Scala analysis: xen09-wilson-marwa-11a-04
Marwa permutation 4 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: 4096/3645 201.956281 narrow diminished 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: 4096/3645 201.9563 narrow diminished third 2: 9/8 203.9100 major whole tone 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: 1 16/15 111.731 cents minor diatonic semitone 1: 1 10/9 182.404 cents minor whole tone 1: 1 4096/3645 201.956 cents narrow diminished third 1: 3 9/8 203.910 cents major whole tone 2: 2 32/27 294.135 cents Pythagorean minor third 2: 1 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: 1 512/405 405.866 cents narrow diminished fourth 2: 1 81/64 407.820 cents Pythagorean major third 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: 1 128/81 792.180 cents Pythagorean minor sixth 5: 1 405/256 794.134 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: 1 2048/1215 903.911 cents narrow diminished seventh 5: 2 27/16 905.865 cents Pythagorean major sixth 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 1 3645/2048 998.044 cents wide augmented sixth 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 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: 6 Average number of different intervals per interval class: 5.00000 = 5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 202.0 405.9 609.8 792.2 903.9 1107.8 1200.0 202.0 : 203.9 407.8 590.2 702.0 905.9 998.0 1200.0 405.9 : 203.9 386.3 498.0 702.0 794.1 996.1 1200.0 609.8 : 182.4 294.1 498.0 590.2 792.2 996.1 1200.0 792.2 : 111.7 315.6 407.8 609.8 813.7 1017.6 1200.0 903.9 : 203.9 296.1 498.0 702.0 905.9 1088.3 1200.0 1107.8: 92.2 294.1 498.0 702.0 884.4 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 92.1787 .. 203.9100 cents 16/15, 111.7313 cents 135/128, 92.1787 cents 2: 294.1350 .. 407.8200 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 3: 407.8200 .. 609.7763 cents 4096/3645, 201.9563 cents 1/1, 0.0000 cents 4: 590.2237 .. 792.1800 cents 4096/3645, 201.9563 cents 2025/2048,-19.5526 cents 5: 792.1800 .. 905.8650 cents 2187/2048, 113.6850 cents 1/1, 0.0000 cents 6: 996.0900 .. 1107.8213 cents 16/15, 111.7313 cents 256/243, 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 : 9/8, 203.9100 cents Average / Smallest step : 1.859741 Largest / Average step : 1.189475 Largest / Smallest step : 2.212116 Median interval of one step : 4096/3645, 201.9563 cents, amount: 1 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 182.70158 cents, oct.: 1278.91109 cents Scale is not proper Step pattern alph. order: ABBCDBE Step pattern size order : DEECBEA Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 1.424875 Lumma stability : 0.304006 Lumma impropriety factor : 0.016294 Rothenberg efficiency : 0.410884 redundancy: 0.589116 Efficiency x scale size : 2.876190 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 5.00000 = 5 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: 3 Number of recognisable fifths : 4, average 701.9550 cents Best minor thirds form a closed circle Length of longest harmonic part : 2 at degree 2 Formal octave complements present : 1 = 14.2857% Limited inverse transpositions with margin 182.4037 cents: 4 -- 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 : 0.179658 Specific harmonicity : 0.146341 Fundamental : 1/3645, -11.8317 octaves, 0.0718 Hz. Guide tone : 4096, 12.0000 octaves, 1071618.315 Hz. Exponens Consonantiae : 1.492992E+07, 23.83170 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 6316.5, average 902.35714 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 14.94576, average 2.13511 Sum of Tenney's harmonic distance : 31.20138, average 4.45734 Vogel's harmonic complexity : 16.85714 Wille's k value : 1822 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 7 Triangular lattice diameter : 7 Lattice compactness : 165.00618, average 5.89308 Lattice compactness (without 2's) : 77.70703, average 2.77525 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 1 .. 12 7.71429 54 1 3: -6 .. 0 -3.42857 24 1 5: -1 .. 0 -0.71429 5 5 Average exponent except 2's :-29 / 7 =-4.14286 Average absolute exponent except 2's: 29 / 7 = 4.14286
