Scala analysis: xen10-wilson-purvi-02a-01
Purvi modulation 1 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: 32/25 427.372572 classic diminished 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: 9/8 203.9100 major whole tone 4: 75/64 274.5824 classic augmented second 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 : 111.7 223.5 427.4 702.0 813.7 925.4 1200.0 111.7 : 111.7 315.6 590.2 702.0 813.7 1088.3 1200.0 223.5 : 203.9 478.5 590.2 702.0 976.5 1088.3 1200.0 427.4 : 274.6 386.3 498.0 772.6 884.4 996.1 1200.0 702.0 : 111.7 223.5 498.0 609.8 721.5 925.4 1200.0 813.7 : 111.7 386.3 498.0 609.8 813.7 1088.3 1200.0 925.4 : 274.6 386.3 498.0 702.0 976.5 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 : 161.92522 cents, oct.: 1133.47655 cents Scale is not proper Step pattern alph. order: AABCAAC Step pattern size order : SSMLSSL 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 Number of recognisable fifths : 4, average 701.9550 cents Scale is Hypolydian octave species of abstract tetrachord Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval classes 1 and 2 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 : 0.227799 Specific harmonicity : 0.168273 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 : 396.5, average 56.64286 Mersenne's string divisions : 862675905 Sum of van Prooijen's expressibility: 7.97737, average 1.13962 Sum of Tenney's harmonic distance : 16.70724, average 2.38675 Vogel's harmonic complexity : 13.85714 Wille's k value : 337 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 5 Lattice compactness : 121.31848, average 4.33280 Lattice compactness (without 2's) : 46.75645, average 1.66987 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 8 3.85714 29 1 3: -2 .. 1 -0.42857 5 1 5: -2 .. 0 -1.14286 8 5 Average exponent except 2's :-11 / 7 =-1.57143 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is JI-epimorphic with val: <7 11 16| = patent
FIT/MODE
7: 1 0 1 2 1 0 2 N T3 SD: 53.7558 c. M: 84.5154 c. 8: 1 1 1 2 0 1 2 N D3 SD: 46.0509 c. M:-76.5374 c. 9: 1 1 1 2 1 1 2 P M ME S SD: 25.5727 c. M:-43.2041 c. 10: 1 1 2 2 1 1 2 P D3 S SD: 27.5823 c. M:-52.6274 c. 12: 1 1 2 3 1 1 3 N SD: 18.0260 c. M: 27.3726 c. Chromatic Phrygian inverse 17: 2 1 3 4 2 1 4 N SD: 17.7610 c. M:-33.3725 c. 19: 2 2 3 4 2 2 4 P SD: 16.3392 c. M:-29.1690 c. 21: 2 2 3 5 2 2 5 N SD: 13.9226 c. M: 27.3726 c. 22: 2 2 4 5 2 2 5 N SD: 5.2136 c. M:-8.9911 c. 31: 3 3 5 7 3 3 7 N SD: 4.4669 c. M:-8.7955 c. 43: 4 4 7 10 4 4 10 N SD: 4.3852 c. M: 8.7679 c. 53: 5 5 9 12 5 5 12 N SD: 2.0401 c. M:-2.9525 c. 65: 6 6 11 15 6 6 15 N SD: 1.6811 c. M: 2.7572 c. 87: 8 8 15 20 8 8 20 N SD: 1.3906 c. M: 2.7729 c. 96: 9 9 16 22 9 9 22 N SD: 1.4136 c. M: 2.3726 c. 118: 11 11 20 27 11 11 27 N SD: 0.1840 c. M:-0.2662 c. 376: 35 35 64 86 35 35 86 N SD: 0.1464 c. M:-0.2870 c. 494: 46 46 84 113 46 46 113 N SD: 0.0795 c. M:-0.1578 c. 612: 57 57 104 140 57 57 140 N SD: 0.0515 c. M:-0.0784 c. 730: 68 68 124 167 68 68 167 N SD: 0.0511 c. M:-0.0991 c. 1171: 109 109 199 268 109 109 268 N SD: 0.0392 c. M: 0.0638 c. 1289: 120 120 219 295 120 120 295 N SD: 0.0364 c. M: 0.0646 c. 1547: 144 144 263 354 144 144 354 N SD: 0.0359 c. M: 0.0624 c. 1665: 155 155 283 381 155 155 381 N SD: 0.0209 c. M: 0.0391 c. 1783: 166 166 303 408 166 166 408 N SD: 0.0096 c. M: 0.0189 c. 1901: 177 177 323 435 177 177 435 N SD: 0.0093 c. M: 0.0185 c. 2395: 223 223 407 548 223 223 548 N SD: 0.0090 c. M:-0.0178 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: 27.2446 cents 4 x x 5:6 x 7:8 S SD: 14.9376 cents 5 x 6 x x 8:9:10 S SD: 32.5901 cents 6 x 7:8:9 x 10:12 S SD: 18.5091 cents 7 x 8:9 x 11:12:14 SD: 6.7867 cents 8 x 9:10:12:13:14:16 S SD: 11.3931 cents 9 x 10:12 x 14:15:18 S SD: 20.7314 cents 10:11 x 13:15:16:17:20 SD: 10.0061 cents 13:14:15:17:20:21:22:26 SD: 9.7380 cents 14:15:16:18:21:22:24:28 S SD: 4.9712 cents 28:30:32:36:42:45:48:56 S SD: 2.4634 cents 42:45:48:54:63:67:72:84 SD: 2.3233 cents 44:47:50:56:66:70:75:88 SD: 2.0699 cents 50:53:57:64:75:80:85:100 SD: 1.8906 cents 58:62:66:74:87:93:99:116 SD: 1.1002 cents 72:77:82:92:108:115:123:144 SD: 0.9485 cents 108:115:123:138:162:173:184:216 SD: 0.8332 cents 118:126:134:151:177:189:201:236 SD: 0.7702 cents 122:130:139:156:183:195:208:244 SD: 0.6107 cents 132:141:150:169:198:211:225:264 SD: 0.6089 cents 150:160:171:192:225:240:256:300 SD: 0.4826 cents 168:179:191:215:252:269:287:336 SD: 0.4545 cents 182:194:207:233:273:291:311:364 SD: 0.4029 cents 210:224:239:269:315:336:358:420 SD: 0.3389 cents 240:256:273:307:360:384:410:480 SD: 0.2964 cents 268:286:305:343:402:429:457:536 SD: 0.2737 cents 282:301:321:361:423:451:481:564 SD: 0.2707 cents 300:320:341:384:450:480:512:600 SD: 0.2416 cents 328:350:373:420:492:525:560:656 SD: 0.2271 cents 378:403:430:484:567:605:645:756 SD: 0.1807 cents 392:418:446:502:588:627:669:784 SD: 0.1627 cents 436:465:496:558:654:698:744:872 SD: 0.1585 cents 450:480:512:576:675:720:768:900 SD: 0.0000 cents