Scala analysis: xen09-wilson-marwa-11a-07
Marwa permutation 7 from Figure 11a, 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: 4096/3645 201.956281 narrow diminished third 2: 512/405 405.866283 narrow diminished fourth 3: 4/3 498.044999 perfect fourth 4: 128/81 792.179997 Pythagorean minor sixth 5: 2048/1215 903.911282 narrow diminished seventh 6: 256/135 1107.821284 octave - major chroma 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 135/128 92.1787 major chroma, major limma 1: 4096/3645 201.9563 narrow diminished third 2: 9/8 203.9100 major whole tone 3: 135/128 92.1787 major chroma, major limma 4: 32/27 294.1350 Pythagorean minor third 5: 16/15 111.7313 minor diatonic semitone 6: 9/8 203.9100 major whole tone 7: 135/128 92.1787 major chroma, major limma
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 : 202.0 405.9 498.0 792.2 903.9 1107.8 1200.0 202.0 : 203.9 296.1 590.2 702.0 905.9 998.0 1200.0 405.9 : 92.2 386.3 498.0 702.0 794.1 996.1 1200.0 498.0 : 294.1 405.9 609.8 702.0 903.9 1107.8 1200.0 792.2 : 111.7 315.6 407.8 609.8 813.7 905.9 1200.0 903.9 : 203.9 296.1 498.0 702.0 794.1 1088.3 1200.0 1107.8: 92.2 294.1 498.0 590.2 884.4 996.1 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 : 180.30734 cents, oct.: 1262.15140 cents Scale is not proper Step pattern alph. order: ABCDEBC Step pattern size order : CDAEBDA 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 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 Formal octave complements present : 1 = 14.2857% 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 : 3645 (O: 3645 U: 3645) Highest odd numerator or denominator: 3645 Scale harmonicity : 0.029070 Average absolute harmonicity : 0.202214 Specific harmonicity : 0.138010 Fundamental : 1/3645, -11.8317 octaves, 0.0718 Hz. Guide tone : 4096, 12.0000 octaves, 1071618.315 Hz. Exponens Consonantiae : 1.492992E+07, 23.83170 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 6265.5, average 895.07143 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 13.76967, average 1.96710 Sum of Tenney's harmonic distance : 28.82117, average 4.11731 Vogel's harmonic complexity : 17.42857 Wille's k value : 1822 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 7 Triangular lattice diameter : 7 Lattice compactness : 176.48264, average 6.30295 Lattice compactness (without 2's) : 80.61930, average 2.87926 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 1 .. 12 7.14286 50 1 3: -6 .. 0 -3.28571 23 2 5: -1 .. 0 -0.57143 4 4 Average exponent except 2's :-27 / 7 =-3.85714 Average absolute exponent except 2's: 27 / 7 = 3.85714
