Scala analysis: xen10-wilson-purvi-02b-06
Purvi modulation 6 from Figure 2b, Helmholtz (16/15 75/64 16/15)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 75/64 274.582429 classic augmented second 2: 5/4 386.313714 major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 5/3 884.358713 major sixth, BP sixth 6: 15/8 1088.268715 classic major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 75/64 274.5824 classic augmented second 2: 16/15 111.7313 minor diatonic semitone 3: 16/15 111.7313 minor diatonic semitone 4: 9/8 203.9100 major whole tone 5: 10/9 182.4037 minor whole tone 6: 9/8 203.9100 major whole tone 7: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 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 75/64 274.582 cents classic augmented second 2: 1 256/225 223.463 cents Neapolitan diminished third 2: 2 6/5 315.641 cents minor third 2: 4 5/4 386.314 cents major third 3: 1 32/25 427.373 cents classic diminished fourth 3: 4 4/3 498.045 cents perfect fourth 3: 2 45/32 590.224 cents diatonic tritone 4: 2 64/45 609.776 cents 2nd tritone 4: 4 3/2 701.955 cents perfect fifth 4: 1 25/16 772.627 cents classic augmented fifth 5: 4 8/5 813.686 cents minor sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 1 225/128 976.537 cents augmented sixth 6: 1 128/75 925.418 cents diminished seventh 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 3 15/8 1088.269 cents classic major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.33333 = 10/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 274.6 386.3 498.0 702.0 884.4 1088.3 1200.0 274.6 : 111.7 223.5 427.4 609.8 813.7 925.4 1200.0 386.3 : 111.7 315.6 498.0 702.0 813.7 1088.3 1200.0 498.0 : 203.9 386.3 590.2 702.0 976.5 1088.3 1200.0 702.0 : 182.4 386.3 498.0 772.6 884.4 996.1 1200.0 884.4 : 203.9 315.6 590.2 702.0 813.7 1017.6 1200.0 1088.3: 111.7 386.3 498.0 609.8 813.7 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 274.5824 cents 1125/1024, 162.8511 cents 16/15, 111.7313 cents 2: 223.4626 .. 386.3137 cents 1125/1024, 162.8511 cents 16384/16875,-51.1199 cents 3: 427.3726 .. 590.2237 cents 1125/1024, 162.8511 cents 128/125, 41.0589 cents 4: 609.7763 .. 772.6274 cents 1125/1024, 162.8511 cents 2048/2025, 19.5526 cents 5: 813.6863 .. 976.5374 cents 1125/1024, 162.8511 cents 128/125, 41.0589 cents 6: 925.4176 .. 1088.2687 cents 1125/1024, 162.8511 cents 16384/16875,-51.1199 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 75/64, 274.5824 cents Average / Smallest step : 1.534293 Largest / Average step : 1.601731 Largest / Smallest step : 2.457525 Median interval of one step : 10/9, 182.4037 cents, amount: 1 Most common interval of one step : 16/15, 111.7313 cents, amount: 3 Least squares average step : 176.43265 cents, oct.: 1235.02854 cents Scale is not proper Step pattern alph. order: ABBCDCB Step pattern size order : DAACBCA Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.448366 Lumma stability : 0.270944 Lumma impropriety factor : 0.085200 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 : 4 Highest interval variety : 4 Mean interval variety : 3.33333 = 10/3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 2048/2025, 19.5526 cents Most common triad is 0.0 386.314 498.045 cents, amount: 3 Number of recognisable fifths : 4, average 701.9550 cents Best fifths form a closed circle Scale contains a complete diamond : 1 3 Length of longest harmonic part : 2 at degree 3 Length of longest subharmonic