Scala analysis: xen10-wilson-purvi-09c-05
Purvi modulation 5 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: 2048/1215 903.911282 narrow diminished seventh 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: 4096/3645 201.9563 narrow diminished third 6: 9/8 203.9100 major whole tone 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: 1 16/15 111.731 cents minor diatonic semitone 1: 1 4096/3645 201.956 cents narrow diminished third 1: 2 9/8 203.910 cents major whole tone 1: 1 32/27 294.135 cents Pythagorean minor third 2: 1 9/8 203.910 cents major whole tone 2: 2 1215/1024 296.089 cents wide augmented second 2: 1 5/4 386.314 cents major third 2: 3 512/405 405.866 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: 3 405/256 794.134 cents wide augmented fifth 5: 1 8/5 813.686 cents minor sixth 5: 2 2048/1215 903.911 cents narrow diminished seventh 5: 1 16/9 996.090 cents Pythagorean minor seventh 6: 1 27/16 905.865 cents Pythagorean major sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 3645/2048 998.044 cents wide augmented sixth 6: 1 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 : 111.7 405.9 498.0 702.0 903.9 1107.8 1200.0 111.7 : 294.1 386.3 590.2 792.2 996.1 1088.3 1200.0 405.9 : 92.2 296.1 498.0 702.0 794.1 905.9 1200.0 498.0 : 203.9 405.9 609.8 702.0 813.7 1107.8 1200.0 702.0 : 202.0 405.9 498.0 609.8 903.9 996.1 1200.0 903.9 : 203.9 296.1 407.8 702.0 794.1 998.0 1200.0 1107.8: 92.2 203.9 498.0 590.2 794.1 996.1 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 : 4096/3645, 201.9563 cents, amount: 1 Least squares average step : 177.08502 cents, oct.: 1239.59515 cents Scale is not proper Step pattern alph. order: ABCDEDC Step pattern size order : BEADCDA Scale is not a Constant Structure Scale diversity : 1.365334 Lumma stability : 0.156887 Lumma impropriety factor : 0.166669 Rothenberg efficiency : 0.451701 redundancy: 0.548299 Efficiency x scale size : 3.161905 Number of different interval sizes : 22 = 3.66667 / class Number of one step interval sizes : 5 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 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 : 1 at degree 0 Formal octave complements present : 3 = 42.8571% Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 5 Odd number limit : 3645 (O: 3645 U: 3645) Highest odd numerator or denominator: 1215 Scale harmonicity : 0.029070 Average absolute harmonicity : 0.239869 Specific harmonicity : 0.144230 Fundamental : 1/2430, -11.2467 octaves, 0.1077 Hz. Guide tone : 6144, 12.5850 octaves, 1607427.473 Hz. Exponens Consonantiae : 1.492992E+07, 23.83170 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 2308.5, average 329.78571 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.95270, average 1.42181 Sum of Tenney's harmonic distance : 20.78978, average 2.96997 Vogel's harmonic complexity : 17.42857 Wille's k value : 1822 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 7 Triangular lattice diameter : 7 Lattice compactness : 169.89400, average 6.06764 Lattice compactness (without 2's) : 74.65964, average 2.66642 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 11 4.85714 36 1 3: -5 .. 1 -1.85714 15 2 5: -1 .. 0 -0.57143 4 4 Average exponent except 2's :-17 / 7 =-2.42857 Average absolute exponent except 2's: 19 / 7 = 2.71429
