Scala analysis: xen10-wilson-purvi-09c-04
Purvi modulation 4 from Figure 9c, Hawkins (135/128 32/27 16/15) (16/15 32/27 135/128)
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: 256/135 1107.821284 octave - major chroma 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 135/128 92.1787 major chroma, major limma 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: 32/27 294.1350 Pythagorean minor third 7: 135/128 92.1787 major chroma, major limma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 135/128 92.179 cents major chroma, major limma 1: 2 16/15 111.731 cents minor diatonic semitone 1: 1 9/8 203.910 cents major whole tone 1: 2 32/27 294.135 cents Pythagorean minor third 2: 1 9/8 203.910 cents major whole tone 2: 1 1215/1024 296.089 cents wide augmented second 2: 1 6/5 315.641 cents minor third 2: 2 5/4 386.314 cents major third 2: 2 512/405 405.866 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: 2 405/256 794.134 cents wide augmented fifth 5: 2 8/5 813.686 cents minor sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 2048/1215 903.911 cents narrow diminished seventh 5: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 27/16 905.865 cents Pythagorean major sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 15/8 1088.269 cents classic major seventh 6: 2 256/135 1107.821 cents octave - major chroma Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 111.7 405.9 498.0 702.0 813.7 1107.8 1200.0 111.7 : 294.1 386.3 590.2 702.0 996.1 1088.3 1200.0 405.9 : 92.2 296.1 407.8 702.0 794.1 905.9 1200.0 498.0 : 203.9 315.6 609.8 702.0 813.7 1107.8 1200.0 702.0 : 111.7 405.9 498.0 609.8 903.9 996.1 1200.0 813.7 : 294.1 386.3 498.0 792.2 884.4 1088.3 1200.0 1107.8: 92.2 203.9 498.0 590.2 794.1 905.9 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: 203.9100 .. 405.8663 cents 4096/3645, 201.9563 cents 243/256,-90.2250 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 .. 996.0900 cents 4096/3645, 201.9563 cents 32805/32768, 1.9537 cents 6: 905.8650 .. 1107.8213 cents 4096/3645, 201.9563 cents 243/256,-90.2250 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 : 16/15, 111.7313 cents, amount: 2 Least squares average step : 173.86270 cents, oct.: 1217.03890 cents Scale is not proper Step pattern alph. order: ABCDABC Step pattern size order : BDACBDA Scale is not a Constant Structure Scale diversity : 1.390463 Lumma stability : 0.156887 Lumma impropriety factor : 0.166669 Rothenberg efficiency : 0.448980 redundancy: 0.551020 Efficiency x scale size : 3.142857 Number of different interval sizes : 22 = 3.66667 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 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 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 : 1215 (O: 1215 U: 1215) Highest odd numerator or denominator: 405 Scale harmonicity : 0.033632 Average absolute harmonicity : 0.250418 Specific harmonicity : 0.174672 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 : 683.5, average 97.64286 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.56709, average 1.08101 Sum of Tenney's harmonic distance : 15.99593, average 2.28513 Vogel's harmonic complexity : 15.42857 Wille's k value : 607 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 6 Triangular lattice diameter : 6 Lattice compactness : 135.11698, average 4.82561 Lattice compactness (without 2's) : 60.08416, average 2.14586 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 9 3.71429 28 1 3: -4 .. 1 -1.14286 10 2 5: -1 .. 0 -0.57143 4 4 Average exponent except 2's :-12 / 7 =-1.71429 Average absolute exponent except 2's: 14 / 7 = 2.00000
