Scala analysis: xen09-wilson-marwa-11a-02
Marwa permutation 2 from Figure 11a, 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: 32/27 294.134997 Pythagorean minor third 2: 512/405 405.866283 narrow diminished fourth 3: 64/45 609.776284 2nd tritone 4: 128/81 792.179997 Pythagorean minor sixth 5: 16/9 996.089998 Pythagorean minor seventh 6: 256/135 1107.821284 octave - major chroma 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 135/128 92.1787 major chroma, major limma 1: 32/27 294.1350 Pythagorean minor third 2: 16/15 111.7313 minor diatonic semitone 3: 9/8 203.9100 major whole tone 4: 10/9 182.4037 minor whole tone 5: 9/8 203.9100 major whole tone 6: 16/15 111.7313 minor diatonic semitone 7: 135/128 92.1787 major chroma, major limma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 135/128 92.179 cents major chroma, major limma 1: 2 16/15 111.731 cents minor diatonic semitone 1: 1 10/9 182.404 cents minor whole tone 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 6/5 315.641 cents minor third 2: 3 5/4 386.314 cents major third 2: 1 512/405 405.866 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: 1 405/256 794.134 cents wide augmented fifth 5: 3 8/5 813.686 cents minor sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 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 9/5 1017.596 cents just minor seventh, BP seventh 6: 2 15/8 1088.269 cents classic major seventh 6: 1 256/135 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 : 294.1 405.9 609.8 792.2 996.1 1107.8 1200.0 294.1 : 111.7 315.6 498.0 702.0 813.7 905.9 1200.0 405.9 : 203.9 386.3 590.2 702.0 794.1 1088.3 1200.0 609.8 : 182.4 386.3 498.0 590.2 884.4 996.1 1200.0 792.2 : 203.9 315.6 407.8 702.0 813.7 1017.6 1200.0 996.1 : 111.7 203.9 498.0 609.8 813.7 996.1 1200.0 1107.8: 92.2 386.3 498.0 702.0 884.4 1088.3 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 : 10/9, 182.4037 cents, amount: 1 Least squares average step : 186.65210 cents, oct.: 1306.56470 cents Scale is not proper Step pattern alph. order: ABCDCBE Step pattern size order : EBDCDBA Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 1.423133 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 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 : 2 at degree 2 Length of longest subharmonic part : 2 at degree 3 Formal octave complements present : 1 = 14.2857% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 5 Odd number limit : 405 (O: 405 U: 405) Highest odd numerator or denominator: 405 Scale harmonicity : 0.038363 Average absolute harmonicity : 0.197152 Specific harmonicity : 0.186770 Fundamental : 1/405, -8.6618 octaves, 0.6460 Hz. Guide tone : 512, 9.0000 octaves, 133952.289 Hz. Exponens Consonantiae : 2.073600E+05, 17.66178 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 856.5, average 122.35714 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.68509, average 1.52644 Sum of Tenney's harmonic distance : 22.72629, average 3.24661 Vogel's harmonic complexity : 12.85714 Wille's k value : 202 Wilson's harmonic complexity : 17 Rectangular lattice diameter : 5 Triangular lattice diameter : 5 Lattice compactness : 124.26749, average 4.43812 Lattice compactness (without 2's) : 58.17189, average 2.07757 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 1 .. 9 5.71429 40 1 3: -4 .. 0 -2.57143 18 3 5: -1 .. 0 -0.42857 3 3 Average exponent except 2's :-21 / 7 =-3.00000 Average absolute exponent except 2's: 21 / 7 = 3.00000
