Scala analysis: xen10-wilson-purvi-02a-02
Purvi modulation 2 from Figure 2a, Helmholtz (75/64 16/15 16/15), (16/15 16/15 75/64)
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: 256/225 223.462571 Neapolitan diminished third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 8/5 813.686286 minor sixth 6: 128/75 925.417571 diminished seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 75/64 274.5824 classic augmented second 1: 16/15 111.7313 minor diatonic semitone 2: 16/15 111.7313 minor diatonic semitone 3: 75/64 274.5824 classic augmented second 4: 9/8 203.9100 major whole tone 5: 16/15 111.7313 minor diatonic semitone 6: 16/15 111.7313 minor diatonic semitone 7: 75/64 274.5824 classic augmented second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 16/15 111.731 cents minor diatonic semitone 1: 1 9/8 203.910 cents major whole tone 1: 2 75/64 274.582 cents classic augmented second 2: 2 256/225 223.463 cents Neapolitan diminished third 2: 1 6/5 315.641 cents minor third 2: 3 5/4 386.314 cents major third 2: 1 675/512 478.492 cents wide augmented 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: 1 1024/675 721.508 cents narrow diminished sixth 5: 3 8/5 813.686 cents minor sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 2 225/128 976.537 cents augmented sixth 6: 2 128/75 925.418 cents diminished seventh 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 4 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 : 111.7 223.5 498.0 702.0 813.7 925.4 1200.0 111.7 : 111.7 386.3 590.2 702.0 813.7 1088.3 1200.0 223.5 : 274.6 478.5 590.2 702.0 976.5 1088.3 1200.0 498.0 : 203.9 315.6 427.4 702.0 813.7 925.4 1200.0 702.0 : 111.7 223.5 498.0 609.8 721.5 996.1 1200.0 813.7 : 111.7 386.3 498.0 609.8 884.4 1088.3 1200.0 925.4 : 274.6 386.3 498.0 772.6 976.5 1088.3 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 .. 478.4924 cents 151875/131072, 255.0299 cents 16384/16875,-51.1199 cents 3: 427.3726 .. 590.2237 cents 1125/1024, 162.8511 cents 16384/16875,-51.1199 cents 4: 609.7763 .. 772.6274 cents 1125/1024, 162.8511 cents 2048/2025, 19.5526 cents 5: 721.5076 .. 976.5374 cents 151875/131072, 255.0299 cents 16384/16875,-51.1199 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 : 16/15, 111.7313 cents, amount: 4 Most common interval of one step : 16/15, 111.7313 cents, amount: 4 Least squares average step : 163.43963 cents, oct.: 1144.07741 cents Scale is not proper Step pattern alph. order: AABCAAB Step pattern size order : SSLMSSL Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.436072 Lumma stability : 0.202513 Lumma impropriety factor : 0.170400 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 : 3 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 0.0 111.731 498.045 cents, amount: 3 Number of recognisable fifths : 4, average 701.9550 cents Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords 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 classes 1 and 2 combined Scale is n-1 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 : 675 (O: 675 U: 675) Highest odd numerator or denominator: 225 Scale harmonicity : 0.033557 Average absolute harmonicity : 0.250386 Specific harmonicity : 0.174291 Fundamental : 1/450, -8.8138 octaves, 0.5814 Hz. Guide tone : 768, 9.5850 octaves, 200928.434 Hz. Exponens Consonantiae : 3.456000E+05, 18.39874 