FIT/MODE
7: 0 2 1 1 1 1 1 N T3 SD: 60.2961 c. M: 111.7313 c. 8: 1 2 0 2 1 1 1 P D3 S SD: 40.3335 c. M: 57.8213 c. 9: 1 2 1 1 2 1 1 P M ME S SD: 28.1601 c. M: 41.1546 c. Pelog Saptanada: Sunda 10: 1 2 1 2 1 2 1 P M ME I SD: 33.1275 c. M: 63.9113 c. 12: 1 3 1 2 2 2 1 N T3 SD: 6.0492 c. M: 11.7313 c. Mela Suryakanta, Bhairubahar That, Raga Supradhipam, Sowrashtram (Sourashtra), Jaganmohini, Major-Melodic Phrygian, Hungarian Gipsy inverse 39: 4 9 3 7 6 7 3 N SD: 7.2074 c. M: 11.6036 c. 41: 4 10 3 7 7 7 3 N SD: 3.2703 c. M:-5.3419 c. 53: 5 13 4 9 9 9 4 N SD: 1.2349 c. M:-1.7491 c. 65: 6 16 5 11 11 11 5 N SD: 0.5165 c. M: 0.9621 c. 183: 17 45 14 31 31 31 14 N SD: 0.5206 c. M:-1.0068 c. 248: 23 61 19 42 42 42 19 N SD: 0.4914 c. M:-0.9274 c. 299: 28 73 23 51 50 51 23 N SD: 0.5080 c. M: 0.9012 c. 311: 29 76 24 53 52 53 24 N SD: 0.5264 c. M: 1.0174 c. 313: 29 77 24 53 53 53 24 N SD: 0.4833 c. M:-0.8811 c. 352: 33 86 27 60 59 60 27 N SD: 0.3958 c. M:-0.7687 c. 364: 34 89 28 62 61 62 28 N SD: 0.3333 c. M: 0.6146 c. 376: 35 92 29 64 63 64 29 N SD: 0.3814 c. M: 0.7198 c. 417: 39 102 32 71 70 71 32 N SD: 0.2539 c. M:-0.4989 c. 429: 40 105 33 73 72 73 33 N SD: 0.2165 c. M: 0.4148 c. 482: 45 118 37 82 81 82 37 N SD: 0.1504 c. M:-0.3019 c. 494: 46 121 38 84 83 84 38 N SD: 0.1400 c. M: 0.2676 c. 547: 51 134 42 93 92 93 42 N SD: 0.0720 c. M:-0.1517 c. 612: 57 150 47 104 103 104 47 N SD: 0.0170 c. M:-0.0334 c. 2395: 223 587 184 407 403 407 184 N SD: 0.0147 c. M: 0.0282 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: 6.5175 cents 4 x 5 x 6:7 x 8 S SD: 16.9488 cents 5 x 6:7 x 8:9:10 S SD: 35.5282 cents 6 x x 8:9:10:11:12 S SD: 12.3283 cents 7:8:9 x 11:12:13:14 SD: 25.6930 cents 8:9:10:11:12:13:15:16 SD: 18.1361 cents 9:10:11:12:14:15:17:18 SD: 16.1651 cents 10:11 x 13:15:17:19:20 SD: 11.7704 cents 12:13:15:16:18:20:23:24 SD: 6.1066 cents 16:17:20:21:24:27:30:32 SD: 5.6382 cents 18:19:23:24:27:30:34:36 SD: 4.7359 cents 26:28:33:35:39:44:49:52 SD: 3.9331 cents 28:30:35:37:42:47:53:56 SD: 3.8993 cents 30:32:38:40:45:51:57:60 SD: 2.2122 cents 42:45:53:56:63:71:80:84 SD: 1.7720 cents 48:51:61:64:72:81:91:96 SD: 1.6416 cents 60:64:76:80:90:101:114:120 SD: 0.7591 cents 102:109:129:136:153:172:193:204 SD: 0.7199 cents 118:126:149:157:177:199:224:236 SD: 0.7157 cents 136:145:172:181:204:229:258:272 SD: 0.5546 cents 162:173:205:216:243:273:307:324 SD: 0.4120 cents 212:226:268:283:318:357:402:424 SD: 0.4049 cents 222:237:281:296:333:374:421:444 SD: 0.3946 cents 238:254:301:317:357:401:451:476 SD: 0.3688 cents 242:258:306:323:363:408:459:484 SD: 0.2994 cents 258:275:326:344:387:435:489:516 SD: 0.2593 cents 270:288:341:360:405:455:512:540 SD: 0.2491 cents 300:320:379:400:450:506:569:600 SD: 0.2357 cents 318:339:402:424:477:536:603:636 SD: 0.1467 cents 420:448:531:560:630:708:796:840 SD: 0.1402 cents 462:493:584:616:693:779:876:924 SD: 0.1336 cents 480:512:607:640:720:809:910:960 SD: 0.1002 cents