Scala analysis: xen09-wilson-marwa-09-06
Marwa permutation 6 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: 45/32 590.223716 diatonic tritone 4: 3/2 701.955001 perfect fifth 5: 405/256 794.133717 wide augmented fifth 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: 32/27 294.1350 Pythagorean minor third 4: 16/15 111.7313 minor diatonic semitone 5: 135/128 92.1787 major chroma, major limma 6: 32/27 294.1350 Pythagorean minor third 7: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 135/128 92.179 cents major chroma, major limma 1: 2 16/15 111.731 cents minor diatonic semitone 1: 1 9/8 203.910 cents major whole tone 1: 2 32/27 294.135 cents Pythagorean minor third 2: 1 9/8 203.910 cents major whole tone 2: 1 1215/1024 296.089 cents wide augmented second 2: 1 6/5 315.641 cents minor third 2: 2 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: 2 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: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 27/16 905.865 cents Pythagorean major sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 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: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 296.1 590.2 702.0 794.1 1088.3 1200.0 203.9 : 92.2 386.3 498.0 590.2 884.4 996.1 1200.0 296.1 : 294.1 405.9 498.0 792.2 903.9 1107.8 1200.0 590.2 : 111.7 203.9 498.0 609.8 813.7 905.9 1200.0 702.0 : 92.2 386.3 498.0 702.0 794.1 1088.3 1200.0 794.1 : 294.1 405.9 609.8 702.0 996.1 1107.8 1200.0 1088.3: 111.7 315.6 407.8 702.0 813.7 905.9 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: 203.9100 .. 405.8663 cents 4096/3645, 201.9563 cents 243/256,-90.2250 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 .. 996.0900 cents 4096/3645, 201.9563 cents 32805/32768, 1.9537 cents 6: 905.8650 .. 1107.8213 cents 4096/3645, 201.9563 cents 243/256,-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 : 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 : 16/15, 111.7313 cents, amount: 2 Least squares average step : 173.39185 cents, oct.: 1213.74297 cents Scale is not proper Step pattern alph. order: ABCDBCD Step pattern size order : CADBADB Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 1.390463 Lumma stability : 0.156887 Lumma impropriety factor : 0.166669 Rothenberg efficiency : 0.448980 redundancy: 0.551020 Efficiency x scale size : 3.142857 Number of different interval sizes : 22 = 3.66667 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 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 Number of recognisable fifths : 4, average 701.9550 cents Scale is Hypodorian octave species of abstract tetrachord Best fifths form a closed circle Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions with margin 201.9563 cents: 1 -- Rational properties -- Prime limit : 5 Odd number limit : 1215 (O: 1215 U: 1215) Highest odd numerator or denominator: 1215 Scale harmonicity : 0.032538 Average absolute harmonicity : 0.229841 Specific harmonicity : 0.164637 Fundamental : 1/1024, -10.0000 octaves, 0.2555 Hz. Guide tone : 2430, 11.2467 octaves, 635750.124 Hz. Exponens Consonantiae : 2.488320E+06, 21.24674 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 1512.5, average 216.07143 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.95270, average 1.42181 Sum of Tenney's harmonic distance : 19.28463, average 2.75495 Vogel's harmonic complexity : 15.14286 Wille's k value : 607 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 6 Triangular lattice diameter : 6 Lattice compactness : 145.32233, average 5.19008 Lattice compactness (without 2's) : 64.25697, average 2.29489 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -10 .. 1 -4.14286 31 1 3: 0 .. 5 2.14286 15 2 5: 0 .. 1 0.57143 4 4 Average exponent except 2's : 19 / 7 = 2.71429 Average absolute exponent except 2's: 19 / 7 = 2.71429
