Scala analysis: xen09-wilson-marwa-09-05
Marwa permutation 5 from Figure 9, Hawkins 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: 9/8 203.910002 major whole tone 2: 1215/1024 296.088718 wide augmented second 3: 45/32 590.223716 diatonic tritone 4: 3/2 701.955001 perfect fifth 5: 27/16 905.865003 Pythagorean major sixth 6: 15/8 1088.268715 classic major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 9/8 203.9100 major whole tone 2: 135/128 92.1787 major chroma, major limma 3: 32/27 294.1350 Pythagorean minor third 4: 16/15 111.7313 minor diatonic semitone 5: 9/8 203.9100 major whole tone 6: 10/9 182.4037 minor whole tone 7: 16/15 111.7313 minor diatonic semitone
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 : 203.9 296.1 590.2 702.0 905.9 1088.3 1200.0 203.9 : 92.2 386.3 498.0 702.0 884.4 996.1 1200.0 296.1 : 294.1 405.9 609.8 792.2 903.9 1107.8 1200.0 590.2 : 111.7 315.6 498.0 609.8 813.7 905.9 1200.0 702.0 : 203.9 386.3 498.0 702.0 794.1 1088.3 1200.0 905.9 : 182.4 294.1 498.0 590.2 884.4 996.1 1200.0 1088.3: 111.7 315.6 407.8 702.0 813.7 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 : 177.38226 cents, oct.: 1241.67579 cents Scale is not proper Step pattern alph. order: ABCDAED Step pattern size order : DAEBDCB Scale is sum-free (all different intervals) 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 Best fifths form a closed circle Length of longest harmonic part : 2 at degree 4 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 14.2857% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 5 Odd number limit : 1215 (O: 1215 U: 1215) Highest odd numerator or denominator: 1215 Scale harmonicity : 0.032538 Average absolute harmonicity : 0.236046 Specific harmonicity : 0.182336 Fundamental : 1/1024, -10.0000 octaves, 0.2555 Hz. Guide tone : 2430, 11.2467 octaves, 635750.124 Hz. Exponens Consonantiae : 2.488320E+06, 21.24674 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 1203.5, average 171.92857 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 : 16.90442, average 2.41492 Vogel's harmonic complexity : 14.57143 Wille's k value : 607 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 6 Triangular lattice diameter : 6 Lattice compactness : 128.02727, average 4.57240 Lattice compactness (without 2's) : 59.49876, average 2.12496 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -10 .. 1 -3.57143 27 1 3: 0 .. 5 2.00000 14 3 5: 0 .. 1 0.42857 3 3 Average exponent except 2's : 17 / 7 = 2.42857 Average absolute exponent except 2's: 17 / 7 = 2.42857
FIT/MODE
7: 1 0 2 1 1 1 1 N T3 SD: 63.8784 c. M: 124.6601 c. 8: 1 1 2 1 1 1 1 P M ME S SD: 31.2236 c. M: 53.9100 c. 10: 2 1 2 1 2 1 1 P M ME S SD: 35.4709 c. M:-63.9113 c. 11: 2 1 2 1 2 2 1 P M ME S SD: 30.5501 c. M: 47.4095 c. 12: 2 1 3 1 2 2 1 P D3 SD: 6.5684 c. M:-11.7313 c. Lydian Diminished, Mela Dharmavati, Raga Ambika, Arunajualita, Dumyaraga, Madhuvanti 41: 7 3 10 4 7 6 4 N SD: 3.0941 c. M: 5.3419 c. 53: 9 4 13 5 9 8 5 N SD: 1.0481 c. M: 1.7491 c. 65: 11 5 16 6 11 10 6 N SD: 0.7698 c. M: 1.2496 c. 118: 20 9 29 11 20 18 11 N SD: 0.5972 c. M: 1.1735 c. 183: 31 14 45 17 31 28 17 N SD: 0.5949 c. M: 1.0068 c. 301: 51 23 74 28 51 46 28 N SD: 0.5862 c. M: 1.0721 c. 311: 53 24 76 29 53 47 29 N SD: 0.5738 c. M:-1.0174 c. 323: 55 25 79 30 55 49 30 N SD: 0.5619 c. M:-1.1249 c. 352: 60 27 86 33 60 53 33 N SD: 0.5928 c. M:-0.9532 c. 364: 62 28 89 34 62 55 34 N SD: 0.4380 c. M:-0.7284 c. 376: 64 29 92 35 64 57 35 N SD: 0.3736 c. M:-0.7198 c. 417: 71 32 102 39 71 63 39 N SD: 0.3805 c. M:-0.6098 c. 429: 73 33 105 40 73 65 40 N SD: 0.2626 c. M:-0.4287 c. 441: 75 34 108 41 75 67 41 N SD: 0.2548 c. M:-0.5099 c. 482: 82 37 118 45 82 73 45 N SD: 0.2256 c. M:-0.3591 c. 494: 84 38 121 46 84 75 46 N SD: 0.1427 c. M:-0.2676 c. 547: 93 42 134 51 93 83 51 N SD: 0.1077 c. M:-0.1679 c. 559: 95 43 137 52 95 85 52 N SD: 0.0848 c. M:-0.1546 c. 612: 104 47 150 57 104 93 57 N SD: 0.0187 c. M: 0.0334 c. 1783: 303 137 437 166 303 271 166 N SD: 0.0207 c. M:-0.0414 c. 1901: 323 146 466 177 323 289 177 N SD: 0.0180 c. M: 0.0340 c. 2395: 407 184 587 223 407 364 223 N SD: 0.0151 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: 31.5514 cents 4 x 5 x 6:7 x 8 S SD: 27.5053 cents 5 x 6:7 x 8:9:10 S SD: 23.6079 cents 6 x 7:8:9:10:11:12 S SD: 17.7379 cents 7:8 x 10:11:12:13:14 S SD: 15.8032 cents 9:10:11:13:14:15:17:18 SD: 14.1698 cents 10:11:12:14:15:17:19:20 SD: 7.3464 cents 12 x 14:17:18:20:23:24 SD: 9.0174 cents 13:15 x 18:20:22:24:26 SD: 12.1421 cents 14:16:17:20:21:24:26:28 SD: 9.1559 cents 15:17:18:21:23:25:28:30 SD: 7.2490 cents 16:18:19:23:24:27:30:32 SD: 5.4396 cents 22:25:26:31:33:37:41:44 SD: 3.2171 cents 32:36:38:45:48:54:60:64 SD: 0.2035 cents 440:495:522:619:660:743:825:880 SD: 0.1970 cents 456:513:541:641:684:770:855:912 SD: 0.1890 cents 472:531:560:664:708:797:885:944 SD: 0.1818 cents 488:549:579:686:732:824:915:976 SD: 0.1754 cents 504:567:598:709:756:851:945:1008 SD: 0.1695 cents 520:585:617:731:780:878:975:1040 SD: 0.1643 cents 536:603:636:754:804:905:1005:1072 SD: 0.1597 cents 552:621:655:776:828:932:1035:1104 SD: 0.1555 cents 568:639:674:799:852:959:1065:1136 SD: 0.1518 cents 584:657:693:821:876:986:1095:1168 SD: 0.1484 cents 600:675:712:844:900:1013:1125:1200 SD: 0.1455 cents