Scala analysis: xen10-wilson-purvi-09a-02
Purvi modulation 2 from Figure 9a, Hawkins (135/128 16/15 32/27), (32/27 135/128 16/15)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 1215/1024 296.088718 wide augmented second 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 405/256 794.133717 wide augmented fifth 6: 27/16 905.865003 Pythagorean major sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 32/27 294.1350 Pythagorean minor third 1: 9/8 203.9100 major whole tone 2: 135/128 92.1787 major chroma, major limma 3: 4096/3645 201.9563 narrow diminished third 4: 9/8 203.9100 major whole tone 5: 135/128 92.1787 major chroma, major limma 6: 16/15 111.7313 minor diatonic semitone 7: 32/27 294.1350 Pythagorean minor third
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: 1 32/27 294.135 cents Pythagorean minor third 2: 2 1215/1024 296.089 cents wide augmented second 2: 2 512/405 405.866 cents narrow diminished fourth 2: 1 4/3 498.045 cents perfect 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 3/2 701.955 cents perfect fifth 5: 2 405/256 794.134 cents wide augmented fifth 5: 2 2048/1215 903.911 cents narrow diminished seventh 5: 1 27/16 905.865 cents Pythagorean major sixth 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: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 296.1 498.0 702.0 794.1 905.9 1200.0 203.9 : 92.2 294.1 498.0 590.2 702.0 996.1 1200.0 296.1 : 202.0 405.9 498.0 609.8 903.9 1107.8 1200.0 498.0 : 203.9 296.1 407.8 702.0 905.9 998.0 1200.0 702.0 : 92.2 203.9 498.0 702.0 794.1 996.1 1200.0 794.1 : 111.7 405.9 609.8 702.0 903.9 1107.8 1200.0 905.9 : 294.1 498.0 590.2 792.2 996.1 1088.3 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 .. 498.0450 cents 32/27, 294.1350 cents 243/256,-90.2250 cents 3: 407.8200 .. 609.7763 cents 4096/3645, 201.9563 cents 243/256,-90.2250 cents 4: 590.2237 .. 792.1800 cents 4096/3645, 201.9563 cents 2025/2048,-19.5526 cents 5: 701.9550 .. 996.0900 cents 32/27, 294.1350 cents 243/256,-90.2250 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 : 163.59929 cents, oct.: 1145.19505 cents Scale is not proper Step pattern alph. order: ABCABDE Step pattern size order : DACDABE Scale is not a Constant Structure Scale diversity : 1.330644 Lumma stability : 0.153631 Lumma impropriety factor : 0.317044 Rothenberg efficiency : 0.540136 redundancy: 0.459864 Efficiency x scale size : 3.780952 Number of different interval sizes : 20 = 3.33333 / 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: 5 Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 5, 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 : 0.251981 Specific harmonicity : 0.155415 Fundamental : 1/3072, -11.5850 octaves, 0.0852 Hz. Guide tone : 4860, 12.2467 octaves, 1271500.247 Hz. Exponens Consonantiae : 1.492992E+07, 23.83170 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 1487.5, average 212.50000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.03188, average 1.29027 Sum of Tenney's harmonic distance : 17.76175, average 2.53739 Vogel's harmonic complexity : 17.14286 Wille's k value : 1822 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 7 Triangular lattice diameter : 7 Lattice compactness : 161.66090, average 5.77360 Lattice compactness (without 2's) : 73.96004, average 2.64143 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -10 .. 2 -3.28571 29 1 3: -1 .. 5 2.00000 16 4 5: 0 .. 1 0.28571 2 2 Average exponent except 2's : 16 / 7 = 2.28571 Average absolute exponent except 2's: 18 / 7 = 2.57143
