Scala analysis: xen10-wilson-purvi-09b-04
Purvi modulation 4 from Figure 9b, Hawkins (32/27 16/15 135/128), (16/15 135/128 32/27)
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: 512/405 405.866283 narrow diminished fourth 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: 32/27 294.1350 Pythagorean minor third 3: 135/128 92.1787 major chroma, major limma 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: 1 135/128 92.179 cents major chroma, major limma 1: 2 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 32/27 294.135 cents Pythagorean minor third 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 1215/1024 296.089 cents wide augmented second 2: 2 6/5 315.641 cents minor third 2: 2 5/4 386.314 cents major third 2: 1 512/405 405.866 cents narrow diminished fourth 3: 1 81/64 407.820 cents Pythagorean major third 3: 4 4/3 498.045 cents perfect fourth 3: 1 45/32 590.224 cents diatonic tritone 3: 1 64/45 609.776 cents 2nd tritone 4: 1 45/32 590.224 cents diatonic tritone 4: 1 64/45 609.776 cents 2nd tritone 4: 4 3/2 701.955 cents perfect fifth 4: 1 128/81 792.180 cents Pythagorean minor sixth 5: 1 405/256 794.134 cents wide augmented fifth 5: 2 8/5 813.686 cents minor sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 1 2048/1215 903.911 cents narrow diminished seventh 5: 1 27/16 905.865 cents Pythagorean major sixth 6: 1 27/16 905.865 cents Pythagorean major sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 2 15/8 1088.269 cents classic major seventh 6: 1 256/135 1107.821 cents octave - major chroma Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 111.7 405.9 498.0 702.0 813.7 996.1 1200.0 111.7 : 294.1 386.3 590.2 702.0 884.4 1088.3 1200.0 405.9 : 92.2 296.1 407.8 590.2 794.1 905.9 1200.0 498.0 : 203.9 315.6 498.0 702.0 813.7 1107.8 1200.0 702.0 : 111.7 294.1 498.0 609.8 903.9 996.1 1200.0 813.7 : 182.4 386.3 498.0 792.2 884.4 1088.3 1200.0 996.1 : 203.9 315.6 609.8 702.0 905.9 1017.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 92.1787 .. 294.1350 cents 4096/3645, 201.9563 cents 135/128, 92.1787 cents 2: 294.1350 .. 405.8663 cents 16/15, 111.7313 cents 1/1, 0.0000 cents 3: 407.8200 .. 609.7763 cents 4096/3645, 201.9563 cents 32805/32768, 1.9537 cents 4: 590.2237 .. 792.1800 cents 4096/3645, 201.9563 cents 2025/2048,-19.5526 cents 5: 794.1337 .. 905.8650 cents 16/15, 111.7313 cents 32805/32768, 1.9537 cents 6: 905.8650 .. 1107.8213 cents 4096/3645, 201.9563 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 135/128, 92.1787 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 32/27, 294.1350 cents Average / Smallest step : 1.859741 Largest / Average step : 1.715787 Largest / Smallest step : 3.190921 Median interval of one step : 10/9, 182.4037 cents, amount: 1 Least squares average step : 169.07422 cents, oct.: 1183.51951 cents Scale is not proper Step pattern alph. order: ABCDAED Step pattern size order : BEADBCD Scale is not a Constant Structure Scale diversity : 1.424003 Lumma stability : 0.156887 Lumma impropriety factor : 0.016294 Rothenberg efficiency : 0.435374 redundancy: 0.564626 Efficiency x scale size : 3.047619 Number of different interval sizes : 24 = 4.00000 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.66667 = 14/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 32805/32768, 1.9537 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 classes 1 and 2 combined 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 : 1215 (O: 1215 U: 1215) Highest odd numerator or denominator: 405 Scale harmonicity : 0.033632 Average absolute harmonicity : 0.259347 Specific harmonicity : 0.195918 Fundamental : 1/810, -9.6618 