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 96.4123 c. M: 138.9471 c. Lebeng 8: 2 1 1 1 2 0 1 N D3 SD: 37.9972 c. M: 57.8213 c. 9: 2 1 1 2 1 1 1 P M ME S SD: 41.9621 c. M: 76.4430 c. 10: 2 1 2 1 2 1 1 P M ME S SD: 42.1161 c. M: 72.1800 c. 11: 3 1 2 1 2 1 1 N T3 SD: 27.6119 c. M:-44.7692 c. 12: 3 1 2 2 2 1 1 N T3 SD: 6.5683 c. M: 9.7763 c. 41: 10 4 7 6 7 4 3 N SD: 3.0391 c. M:-4.8579 c. 53: 13 5 9 8 9 5 4 N SD: 1.0655 c. M:-1.6809 c. 65: 16 6 11 10 11 6 5 N SD: 0.8806 c. M:-1.6662 c. 118: 29 11 20 18 20 11 9 N SD: 0.6946 c. M:-1.0403 c. 289: 71 27 49 44 49 27 22 N SD: 0.7202 c. M:-1.0541 c. 301: 74 28 51 46 51 28 23 N SD: 0.6950 c. M:-1.1755 c. 311: 76 29 53 47 53 29 24 N SD: 0.6821 c. M: 1.1832 c. 323: 79 30 55 49 55 30 25 N SD: 0.6401 c. M: 0.9127 c. 364: 89 34 62 55 62 34 28 N SD: 0.5179 c. M: 0.9712 c. 376: 92 35 64 57 64 35 29 N SD: 0.4383 c. M: 0.6906 c. 417: 102 39 71 63 71 39 32 N SD: 0.4320 c. M: 0.8131 c. 429: 105 40 73 65 73 40 33 N SD: 0.3124 c. M: 0.5716 c. 441: 108 41 75 67 75 41 34 N SD: 0.2858 c. M: 0.4241 c. 482: 118 45 82 73 82 45 37 N SD: 0.2552 c. M: 0.4788 c. 494: 121 46 84 75 84 46 38 N SD: 0.1685 c. M: 0.2772 c. 547: 134 51 93 83 93 51 42 N SD: 0.1206 c. M: 0.2239 c. 559: 137 52 95 85 95 52 43 N SD: 0.0886 c. M: 0.1418 c. 612: 150 57 104 93 104 57 47 N SD: 0.0188 c. M:-0.0276 c. 2395: 587 223 407 364 407 223 184 N SD: 0.0179 c. M: 0.0297 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: 45.1125 cents 3 x 4 x 5 x x 6 S SD: 43.4535 cents 4 x 5 x 6:7 x 8 S SD: 24.0653 cents 5:6 x 7:8:9 x 10 S SD: 9.2323 cents 6:7:8 x 9:11 x 12 SD: 28.4386 cents 7:8:9:10:11:12:13:14 H SD: 14.4560 cents 9:11 x 13:14:16:17:18 SD: 10.9895 cents 10:12:13:14:16:18:19:20 S SD: 9.5616 cents 12:14:15:17:19:21:23:24 SD: 6.8041 cents 16:19:20:23:25:28:30:32 SD: 6.7670 cents 19:23:24:27:30:34:36:38 SD: 5.4930 cents 21:25:27:30:33:37:40:42 SD: 5.2819 cents 22:26:28:31:35:39:42:44 SD: 3.8145 cents 26:31:33:37:41:46:49:52 SD: 2.6853 cents 31:37:39:44:49:55:59:62 SD: 2.4056 cents 38:45:48:54:60:68:72:76 SD: 1.6844 cents 50:59:63:71:79:89:95:100 SD: 1.5271 cents 64:76:81:91:101:114:121:128 SD: 1.0984 cents 76:90:96:108:120:135:144:152 SD: 0.4984 cents 185:219:234:263:292:329:351:370 SD: 0.4724 cents 189:224:239:269:299:336:358:378 SD: 0.4370 cents 211:250:267:300:333:375:400:422 SD: 0.4241 cents 216:256:273:307:341:384:410:432 SD: 0.3824 cents 239:283:302:340:378:425:453:478 SD: 0.3623 cents 243:288:307:346:384:432:461:486 SD: 0.3454 cents 253:300:320:360:400:450:480:506 SD: 0.2992 cents 265:314:335:377:419:471:503:530 SD: 0.2958 cents 291:345:368:414:460:517:552:582 SD: 0.2390 cents 329:390:416:468:520:585:624:658 SD: 0.1151 cents 405:480:512:576:640:720:768:810 SD: 0.0000 cents