Scala analysis: xen09-wilson-marwa-09-03
Marwa permutation 3 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: 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: 135/128 92.1787 major chroma, major limma 6: 9/8 203.9100 major whole tone 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 9/8 203.910 cents major whole tone 2: 2 1215/1024 296.089 cents wide augmented second 2: 1 5/4 386.314 cents major third 2: 3 512/405 405.866 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: 3 405/256 794.134 cents wide augmented fifth 5: 1 8/5 813.686 cents minor sixth 5: 2 2048/1215 903.911 cents narrow diminished seventh 5: 1 16/9 996.090 cents Pythagorean minor seventh 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: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 296.1 590.2 702.0 794.1 998.0 1200.0 203.9 : 92.2 386.3 498.0 590.2 794.1 996.1 1200.0 296.1 : 294.1 405.9 498.0 702.0 903.9 1107.8 1200.0 590.2 : 111.7 203.9 407.8 609.8 813.7 905.9 1200.0 702.0 : 92.2 296.1 498.0 702.0 794.1 1088.3 1200.0 794.1 : 203.9 405.9 609.8 702.0 996.1 1107.8 1200.0 998.0 : 202.0 405.9 498.0 792.2 903.9 996.1 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 : 4096/3645, 201.9563 cents, amount: 1 Least squares average step : 169.52507 cents, oct.: 1186.67547 cents Scale is not proper Step pattern alph. order: ABCDBAE Step pattern size order : DAEBADC Scale is not a Constant Structure Scale diversity : 1.365334 Lumma stability : 0.156887 Lumma impropriety factor : 0.166669 Rothenberg efficiency : 0.451701 redundancy: 0.548299 Efficiency x scale size : 3.161905 Number of different interval sizes : 22 = 3.66667 / class Number of one step interval sizes : 5 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 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 -- 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 : 0.222279 Specific harmonicity : 0.138508 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 : 4347.5, average 621.07143 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 12.33831, average 1.76262 Sum of Tenney's harmonic distance : 24.07847, average 3.43978 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 : 176.46277, average 6.30224 Lattice compactness (without 2's) : 79.40198, average 2.83578 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -11 .. 1 -5.28571 39 1 3: 0 .. 6 2.85714 20 2 5: 0 .. 1 0.57143 4 4 Average exponent except 2's : 24 / 7 = 3.42857 Average absolute exponent except 2's: 24 / 7 = 3.42857
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 44.9996 c. M: 75.9380 c. Lebeng 8: 1 1 2 1 0 2 1 N D3 SD: 37.7449 c. M: 53.9100 c. 10: 2 0 3 1 1 1 2 N SD: 34.6836 c. M: 56.0887 c. 12: 2 1 3 1 1 2 2 N T3 SD: 4.9022 c. M:-9.7763 c. Minor Gipsy, Mela Sanmukhapriya, Raga Camara, Chinthamani 41: 7 3 10 4 3 7 7 N SD: 2.9286 c. M: 4.8579 c. 53: 9 4 13 5 4 9 9 N SD: 1.2871 c. M: 1.8173 c. 65: 11 5 16 6 5 11 11 N SD: 0.6546 c. M: 1.1206 c. 183: 31 14 45 17 14 31 31 N SD: 0.7311 c. M: 1.3224 c. 207: 35 16 51 19 16 35 35 N SD: 0.7101 c. M:-1.0806 c. 248: 42 19 61 23 19 42 42 N SD: 0.6979 c. M: 1.2695 c. 272: 46 21 67 25 21 46 46 N SD: 0.6868 c. M: 0.9849 c. 311: 53 24 76 29 24 53 52 N SD: 0.7304 c. M:-1.3132 c. 313: 53 24 77 29 24 53 53 N SD: 0.6825 c. M: 1.2386 c. 337: 57 26 83 31 26 57 57 N SD: 0.6754 c. M: 1.0111 c. 340: 58 26 83 32 26 58 57 N SD: 0.5613 c. M: 0.8120 c. 352: 60 27 86 33 27 60 59 N SD: 0.4879 c. M:-0.8199 c. 364: 62 28 89 34 28 62 61 N SD: 0.4719 c. M:-0.8574 c. 376: 64 29 92 35 29 64 63 N SD: 0.5076 c. M:-0.8925 c. 393: 67 30 96 37 30 67 66 N SD: 0.4843 c. M: 0.9107 c. 405: 69 31 99 38 31 69 68 N SD: 0.3746 c. M: 0.5941 c. 417: 71 32 102 39 32 71 70 N SD: 0.3100 c. M:-0.5174 c. 429: 73 33 105 40 33 73 72 N SD: 0.3069 c. M:-0.5577 c. 470: 80 36 115 44 36 80 79 N SD: 0.2447 c. M: 0.4365 c. 482: 82 37 118 45 37 82 81 N SD: 0.1802 c. M:-0.2965 c. 494: 84 38 121 46 38 84 83 N SD: 0.1897 c. M:-0.3368 c. 535: 91 41 131 50 41 91 90 N SD: 0.1571 c. M: 0.3172 c. 547: 93 42 134 51 42 93 92 N SD: 0.0817 c. M:-0.1281 c. 612: 104 47 150 57 47 104 103 N SD: 0.0137 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: 42.9954 cents 4 x 5 x 6 x 7:8 S SD: 23.7095 cents 5 x 6:7 x 8:9:10 S SD: 6.9466 cents 6 x 7:8:9:10:11:12 S SD: 23.6437 cents 7:8 x 10 x 11:12:14 S SD: 15.2789 cents 9:10:11:13 x 14:16:18 SD: 13.0236 cents 10:11:12:14:15:16:18:20 S SD: 7.4506 cents 11:12:13:15 x 17:20:22 SD: 15.5713 cents 12 x 14:17:18:19:21:24 SD: 7.2123 cents 13:15 x 18:20:21:23:26 SD: 12.8813 cents 14:16:17:20:21:22:25:28 SD: 8.1549 cents 15:17:18:21:23:24:27:30 SD: 7.5828 cents 16:18:19:23:24:25:28:32 SD: 7.5134 cents 17:19:20:24:26:27:30:34 SD: 6.0353 cents 22:25:26:31:33:35:39:44 SD: 3.2054 cents 32:36:38:45:48:51:57:64 SD: 1.8478 cents 54:61:64:76:81:85:96:108 SD: 1.6685 cents 64:72:76:90:96:101:114:128 SD: 0.6757 cents 86:97:102:121:129:136:153:172 SD: 0.6733 cents 96:108:114:135:144:152:171:192 SD: 0.3524 cents 160:180:190:225:240:253:285:320 SD: 0.3126 cents 246:277:292:346:369:389:438:492 SD: 0.2898 cents 256:288:304:360:384:405:456:512 SD: 0.2878 cents 278:313:330:391:417:440:495:556 SD: 0.2771 cents 290:326:344:408:435:459:516:580 SD: 0.2655 cents 328:369:389:461:492:519:584:656 SD: 0.2063 cents 354:398:420:498:531:560:630:708 SD: 0.1835 cents 376:423:446:529:564:595:669:752 SD: 0.1695 cents 440:495:522:619:660:696:783:880 SD: 0.1154 cents 536:603:636:754:804:848:954:1072 SD: 0.0835 cents