents Pythagorean major sixth 5: 2 128/75 925.418 cents diminished seventh 5: 1 9/5 1017.596 cents just minor seventh, BP 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 : 70.7 182.4 498.0 702.0 772.6 996.1 1200.0 70.7 : 111.7 427.4 631.3 702.0 925.4 1129.3 1200.0 182.4 : 315.6 519.6 590.2 813.7 1017.6 1088.3 1200.0 498.0 : 203.9 274.6 498.0 702.0 772.6 884.4 1200.0 702.0 : 70.7 294.1 498.0 568.7 680.4 996.1 1200.0 772.6 : 223.5 427.4 498.0 609.8 925.4 1129.3 1200.0 996.1 : 203.9 274.6 386.3 702.0 905.9 976.5 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 : 9/8, 203.9100 cents, amount: 2 Least squares average step : 164.12223 cents, oct.: 1148.85560 cents Scale is not proper Step pattern alph. order: ABCDAED Step pattern size order : ABECADC Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.613265 Lumma stability : 0.117787 Lumma impropriety factor : 0.496263 Rothenberg efficiency : 0.408163 redundancy: 0.591837 Efficiency x scale size : 2.857143 Number of different interval sizes : 28 = 4.66667 / 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 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 : 0.255195 Specific harmonicity : 0.180722 Fundamental : 1/144, -7.1699 octaves, 1.8168 Hz. Guide tone : 1200, 10.2288 octaves, 313950.678 Hz. Exponens Consonantiae : 1.728000E+05, 17.39874 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 74.5, average 10.64286 Mersenne's string divisions : 2862825 Sum of van Prooijen's expressibility: 5.65861, average 0.80837 Sum of Tenney's harmonic distance : 11.65118, average 1.66445 Vogel's harmonic complexity : 11.42857 Wille's k value : 112 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 105.51578, average 3.76842 Lattice compactness (without 2's) : 51.53610, average 1.84058 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 4 0.00000 16 1 3: -2 .. 1 -0.71429 7 3 5: 0 .. 2 0.71429 5 3 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 12 / 7 = 1.71429
FIT/MODE
7: 0 1 2 1 1 1 1 N T3 SD: 44.4658 c. M:-84.5154 c. 9: 0 1 3 1 1 1 2 N SD: 45.6394 c. M: 70.6724 c. 11: 0 1 3 2 1 2 2 N SD: 48.8528 c. M: 73.3128 c. 12: 1 1 3 2 1 2 2 N SD: 16.6559 c. M:-29.3276 c. Mela Ratnangi, Raga Phenadyuti 14: 1 1 4 2 1 3 2 N SD: 16.6077 c. M:-32.4814 c. 17: 1 2 4 3 1 3 3 N SD: 11.7679 c. M:-29.3610 c. 19: 1 2 5 3 1 4 3 N SD: 9.5328 c. M: 14.7327 c. 29: 2 2 8 5 2 5 5 N SD: 9.4794 c. M: 16.8865 c. 31: 2 3 8 5 2 6 5 N SD: 6.8995 c. M:-11.1447 c. 34: 2 3 9 6 2 6 6 N SD: 4.5123 c. M: 7.8547 c. 48: 3 4 13 8 3 9 8 N SD: 3.8192 c. M: 7.4037 c. 53: 3 5 14 9 3 10 9 N SD: 1.5642 c. M: 2.8161 c. 118: 7 11 31 20 7 22 20 N SD: 0.4059 c. M:-0.6471 c. 171: 10 16 45 29 10 32 29 N SD: 0.3738 c. M: 0.6976 c. 289: 17 27 76 49 17 54 49 N SD: 0.2655 c. M:-0.4498 c. 323: 19 30 85 55 19 60 55 N SD: 0.2460 c. M: 0.4244 c. 441: 26 41 116 75 26 82 75 N SD: 0.1098 c. M: 0.1716 c. 559: 33 52 147 95 33 104 95 N SD: 0.0974 c. M:-0.1812 c. 612: 36 57 161 104 36 114 104 N SD: 0.0478 c. M: 0.0842 c. 730: 43 68 192 124 43 136 124 N SD: 0.0430 c. M:-0.0744 c. 1171: 69 109 308 199 69 218 199 N SD: 0.0236 c. M:-0.0455 c. 1783: 105 166 469 303 105 332 303 N SD: 0.0095 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 x 5:6 S SD: 37.2438 cents 4 x x 5:6 x 7:8 S SD: 28.7524 cents 5 x 6:7 x 8:9:10 S SD: 32.8848 cents 6 x 7:8:9 x 11:12 SD: 19.9727 cents 7 x 8:9 x 11:12:14 SD: 20.4000 cents 8 x 9:11:12:13:14:16 SD: 15.5047 cents 9 x 10:12 x 14:16:18 S SD: 1.5423 cents 10 x 11:13:15:16:18:20 SD: 11.0205 cents 11 x 12:15 x 17:20:22 SD: 13.2621 cents 12 x 13:16:18:19:21:24 SD: 9.4138 cents 13 x 14:17 x 20:23:26 SD: 13.9249 cents 14:15:16:19:21:22:25:28 SD: 10.9291 cents 15:16:17:20 x 23:27:30 SD: 11.0401 cents 16:17:18:21:24:25:28:32 SD: 7.9853 cents 18:19:20:24:27:28:32:36 S SD: 3.4561 cents 27:28:30:36:41:42:48:54 SD: 3.4112 cents 28:29:31:37:42:44:50:56 SD: 3.3032 cents 42:44:47:56:63:66:75:84 SD: 2.8782 cents 44:46:49:59:66:69:78:88 SD: 2.0942 cents 46:48:51:61:69:72:82:92 SD: 1.7106 cents 54:56:60:72:81:84:96:108 S SD: 1.5580 cents 72:75:80:96:108:113:128:144 SD: 1.0968 cents 90:94:100:120:135:141:160:180 SD: 0.9315 cents 96:100:107:128:144:150:171:192 SD: 0.9101 cents 98:102:109:131:147:153:174:196 SD: 0.8012 cents 116:121:129:155:174:181:206:232 SD: 0.7955 cents 117:122:130:156:176:183:208:234 SD: 0.7897 cents 126:131:140:168:189:197:224:252 SD: 0.4970 cents 144:150:160:192:216:225:256:288 SD: 0.0000 cents