Scala analysis: xen10-wilson-purvi-02a-06
Purvi modulation 6 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: 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: 16/9 996.089998 Pythagorean minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 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: 16/15 111.7313 minor diatonic semitone 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 : 274.6 386.3 498.0 702.0 884.4 996.1 1200.0 274.6 : 111.7 223.5 427.4 609.8 721.5 925.4 1200.0 386.3 : 111.7 315.6 498.0 609.8 813.7 1088.3 1200.0 498.0 : 203.9 386.3 498.0 702.0 976.5 1088.3 1200.0 702.0 : 182.4 294.1 498.0 772.6 884.4 996.1 1200.0 884.4 : 111.7 315.6 590.2 702.0 813.7 1017.6 1200.0 996.1 : 203.9 478.5 590.2 702.0 905.9 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 : 10/9, 182.4037 cents, amount: 1 Most common interval of one step : 16/15, 111.7313 cents, amount: 3 Least squares average step : 172.48213 cents, oct.: 1207.37492 cents Scale is not proper Step pattern alph. order: ABBCDBC Step pattern size order : DAACBAC 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 Number of recognisable fifths : 4, average 701.9550 cents Scale contains a complete diamond : 1 3 Length of longest harmonic part : 2 at degree 3 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 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 5 Odd number limit : 675 (O: 675 U: 675) Highest odd numerator or denominator: 75 Scale harmonicity : 0.032468 Average absolute harmonicity : 0.267154 Specific harmonicity : 0.195439 Fundamental : 1/576, -9.1699 octaves, 0.4542 Hz. Guide tone : 1200, 10.2288 octaves, 313950.678 Hz. Exponens Consonantiae : 6.912000E+05, 19.39874 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 98.0, average 14.00000 Mersenne's string divisions : 1751400 Sum of van Prooijen's expressibility: 5.18149, average 0.74021 Sum of Tenney's harmonic distance : 10.47509, average 1.49644 Vogel's harmonic complexity : 13.71429 Wille's k value : 337 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 5 Lattice compactness : 109.03546, average 3.89412 Lattice compactness (without 2's) : 46.09960, average 1.64641 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -6 .. 4 -0.28571 16 1 3: -2 .. 1 -0.28571 6 3 5: 0 .. 2 0.57143 4 3 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 10 / 7 = 1.42857 Scale is JI-epimorphic with val: <7 11 16| = patent
FIT/MODE
7: 2 0 1 1 1 1 1 N T3 SD: 35.6033 c. M:-68.2747 c. 8: 2 1 0 2 1 1 1 N D3 SD: 42.2063 c. M:-63.6863 c. 9: 2 1 1 1 2 0 2 N T3 SD: 36.0108 c. M: 62.7567 c. 10: 2 1 1 2 1 1 2 P D3 I SD: 28.8092 c. M: 44.3587 c. 12: 3 1 1 2 2 1 2 N SD: 12.5411 c. M:-25.4176 c. Mela Vagadhisvari, Raga Bhogachayanata, Nandkauns, Ganavaridhi, Chayanata, Bluesy Rock 'n Roll 19: 4 2 2 3 3 2 3 P SD: 11.0113 c. M: 21.9508 c. 22: 5 2 2 4 3 2 4 N SD: 8.1457 c. M: 14.2718 c. 31: 7 3 3 5 5 3 5 N SD: 5.4810 c. M:-10.3616 c. 34: 8 3 3 6 5 3 6 N SD: 4.7905 c. M: 7.8547 c. 41: 9 4 4 7 6 4 7 N SD: 5.3436 c. M: 11.1678 c. 53: 12 5 5 9 8 5 9 N SD: 1.3161 c. M: 2.8843 c. 65: 15 6 6 11 10 6 11 N SD: 1.2897 c. M:-2.3406 c. 118: 27 11 11 20 18 11 20 N SD: 0.2858 c. M:-0.5202 c. 323: 74 30 30 55 49 30 55 N SD: 0.2426 c. M: 0.4244 c. 376: 86 35 35 64 57 35 64 N SD: 0.2113 c. M: 0.3453 c. 441: 101 41 41 75 67 41 75 N SD: 0.1265 c. M:-0.2475 c. 494: 113 46 46 84 75 46 84 N SD: 0.0962 c. M: 0.1482 c. 559: 128 52 52 95 85 52 95 N SD: 0.0869 c. M:-0.1940 c. 612: 140 57 57 104 93 57 104 N SD: 0.0359 c. M: 0.0726 c. 1171: 268 109 109 199 178 109 199 N SD: 0.0245 c. M:-0.0546 c. 1289: 295 120 120 219 196 120 219 N SD: 0.0320 c. M:-0.0491 c. 1342: 307 125 125 228 204 125 228 N SD: 0.0316 c. M: 0.0668 c. 1665: 381 155 155 283 253 155 283 N SD: 0.0287 c. M: 0.0540 c. 1783: 408 166 166 303 271 166 303 N SD: 0.0088 c. M: 0.0160 c. 2395: 548 223 223 407 364 223 407 N SD: 0.0106 c. M: 0.0163 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 x 7:8 S SD: 6.8160 cents 5:6 x 7 x 8:9:10 S SD: 23.8978 cents 6:7 x 8:9:10:11:12 S SD: 8.9714 cents 7:8:9 x 11:12 x 14 SD: 22.9151 cents 8:9:10:11:12:13:14:16 S SD: 14.6365 cents 9 x 11:12:14:15:16:18 SD: 12.3353 cents 10:12 x 13:15:17:18:20 SD: 12.0702 cents 12:14:15:16:18:20:21:24 S SD: 4.0477 cents 24:28:30:32:36:40:43:48 SD: 2.2177 cents 36:42:45:48:54:60:64:72 S SD: 1.1016 cents 76:89:95:101:114:127:135:152 SD: 1.0761 cents 99:116:124:132:149:165:176:198 SD: 0.9702 cents 100:117:125:133:150:167:178:200 SD: 0.9379 cents 104:122:130:139:156:173:185:208 SD: 0.8158 cents 116:136:145:155:174:193:206:232 SD: 0.7414 cents 132:155:165:176:198:220:235:264 SD: 0.6102 cents 140:164:175:187:210:233:249:280 SD: 0.5838 cents 144:169:180:192:216:240:256:288 SD: 0.3661 cents 168:197:210:224:252:280:299:336 SD: 0.3174 cents 180:211:225:240:270:300:320:360 SD: 0.0733 cents 396:464:495:528:594:660:704:792 SD: 0.0333 cents 576:675:720:768:864:960:1024:1152 SD: 0.0000 cents