Scala analysis: xen09-wilson-marwa-09-12
Marwa permutation 12 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: 4/3 498.044999 perfect fourth 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: 4096/3645 201.9563 narrow diminished third 4: 9/8 203.9100 major whole tone 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: 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 : 203.9 296.1 498.0 702.0 794.1 1088.3 1200.0 203.9 : 92.2 294.1 498.0 590.2 884.4 996.1 1200.0 296.1 : 202.0 405.9 498.0 792.2 903.9 1107.8 1200.0 498.0 : 203.9 296.1 590.2 702.0 905.9 998.0 1200.0 702.0 : 92.2 386.3 498.0 702.0 794.1 996.1 1200.0 794.1 : 294.1 405.9 609.8 702.0 903.9 1107.8 1200.0 1088.3: 111.7 315.6 407.8 609.8 813.7 905.9 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: 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 : 171.41660 cents, oct.: 1199.91617 cents Scale is not proper Step pattern alph. order: ABCABDE Step pattern size order : DACDAEB 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 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 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: 1215 Scale harmonicity : 0.029070 Average absolute harmonicity : 0.251916 Specific harmonicity : 0.153354 Fundamental : 1/3072, -11.5850 octaves, 0.0852 Hz. Guide tone : 4860, 12.2467 octaves, 1271500.247 Hz. Exponens Consonantiae : 1.492992E+07, 23.83170 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 1477.5, average 211.07143 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.77661, average 1.25380 Sum of Tenney's harmonic distance : 17.20545, average 2.45792 Vogel's harmonic complexity : 17.14286 Wille's k value : 1822 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 7 Triangular lattice diameter : 7 Lattice compactness : 158.53330, average 5.66190 Lattice compactness (without 2's) : 71.78847, average 2.56387 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -10 .. 2 -3.14286 28 1 3: -1 .. 5 1.71429 14 3 5: 0 .. 1 0.42857 3 3 Average exponent except 2's : 15 / 7 = 2.14286 Average absolute exponent except 2's: 17 / 7 = 2.42857
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 40.1849 c. M:-63.0091 c. Lebeng 9: 2 0 2 1 1 2 1 N D3 SD: 33.3716 c. M:-62.7567 c. 10: 2 0 2 2 1 2 1 N T3 SD: 32.2308 c. M: 56.0887 c. 11: 2 1 2 1 1 3 1 N T3 SD: 30.7258 c. M:-47.4095 c. 12: 2 1 2 2 1 3 1 P D3 SD: 5.4807 c. M:-11.7313 c. Harmonic Minor, Mischung 4, Pilu That, Mela Kiravani, Raga Kiranavali, Kirvani (Kirwani), Kalyana Vasantha, Deshi(3), Maqam Bayat-e-Esfahan, Sultani Yakah, Zhalibny Minor, Armoniko minore: Greece 39: 7 3 6 7 3 9 4 N SD: 8.4116 c. M:-11.6036 c. 41: 7 3 7 7 3 10 4 N SD: 2.8453 c. M: 5.3419 c. 53: 9 4 9 9 4 13 5 N SD: 1.0752 c. M: 1.7491 c. Makam Sehnaz Buselik 65: 11 5 11 11 5 16 6 N SD: 0.6030 c. M:-0.9621 c. 118: 20 9 20 20 9 29 11 N SD: 0.6135 c. M: 1.1735 c. 183: 31 14 31 31 14 45 17 N SD: 0.5548 c. M: 1.0068 c. 248: 42 19 42 42 19 61 23 N SD: 0.5476 c. M: 0.9274 c. 299: 51 23 50 51 23 73 28 N SD: 0.5838 c. M:-0.9012 c. 301: 51 23 51 51 23 74 28 N SD: 0.5712 c. M: 1.0721 c. 311: 53 24 52 53 24 76 29 N SD: 0.5488 c. M:-1.0174 c. 313: 53 24 53 53 24 77 29 N SD: 0.5502 c. M: 0.8811 c. 323: 55 25 54 55 25 79 30 N SD: 0.5910 c. M:-1.1249 c. 352: 60 27 59 60 27 86 33 N SD: 0.4603 c. M: 0.7687 c. 364: 62 28 61 62 28 89 34 N SD: 0.3774 c. M:-0.6146 c. 376: 64 29 63 64 29 92 35 N SD: 0.3774 c. M:-0.7198 c. 417: 71 32 70 71 32 102 39 N SD: 0.2947 c. M: 0.4989 c. 429: 73 33 72 73 33 105 40 N SD: 0.2370 c. M:-0.4148 c. 441: 75 34 74 75 34 108 41 N SD: 0.2704 c. M:-0.5099 c. 482: 82 37 81 82 37 118 45 N SD: 0.1739 c. M: 0.3019 c. 494: 84 38 83 84 38 121 46 N SD: 0.1413 c. M:-0.2676 c. 547: 93 42 92 93 42 134 51 N SD: 0.0822 c. M: 0.1517 c. 559: 95 43 94 95 43 137 52 N SD: 0.0892 c. M:-0.1546 c. 612: 104 47 103 104 47 150 57 N SD: 0.0155 c. M: 0.0334 c. 2395: 407 184 403 407 184 587 223 N SD: 0.0149 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: 30.0750 cents 4 x 5 x 6 x x 8 S SD: 30.0750 cents 5 x 6:7 x 8:9:10 S SD: 22.7103 cents 6 x 7:8:9:10:11:12 S SD: 17.0847 cents 7:8 x 9 x 11:13:14 SD: 14.3072 cents 9:10:11:12 x 14:17:18 SD: 10.6889 cents 10:11:12:13:15:16:19:20 SD: 9.8201 cents 11:12:13:15 x 17:21:22 SD: 13.9563 cents 12 x 14:16:18:19:23:24 SD: 7.9992 cents 13:15 x 17:20:21:24:26 SD: 13.9419 cents 14:16:17:19:21:22:26:28 SD: 8.6844 cents 15:17:18:20:23:24:28:30 SD: 7.0496 cents 16:18:19:21:24:25:30:32 SD: 4.9649 cents 22:25:26:29:33:35:41:44 SD: 4.3942 cents 24:27:28:32:36:38:45:48 SD: 4.1789 cents 26:29:31:35:39:41:49:52 SD: 3.7141 cents 32:36:38:43:48:51:60:64 SD: 2.6603 cents 38:43:45:51:57:60:71:76 SD: 2.4354 cents 42:47:50:56:63:66:79:84 SD: 2.4038 cents 48:54:57:64:72:76:90:96 SD: 0.2878 cents 258:290:306:344:387:408:484:516 SD: 0.2855 cents 264:297:313:352:396:418:495:528 SD: 0.2793 cents 280:315:332:373:420:443:525:560 SD: 0.2785 cents 294:331:349:392:441:465:551:588 SD: 0.2542 cents 306:344:363:408:459:484:574:612 SD: 0.2220 cents 354:398:420:472:531:560:664:708 SD: 0.1827 cents 392:441:465:523:588:620:735:784 SD: 0.1806 cents 402:452:477:536:603:636:754:804 SD: 0.1600 cents 440:495:522:587:660:696:825:880 SD: 0.1482 cents 456:513:541:608:684:721:855:912 SD: 0.1415 cents 488:549:579:651:732:772:915:976 SD: 0.1275 cents 504:567:598:672:756:797:945:1008 SD: 0.1067 cents 552:621:655:736:828:873:1035:1104 SD: 0.0810 cents 600:675:712:800:900:949:1125:1200 SD: 0.0643 cents