octaves, 0.3230 Hz. Guide tone : 1536, 10.5850 octaves, 401856.868 Hz. Exponens Consonantiae : 1.244160E+06, 20.24674 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 500.5, average 71.50000 Mersenne's string divisions : 27716325 Sum of van Prooijen's expressibility: 6.39100, average 0.91300 Sum of Tenney's harmonic distance : 13.61572, average 1.94510 Vogel's harmonic complexity : 16.00000 Wille's k value : 607 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 6 Triangular lattice diameter : 6 Lattice compactness : 116.29923, average 4.15354 Lattice compactness (without 2's) : 55.28678, average 1.97453 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 9 3.14286 24 1 3: -4 .. 1 -1.00000 9 3 5: -1 .. 0 -0.42857 3 3 Average exponent except 2's :-10 / 7 =-1.42857 Average absolute exponent except 2's: 12 / 7 = 1.71429
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 39.6502 c. M: 63.0091 c. Lebeng 9: 1 2 1 1 1 1 2 N D3 S SD: 31.8866 c. M: 62.7567 c. 10: 1 2 1 2 1 1 2 P M ME S SD: 26.2358 c. M: 45.8663 c. 12: 1 3 1 2 1 2 2 P D3 SD: 7.3900 c. M: 13.6863 c. Phrygian Dominant, Phrygian Major, Mela Vakulabharanam, Raga Ahiri, Basant Mukhari, Jogiya, Vativasantabhairavi, Zilof, Ahava Rabba, Freygish: Jewish, Maqam Hijaz-Nahawand, Humayun, Spanish Gipsy, Dorico Flamenco: Spain, Hitzaz: Greece, Harmonic Major inverse, Mixolydian flat 2 flat 6 41: 4 10 3 7 4 6 7 N SD: 3.3597 c. M:-5.8259 c. 53: 5 13 4 9 5 8 9 N SD: 1.0011 c. M:-1.6809 c. 65: 6 16 5 11 6 10 11 N SD: 0.7512 c. M: 1.3786 c. 118: 11 29 9 20 11 18 20 N SD: 0.4266 c. M:-0.9134 c. 183: 17 45 14 31 17 28 31 N SD: 0.4579 c. M:-0.6911 c. 301: 28 74 23 51 28 46 51 N SD: 0.4297 c. M:-0.7782 c. 311: 29 76 24 53 29 47 53 N SD: 0.4287 c. M: 0.7216 c. 323: 30 79 25 55 30 49 55 N SD: 0.4112 c. M: 0.9127 c. 364: 34 89 28 62 34 55 62 N SD: 0.3739 c. M:-0.5994 c. 376: 35 92 29 64 35 57 64 N SD: 0.2672 c. M: 0.5471 c. 429: 40 105 33 73 40 65 73 N SD: 0.2107 c. M:-0.2997 c. 441: 41 108 34 75 41 67 75 N SD: 0.1921 c. M: 0.4241 c. 494: 46 121 38 84 46 75 84 N SD: 0.1031 c. M: 0.1983 c. 559: 52 137 43 95 52 85 95 N SD: 0.0756 c. M: 0.1418 c. 612: 57 150 47 104 57 93 104 N SD: 0.0211 c. M:-0.0392 c. 1289: 120 316 99 219 120 196 219 N SD: 0.0228 c. M: 0.0323 c. 1783: 166 437 137 303 166 271 303 N SD: 0.0151 c. M: 0.0334 c. 1901: 177 466 146 323 177 289 323 N SD: 0.0130 c. M:-0.0254 c. 2395: 223 587 184 407 223 364 407 N SD: 0.0110 c. M: 0.0208 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 5 x 6 x 7:8 S SD: 8.3876 cents 5 x 6:7 x 8:9:10 S SD: 25.0901 cents 6 x x 8:9:10:11:12 S SD: 17.7004 cents 7:8:9 x x 11:12:14 SD: 28.3248 cents 8:9:10:11:12:13:14:16 S SD: 16.4012 cents 9:10:11:12 x 14:16:18 S SD: 17.3129 cents 10:11 x 13:15:16:18:20 SD: 12.0435 cents 12:13:15:16:18:19:21:24 SD: 6.6620 cents 15:16:19:20:23:24:27:30 SD: 6.2626 cents 18:19:23:24:27:29:32:36 SD: 4.0767 cents 27:29:34:36:41:43:48:54 SD: 3.7937 cents 30:32:38:40:45:48:53:60 SD: 1.6240 cents 60:64:76:80:90:96:107:120 SD: 0.9101 cents 72:77:91:96:108:115:128:144 SD: 0.7759 cents 90:96:114:120:135:144:160:180 SD: 0.4826 cents 162:173:205:216:243:259:288:324 SD: 0.4202 cents 198:211:250:264:297:317:352:396 SD: 0.4170 cents 208:222:263:277:312:333:370:416 SD: 0.3958 cents 212:226:268:283:318:339:377:424 SD: 0.3646 cents 238:254:301:317:357:381:423:476 SD: 0.3397 cents 258:275:326:344:387:413:459:516 SD: 0.3070 cents 270:288:341:360:405:432:480:540 SD: 0.2416 cents 288:307:364:384:432:461:512:576 SD: 0.2027 cents 330:352:417:440:495:528:587:660 SD: 0.1783 cents 360:384:455:480:540:576:640:720 SD: 0.0604 cents 450:480:569:600:675:720:800:900 SD: 0.0483 cents