Scala analysis: xen09-wilson-marwa-11b-03
Marwa permutation 3 from Figure 11b, Hawkins 135/128 16/15 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: 5/4 386.313714 major third 3: 45/32 590.223716 diatonic tritone 4: 128/81 792.179997 Pythagorean minor sixth 5: 5/3 884.358713 major sixth, BP sixth 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: 32/27 294.1350 Pythagorean minor third 2: 135/128 92.1787 major chroma, major limma 3: 9/8 203.9100 major whole tone 4: 4096/3645 201.9563 narrow diminished third 5: 135/128 92.1787 major chroma, major limma 6: 9/8 203.9100 major whole tone 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 : 294.1 386.3 590.2 792.2 884.4 1088.3 1200.0 294.1 : 92.2 296.1 498.0 590.2 794.1 905.9 1200.0 386.3 : 203.9 405.9 498.0 702.0 813.7 1107.8 1200.0 590.2 : 202.0 294.1 498.0 609.8 903.9 996.1 1200.0 792.2 : 92.2 296.1 407.8 702.0 794.1 998.0 1200.0 884.4 : 203.9 315.6 609.8 702.0 905.9 1107.8 1200.0 1088.3: 111.7 405.9 498.0 702.0 903.9 996.1 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: 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 : 181.12542 cents, oct.: 1267.87797 cents Scale is not proper Step pattern alph. order: ABCDBCE Step pattern size order : EADCADB Scale is sum-free (all different intervals) 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 Formal octave complements present : 1 = 14.2857% Scale is n-1 differentially coherent in interval classes 2 and 3 combined 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: 81 Scale harmonicity : 0.029070 Average absolute harmonicity : 0.215071 Specific harmonicity : 0.156581 Fundamental : 1/2592, -11.3399 octaves, 0.1009 Hz. Guide tone : 5760, 12.4919 octaves, 1506963.256 Hz. Exponens Consonantiae : 1.492992E+07, 23.83170 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 194.0, average 27.71429 Mersenne's string divisions : 142940952 Sum of van Prooijen's expressibility: 7.56709, average 1.08101 Sum of Tenney's harmonic distance : 14.96790, average 2.13827 Vogel's harmonic complexity : 18.14286 Wille's k value : 1822 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 7 Triangular lattice diameter : 7 Lattice compactness : 151.89559, average 5.42484 Lattice compactness (without 2's) : 70.21663, average 2.50774 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 7 0.42857 23 1 3: -4 .. 2 -0.71429 11 2 5: 0 .. 1 0.57143 4 4 Average exponent except 2's :-1 / 7 =-0.14286 Average absolute exponent except 2's: 15 / 7 = 2.14286