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 59.7239 c. M: 106.4657 c. Lebeng 8: 1 1 1 2 1 1 1 P M ME I SD: 55.2309 c. M: 105.8663 c. 9: 2 1 1 2 1 1 1 P M ME S SD: 33.9908 c. M:-64.7104 c. 11: 2 2 1 2 1 2 1 P M ME S SD: 28.0668 c. M:-47.4095 c. 12: 2 2 1 3 1 2 1 P D3 SD: 5.0665 c. M: 7.8213 c. Ionian Augmented, Ionian sharp 5 41: 7 7 3 10 4 7 3 N SD: 2.8879 c. M:-4.3738 c. 53: 9 9 4 13 5 9 4 N SD: 1.3020 c. M:-1.8173 c. 65: 11 11 5 16 6 11 5 N SD: 0.8281 c. M:-1.6662 c. 118: 20 20 9 29 11 20 9 N SD: 0.9136 c. M:-1.4335 c. 183: 31 31 14 45 17 31 14 N SD: 0.8514 c. M:-1.3224 c. 248: 42 42 19 61 23 42 19 N SD: 0.8335 c. M:-1.3684 c. 301: 51 51 23 74 28 51 23 N SD: 0.8721 c. M:-1.3660 c. 304: 51 52 23 75 28 52 23 N SD: 0.8322 c. M:-1.3892 c. 308: 52 52 24 75 29 52 24 N SD: 0.8169 c. M: 1.3278 c. 311: 52 53 24 76 29 53 24 N SD: 0.8408 c. M: 1.3132 c. 313: 53 53 24 77 29 53 24 N SD: 0.8268 c. M:-1.4302 c. 316: 53 54 24 78 29 54 24 N SD: 0.7874 c. M:-1.4909 c. 323: 54 55 25 79 30 55 25 N SD: 0.8571 c. M: 1.3371 c. 327: 55 56 25 80 30 56 25 N SD: 0.8473 c. M:-1.4732 c. 328: 55 56 25 81 30 56 25 N SD: 0.7904 c. M:-1.7224 c. 339: 57 58 26 83 31 58 26 N SD: 0.8280 c. M: 1.2564 c. 340: 57 58 26 83 32 58 26 N SD: 0.7189 c. M: 1.5918 c. 349: 59 59 27 85 33 59 27 N SD: 0.7091 c. M: 1.3491 c. 352: 59 60 27 86 33 60 27 N SD: 0.6202 c. M: 1.2709 c. 361: 61 61 28 88 34 61 28 N SD: 0.6597 c. M: 1.0443 c. 364: 61 62 28 89 34 62 28 N SD: 0.5694 c. M: 0.9712 c. 376: 63 64 29 92 35 64 29 N SD: 0.5683 c. M: 0.8925 c. 405: 68 69 31 99 38 69 31 N SD: 0.4770 c. M: 1.0689 c. 417: 70 71 32 102 39 71 32 N SD: 0.3946 c. M: 0.8131 c. 429: 72 73 33 105 40 73 33 N SD: 0.3627 c. M: 0.5716 c. 441: 74 75 34 108 41 75 34 N SD: 0.3844 c. M: 0.5957 c. 470: 79 80 36 115 44 80 36 N SD: 0.3061 c. M: 0.6906 c. 482: 81 82 37 118 45 82 37 N SD: 0.2299 c. M: 0.4788 c. 494: 83 84 38 121 46 84 38 N SD: 0.2147 c. M: 0.3368 c. 535: 90 91 41 131 50 91 41 N SD: 0.1857 c. M: 0.4043 c. 547: 92 93 42 134 51 93 42 N SD: 0.1047 c. M: 0.2239 c. 559: 94 95 43 137 52 95 43 N SD: 0.1143 c. M: 0.1674 c. 612: 103 104 47 150 57 104 47 N SD: 0.0143 c. M: 0.0231 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: 45.1125 cents 3 x x 4 x 5 x 6 S SD: 6.5175 cents 4 x 5 x 6:7 x 8 S SD: 28.2143 cents 5 x 6:7:8 x 9:10 S SD: 30.9052 cents 6:7 x 8:9:10:11:12 S SD: 21.1832 cents 7:8:9 x 11:12:13:14 SD: 10.4875 cents 8:9:10:11:13 x 15:16 SD: 12.8495 cents 9:10:11:12:14:15:17:18 SD: 10.0724 cents 10:11 x 13:16:17:19:20 SD: 10.5113 cents 12:13:15:16:19:20:23:24 SD: 10.2377 cents 14:16:18:19:22:24:27:28 SD: 9.5271 cents 15:17:19:20:24:25:28:30 SD: 6.0887 cents 19:21:24:25:30:32:36:38 SD: 5.2624 cents 22:25:28:29:35:37:42:44 SD: 4.9233 cents 23:26:29:31:36:39:44:46 SD: 4.7134 cents 26:29:33:35:41:44:49:52 SD: 3.6795 cents 31:35:39:41:49:52:59:62 SD: 3.0127 cents 38:43:48:51:60:64:72:76 SD: 2.3996 cents 41:46:52:55:65:69:78:82 SD: 2.1183 cents 48:54:61:64:76:81:91:96 SD: 1.4383 cents 57:64:72:76:90:96:108:114 SD: 0.4550 cents 162:182:205:216:256:273:307:324 SD: 0.3025 cents 219:246:277:292:346:369:415:438 SD: 0.2594 cents 300:337:379:400:474:506:569:600 SD: 0.2544 cents 315:354:398:420:498:531:597:630 SD: 0.2256 cents 348:391:440:464:550:587:660:696 SD: 0.1868 cents 405:455:512:540:640:683:768:810 SD: 0.1350 cents 462:519:584:616:730:779:876:924 SD: 0.1204 cents 534:600:675:712:844:900:1013:1068 SD: 0.1143 cents 591:664:747:788:934:996:1121:1182 SD: 0.1047 cents 598:672:756:797:945:1008:1134:1196 SD: 0.1037 cents