Scala analysis: xen10-wilson-purvi-09b-05
Purvi modulation 5 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: 2048/1215 903.911282 narrow diminished seventh 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: 4096/3645 201.9563 narrow diminished third 6: 135/128 92.1787 major chroma, major limma 7: 9/8 203.9100 major whole tone
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 32/27 294.135 cents Pythagorean minor third 2: 2 1215/1024 296.089 cents wide augmented second 2: 1 6/5 315.641 cents minor third 2: 1 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: 1 8/5 813.686 cents minor sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 2 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 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: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 111.7 405.9 498.0 702.0 903.9 996.1 1200.0 111.7 : 294.1 386.3 590.2 792.2 884.4 1088.3 1200.0 405.9 : 92.2 296.1 498.0 590.2 794.1 905.9 1200.0 498.0 : 203.9 405.9 498.0 702.0 813.7 1107.8 1200.0 702.0 : 202.0 294.1 498.0 609.8 903.9 996.1 1200.0 903.9 : 92.2 296.1 407.8 702.0 794.1 998.0 1200.0 996.1 : 203.9 315.6 609.8 702.0 905.9 1107.8 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 : 4096/3645, 201.9563 cents, amount: 1 Least squares average step : 172.29654 cents, oct.: 1206.07576 cents Scale is not proper Step pattern alph. order: ABCDECD Step pattern size order : BEADCAD Scale is not a Constant Structure Scale diversity : 1.394243 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 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 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 : 3645 (O: 3645 U: 3645) Highest odd numerator or denominator: 1215 Scale harmonicity : 0.029070 Average absolute harmonicity : 0.248798 Specific harmonicity : 0.153354 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 : 2125.5, average 303.64286 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.77661, average 1.25380 Sum of Tenney's harmonic distance : 18.40957, average 2.62994 Vogel's harmonic complexity : 18.00000 Wille's k value : 1822 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 7 Triangular lattice diameter : 7 Lattice compactness : 158.53330, average 5.66190 Lattice compactness (without 2's) : 71.78847, average 2.56387 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 11 4.28571 32 1 3: -5 .. 1 -1.71429 14 3 5: -1 .. 0 -0.42857 3 3 Average exponent except 2's :-15 / 7 =-2.14286 Average absolute exponent except 2's: 17 / 7 = 2.42857
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 40.1849 c. M: 63.0091 c. Lebeng 8: 1 2 0 2 1 1 1 P D3 S SD: 39.5520 c. M:-53.9100 c. 9: 1 2 1 1 2 0 2 N D3 SD: 33.3716 c. M: 62.7567 c. 10: 1 2 1 2 1 1 2 P M ME S SD: 34.2480 c. M: 63.9113 c. 11: 1 3 1 1 2 1 2 N T3 SD: 30.7258 c. M:-47.4095 c. 12: 1 3 1 2 2 1 2 P D3 SD: 5.4807 c. M: 11.7313 c. Harmonic Minor inverse, Mixolydian flat 2, Mela Cakravaka, Raga Ahir Bhairav, Bindumalini, Hevitri, Vegavahini, Makam Hicaz, Zanjaran 41: 4 10 3 7 7 3 7 N SD: 2.8453 c. M:-5.3419 c. 53: 5 13 4 9 9 4 9 N SD: 1.0752 c. M:-1.7491 c. 65: 6 16 5 11 11 5 11 N SD: 0.6030 c. M: 0.9621 c. 118: 11 29 9 20 20 9 20 N SD: 0.6135 c. M:-1.1735 c. 183: 17 45 14 31 31 14 31 N SD: 0.5548 c. M:-1.0068 c. 248: 23 61 19 42 42 19 42 N SD: 0.5476 c. M:-0.9274 c. 299: 28 73 23 51 50 23 51 N SD: 0.5838 c. M: 0.9012 c. 301: 28 74 23 51 51 23 51 N SD: 0.5712 c. M:-1.0721 c. 311: 29 76 24 53 52 24 53 N SD: 0.5488 c. M: 1.0174 c. 313: 29 77 24 53 53 24 53 N SD: 0.5502 c. M:-0.8811 c. 323: 30 79 25 55 54 25 55 N SD: 0.5910 c. M: 1.1249 c. 352: 33 86 27 60 59 27 60 N SD: 0.4603 c. M:-0.7687 c. 364: 34 89 28 62 61 28 62 N SD: 0.3774 c. M: 0.6146 c. 376: 35 92 29 64 63 29 64 N SD: 0.3774 c. M: 0.7198 c. 417: 39 102 32 71 70 32 71 N SD: 0.2947 c. M:-0.4989 c. 429: 40 105 33 73 72 33 73 N SD: 0.2370 c. M: 0.4148 c. 441: 41 108 34 75 74 34 75 N SD: 0.2704 c. M: 0.5099 c. 482: 45 118 37 82 81 37 82 N SD: 0.1739 c. M:-0.3019 c. 494: 46 121 38 84 83 38 84 N SD: 0.1413 c. M: 0.2676 c. 547: 51 134 42 93 92 42 93 N SD: 0.0822 c. M:-0.1517 c. 559: 52 137 43 95 94 43 95 N SD: 0.0892 c. M: 0.1546 c. 612: 57 150 47 104 103 47 104 N SD: 0.0155 c. M:-0.0334 c. 2395: 223 587 184 407 403 184 407 N SD: 0.0149 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 x 7:8 S SD: 8.3876 cents 5 x 6:7 x 8:9:10 S SD: 30.9052 cents 6 x x 8:9:10:11:12 S SD: 11.3496 cents 7:8:9 x 11:12 x 14 SD: 29.9734 cents 8:9:10:11:12:13:14:16 S SD: 18.3381 cents 9:10:11:12:14:15:16:18 S SD: 16.1361 cents 10:11 x 13:15:17:18:20 SD: 12.2912 cents 12:13:15:16:18:20:21:24 SD: 6.7437 cents 16:17:20:21:24:27:28:32 SD: 6.2576 cents 18:19:23:24:27:30:32:36 SD: 4.6360 cents 26:28:33:35:39:44:46:52 SD: 3.8151 cents 30:32:38:40:45:51:53:60 SD: 2.6581 cents 42:45:53:56:63:71:75:84 SD: 1.7720 cents 58:62:73:77:87:98:103:116 SD: 1.7451 cents 60:64:76:80:90:101:107:120 SD: 0.9689 cents 76:81:96:101:114:128:135:152 SD: 0.9109 cents 90:96:114:120:135:152:160:180 SD: 0.6825 cents 102:109:129:136:153:172:181:204 SD: 0.6581 cents 136:145:172:181:204:229:242:272 SD: 0.5910 cents 152:162:192:203:228:256:270:304 SD: 0.5751 cents 162:173:205:216:243:273:288:324 SD: 0.3792 cents 238:254:301:317:357:401:423:476 SD: 0.3313 cents 242:258:306:323:363:408:430:484 SD: 0.3213 cents 258:275:326:344:387:435:459:516 SD: 0.2902 cents 270:288:341:360:405:455:480:540 SD: 0.2491 cents 318:339:402:424:477:536:565:636 SD: 0.2067 cents 360:384:455:480:540:607:640:720 SD: 0.0967 cents