Scala analysis: xen09-wilson-marwa-09-02
Marwa permutation 2 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: 27/16 905.865003 Pythagorean major sixth 6: 3645/2048 998.043719 wide augmented sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 4096/3645 201.9563 narrow diminished third 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: 9/8 203.9100 major whole tone 6: 135/128 92.1787 major chroma, major limma 7: 4096/3645 201.9563 narrow diminished third
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 : 203.9 296.1 590.2 702.0 905.9 998.0 1200.0 203.9 : 92.2 386.3 498.0 702.0 794.1 996.1 1200.0 296.1 : 294.1 405.9 609.8 702.0 903.9 1107.8 1200.0 590.2 : 111.7 315.6 407.8 609.8 813.7 905.9 1200.0 702.0 : 203.9 296.1 498.0 702.0 794.1 1088.3 1200.0 905.9 : 92.2 294.1 498.0 590.2 884.4 996.1 1200.0 998.0 : 202.0 405.9 498.0 792.2 903.9 1107.8 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 : 173.51547 cents, oct.: 1214.60830 cents Scale is not proper Step pattern alph. order: ABCDABE Step pattern size order : DAEBDAC 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 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 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 : 0.228484 Specific harmonicity : 0.146230 Fundamental : 1/2048, -11.0000 octaves, 0.1277 Hz. Guide tone : 7290, 12.8317 octaves, 1907250.371 Hz. Exponens Consonantiae : 1.492992E+07, 23.83170 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 4038.5, average 576.92857 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.16221, average 1.59460 Sum of Tenney's harmonic distance : 21.69826, average 3.09975 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 : 166.62477, average 5.95088 Lattice compactness (without 2's) : 76.56998, average 2.73464 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -11 .. 1 -4.71429 35 1 3: 0 .. 6 2.71429 19 3 5: 0 .. 1 0.42857 3 3 Average exponent except 2's : 22 / 7 = 3.14286 Average absolute exponent except 2's: 22 / 7 = 3.14286
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 42.3901 c. M: 75.9380 c. Lebeng 8: 1 1 2 1 1 1 1 P M ME S SD: 33.9313 c. M: 53.9100 c. 12: 2 1 3 1 2 1 2 P D3 SD: 4.9020 c. M:-9.7763 c. Mela Hemavati, Raga Desisimharavam, Maqam Nakriz, Tunisian, Dorian sharp 4, Misheberekh: Jewish, Nigriz, Pimenikos, Souzinak (Peiraiotikos Minor): Greece, Ukrainian Dorian, Ukrainian Minor, Kaffa, Gnossiennes 41: 7 3 10 4 7 3 7 N SD: 2.5916 c. M: 4.8579 c. 53: 9 4 13 5 9 4 9 N SD: 1.1220 c. M: 1.8173 c. 65: 11 5 16 6 11 5 11 N SD: 0.7998 c. M: 1.2496 c. 118: 20 9 29 11 20 9 20 N SD: 0.8048 c. M: 1.4335 c. 183: 31 14 45 17 31 14 31 N SD: 0.7710 c. M: 1.3224 c. 248: 42 19 61 23 42 19 42 N SD: 0.7672 c. M: 1.2695 c. 301: 51 23 74 28 51 23 51 N SD: 0.7802 c. M: 1.3660 c. 311: 53 24 76 29 53 24 52 N SD: 0.7561 c. M:-1.3132 c. 313: 53 24 77 29 53 24 53 N SD: 0.7688 c. M: 1.2386 c. 323: 55 25 79 30 55 25 54 N SD: 0.7485 c. M:-1.3371 c. 340: 58 26 83 32 58 26 57 N SD: 0.7201 c. M:-1.1938 c. 352: 60 27 86 33 60 27 59 N SD: 0.6025 c. M:-0.9532 c. 364: 62 28 89 34 62 28 61 N SD: 0.5279 c. M:-0.8574 c. 376: 64 29 92 35 64 29 63 N SD: 0.5032 c. M:-0.8925 c. 405: 69 31 99 38 69 31 68 N SD: 0.4812 c. M:-0.8017 c. 417: 71 32 102 39 71 32 70 N SD: 0.3840 c. M:-0.6098 c. 429: 73 33 105 40 73 33 72 N SD: 0.3315 c. M:-0.5577 c. 441: 75 34 108 41 75 34 74 N SD: 0.3342 c. M:-0.5957 c. 470: 80 36 115 44 80 36 79 N SD: 0.3115 c. M:-0.5180 c. 482: 82 37 118 45 82 37 81 N SD: 0.2246 c. M:-0.3591 c. 494: 84 38 121 46 84 38 83 N SD: 0.1912 c. M:-0.3368 c. 535: 91 41 131 50 91 41 90 N SD: 0.1895 c. M: 0.3172 c. 547: 93 42 134 51 93 42 92 N SD: 0.1033 c. M:-0.1679 c. 559: 95 43 137 52 95 43 94 N SD: 0.0983 c. M:-0.1674 c. 612: 104 47 150 57 104 47 103 N SD: 0.0139 c. M: 0.0276 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: 31.5514 cents 4 x 5 x 6 x 7:8 S SD: 23.7095 cents 5 x 6:7 x 8:9:10 S SD: 19.3091 cents 6 x 7:8:9:10:11:12 S SD: 18.5942 cents 7:8 x 10:11:12 x 14 S SD: 18.6721 cents 8:9:10:11:12 x 14:16 S SD: 17.0847 cents 9:10:11:13:14:15:16:18 SD: 14.0546 cents 10:11:12:14:15:17:18:20 SD: 7.1443 cents 12 x 14:17:18:20:21:24 SD: 8.0504 cents 13:15 x 18:20:22:23:26 SD: 11.4177 cents 14:16:17:20:21:24:25:28 SD: 8.8829 cents 15:17:18:21:23:25:27:30 SD: 7.6900 cents 16:18:19:23:24:27:28:32 SD: 6.8565 cents 17:19:20:24:26:29:30:34 SD: 6.5320 cents 22:25:26:31:33:37:39:44 SD: 3.0091 cents 32:36:38:45:48:54:57:64 SD: 0.2878 cents 246:277:292:346:369:415:438:492 SD: 0.2765 cents 278:313:330:391:417:469:495:556 SD: 0.2628 cents 310:349:368:436:465:523:552:620 SD: 0.2544 cents 342:385:406:481:513:577:609:684 SD: 0.2493 cents 354:398:420:498:531:597:630:708 SD: 0.2398 cents 386:434:458:543:579:651:687:772 SD: 0.2188 cents 418:470:496:588:627:705:744:836 SD: 0.2034 cents 440:495:522:619:660:743:783:880 SD: 0.1998 cents 450:506:534:633:675:759:801:900 SD: 0.1923 cents 472:531:560:664:708:797:840:944 SD: 0.1826 cents 504:567:598:709:756:851:897:1008 SD: 0.1696 cents 536:603:636:754:804:905:954:1072 SD: 0.1599 cents 568:639:674:799:852:959:1011:1136 SD: 0.1531 cents 586:659:695:824:879:989:1043:1172 SD: 0.1478 cents