FIT/MODE
7: 1 0 2 1 0 2 1 N T3 SD: 73.6246 c. M: 124.6601 c. 8: 1 1 2 1 0 2 1 N D3 SD: 35.3306 c. M: 53.9100 c. 9: 1 1 2 1 1 2 1 P M ME S SD: 39.3330 c. M: 70.5767 c. 10: 2 1 2 1 1 2 1 P M ME S SD: 33.7648 c. M:-63.9113 c. 11: 2 1 2 1 1 3 1 N T3 SD: 30.1547 c. M: 47.4095 c. 12: 2 1 3 1 1 3 1 N T3 S SD: 6.5685 c. M:-11.7313 c. Double Harmonic Minor, Hungarian Minor, Egyptian Heptatonic, Mela Simhendramadhyama, Raga Madhava Manohari, Shimendra Madyam, Maqam Nawa Athar, Hisar, Flamenco Mode, Niavent: Greece 39: 7 3 9 4 3 9 4 N SD: 8.3991 c. M:-11.6036 c. 41: 7 3 10 4 3 10 4 N SD: 3.3814 c. M: 5.3419 c. 53: 9 4 13 5 4 13 5 N SD: 1.2232 c. M: 1.7491 c. Makam Rengidil 65: 11 5 16 6 5 16 6 N SD: 0.6175 c. M:-0.9621 c. 118: 20 9 29 11 9 29 11 N SD: 0.6236 c. M: 1.1735 c. 183: 31 14 45 17 14 45 17 N SD: 0.5423 c. M: 1.0068 c. 248: 42 19 61 23 19 61 23 N SD: 0.5335 c. M: 0.9274 c. 299: 51 23 73 28 23 73 28 N SD: 0.5736 c. M:-0.9012 c. 301: 51 23 74 28 23 74 28 N SD: 0.5649 c. M: 1.0721 c. 311: 53 24 76 29 24 76 29 N SD: 0.5395 c. M:-1.0174 c. 313: 53 24 77 29 24 77 29 N SD: 0.5382 c. M: 0.8811 c. 323: 55 25 79 30 25 79 30 N SD: 0.6139 c. M:-1.1249 c. 352: 60 27 86 33 27 86 33 N SD: 0.4759 c. M: 0.7687 c. 364: 62 28 89 34 28 89 34 N SD: 0.3686 c. M:-0.6146 c. 376: 64 29 92 35 29 92 35 N SD: 0.3795 c. M:-0.7198 c. 417: 71 32 102 39 32 102 39 N SD: 0.3056 c. M: 0.4989 c. 429: 73 33 105 40 33 105 40 N SD: 0.2308 c. M:-0.4148 c. 482: 82 37 118 45 37 118 45 N SD: 0.1815 c. M: 0.3019 c. 494: 84 38 121 46 38 121 46 N SD: 0.1407 c. M:-0.2676 c. 547: 93 42 134 51 42 134 51 N SD: 0.0873 c. M: 0.1517 c. 559: 95 43 137 52 43 137 52 N SD: 0.0993 c. M:-0.1546 c. 612: 104 47 150 57 47 150 57 N SD: 0.0186 c. M: 0.0334 c. 1901: 323 146 466 177 146 466 177 N SD: 0.0179 c. M: 0.0340 c. 2395: 407 184 587 223 184 587 223 N SD: 0.0148 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: 42.9954 cents 4 x 5 x 6 x x 8 S SD: 30.0750 cents 5 x 6:7 x 8:9:10 S SD: 15.2560 cents 6 x 7:8:9:10:11:12 S SD: 22.9763 cents 7:8 x 10 x 11:13:14 SD: 8.7101 cents 9:10:11:13 x 14:17:18 SD: 13.1925 cents 10:11:12:14:15:16:19:20 SD: 7.6446 cents 11:12:13:15 x 17:21:22 SD: 15.2173 cents 12 x 14:17:18:19:23:24 SD: 8.2778 cents 13:15 x 18:20:21:24:26 SD: 13.5276 cents 14:16:17:20:21:22:26:28 SD: 8.4514 cents 15:17:18:21:23:24:28:30 SD: 7.1352 cents 16:18:19:23:24:25:30:32 SD: 6.2473 cents 17:19:20:24:26:27:32:34 SD: 5.7387 cents 22:25:26:31:33:35:41:44 SD: 3.4013 cents 32:36:38:45:48:51:60:64 SD: 1.8365 cents 54:61:64:76:81:85:101:108 SD: 1.7550 cents 64:72:76:90:96:101:120:128 SD: 0.6444 cents 96:108:114:135:144:152:180:192 SD: 0.2878 cents 160:180:190:225:240:253:300:320 SD: 0.2373 cents 256:288:304:360:384:405:480:512 SD: 0.2035 cents 328:369:389:461:492:519:615:656 SD: 0.1817 cents 376:423:446:529:564:595:705:752 SD: 0.1527 cents 392:441:465:551:588:620:735:784 SD: 0.1427 cents 424:477:503:596:636:671:795:848 SD: 0.1380 cents 440:495:522:619:660:696:825:880 SD: 0.1105 cents 488:549:579:686:732:772:915:976 SD: 0.0912 cents 536:603:636:754:804:848:1005:1072 SD: 0.0830 cents