Scala analysis: xen10-wilson-purvi-10c-06
Purvi modulation 6 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: 3/2 701.955001 perfect fifth 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: 9/8 203.9100 major whole tone 5: 256/225 223.4626 Neapolitan diminished third 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: 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 5/4 386.314 cents major third 2: 3 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: 3 25/16 772.627 cents classic augmented fifth 5: 1 8/5 813.686 cents minor 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: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 315.6 427.4 498.0 702.0 925.4 1129.3 1200.0 315.6 : 111.7 182.4 386.3 609.8 813.7 884.4 1200.0 427.4 : 70.7 274.6 498.0 702.0 772.6 1088.3 1200.0 498.0 : 203.9 427.4 631.3 702.0 1017.6 1129.3 1200.0 702.0 : 223.5 427.4 498.0 813.7 925.4 996.1 1200.0 925.4 : 203.9 274.6 590.2 702.0 772.6 976.5 1200.0 1129.3: 70.7 386.3 498.0 568.7 772.6 996.1 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 : 9/8, 203.9100 cents, amount: 2 Least squares average step : 180.53853 cents, oct.: 1263.76974 cents Scale is not proper Step pattern alph. order: ABCDEDC Step pattern size order : EBACDCA Scale is not a Constant Structure Scale diversity : 1.566731 Lumma stability : 0.117787 Lumma impropriety factor : 0.342632 Rothenberg efficiency : 0.436735 redundancy: 0.563265 Efficiency x scale size : 3.057143 Number of different interval sizes : 24 = 4.00000 / 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 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: 75 Scale harmonicity : 0.038265 Average absolute harmonicity : 0.248344 Specific harmonicity : 0.177089 Fundamental : 1/150, -7.2288 octaves, 1.7442 Hz. Guide tone : 384, 8.5850 octaves, 100464.217 Hz. Exponens Consonantiae : 5.760000E+04, 15.81378 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 179.5, average 25.64286 Mersenne's string divisions : 46457565 Sum of van Prooijen's expressibility: 6.32415, average 0.90345 Sum of Tenney's harmonic distance : 13.60003, average 1.94286 Vogel's harmonic complexity : 12.14286 Wille's k value : 112 Wilson's harmonic complexity : 16 Rectangular lattice diameter : 4 Triangular lattice diameter : 4 Lattice compactness : 105.59943, average 3.77141 Lattice compactness (without 2's) : 47.78804, average 1.70672 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 7 2.71429 21 1 3: -1 .. 1 0.14286 5 2 5: -2 .. 0 -1.00000 7 4 Average exponent except 2's :-6 / 7 =-0.85714 Average absolute exponent except 2's: 12 / 7 = 1.71429
FIT/MODE
7: 2 0 1 1 1 2 0 N T3 SD: 50.8037 c. M: 84.5154 c. 8: 2 1 0 2 1 2 0 N T3 SD: 39.6664 c. M:-70.6724 c. 9: 2 1 1 1 2 1 1 P M ME S SD: 37.0855 c. M: 62.6609 c. 11: 3 1 0 2 2 2 1 N G SD: 38.7679 c. M: 61.6814 c. 12: 3 1 1 2 2 2 1 N T3 SD: 18.9273 c. M: 29.3276 c. Mela Sulini, Raga Sailadesakshi, Raga Trishuli, Houzam: Greece 14: 4 1 1 2 3 2 1 N SD: 16.0359 c. M:-27.2159 c. 17: 4 2 1 3 3 3 1 N SD: 13.1699 c. M: 33.2883 c. 19: 5 2 1 3 4 3 1 N SD: 11.0814 c. M:-21.9508 c. 22: 6 2 1 4 4 4 1 N SD: 9.1143 c. M:-16.1270 c. 31: 8 3 2 5 6 5 2 N SD: 4.6336 c. M: 6.7469 c. 34: 9 3 2 6 6 6 2 N SD: 3.9646 c. M: 7.7705 c. 53: 14 5 3 9 10 9 3 N SD: 1.9126 c. M:-2.8843 c. 84: 22 8 5 14 16 14 5 N SD: 1.7500 c. M:-3.1539 c. 87: 23 8 5 15 16 15 5 N SD: 1.2882 c. M:-1.7069 c. 118: 31 11 7 20 22 20 7 N SD: 0.2961 c. M: 0.5140 c. 289: 76 27 17 49 54 49 17 N SD: 0.2656 c. M:-0.5340 c. 323: 85 30 19 55 60 55 19 N SD: 0.1894 c. M: 0.3402 c. 441: 116 41 26 75 82 75 26 N SD: 0.1242 c. M: 0.2475 c. 494: 130 46 29 84 92 84 29 N SD: 0.1287 c. M:-0.2271 c. 559: 147 52 33 95 104 95 33 N SD: 0.1226 c. M: 0.1940 c. 612: 161 57 36 104 114 104 36 N SD: 0.0542 c. M:-0.0842 c. 730: 192 68 43 124 136 124 43 N SD: 0.0338 c. M:-0.0619 c. 1053: 277 98 62 179 196 179 62 N SD: 0.0347 c. M: 0.0614 c. 1171: 308 109 69 199 218 199 69 N SD: 0.0310 c. M: 0.0546 c. 1665: 438 155 98 283 310 283 98 N SD: 0.0261 c. M:-0.0418 c. 1783: 469 166 105 303 332 303 105 N SD: 0.0068 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: 0.0000 cents 3 x x 4 x 5 x 6 S SD: 13.6863 cents 4 x 5 x 6:7 x 8 S SD: 14.9376 cents 5:6 x 7:8:9 x 10 S SD: 33.5354 cents 6:7 x 8:9:10 x 12 S SD: 12.7505 cents 7:8:9 x 11:12:13:14 SD: 21.7694 cents 8 x 10:11:12:14:15:16 S SD: 14.9944 cents 9:11 x 12:14:15:17:18 SD: 14.3942 cents 10:12:13 x 15:17:19:20 SD: 5.5151 cents 13:16 x 17:20:22:25:26 SD: 12.0117 cents 14:17:18:19:21:24:27:28 SD: 5.6009 cents 21:25:27:28:32:36:40:42 SD: 5.0363 cents 24:29:31:32:36:41:46:48 SD: 2.8649 cents 36:43:46:48:54:61:69:72 SD: 2.2014 cents 40:48:51:53:60:68:77:80 SD: 2.1661 cents 50:60:64:67:75:85:96:100 SD: 1.5680 cents 54:65:69:72:81:92:104:108 SD: 1.2374 cents 75:90:96:100:113:128:144:150 SD: 1.0968 cents 86:103:110:115:129:147:165:172 SD: 0.9777 cents 90:108:115:120:135:154:173:180 SD: 0.8248 cents 96:115:123:128:144:164:184:192 SD: 0.6971 cents 114:137:146:152:171:195:219:228 SD: 0.6924 cents 126:151:161:168:189:215:242:252 SD: 0.5483 cents 150:180:192:200:225:256:288:300 SD: 0.0000 cents