Scala analysis: xen09-wilson-marwa-11b-02
Marwa permutation 2 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: 16/9 996.089998 Pythagorean minor seventh 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: 9/8 203.9100 major whole tone 6: 135/128 92.1787 major chroma, major limma 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 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 : 294.1 386.3 590.2 792.2 996.1 1088.3 1200.0 294.1 : 92.2 296.1 498.0 702.0 794.1 905.9 1200.0 386.3 : 203.9 405.9 609.8 702.0 813.7 1107.8 1200.0 590.2 : 202.0 405.9 498.0 609.8 903.9 996.1 1200.0 792.2 : 203.9 296.1 407.8 702.0 794.1 998.0 1200.0 996.1 : 92.2 203.9 498.0 590.2 794.1 996.1 1200.0 1088.3: 111.7 405.9 498.0 702.0 903.9 1107.8 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 : 185.11583 cents, oct.: 1295.81079 cents Scale is not proper Step pattern alph. order: ABCDCBE Step pattern size order : EADCDAB Scale is sum-free (all different intervals) 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 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 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 : 0.214621 Specific harmonicity : 0.152260 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 : 202.5, average 28.92857 Mersenne's string divisions : 446690475 Sum of van Prooijen's expressibility: 7.82237, average 1.11748 Sum of Tenney's harmonic distance : 15.95017, average 2.27860 Vogel's harmonic complexity : 17.57143 Wille's k value : 1822 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 7 Triangular lattice diameter : 7 Lattice compactness : 160.99960, average 5.74999 Lattice compactness (without 2's) : 72.51130, average 2.58969 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 7 1.00000 27 1 3: -4 .. 2 -0.85714 12 3 5: 0 .. 1 0.42857 3 3 Average exponent except 2's :-3 / 7 =-0.42857 Average absolute exponent except 2's: 15 / 7 = 2.14286
FIT/MODE
7: 2 0 1 2 1 0 1 N T3 SD: 51.9174 c. M: 75.9380 c. 8: 2 1 1 1 2 0 1 N D3 SD: 38.4259 c. M:-63.6863 c. 9: 2 1 1 2 1 1 1 P M ME S SD: 35.1416 c. M: 62.7567 c. 10: 2 1 2 1 2 1 1 P M ME S SD: 38.3581 c. M: 72.1800 c. 12: 3 1 2 2 2 1 1 N T3 SD: 8.7125 c. M:-13.6863 c. 29: 7 2 5 5 5 2 3 N SD: 8.7088 c. M: 13.8999 c. 35: 9 2 6 6 6 3 3 N SD: 7.9445 c. M:-14.4364 c. 40: 10 3 7 6 7 3 4 N SD: 7.5344 c. M: 12.1800 c. 41: 10 3 7 7 7 3 4 N SD: 3.6424 c. M: 5.8259 c. 53: 13 4 9 9 9 4 5 N SD: 0.9770 c. M: 1.5445 c. 65: 16 5 11 11 11 5 6 N SD: 1.0794 c. M:-1.6662 c. 118: 29 9 20 20 20 9 11 N SD: 0.5542 c. M:-1.0403 c. 171: 42 13 29 29 29 13 16 N SD: 0.5546 c. M:-0.8025 c. 289: 71 22 49 49 49 22 27 N SD: 0.5345 c. M:-0.8996 c. 311: 76 24 53 52 53 24 29 N SD: 0.6319 c. M: 1.1832 c. 323: 79 25 55 54 55 25 30 N SD: 0.4817 c. M: 0.8487 c. 364: 89 28 62 61 62 28 34 N SD: 0.5618 c. M: 0.9712 c. 376: 92 29 64 63 64 29 35 N SD: 0.3638 c. M: 0.6906 c. 388: 95 30 66 65 66 30 36 N SD: 0.3408 c. M:-0.4979 c. 429: 105 33 73 72 73 33 40 N SD: 0.3178 c. M: 0.5716 c. 441: 108 34 75 74 75 34 41 N SD: 0.2110 c. M: 0.3433 c. 494: 121 38 84 83 84 38 46 N SD: 0.1460 c. M: 0.2772 c. 547: 134 42 93 92 93 42 51 N SD: 0.1541 c. M: 0.2239 c. 559: 137 43 95 94 95 43 52 N SD: 0.0728 c. M:-0.1162 c. 612: 150 47 104 103 104 47 57 N SD: 0.0250 c. M: 0.0392 c. 1783: 437 137 303 300 303 137 166 N SD: 0.0179 c. M: 0.0319 c. 2395: 587 184 407 403 407 184 223 N SD: 0.0156 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 4:5 x x 6 S SD: 43.4535 cents 4 x 5 x 6:7 x 8 S SD: 23.5636 cents 5:6 x 7:8:9 x 10 S SD: 7.6080 cents 6:7 x 8:9 x 11:12 SD: 27.4914 cents 7:8:9:10:11:12:13:14 H SD: 15.2652 cents 9 x 11:13:14:16:17:18 SD: 11.2702 cents 12:14:15:17:19:21:23:24 SD: 7.9657 cents 15:18:19:21:24:27:28:30 SD: 6.4402 cents 17:20:21:24:27:30:32:34 SD: 4.3196 cents 27:32:34:38:43:48:51:54 SD: 3.2263 cents 32:38:40:45:51:57:60:64 SD: 2.2122 cents 48:57:60:68:76:85:90:96 SD: 2.1758 cents 49:58:61:69:77:87:92:98 SD: 1.8341 cents 55:65:69:77:87:98:103:110 SD: 1.7263 cents 59:70:74:83:93:105:111:118 SD: 1.3910 cents 64:76:80:90:101:114:120:128 SD: 0.7591 cents 81:96:101:114:128:144:152:162 SD: 0.6757 cents 135:160:169:190:213:240:253:270 SD: 0.5830 cents 136:161:170:191:215:242:255:272 SD: 0.4970 cents 152:180:190:214:240:270:285:304 SD: 0.4558 cents 167:198:209:235:264:297:313:334 SD: 0.3875 cents 184:218:230:259:291:327:345:368 SD: 0.3331 cents 216:256:270:304:341:384:405:432 SD: 0.3159 cents 248:294:310:349:392:441:465:496 SD: 0.2075 cents 352:417:440:495:556:626:660:704 SD: 0.1784 cents 384:455:480:540:607:683:720:768 SD: 0.1547 cents 448:531:560:630:708:796:840:896 SD: 0.1402 cents 512:607:640:720:809:910:960:1024 SD: 0.1002 cents