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 371.5, average 53.07143 Mersenne's string divisions : 45403995 Sum of van Prooijen's expressibility: 7.05655, average 1.00808 Sum of Tenney's harmonic distance : 14.88333, average 2.12619 Vogel's harmonic complexity : 14.42857 Wille's k value : 337 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 5 Lattice compactness : 118.26056, average 4.22359 Lattice compactness (without 2's) : 45.75645, average 1.63416 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 8 3.42857 26 1 3: -2 .. 1 -0.57143 6 2 5: -2 .. 0 -0.85714 6 4 Average exponent except 2's :-10 / 7 =-1.42857 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is JI-epimorphic with val: <7 11 16| = patent
FIT/MODE
7: 1 0 2 1 1 0 2 N T3 SD: 43.6688 c. M: 68.2747 c. 9: 1 1 2 1 1 1 2 P M ME S SD: 26.9225 c. M:-43.2041 c. Pseudo Pelog, Pelogic-7, Antiionian 10: 1 1 2 2 1 1 2 P D3 S SD: 20.2888 c. M:-34.5824 c. 12: 1 1 3 2 1 1 3 N SD: 14.7799 c. M: 25.4176 c. Chromatic Dorian, Mela Kanakangi, Raga Kanakambari 21: 2 2 5 3 2 2 5 N SD: 11.1572 c. M:-16.2407 c. 22: 2 2 5 4 2 2 5 N SD: 4.7862 c. M:-7.1359 c. 31: 3 3 7 5 3 3 7 N SD: 4.8412 c. M:-8.7955 c. 43: 4 4 10 7 4 4 10 N SD: 3.2962 c. M: 4.4873 c. 53: 5 5 12 9 5 5 12 N SD: 1.7406 c. M:-2.9525 c. 65: 6 6 15 11 6 6 15 N SD: 1.3285 c. M: 2.3406 c. 96: 9 9 22 16 9 9 22 N SD: 1.3191 c. M: 1.9550 c. 118: 11 11 27 20 11 11 27 N SD: 0.1852 c. M:-0.2662 c. 376: 35 35 86 64 35 35 86 N SD: 0.1180 c. M:-0.1727 c. 494: 46 46 113 84 46 46 113 N SD: 0.0587 c. M:-0.0885 c. 612: 57 57 140 104 57 57 140 N SD: 0.0422 c. M:-0.0726 c. 1171: 109 109 268 199 109 109 268 N SD: 0.0354 c. M: 0.0638 c. 1289: 120 120 295 219 120 120 295 N SD: 0.0276 c. M: 0.0491 c. 1407: 131 131 322 239 131 131 322 N SD: 0.0299 c. M: 0.0444 c. 1665: 155 155 381 283 155 155 381 N SD: 0.0226 c. M: 0.0391 c. 1783: 166 166 408 303 166 166 408 N SD: 0.0100 c. M: 0.0189 c. 1901: 177 177 435 323 177 177 435 N SD: 0.0069 c. M: 0.0099 c. 2395: 223 223 548 407 223 223 548 N SD: 0.0066 c. M:-0.0104 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: 13.6863 cents 4 x x 5:6 x 7:8 S SD: 29.9668 cents 5 x 6:7 x 8:9:10 S SD: 31.0667 cents 6 x 7:8:9 x 10:12 S SD: 11.9501 cents 7 x 8:9 x 11:12:14 SD: 14.2212 cents 8 x 9:11:12:13:14:16 SD: 12.7203 cents 9 x 10:12 x 14:15:18 S SD: 15.1660 cents 10:11 x 13:15:16:17:20 SD: 11.5531 cents 12:13:14:16:18:19:20:24 S SD: 9.7092 cents 13:14:15:17:20:21:22:26 SD: 9.4800 cents 14:15:16:19:21:22:24:28 SD: 6.5316 cents 20:21:23:27:30:32:34:40 SD: 5.7035 cents 24:26:27:32:36:38:41:48 SD: 5.4102 cents 27:29:31:36:41:43:46:54 SD: 4.3215 cents 28:30:32:37:42:45:48:56 SD: 3.1264 cents 30:32:34:40:45:48:51:60 SD: 1.3689 cents 58:62:66:77:87:93:99:116 SD: 1.3079 cents 72:77:82:96:108:115:123:144 SD: 0.8456 cents 102:109:116:136:153:163:174:204 SD: 0.5693 cents 150:160:171:200:225:240:256:300 SD: 0.4826 cents 168:179:191:224:252:269:287:336 SD: 0.4521 cents 180:192:205:240:270:288:307:360 SD: 0.2902 cents 210:224:239:280:315:336:358:420 SD: 0.2847 cents 240:256:273:320:360:384:410:480 SD: 0.2488 cents 270:288:307:360:405:432:461:540 SD: 0.1935 cents 348:371:396:464:522:557:594:696 SD: 0.1670 cents 378:403:430:504:567:605:645:756 SD: 0.1612 cents 420:448:478:560:630:672:717:840 SD: 0.0976 cents 450:480:512:600:675:720:768:900 SD: 0.0000 cents