Scala analysis: xen09-wilson-marwa-09-19
Marwa permutation 19 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: 135/128 92.178716 major chroma, major limma 2: 5/4 386.313714 major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 5/3 884.358713 major sixth, BP sixth 6: 16/9 996.089998 Pythagorean minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 135/128 92.1787 major chroma, major limma 2: 32/27 294.1350 Pythagorean minor third 3: 16/15 111.7313 minor diatonic semitone 4: 9/8 203.9100 major whole tone 5: 10/9 182.4037 minor whole tone 6: 16/15 111.7313 minor diatonic semitone 7: 9/8 203.9100 major whole tone
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 : 92.2 386.3 498.0 702.0 884.4 996.1 1200.0 92.2 : 294.1 405.9 609.8 792.2 903.9 1107.8 1200.0 386.3 : 111.7 315.6 498.0 609.8 813.7 905.9 1200.0 498.0 : 203.9 386.3 498.0 702.0 794.1 1088.3 1200.0 702.0 : 182.4 294.1 498.0 590.2 884.4 996.1 1200.0 884.4 : 111.7 315.6 407.8 702.0 813.7 1017.6 1200.0 996.1 : 203.9 296.1 590.2 702.0 905.9 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: 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 : 171.17925 cents, oct.: 1198.25473 cents Scale is not proper Step pattern alph. order: ABCDECD Step pattern size order : AEBDCBD 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 Scale contains a complete diamond : 1 3 Length of longest harmonic part : 2 at degree 3 Formal octave complements present : 3 = 42.8571% 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: 135 Scale harmonicity : 0.032538 Average absolute harmonicity : 0.267175 Specific harmonicity : 0.195718 Fundamental : 1/1152, -10.1699 octaves, 0.2271 Hz. Guide tone : 2160, 11.0768 octaves, 565111.221 Hz. Exponens Consonantiae : 2.488320E+06, 21.24674 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 160.0, average 22.85714 Mersenne's string divisions : 3313800 Sum of van Prooijen's expressibility: 5.43676, average 0.77668 Sum of Tenney's harmonic distance : 11.03139, average 1.57591 Vogel's harmonic complexity : 14.71429 Wille's k value : 607 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 6 Triangular lattice diameter : 6 Lattice compactness : 118.74117, average 4.24076 Lattice compactness (without 2's) : 54.32595, average 1.94021 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -7 .. 4 -0.42857 17 1 3: -2 .. 3 0.00000 8 3 5: 0 .. 1 0.42857 3 3 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 11 / 7 = 1.57143
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 38.7156 c. M:-79.2499 c. Lebeng 10: 1 2 1 2 1 1 2 P M ME S SD: 27.7434 c. M: 44.3587 c. 12: 1 3 1 2 2 1 2 P D3 SD: 8.5863 c. M:-15.6413 c. Harmonic Minor inverse, Mixolydian flat 2, Mela Cakravaka, Raga Ahir Bhairav, Bindumalini, Hevitri, Vegavahini, Makam Hicaz, Zanjaran 29: 2 7 3 5 4 3 5 N SD: 8.7201 c. M: 15.3932 c. 31: 2 8 3 5 5 3 5 N SD: 7.7003 c. M: 14.7594 c. 34: 3 8 3 6 5 3 6 P SD: 6.4148 c. M:-13.7036 c. 37: 3 9 3 7 5 4 6 N SD: 8.1402 c. M:-11.5585 c. 38: 3 9 4 6 6 4 6 P SD: 7.3040 c. M:-14.4363 c. 41: 3 10 4 7 6 4 7 N SD: 3.6702 c. M: 6.3099 c. 53: 4 13 5 9 8 5 9 N SD: 0.9567 c. M: 1.6127 c. 65: 5 16 6 11 10 6 11 N SD: 0.9397 c. M:-1.7951 c. 118: 9 29 11 20 18 11 20 N SD: 0.3777 c. M: 0.6533 c. 323: 25 79 30 55 49 30 55 N SD: 0.3353 c. M:-0.7005 c. 376: 29 92 35 64 57 35 64 N SD: 0.2506 c. M:-0.3745 c. 429: 33 105 40 73 65 40 73 N SD: 0.2464 c. M: 0.4426 c. 441: 34 108 41 75 67 41 75 N SD: 0.1536 c. M:-0.3383 c. 494: 38 121 46 84 75 46 84 N SD: 0.1026 c. M: 0.1482 c. 559: 43 137 52 95 85 52 95 N SD: 0.0675 c. M:-0.1290 c. 612: 47 150 57 104 93 57 104 N SD: 0.0246 c. M: 0.0450 c. 1171: 90 287 109 199 178 109 199 N SD: 0.0230 c. M:-0.0501 c. 1783: 137 437 166 303 271 166 303 N SD: 0.0124 c. M:-0.0254 c. 1901: 146 466 177 323 289 177 323 N SD: 0.0127 c. M:-0.0179 c. 2395: 184 587 223 407 364 223 407 N SD: 0.0111 c. M: 0.0163 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: 0.0000 cents 4 x 5 x 6 x 7:8 S SD: 6.8160 cents 5 x 6:7 x 8:9:10 S SD: 26.5228 cents 6 x x 8:9:10:11:12 S SD: 10.6546 cents 7:8:9 x 11:12 x 14 SD: 34.9646 cents 8:9:10:11:12:13:14:16 S SD: 19.1590 cents 9:10:11:12:14:15:16:18 S SD: 16.6711 cents 10:11 x 13:15:17:18:20 SD: 15.6902 cents 11:12:14:15:17:18:20:22 SD: 15.0496 cents 12:13:15:16:18:20:21:24 SD: 7.6874 cents 15:16:19:20:23:25:27:30 SD: 7.5842 cents 16:17:20:21:24:27:28:32 SD: 6.5659 cents 18:19:23:24:27:30:32:36 SD: 5.4396 cents 20:21:25:27:30:33:36:40 SD: 5.1255 cents 24:25:30:32:36:40:43:48 SD: 3.6254 cents 32:34:40:43:48:53:57:64 SD: 3.1102 cents 36:38:45:48:54:60:64:72 SD: 0.2035 cents 276:291:345:368:414:460:491:552 SD: 0.1859 cents 312:329:390:416:468:520:555:624 SD: 0.1558 cents 348:367:435:464:522:580:619:696 SD: 0.1349 cents 384:405:480:512:576:640:683:768 SD: 0.1207 cents 420:443:525:560:630:700:747:840 SD: 0.1118 cents 456:481:570:608:684:760:811:912 SD: 0.1066 cents 492:519:615:656:738:820:875:984 SD: 0.1043 cents 528:557:660:704:792:880:939:1056 SD: 0.1039 cents 588:620:735:784:882:980:1045:1176 SD: 0.1005 cents