Scala analysis: xen09-wilson-marwa-09-01
Marwa permutation 1 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: 81/64 407.820003 Pythagorean major third 3: 45/32 590.223716 diatonic tritone 4: 3/2 701.955001 perfect fifth 5: 27/16 905.865003 Pythagorean major sixth 6: 3645/2048 998.043719 wide augmented sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 4096/3645 201.9563 narrow diminished third 1: 9/8 203.9100 major whole tone 2: 9/8 203.9100 major whole tone 3: 10/9 182.4037 minor whole tone 4: 16/15 111.7313 minor diatonic semitone 5: 9/8 203.9100 major whole tone 6: 135/128 92.1787 major chroma, major limma 7: 4096/3645 201.9563 narrow diminished third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 135/128 92.179 cents major chroma, major limma 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 10/9 182.404 cents minor whole tone 1: 1 4096/3645 201.956 cents narrow diminished third 1: 3 9/8 203.910 cents major whole tone 2: 2 32/27 294.135 cents Pythagorean minor third 2: 1 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: 1 512/405 405.866 cents narrow diminished fourth 2: 1 81/64 407.820 cents Pythagorean major third 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: 1 128/81 792.180 cents Pythagorean minor sixth 5: 1 405/256 794.134 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: 1 2048/1215 903.911 cents narrow diminished seventh 5: 2 27/16 905.865 cents Pythagorean major sixth 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 1 3645/2048 998.044 cents wide augmented sixth 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 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: 6 Average number of different intervals per interval class: 5.00000 = 5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 407.8 590.2 702.0 905.9 998.0 1200.0 203.9 : 203.9 386.3 498.0 702.0 794.1 996.1 1200.0 407.8 : 182.4 294.1 498.0 590.2 792.2 996.1 1200.0 590.2 : 111.7 315.6 407.8 609.8 813.7 1017.6 1200.0 702.0 : 203.9 296.1 498.0 702.0 905.9 1088.3 1200.0 905.9 : 92.2 294.1 498.0 702.0 884.4 996.1 1200.0 998.0 : 202.0 405.9 609.8 792.2 903.9 1107.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 92.1787 .. 203.9100 cents 16/15, 111.7313 cents 135/128, 92.1787 cents 2: 294.1350 .. 407.8200 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 3: 407.8200 .. 609.7763 cents 4096/3645, 201.9563 cents 1/1, 0.0000 cents 4: 590.2237 .. 792.1800 cents 4096/3645, 201.9563 cents 2025/2048,-19.5526 cents 5: 792.1800 .. 905.8650 cents 2187/2048, 113.6850 cents 1/1, 0.0000 cents 6: 996.0900 .. 1107.8213 cents 16/15, 111.7313 cents 256/243, 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 : 9/8, 203.9100 cents Average / Smallest step : 1.859741 Largest / Average step : 1.189475 Largest / Smallest step : 2.212116 Median interval of one step : 4096/3645, 201.9563 cents, amount: 1 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 175.11163 cents, oct.: 1225.78142 cents Scale is not proper Step pattern alph. order: AABCADE Step pattern size order : EECBEAD Scale is not a Constant Structure Scale diversity : 1.424875 Lumma stability : 0.304006 Lumma impropriety factor : 0.016294 Rothenberg efficiency : 0.410884 redundancy: 0.589116 Efficiency x scale size : 2.876190 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 5.00000 = 5 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: 3 Number of recognisable fifths : 4, average 701.9550 cents Best minor thirds form a closed circle Length of longest harmonic part : 2 at degree 1 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 14.2857% Limited inverse transpositions with margin 182.4037 cents: 2 -- Rational properties -- Prime limit : 5 Odd number limit : 3645 (O: 3645 U: 3645) Highest