Scala analysis: xen09-wilson-marwa-11a-03
Marwa permutation 3 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: 2048/1215 903.911282 narrow diminished 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: 16/15 111.7313 minor diatonic semitone 6: 9/8 203.9100 major whole tone 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 32/27 294.135 cents Pythagorean minor third 2: 1 1215/1024 296.089 cents wide augmented second 2: 2 6/5 315.641 cents minor third 2: 2 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: 2 8/5 813.686 cents minor sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 1 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 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: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 294.1 405.9 609.8 792.2 903.9 1107.8 1200.0 294.1 : 111.7 315.6 498.0 609.8 813.7 905.9 1200.0 405.9 : 203.9 386.3 498.0 702.0 794.1 1088.3 1200.0 609.8 : 182.4 294.1 498.0 590.2 884.4 996.1 1200.0 792.2 : 111.7 315.6 407.8 702.0 813.7 1017.6 1200.0 903.9 : 203.9 296.1 590.2 702.0 905.9 1088.3 1200.0 1107.8: 92.2 386.3 498.0 702.0 884.4 996.1 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: 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 : 10/9, 182.4037 cents, amount: 1 Least squares average step : 183.36000 cents, oct.: 1283.52003 cents Scale is not proper Step pattern alph. order: ABCDBCE Step pattern size order : EBDCBDA Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 1.424003 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 : 2 at degree 2 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 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 : 1215 (O: 1215 U: 1215) Highest odd numerator or denominator: 1215 Scale harmonicity : 0.032538 Average absolute harmonicity : 0.186494 Specific harmonicity : 0.163237 Fundamental : 1/1215, -10.2467 octaves, 0.2153 Hz. Guide tone : 2048, 11.0000 octaves, 535809.158 Hz. Exponens Consonantiae : 2.488320E+06, 21.24674 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 2475.5, average 353.64286 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 12.81543, average 1.83078 Sum of Tenney's harmonic distance : 26.96384, average 3.85198 Vogel's harmonic complexity : 14.85714 Wille's k value : 607 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 6 Triangular lattice diameter : 6 Lattice compactness : 144.88177, average 5.17435 Lattice compactness (without 2's) : 66.36993, average 2.37035 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 1 .. 11 6.71429 47 1 3: -5 .. 0 -3.00000 21 2 5: -1 .. 0 -0.57143 4 4 Average exponent except 2's :-25 / 7 =-3.57143 Average absolute exponent except 2's: 25 / 7 = 3.57143
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 82.7632 c. M: 122.7064 c. Lebeng 8: 2 1 1 1 1 1 1 P M ME S SD: 32.1059 c. M: 57.8213 c. 9: 2 1 2 1 1 1 1 N D3 S SD: 30.8127 c. M:-56.8904 c. 12: 3 1 2 2 1 2 1 P D3 SD: 6.5684 c. M: 9.7763 c. Aeolian flat 1 41: 10 4 7 6 4 7 3 N SD: 3.2802 c. M:-4.8579 c. 53: 13 5 9 8 5 9 4 N SD: 1.2528 c. M:-1.7491 c. 65: 16 6 11 10 6 11 5 N SD: 0.8644 c. M:-1.6662 c. 118: 29 11 20 18 11 20 9 N SD: 0.8003 c. M:-1.1735 c. 183: 45 17 31 28 17 31 14 N SD: 0.7678 c. M:-1.2626 c. 311: 76 29 53 47 29 53 24 N SD: 0.7504 c. M: 1.1832 c. 323: 79 30 55 49 30 55 25 N SD: 0.7515 c. M: 1.1249 c. 348: 85 33 59 53 32 59 27 N SD: 0.7902 c. M: 1.0315 c. 350: 86 32 60 53 33 59 27 N SD: 0.7710 c. M: 1.2949 c. 352: 86 33 60 53 33 60 27 N SD: 0.6580 c. M: 1.2709 c. 364: 89 34 62 55 34 62 28 N SD: 0.5371 c. M: 0.9712 c. 376: 92 35 64 57 35 64 29 N SD: 0.4991 c. M: 0.7198 c. 417: 102 39 71 63 39 71 32 N SD: 0.4209 c. M: 0.8131 c. 429: 105 40 73 65 40 73 33 N SD: 0.3324 c. M: 0.5716 c. 441: 108 41 75 67 41 75 34 N SD: 0.3385 c. M: 0.5099 c. 482: 118 45 82 73 45 82 37 N SD: 0.2478 c. M: 0.4788 c. 494: 121 46 84 75 46 84 38 N SD: 0.1894 c. M: 0.2772 c. 547: 134 51 93 83 51 93 42 N SD: 0.1162 c. M: 0.2239 c. 559: 137 52 95 85 52 95 43 N SD: 0.1057 c. M: 0.1546 c. 612: 150 57 104 93 57 104 47 N SD: 0.0187 c. M:-0.0276 c. 2395: 587 223 407 364 223 407 184 N SD: 0.0201 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 x 5 x 6 S SD: 31.4099 cents 4 x 5 x 6:7 x 8 S SD: 28.2143 cents 5:6 x 7:8 x 9:10 S SD: 19.8080 cents 6:7:8 x 9:10:11:12 S SD: 24.2559 cents 7:8:9:10:11:12:13:14 H SD: 12.0622 cents 8:9:10:11:13 x 15:16 SD: 20.1798 cents 9:11 x 13:14:15:17:18 SD: 11.4625 cents 10:12:13:14:16:17:19:20 SD: 9.2959 cents 12:14:15:17:19:20:23:24 SD: 6.2392 cents 16:19:20:23:25:27:30:32 SD: 5.5408 cents 19:23:24:27:30:32:36:38 SD: 5.2521 cents 22:26:28:31:35:37:42:44 SD: 3.7899 cents 26:31:33:37:41:44:49:52 SD: 2.5992 cents 38:45:48:54:60:64:72:76 SD: 0.4984 cents 178:211:225:253:281:300:338:356 SD: 0.4497 cents 201:238:254:286:318:339:381:402 SD: 0.4362 cents 204:242:258:290:322:344:387:408 SD: 0.4184 cents 216:256:273:307:341:364:410:432 SD: 0.3872 cents 232:275:293:330:367:391:440:464 SD: 0.3643 cents 242:287:306:344:382:408:459:484 SD: 0.3517 cents 258:306:326:367:408:435:489:516 SD: 0.3186 cents 270:320:341:384:427:455:512:540 SD: 0.3152 cents 291:345:368:414:460:491:552:582 SD: 0.3050 cents 296:351:374:421:468:499:561:592 SD: 0.2666 cents 303:359:383:431:479:511:575:606 SD: 0.2588 cents 329:390:416:468:520:555:624:658 SD: 0.2220 cents 341:404:431:485:539:575:647:682 SD: 0.2062 cents 367:435:464:522:580:619:696:734 SD: 0.1613 cents 405:480:512:576:640:683:768:810 SD: 0.1207 cents 443:525:560:630:700:747:840:886 SD: 0.1008 cents 481:570:608:684:760:811:912:962 SD: 0.1000 cents