Scala analysis: xen09-wilson-marwa-09-18
Marwa permutation 18 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: 405/256 794.133717 wide augmented fifth 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: 135/128 92.1787 major chroma, major limma 6: 4096/3645 201.9563 narrow diminished third 7: 9/8 203.9100 major whole tone
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 : 92.2 386.3 498.0 702.0 794.1 996.1 1200.0 92.2 : 294.1 405.9 609.8 702.0 903.9 1107.8 1200.0 386.3 : 111.7 315.6 407.8 609.8 813.7 905.9 1200.0 498.0 : 203.9 296.1 498.0 702.0 794.1 1088.3 1200.0 702.0 : 92.2 294.1 498.0 590.2 884.4 996.1 1200.0 794.1 : 202.0 405.9 498.0 792.2 903.9 1107.8 1200.0 996.1 : 203.9 296.1 590.2 702.0 905.9 998.0 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 : 167.95693 cents, oct.: 1175.69849 cents Scale is not proper Step pattern alph. order: ABCDAED Step pattern size order : AEBDACD 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 Scale contains a complete diamond : 1 3 Formal octave complements present : 3 = 42.8571% 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: 405 Scale harmonicity : 0.029070 Average absolute harmonicity : 0.257118 Specific harmonicity : 0.156734 Fundamental : 1/2304, -11.1699 octaves, 0.1136 Hz. Guide tone : 6480, 12.6618 octaves, 1695333.663 Hz. Exponens Consonantiae : 1.492992E+07, 23.83170 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 486.5, average 69.50000 Mersenne's string divisions : 273802725 Sum of van Prooijen's expressibility: 7.34524, average 1.04932 Sum of Tenney's harmonic distance : 14.87099, average 2.12443 Vogel's harmonic complexity : 16.71429 Wille's k value : 1822 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 7 Triangular lattice diameter : 7 Lattice compactness : 156.25293, average 5.58046 Lattice compactness (without 2's) : 69.43751, average 2.47991 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -8 .. 4 -1.57143 25 1 3: -2 .. 4 0.71429 11 3 5: 0 .. 1 0.42857 3 3 Average exponent except 2's : 8 / 7 = 1.14286 Average absolute exponent except 2's: 14 / 7 = 2.00000
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 44.2747 c. M:-79.2499 c. Lebeng 9: 1 2 1 1 1 1 2 N D3 S SD: 34.5261 c. M: 62.7567 c. 10: 1 2 1 2 1 1 2 P M ME S SD: 28.0914 c. M:-45.8663 c. 12: 1 3 1 2 1 2 2 P D3 SD: 6.6099 c. M:-13.6863 c. Phrygian Dominant, Phrygian Major, Mela Vakulabharanam, Raga Ahiri, Basant Mukhari, Jogiya, Vativasantabhairavi, Zilof, Ahava Rabba, Freygish: Jewish, Maqam Hijaz-Nahawand, Humayun, Spanish Gipsy, Dorico Flamenco: Spain, Hitzaz: Greece, Harmonic Major inverse, Mixolydian flat 2 flat 6 41: 3 10 4 7 3 7 7 N SD: 3.1534 c. M: 5.8259 c. 53: 4 13 5 9 4 9 9 N SD: 1.0307 c. M: 1.6809 c. 65: 5 16 6 11 5 11 11 N SD: 0.6591 c. M:-1.3786 c. 118: 9 29 11 20 9 20 20 N SD: 0.4903 c. M: 0.9134 c. 183: 14 45 17 31 14 31 31 N SD: 0.4695 c. M: 0.6911 c. 301: 23 74 28 51 23 51 51 N SD: 0.4654 c. M: 0.7782 c. 311: 24 76 29 53 24 52 53 N SD: 0.4536 c. M:-0.7216 c. 323: 25 79 30 55 25 54 55 N SD: 0.4778 c. M:-0.9127 c. 364: 28 89 34 62 28 61 62 N SD: 0.3521 c. M: 0.5994 c. 376: 29 92 35 64 29 63 64 N SD: 0.3021 c. M:-0.5471 c. 417: 32 102 39 71 32 70 71 N SD: 0.3299 c. M: 0.7022 c. 429: 33 105 40 73 33 72 73 N SD: 0.2080 c. M: 0.2997 c. 441: 34 108 41 75 34 74 75 N SD: 0.2220 c. M:-0.4241 c. 482: 37 118 45 82 37 81 82 N SD: 0.1967 c. M: 0.4216 c. 494: 38 121 46 84 38 83 84 N SD: 0.1140 c. M:-0.1983 c. 547: 42 134 51 93 42 92 93 N SD: 0.0954 c. M: 0.2077 c. 559: 43 137 52 95 43 94 95 N SD: 0.0810 c. M:-0.1418 c. 612: 47 150 57 104 47 103 104 N SD: 0.0188 c. M: 0.0392 c. 1289: 99 316 120 219 99 217 219 N SD: 0.0226 c. M:-0.0323 c. 1783: 137 437 166 303 137 300 303 N SD: 0.0175 c. M:-0.0334 c. 1901: 146 466 177 323 146 320 323 N SD: 0.0144 c. M: 0.0254 c. 2395: 184 587 223 407 184 403 407 N SD: 0.0121 c. M:-0.0208 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: 30.0750 cents 4 x 5 x 6 x 7:8 S SD: 6.8160 cents 5 x 6:7 x 8:9:10 S SD: 22.7808 cents 6 x x 8:9:10:11:12 S SD: 20.9557 cents 7:8:9 x x 11:12:14 SD: 32.1234 cents 8:9:10:11:12:13:14:16 S SD: 19.2818 cents 9:10:11:12 x 14:16:18 S SD: 17.0847 cents 10:11 x 13:15:16:18:20 SD: 14.9718 cents 11:12:14:15 x 17:20:22 SD: 15.8620 cents 12:13:15:16:18:19:21:24 SD: 7.6901 cents 16:17:20:21:24:25:28:32 SD: 6.5659 cents 19:20:24:25:29:30:34:38 SD: 6.2478 cents 20:21:25:27:30:32:36:40 SD: 5.2815 cents 24:25:30:32:36:38:43:48 SD: 3.6311 cents 32:34:40:43:48:51:57:64 SD: 3.2558 cents 36:38:45:48:54:57:64:72 SD: 0.2878 cents 256:270:320:341:384:405:455:512 SD: 0.2491 cents 292:308:365:389:438:462:519:584 SD: 0.2212 cents 328:346:410:437:492:519:583:656 SD: 0.2044 cents 364:384:455:485:546:576:647:728 SD: 0.1949 cents 400:422:500:533:600:633:711:800 SD: 0.1901 cents 404:426:505:539:606:639:718:808 SD: 0.1876 cents 440:464:550:587:660:696:782:880 SD: 0.1640 cents 476:502:595:635:714:753:846:952 SD: 0.1468 cents 512:540:640:683:768:810:910:1024 SD: 0.1350 cents 548:578:685:731:822:867:974:1096 SD: 0.1275 cents 584:616:730:779:876:924:1038:1168 SD: 0.1236 cents 588:620:735:784:882:930:1045:1176 SD: 0.1183 cents