odd numerator or denominator: 3645 Scale harmonicity : 0.029070 Average absolute harmonicity : 0.232251 Specific harmonicity : 0.166176 Fundamental : 1/2048, -11.0000 octaves, 0.1277 Hz. Guide tone : 7290, 12.8317 octaves, 1907250.371 Hz. Exponens Consonantiae : 1.492992E+07, 23.83170 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 2991.5, average 427.35714 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.98612, average 1.42659 Sum of Tenney's harmonic distance : 19.31805, average 2.75972 Vogel's harmonic complexity : 16.00000 Wille's k value : 1822 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 7 Triangular lattice diameter : 7 Lattice compactness : 146.91916, average 5.24711 Lattice compactness (without 2's) : 71.32263, average 2.54724 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -11 .. 1 -4.14286 31 1 3: 0 .. 6 2.57143 18 4 5: 0 .. 1 0.28571 2 2 Average exponent except 2's : 20 / 7 = 2.85714 Average absolute exponent except 2's: 20 / 7 = 2.85714
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 45.6874 c. M: 75.9380 c. Lebeng 8: 1 2 1 1 1 1 1 P M ME S SD: 37.4608 c. M: 53.9100 c. 10: 2 1 2 1 2 0 2 N T3 SD: 34.6170 c. M:-54.1350 c. 11: 2 2 1 1 2 1 2 N D3 SD: 30.7797 c. M: 47.4095 c. 12: 2 2 2 1 2 1 2 P D3 S SD: 5.5300 c. M:-9.7763 c. Lydian Dominant, Mela Vacaspati, Raga Bhusavati, Bhusavali, Vachaspati, Overtone, Lydian-Mixolydian, Bartok 29: 5 5 4 3 5 2 5 N SD: 5.4825 c. M: 10.9134 c. 41: 7 7 6 4 7 3 7 N SD: 2.3653 c. M: 4.8579 c. 53: 9 9 8 5 9 4 9 N SD: 0.9124 c. M: 1.8173 c. 65: 11 11 10 6 11 5 11 N SD: 0.9826 c. M: 1.6662 c. 118: 20 20 18 11 20 9 20 N SD: 0.7782 c. M: 1.4335 c. 171: 29 29 26 16 29 13 29 N SD: 0.7728 c. M: 1.5525 c. 183: 31 31 28 17 31 14 31 N SD: 0.8230 c. M: 1.3224 c. 224: 38 38 34 21 38 17 38 N SD: 0.7882 c. M: 1.6151 c. 289: 49 49 44 27 49 22 49 N SD: 0.7695 c. M: 1.5039 c. 311: 53 53 47 29 53 24 52 N SD: 0.7898 c. M:-1.3132 c. 323: 55 55 49 30 55 25 54 N SD: 0.6946 c. M:-1.3371 c. 335: 57 57 51 31 57 26 56 N SD: 0.6617 c. M:-1.3593 c. 351: 60 59 54 32 60 27 59 N SD: 0.8657 c. M:-1.2293 c. 352: 60 60 53 33 60 27 59 N SD: 0.7468 c. M:-1.2709 c. 364: 62 62 55 34 62 28 61 N SD: 0.5996 c. M:-0.9712 c. 376: 64 64 57 35 64 29 63 N SD: 0.4974 c. M:-0.8925 c. 388: 66 66 59 36 66 30 65 N SD: 0.4546 c. M:-0.9254 c. 417: 71 71 63 39 71 32 70 N SD: 0.4773 c. M:-0.8131 c. 429: 73 73 65 40 73 33 72 N SD: 0.3633 c. M:-0.5716 c. 441: 75 75 67 41 75 34 74 N SD: 0.3023 c. M:-0.5957 c. 482: 82 82 73 45 82 37 81 N SD: 0.2805 c. M:-0.4788 c. 494: 84 84 75 46 84 38 83 N SD: 0.1931 c. M:-0.3368 c. 506: 86 86 77 47 86 39 85 N SD: 0.1846 c. M:-0.3753 c. 547: 93 93 83 51 93 42 92 N SD: 0.1307 c. M:-0.2239 c. 559: 95 95 85 52 95 43 94 N SD: 0.0814 c. M:-0.1674 c. 612: 104 104 93 57 104 47 103 N SD: 0.0160 c. M: 0.0276 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 4 x x 5 x 6 S SD: 30.9176 cents 4 x 5 x 6 x 7:8 S SD: 9.0699 cents 5 x 6:7 x 8:9:10 S SD: 26.4088 cents 6:7:8 x 9:10:11:12 S SD: 20.5486 cents 7:8:9:10:11:12 x 14 S SD: 16.2100 cents 8:9:10:11:12 x 14:16 S SD: 8.8661 cents 14:16:18:20:21:24:25:28 SD: 7.8330 cents 15:17:19:21:23:25:27:30 SD: 7.1677 cents 18:20:23:25:27:30:32:36 SD: 5.8294 cents 22:25:28:31:33:37:39:44 SD: 3.1630 cents 32:36:41:45:48:54:57:64 SD: 3.0414 cents 38:43:48:53:57:64:68:76 SD: 2.9124 cents 40:45:51:56:60:68:71:80 SD: 2.8844 cents 41:46:52:58:62:69:73:82 SD: 2.7117 cents 42:47:53:59:63:71:75:84 SD: 1.7851 cents 54:61:68:76:81:91:96:108 SD: 1.6797 cents 64:72:81:90:96:108:114:128 SD: 0.2035 cents 384:432:486:540:576:648:683:768 SD: 0.1584 cents 448:504:567:630:672:756:797:896 SD: 0.1066 cents 512:576:648:720:768:864:911:1024 SD: 0.0679 cents 576:648:729:810:864:972:1025:1152 SD: 0.0377 cents