Scala analysis: xen10-wilson-purvi-02a-03
Purvi modulation 3 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: 16/9 996.089998 Pythagorean minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 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: 10/9 182.4037 minor whole tone 7: 9/8 203.9100 major whole tone
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: 1 32/27 294.135 cents Pythagorean minor third 2: 2 6/5 315.641 cents minor third 2: 2 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: 2 8/5 813.686 cents minor sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 1 27/16 905.865 cents Pythagorean major 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: 5 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 111.7 223.5 498.0 702.0 813.7 996.1 1200.0 111.7 : 111.7 386.3 590.2 702.0 884.4 1088.3 1200.0 223.5 : 274.6 478.5 590.2 772.6 976.5 1088.3 1200.0 498.0 : 203.9 315.6 498.0 702.0 813.7 925.4 1200.0 702.0 : 111.7 294.1 498.0 609.8 721.5 996.1 1200.0 813.7 : 182.4 386.3 498.0 609.8 884.4 1088.3 1200.0 996.1 : 203.9 315.6 427.4 702.0 905.9 1017.6 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 : 10/9, 182.4037 cents, amount: 1 Most common interval of one step : 16/15, 111.7313 cents, amount: 3 Least squares average step : 166.46845 cents, oct.: 1165.27914 cents Scale is not proper Step pattern alph. order: AABCADC Step pattern size order : AADCABC Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.483493 Lumma stability : 0.202513 Lumma impropriety factor : 0.170400 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 : 4 Highest interval variety : 5 Mean interval variety : 4.00000 = 4 Median interval variety : 3 Lowest interval variety : 3 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 : 2 at degree 5 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 classes 2 and 3 combined Scale is n-1 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 : 0.259333 Specific harmonicity : 0.195638 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 : 282.5, average 40.35714 Mersenne's string divisions : 7828275 Sum of van Prooijen's expressibility: 6.13573, average 0.87653 Sum of Tenney's harmonic distance : 13.05942, average 1.86563 Vogel's harmonic complexity : 15.00000 Wille's k value : 337 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 5 Lattice compactness : 106.29994, average 3.79643 Lattice compactness (without 2's) : 46.69196, average 1.66757 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 8 3.00000 23 1 3: -2 .. 1 -0.71429 7 3 5: -2 .. 0 -0.57143 4 3 Average exponent except 2's :-9 / 7 =-1.28571 Average absolute exponent except 2's: 11 / 7 = 1.57143 Scale is JI-epimorphic with val: <7 11 16| = patent
FIT/MODE
7: 1 0 2 1 1 1 1 N T3 SD: 37.3063 c. M:-59.6973 c. 9: 1 1 2 1 1 1 2 P M ME S SD: 35.7561 c. M: 62.7567 c. Pseudo Pelog, Pelogic-7, Antiionian 10: 1 1 2 2 1 1 2 P D3 S SD: 20.6605 c. M: 36.0900 c. 12: 1 1 3 2 1 2 2 N SD: 11.3286 c. M: 23.4626 c. Mela Ratnangi, Raga Phenadyuti 22: 2 2 5 4 2 3 4 N SD: 7.1773 c. M: 14.2718 c. 31: 3 3 7 5 3 5 5 N SD: 6.0752 c. M:-10.3616 c. 34: 3 3 8 6 3 5 6 N SD: 6.1793 c. M: 11.6979 c. 41: 4 4 9 7 4 6 7 N SD: 5.0430 c. M:-10.6838 c. 43: 4 4 10 7 4 7 7 N SD: 4.2964 c. M:-8.5612 c. 53: 5 5 12 9 5 8 9 N SD: 1.3579 c. M:-2.9525 c. 65: 6 6 15 11 6 10 11 N SD: 1.0399 c. M: 1.9241 c. 118: 11 11 27 20 11 18 20 N SD: 0.2701 c. M:-0.5202 c. 323: 30 30 74 55 30 49 55 N SD: 0.3060 c. M: 0.5524 c. 376: 35 35 86 64 35 57 64 N SD: 0.1706 c. M: 0.3453 c. 429: 40 40 98 73 40 65 73 N SD: 0.2189 c. M:-0.3137 c. 441: 41 41 101 75 41 67 75 N SD: 0.1646 c. M: 0.3333 c. 494: 46 46 113 84 46 75 84 N SD: 0.0712 c. M: 0.1386 c. 612: 57 57 140 104 57 93 104 N SD: 0.0323 c. M:-0.0668 c. 1171: 109 109 268 199 109 178 199 N SD: 0.0295 c. M: 0.0638 c. 1289: 120 120 295 219 120 196 219 N SD: 0.0236 c. M: 0.0336 c. 1783: 166 166 408 303 166 271 303 N SD: 0.0109 c. M: 0.0189 c. 1901: 177 177 435 323 177 289 323 N SD: 0.0088 c. M:-0.0173 c. 2395: 223 223 548 407 223 364 407 N SD: 0.0078 c. M: 0.0148 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: 23.5575 cents 4 x x 5:6 x 7:8 S SD: 28.7524 cents 5 x 6:7 x 8:9:10 S SD: 25.3725 cents 6 x 7:8:9:10:11:12 S SD: 16.4290 cents 7 x 8:9 x 11:12:14 SD: 18.9322 cents 8 x 9:11:12:13:14:16 SD: 11.4067 cents 9 x 10:12 x 14:16:18 S SD: 12.7505 cents 10:11 x 13:15:16:18:20 SD: 12.0435 cents 12:13:14:16:18:19:21:24 SD: 8.6623 cents 14:15:16:19:21:22:25:28 SD: 6.5316 cents 15:16:17:20:23:24:27:30 SD: 6.3186 cents 22:23:25:29:33:35:39:44 SD: 5.9367 cents 24:26:27:32:36:38:43:48 SD: 5.7373 cents 26:28:30:35:39:42:46:52 SD: 5.5004 cents 27:29:31:36:41:43:48:54 SD: 4.3001 cents 28:30:32:37:42:45:50:56 SD: 3.1264 cents 30:32:34:40:45:48:53:60 SD: 1.8279 cents 58:62:66:77:87:93:103:116 SD: 1.3344 cents 60:64:68:80:90:96:107:120 SD: 1.2379 cents 72:77:82:96:108:115:128:144 SD: 0.8104 cents 102:109:116:136:153:163:181:204 SD: 0.7199 cents 108:115:123:144:162:173:192:216 SD: 0.5699 cents 138:147:157:184:207:221:245:276 SD: 0.5260 cents 168:179:191:224:252:269:299:336 SD: 0.4714 cents 180:192:205:240:270:288:320:360 SD: 0.2414 cents 210:224:239:280:315:336:373:420 SD: 0.2314 cents 240:256:273:320:360:384:427:480 SD: 0.2024 cents 270:288:307:360:405:432:480:540 SD: 0.1611 cents 378:403:430:504:567:605:672:756 SD: 0.1545 cents 420:448:478:560:630:672:747:840 SD: 0.1302 cents 450:480:512:600:675:720:800:900 SD: 0.0000 cents