Scala analysis: xen09-wilson-marwa-09-11
Marwa permutation 11 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: 4/3 498.044999 perfect fourth 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: 4096/3645 201.9563 narrow diminished third 4: 9/8 203.9100 major whole tone 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: 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 : 203.9 296.1 498.0 702.0 905.9 1088.3 1200.0 203.9 : 92.2 294.1 498.0 702.0 884.4 996.1 1200.0 296.1 : 202.0 405.9 609.8 792.2 903.9 1107.8 1200.0 498.0 : 203.9 407.8 590.2 702.0 905.9 998.0 1200.0 702.0 : 203.9 386.3 498.0 702.0 794.1 996.1 1200.0 905.9 : 182.4 294.1 498.0 590.2 792.2 996.1 1200.0 1088.3: 111.7 315.6 407.8 609.8 813.7 1017.6 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 : 175.40700 cents, oct.: 1227.84899 cents Scale is not proper Step pattern alph. order: ABCAADE Step pattern size order : EADEECB 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 Scale contains a complete diamond : 1 3 Length of longest harmonic part : 2 at degree 4 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% Limited inverse transpositions with margin 113.6850 cents: 1 -- 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 : 0.258121 Specific harmonicity : 0.175438 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 : 1168.5, average 166.92857 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.60052, average 1.08579 Sum of Tenney's harmonic distance : 14.82524, average 2.11789 Vogel's harmonic complexity : 16.57143 Wille's k value : 1822 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 7 Triangular lattice diameter : 7 Lattice compactness : 139.09788, average 4.96778 Lattice compactness (without 2's) : 66.51703, average 2.37561 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -10 .. 2 -2.57143 24 1 3: -1 .. 5 1.57143 13 4 5: 0 .. 1 0.28571 2 2 Average exponent except 2's : 13 / 7 = 1.85714 Average absolute exponent except 2's: 15 / 7 = 2.14286
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 37.2395 c. M: 59.6973 c. Lebeng 8: 1 1 1 2 1 1 1 P M ME I SD: 35.9307 c. M: 53.9100 c. 9: 2 0 2 1 2 1 1 N D3 SD: 34.8789 c. M:-62.7567 c. 10: 2 0 2 2 2 1 1 N SD: 34.0140 c. M: 56.0887 c. 11: 2 1 2 1 2 2 1 P M ME S SD: 31.1139 c. M:-47.4095 c. 12: 2 1 2 2 2 2 1 P D3 S SD: 5.4805 c. M:-11.7313 c. Melodic Minor ascending, Jazz Minor, Minor-Major, Mela Gaurimanohari, Raga Kedar Bahar, Patdip (Patadeep), Velavali, Deshi(2), Mischung 1, Hawaiian 41: 7 3 7 7 7 6 4 N SD: 2.4971 c. M: 5.3419 c. 53: 9 4 9 9 9 8 5 N SD: 0.8708 c. M: 1.7491 c. 65: 11 5 11 11 11 10 6 N SD: 0.7582 c. M: 1.2496 c. 118: 20 9 20 20 20 18 11 N SD: 0.5867 c. M: 1.1735 c. 183: 31 14 31 31 31 28 17 N SD: 0.6063 c. M: 1.0068 c. 289: 49 22 49 49 49 44 27 N SD: 0.6022 c. M: 1.2790 c. 301: 51 23 51 51 51 46 28 N SD: 0.5923 c. M: 1.0721 c. 311: 53 24 52 53 53 47 29 N SD: 0.5825 c. M:-1.0174 c. 323: 55 25 54 55 55 49 30 N SD: 0.5368 c. M:-1.1249 c. 352: 60 27 59 60 60 53 33 N SD: 0.5803 c. M:-0.9532 c. 364: 62 28 61 62 62 55 34 N SD: 0.4455 c. M:-0.7284 c. 376: 64 29 63 64 64 57 35 N SD: 0.3715 c. M:-0.7198 c. 388: 66 30 65 66 66 59 36 N SD: 0.3769 c. M:-0.8185 c. 417: 71 32 70 71 71 63 39 N SD: 0.3718 c. M:-0.6098 c. 429: 73 33 72 73 73 65 40 N SD: 0.2680 c. M:-0.4287 c. 441: 75 34 74 75 75 67 41 N SD: 0.2385 c. M:-0.5099 c. 482: 82 37 81 82 82 73 45 N SD: 0.2195 c. M:-0.3591 c. 494: 84 38 83 84 84 75 46 N SD: 0.1433 c. M:-0.2676 c. 547: 93 42 92 93 93 83 51 N SD: 0.1037 c. M:-0.1679 c. 559: 95 43 94 95 95 85 52 N SD: 0.0727 c. M:-0.1546 c. 612: 104 47 103 104 104 93 57 N SD: 0.0157 c. M: 0.0334 c. 1901: 323 146 320 323 323 289 177 N SD: 0.0181 c. M: 0.0340 c. 2395: 407 184 403 407 407 364 223 N SD: 0.0152 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: 7.1688 cents 4 x 5 x 6:7 x 8 S SD: 27.5053 cents 5 x 6:7 x 8:9:10 S SD: 28.9886 cents 6 x 7:8:9:10:11:12 S SD: 8.8661 cents 7:8 x 9:11:12:13:14 SD: 18.4175 cents 8:9:10:11:12:14:15:16 S SD: 17.4629 cents 9:10:11:12:14:15:17:18 SD: 12.5243 cents 10:11:12:13:15:17:19:20 SD: 9.5897 cents 12 x 14:16:18:20:23:24 SD: 8.7624 cents 13:15 x 17:20:22:24:26 SD: 12.6020 cents 14:16:17:19:21:24:26:28 SD: 9.3714 cents 15:17:18:20:23:25:28:30 SD: 7.1648 cents 16:18:19:21:24:27:30:32 SD: 3.9002 cents 26:29:31:35:39:44:49:52 SD: 3.6946 cents 32:36:38:43:48:54:60:64 SD: 1.9354 cents 42:47:50:56:63:71:79:84 SD: 1.7895 cents 48:54:57:64:72:81:90:96 SD: 0.2035 cents 408:459:484:544:612:689:765:816 SD: 0.1869 cents 456:513:541:608:684:770:855:912 SD: 0.1626 cents 504:567:598:672:756:851:945:1008 SD: 0.1454 cents 552:621:655:736:828:932:1035:1104 SD: 0.1335 cents 600:675:712:800:900:1013:1125:1200 SD: 0.1257 cents