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 74.0187 c. M: 122.7064 c. Lebeng 8: 2 1 1 1 1 1 1 P M ME S SD: 33.1107 c. M:-63.6863 c. 9: 2 1 1 2 1 1 1 P M ME S SD: 31.8583 c. M: 56.8904 c. 12: 3 1 2 2 1 2 1 P D3 SD: 10.4247 c. M:-15.6413 c. Aeolian flat 1 29: 7 2 5 5 2 5 3 N SD: 10.4124 c. M: 15.3932 c. 30: 7 3 5 5 2 5 3 P SD: 9.4959 c. M: 14.1350 c. 32: 8 2 6 5 3 5 3 P SD: 8.6612 c. M:-15.6413 c. 33: 8 3 5 6 2 6 3 N SD: 8.2096 c. M:-13.6863 c. 38: 9 3 7 6 3 6 4 P SD: 8.1800 c. M: 14.5845 c. 41: 10 3 7 7 3 7 4 N SD: 4.3383 c. M: 6.3099 c. 53: 13 4 9 9 4 9 5 N SD: 1.0993 c. M: 1.5445 c. 65: 16 5 11 11 5 11 6 N SD: 1.2354 c. M:-1.7951 c. 118: 29 9 20 20 9 20 11 N SD: 0.5384 c. M:-1.0403 c. 171: 42 13 29 29 13 29 16 N SD: 0.5364 c. M:-0.8025 c. 289: 71 22 49 49 22 49 27 N SD: 0.5074 c. M:-0.8996 c. 323: 79 25 55 54 25 55 30 N SD: 0.4577 c. M: 0.8487 c. 376: 92 29 64 63 29 64 35 N SD: 0.3600 c. M: 0.6906 c. 388: 95 30 66 65 30 66 36 N SD: 0.3378 c. M:-0.4979 c. 429: 105 33 73 72 33 73 40 N SD: 0.3425 c. M: 0.5716 c. 441: 108 34 75 74 34 75 41 N SD: 0.2008 c. M: 0.3433 c. 494: 121 38 84 83 38 84 46 N SD: 0.1473 c. M: 0.2772 c. 547: 134 42 93 92 42 93 51 N SD: 0.1785 c. M: 0.2636 c. 559: 137 43 95 94 43 95 52 N SD: 0.0780 c. M:-0.1162 c. 612: 150 47 104 103 47 104 57 N SD: 0.0299 c. M: 0.0450 c. 1171: 287 90 199 197 90 199 109 N SD: 0.0280 c. M:-0.0410 c. 1783: 437 137 303 300 137 303 166 N SD: 0.0170 c. M: 0.0319 c. 2395: 587 184 407 403 184 407 223 N SD: 0.0159 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 x 4 x 5 x 6 S SD: 30.7262 cents 4 x 5 x 6:7 x 8 S SD: 30.8983 cents 5:6 x 7:8 x 9:10 S SD: 15.4649 cents 6:7 x 8:9:10:11:12 S SD: 22.9095 cents 7:8:9:10:11:12:13:14 H SD: 14.1658 cents 8:9:10:11 x 13:15:16 SD: 17.9315 cents 9 x 11:13:14:15:17:18 SD: 11.2702 cents 12:14:15:17:19:20:23:24 SD: 6.9486 cents 15:18:19:21:24:25:28:30 SD: 5.6601 cents 17:20:21:24:27:28:32:34 SD: 4.8882 cents 24:28:30:34:38:40:45:48 SD: 4.3283 cents 27:32:34:38:43:45:51:54 SD: 3.2263 cents 32:38:40:45:51:53:60:64 SD: 2.6581 cents 39:46:49:55:62:65:73:78 SD: 2.4271 cents 47:56:59:66:74:78:88:94 SD: 2.2370 cents 48:57:60:68:76:80:90:96 SD: 1.9487 cents 55:65:69:77:87:92:103:110 SD: 1.8630 cents 59:70:74:83:93:98:111:118 SD: 1.6036 cents 64:76:80:90:101:107:120:128 SD: 0.9689 cents 81:96:101:114:128:135:152:162 SD: 0.6757 cents 135:160:169:190:213:225:253:270 SD: 0.5830 cents 136:161:170:191:215:227:255:272 SD: 0.5722 cents 145:172:181:204:229:242:272:290 SD: 0.5705 cents 152:180:190:214:240:253:285:304 SD: 0.5219 cents 167:198:209:235:264:278:313:334 SD: 0.4790 cents 184:218:230:259:291:307:345:368 SD: 0.4196 cents 200:237:250:281:316:333:375:400 SD: 0.3355 cents 216:256:270:304:341:360:405:432 SD: 0.3159 cents 248:294:310:349:392:413:465:496 SD: 0.2811 cents 264:313:330:371:417:440:495:528 SD: 0.2180 cents 312:370:390:439:493:520:585:624 SD: 0.2056 cents 345:409:431:485:545:575:647:690 SD: 0.2019 cents 384:455:480:540:607:640:720:768 SD: 0.0967 cents 600:711:750:844:948:1000:1125:1200 SD: 0.0914 cents