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 48.1522 c. M: 79.2499 c. Lebeng 8: 1 2 0 2 0 2 1 N D3 I SD: 46.9470 c. M: 63.6863 c. 9: 1 2 1 1 1 2 1 P M ME I SD: 26.3835 c. M: 41.1546 c. 10: 1 2 1 2 1 2 1 P M ME I SD: 24.7553 c. M: 45.8663 c. 12: 1 3 1 2 1 3 1 N T3 I SD: 7.8209 c. M: 13.6863 c. Double Harmonic Major, Major Gipsy, Bhairav That, Mela Mayamalavagaula, Raga Paraj, Kalingada, Gaulipantu, Lalitapancamam, Gandhakriya, Kalingda, Manjiri, Chromatic 2nd Byzantine Liturgical, Hitzazkiar: Greece, Maqam Zengule, Hijaz Kar, Suzidil 38: 4 9 3 6 4 9 3 N SD: 7.5539 c. M:-14.5845 c. 41: 4 10 3 7 4 10 3 N SD: 3.7265 c. M:-5.8259 c. 53: 5 13 4 9 5 13 4 N SD: 1.1709 c. M:-1.6809 c. Makam Evcara (Evicara) 65: 6 16 5 11 6 16 5 N SD: 0.6837 c. M: 1.3786 c. 118: 11 29 9 20 11 29 9 N SD: 0.4520 c. M:-0.9134 c. 183: 17 45 14 31 17 45 14 N SD: 0.4158 c. M:-0.6911 c. 301: 28 74 23 51 28 74 23 N SD: 0.4108 c. M:-0.7782 c. 311: 29 76 24 53 29 76 24 N SD: 0.3996 c. M: 0.7216 c. 323: 30 79 25 55 30 79 25 N SD: 0.4620 c. M: 0.9127 c. 364: 34 89 28 62 34 89 28 N SD: 0.3293 c. M:-0.5994 c. 376: 35 92 29 64 35 92 29 N SD: 0.2727 c. M: 0.5471 c. 429: 40 105 33 73 40 105 33 N SD: 0.1874 c. M:-0.2997 c. 441: 41 108 34 75 41 108 34 N SD: 0.2215 c. M: 0.4241 c. 482: 45 118 37 82 45 118 37 N SD: 0.2086 c. M:-0.4216 c. 494: 46 121 38 84 46 121 38 N SD: 0.1013 c. M: 0.1983 c. 547: 51 134 42 93 51 134 42 N SD: 0.1030 c. M:-0.2077 c. 559: 52 137 43 95 52 137 43 N SD: 0.0894 c. M: 0.1418 c. 612: 57 150 47 104 57 150 47 N SD: 0.0222 c. M:-0.0392 c. 1289: 120 316 99 219 120 316 99 N SD: 0.0203 c. M: 0.0323 c. 1783: 166 437 137 303 166 437 137 N SD: 0.0168 c. M: 0.0334 c. 1901: 177 466 146 323 177 466 146 N SD: 0.0129 c. M:-0.0254 c. 2395: 223 587 184 407 223 587 184 N SD: 0.0107 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 x 8 S SD: 6.5175 cents 5 x 6:7 x 8:9:10 S SD: 30.6044 cents 6 x x 8:9:10:11:12 S SD: 18.3434 cents 7:8:9 x x 11:13:14 SD: 26.3803 cents 8:9:10:11:12:13:15:16 SD: 16.1751 cents 9:10:11:12 x 14:17:18 SD: 17.3497 cents 10:11 x 13:15:16:19:20 SD: 11.5116 cents 12:13:15:16:18:19:23:24 SD: 6.0163 cents 18:19:23:24:27:29:34:36 SD: 4.1900 cents 27:29:34:36:41:43:51:54 SD: 3.9153 cents 30:32:38:40:45:48:57:60 SD: 0.6825 cents 132:141:167:176:198:211:250:264 SD: 0.5546 cents 162:173:205:216:243:259:307:324 SD: 0.4500 cents 182:194:230:243:273:291:345:364 SD: 0.4351 cents 192:205:243:256:288:307:364:384 SD: 0.4071 cents 212:226:268:283:318:339:402:424 SD: 0.3573 cents 240:256:303:320:360:384:455:480 SD: 0.3378 cents 242:258:306:323:363:387:459:484 SD: 0.3213 cents 258:275:326:344:387:413:489:516 SD: 0.2779 cents 270:288:341:360:405:432:512:540 SD: 0.2416 cents 288:307:364:384:432:461:546:576 SD: 0.2116 cents 300:320:379:400:450:480:569:600 SD: 0.1759 cents 318:339:402:424:477:509:603:636 SD: 0.1758 cents 330:352:417:440:495:528:626:660 SD: 0.1406 cents 360:384:455:480:540:576:683:720 SD: 0.1350 cents 450:480:569:600:675:720:853:900 SD: 0.1080 cents 480:512:607:640:720:768:910:960 SD: 0.0967 cents