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 69.5119 c. M: 106.4657 c. Lebeng 8: 1 2 1 1 1 1 1 P M ME S SD: 37.5701 c. M: 57.8213 c. 11: 2 2 2 1 1 2 1 N D3 SD: 27.4404 c. M:-44.7692 c. 12: 2 2 2 2 1 2 1 P D3 S SD: 6.2271 c. M: 9.7763 c. Lydian Augmented, Lydian sharp 5 41: 7 7 7 6 4 7 3 N SD: 3.4173 c. M:-4.8579 c. 53: 9 9 9 8 5 9 4 N SD: 1.4267 c. M:-1.8173 c. 65: 11 11 11 10 6 11 5 N SD: 0.8388 c. M:-1.6662 c. 118: 20 20 20 18 11 20 9 N SD: 0.9204 c. M:-1.4335 c. 183: 31 31 31 28 17 31 14 N SD: 0.8433 c. M:-1.3224 c. 248: 42 42 42 38 23 42 19 N SD: 0.8243 c. M:-1.3684 c. 311: 52 53 53 47 29 53 24 N SD: 0.8348 c. M: 1.3132 c. 313: 53 53 53 48 29 53 24 N SD: 0.8189 c. M:-1.4302 c. 323: 54 55 55 49 30 55 25 N SD: 0.8731 c. M: 1.3371 c. 327: 55 56 55 50 30 56 25 N SD: 0.7848 c. M:-1.4732 c. 339: 57 58 57 52 31 58 26 N SD: 0.8029 c. M: 1.2564 c. 340: 57 58 58 51 32 58 26 N SD: 0.7671 c. M: 1.5918 c. 350: 59 59 60 53 33 59 27 N SD: 0.7317 c. M: 1.2949 c. 352: 59 60 60 53 33 60 27 N SD: 0.6319 c. M: 1.2709 c. 364: 61 62 62 55 34 62 28 N SD: 0.5636 c. M: 0.9712 c. 376: 63 64 64 57 35 64 29 N SD: 0.5697 c. M: 0.8925 c. 388: 65 66 66 59 36 66 30 N SD: 0.6357 c. M: 0.9254 c. 405: 68 69 69 61 38 69 31 N SD: 0.5175 c. M: 1.0689 c. 417: 70 71 71 63 39 71 32 N SD: 0.4028 c. M: 0.8131 c. 429: 72 73 73 65 40 73 33 N SD: 0.3587 c. M: 0.5716 c. 441: 74 75 75 67 41 75 34 N SD: 0.3948 c. M: 0.5957 c. 470: 79 80 80 71 44 80 36 N SD: 0.3416 c. M: 0.6906 c. 482: 81 82 82 73 45 82 37 N SD: 0.2357 c. M: 0.4788 c. 494: 83 84 84 75 46 84 38 N SD: 0.2143 c. M: 0.3368 c. 547: 92 93 93 83 51 93 42 N SD: 0.1087 c. M: 0.2239 c. 559: 94 95 95 85 52 95 43 N SD: 0.1223 c. M: 0.1674 c. 612: 103 104 104 93 57 104 47 N SD: 0.0176 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: 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 x 6:7:8 x 9:10 S SD: 26.4476 cents 6:7:8 x 9:10:11:12 S SD: 26.1678 cents 7:8:9:10:11:12:13:14 H SD: 9.0565 cents 8:9:10:11:13 x 15:16 SD: 13.4612 cents 9:10:11:13:14:15:17:18 SD: 10.7776 cents 10:11:13:14:16:17:19:20 SD: 10.2392 cents 14:16:18:20:22:24:27:28 S SD: 8.5333 cents 15:17:19:21:24:25:28:30 SD: 7.2279 cents 16:18:20:23:25:27:30:32 SD: 5.5268 cents 19:21:24:27:30:32:36:38 SD: 4.1235 cents 26:29:33:37:41:44:49:52 SD: 2.8213 cents 31:35:39:44:49:52:59:62 SD: 2.3054 cents 38:43:48:54:60:64:72:76 SD: 1.7803 cents 48:54:61:68:76:81:91:96 SD: 1.7337 cents 50:56:63:71:79:84:95:100 SD: 1.5536 cents 57:64:72:81:90:96:108:114 SD: 0.4984 cents 178:200:225:253:281:300:338:356 SD: 0.4486 cents 185:208:234:263:292:312:351:370 SD: 0.4058 cents 201:226:254:286:318:339:381:402 SD: 0.3966 cents 220:247:278:313:348:371:417:440 SD: 0.3921 cents 235:264:297:334:371:396:446:470 SD: 0.3765 cents 242:272:306:344:382:408:459:484 SD: 0.3176 cents 258:290:326:367:408:435:489:516 SD: 0.2712 cents 315:354:398:448:498:531:597:630 SD: 0.2256 cents 341:383:431:485:539:575:647:682 SD: 0.2230 cents 348:391:440:495:550:587:660:696 SD: 0.1898 cents 379:426:479:539:599:639:719:758 SD: 0.1563 cents 405:455:512:576:640:683:768:810 SD: 0.1350 cents 436:490:551:620:689:735:827:872 SD: 0.1189 cents 500:562:632:711:790:843:948:1000 SD: 0.1139 cents