FIT/MODE
7: 1 1 1 1 1 0 2 N T3 SD: 38.0110 c. M:-63.0091 c. 8: 1 1 1 2 0 1 2 N D3 SD: 36.8790 c. M: 53.9100 c. 9: 2 0 2 1 1 1 2 N T3 SD: 33.9822 c. M:-62.7567 c. 11: 2 1 2 1 1 1 3 N SD: 33.1655 c. M:-47.4095 c. 12: 2 1 2 2 1 1 3 N SD: 3.9105 c. M:-5.8663 c. Mela Jhankaradhvani, Raga Jhankara Bhramavi 41: 7 3 7 7 3 4 10 N SD: 2.0786 c. M: 3.8898 c. 53: 9 4 9 9 4 5 13 N SD: 0.9223 c. M: 1.7491 c. 65: 11 5 11 11 5 6 16 N SD: 0.6741 c. M: 1.2496 c. 118: 20 9 20 20 9 11 29 N SD: 0.6789 c. M: 1.1735 c. 183: 31 14 31 31 14 17 45 N SD: 0.6531 c. M: 1.0068 c. 248: 42 19 42 42 19 23 61 N SD: 0.6501 c. M: 1.0263 c. 311: 53 24 52 53 24 29 76 N SD: 0.6401 c. M:-1.0174 c. 323: 55 25 54 55 25 30 79 N SD: 0.6295 c. M:-1.1249 c. 340: 58 26 57 58 26 32 83 N SD: 0.6002 c. M:-1.1938 c. 352: 60 27 59 60 27 33 86 N SD: 0.5072 c. M:-0.9532 c. 364: 62 28 61 62 28 34 89 N SD: 0.4472 c. M:-0.7284 c. 376: 64 29 63 64 29 35 92 N SD: 0.4250 c. M:-0.7198 c. 405: 69 31 68 69 31 38 99 N SD: 0.3996 c. M:-0.8017 c. 417: 71 32 70 71 32 39 102 N SD: 0.3231 c. M:-0.6098 c. 429: 73 33 72 73 33 40 105 N SD: 0.2809 c. M:-0.4287 c. 441: 75 34 74 75 34 41 108 N SD: 0.2804 c. M:-0.5099 c. 470: 80 36 79 80 36 44 115 N SD: 0.2569 c. M:-0.5180 c. 482: 82 37 81 82 37 45 118 N SD: 0.1888 c. M:-0.3591 c. 494: 84 38 83 84 38 46 121 N SD: 0.1616 c. M:-0.2676 c. 535: 91 41 90 91 41 50 131 N SD: 0.1543 c. M:-0.3032 c. 547: 93 42 92 93 42 51 134 N SD: 0.0866 c. M:-0.1679 c. 559: 95 43 94 95 43 52 137 N SD: 0.0815 c. M:-0.1546 c. 600: 102 46 101 102 46 56 147 N SD: 0.0895 c. M:-0.1350 c. 612: 104 47 103 104 47 57 150 N SD: 0.0111 c. M:-0.0174 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 x 5:6 S SD: 7.1688 cents 4 x 5 x 6 x 7:8 S SD: 27.5053 cents 5 x 6:7 x 8 x 10 S SD: 22.2195 cents 6 x 7:8:9 x 10:12 S SD: 7.2559 cents 7:8 x 9 x 11:12:14 SD: 14.9483 cents 9:10:11:12 x 14:15:18 S SD: 11.0710 cents 10:11:12:13:15:16:17:20 SD: 9.4358 cents 11:12:13:15 x 17:19:22 SD: 14.5921 cents 12 x 14:16:18:19:20:24 S SD: 6.0512 cents 13:15 x 17:20:21:22:26 SD: 13.2301 cents 14:16:17:19:21:22:24:28 SD: 9.2189 cents 15:17:18:20:23:24:25:30 SD: 7.6107 cents 16:18:19:21:24:25:27:32 SD: 4.9649 cents 22:25:26:29:33:35:37:44 SD: 4.2124 cents 26:29:31:35:39:41:44:52 SD: 3.5622 cents 32:36:38:43:48:51:54:64 SD: 2.6603 cents 38:43:45:51:57:60:64:76 SD: 2.3256 cents 42:47:50:56:63:66:71:84 SD: 2.3138 cents 48:54:57:64:72:76:81:96 SD: 0.2878 cents 246:277:292:328:369:389:415:492 SD: 0.2793 cents 294:331:349:392:441:465:496:588 SD: 0.2364 cents 342:385:406:456:513:541:577:684 SD: 0.2133 cents 390:439:463:520:585:617:658:780 SD: 0.2019 cents 402:452:477:536:603:636:678:804 SD: 0.1938 cents 450:506:534:600:675:712:759:900 SD: 0.1778 cents 498:560:591:664:747:788:840:996 SD: 0.1694 cents 510:574:605:680:765:807:861:1020 SD: 0.1686 cents 546:614:648:728:819:864:921:1092 SD: 0.1660 cents 552:621:655:736:828:873:932:1104 SD: 0.1555 cents 600:675:712:800:900:949:1013:1200 SD: 0.1380 cents