part : 2 at degree 4 Formal octave complements present : 3 = 42.8571% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 Scale is n-1 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 : 0.263687 Specific harmonicity : 0.211780 Fundamental : 1/192, -7.5850 octaves, 1.3626 Hz. Guide tone : 300, 8.2288 octaves, 78487.670 Hz. Exponens Consonantiae : 5.760000E+04, 15.81378 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 97.0, average 13.85714 Mersenne's string divisions : 8056440 Sum of van Prooijen's expressibility: 5.40334, average 0.77191 Sum of Tenney's harmonic distance : 10.39591, average 1.48513 Vogel's harmonic complexity : 11.71429 Wille's k value : 112 Wilson's harmonic complexity : 16 Rectangular lattice diameter : 4 Triangular lattice diameter : 4 Lattice compactness : 95.06945, average 3.39534 Lattice compactness (without 2's) : 40.90826, average 1.46101 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -6 .. 2 -1.28571 15 1 3: -1 .. 1 0.14286 5 2 5: 0 .. 2 0.71429 5 4 Average exponent except 2's : 6 / 7 = 0.85714 Average absolute exponent except 2's: 10 / 7 = 1.42857 Scale is JI-epimorphic with val: <7 11 16| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 49.8013 c. M: 103.1539 c. Lebeng 8: 2 1 0 2 1 1 1 N D3 SD: 39.6913 c. M:-63.6863 c. 9: 2 1 1 1 2 1 1 P M ME S SD: 28.2986 c. M:-48.9746 c. 10: 2 1 1 2 1 2 1 P M ME S SD: 25.5669 c. M: 44.3587 c. Sethares Neutral, Beatles-7, Dichotic-7 12: 3 1 1 2 2 2 1 N T3 SD: 13.2195 c. M:-25.4176 c. Mela Sulini, Raga Sailadesakshi, Raga Trishuli, Houzam: Greece 19: 4 2 2 3 3 3 2 P T3 SD: 11.0391 c. M: 21.9508 c. 22: 5 2 2 4 3 4 2 N SD: 6.1847 c. M: 11.6314 c. 31: 7 3 3 5 5 5 3 N T3 SD: 4.1793 c. M:-5.9639 c. 34: 8 3 3 6 5 6 3 N SD: 4.3614 c. M:-7.7705 c. 43: 10 4 4 7 7 7 4 N T3 SD: 4.6458 c. M:-8.6645 c. 53: 12 5 5 9 8 9 5 N SD: 1.4286 c. M: 2.8843 c. 65: 15 6 6 11 10 11 6 N SD: 1.3024 c. M:-2.3406 c. 87: 20 8 8 15 13 15 8 N SD: 1.2301 c. M: 1.6001 c. 118: 27 11 11 20 18 20 11 N SD: 0.2135 c. M:-0.3870 c. 323: 74 30 30 55 49 55 30 N SD: 0.2098 c. M:-0.3402 c. 376: 86 35 35 64 57 64 35 N SD: 0.1665 c. M: 0.3162 c. 441: 101 41 41 75 67 75 41 N SD: 0.1255 c. M:-0.2475 c. 494: 113 46 46 84 75 84 46 N SD: 0.0808 c. M: 0.1482 c. 612: 140 57 57 104 93 104 57 N SD: 0.0378 c. M: 0.0726 c. 730: 167 68 68 124 111 124 68 N SD: 0.0375 c. M: 0.0619 c. 1053: 241 98 98 179 160 179 98 N SD: 0.0384 c. M:-0.0614 c. 1171: 268 109 109 199 178 199 109 N SD: 0.0264 c. M:-0.0546 c. 1289: 295 120 120 219 196 219 120 N SD: 0.0305 c. M:-0.0491 c. 1665: 381 155 155 283 253 283 155 N SD: 0.0215 c. M: 0.0344 c. 1783: 408 166 166 303 271 303 166 N SD: 0.0074 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: 0.0000 cents 4 x 5 x 6:7 x 8 S SD: 21.1168 cents 5:6 x 7 x 8:9:10 S SD: 27.4297 cents 6:7 x 8:9:10:11:12 S SD: 6.6104 cents 7:8:9 x 11:12:13:14 SD: 19.2945 cents 8:9:10:11:12:13:15:16 SD: 14.1087 cents 9 x 11:12:14:15:17:18 SD: 12.5177 cents 10:12 x 13:15:17:19:20 SD: 12.1428 cents 12:14:15:16:18:20:23:24 SD: 5.5463 cents 23:27:29:31:35:38:43:46 SD: 5.4556 cents 24:28:30:32:36:40:45:48 S SD: 1.1016 cents 88:103:110:117:132:147:165:176 SD: 0.9488 cents 104:122:130:139:156:173:195:208 SD: 0.8022 cents 120:141:150:160:180:200:225:240 SD: 0.6586 cents 128:150:160:171:192:213:240:256 SD: 0.6184 cents 144:169:180:192:216:240:270:288 SD: 0.3661 cents 168:197:210:224:252:280:315:336 SD: 0.1570 cents 192:225:240:256:288:320:360:384 SD: 0.0000 cents