Scala analysis: xen09-wilson-marwa-11b-07
Marwa permutation 7 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: 10/9 182.403712 minor whole tone 2: 5/4 386.313714 major third 3: 4/3 498.044999 perfect fourth 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: 10/9 182.4037 minor whole tone 2: 9/8 203.9100 major whole tone 3: 16/15 111.7313 minor diatonic semitone 4: 32/27 294.1350 Pythagorean minor 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: 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 : 182.4 386.3 498.0 792.2 884.4 1088.3 1200.0 182.4 : 203.9 315.6 609.8 702.0 905.9 1017.6 1200.0 386.3 : 111.7 405.9 498.0 702.0 813.7 996.1 1200.0 498.0 : 294.1 386.3 590.2 702.0 884.4 1088.3 1200.0 792.2 : 92.2 296.1 407.8 590.2 794.1 905.9 1200.0 884.4 : 203.9 315.6 498.0 702.0 813.7 1107.8 1200.0 1088.3: 111.7 294.1 498.0 609.8 903.9 996.1 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 : 10/9, 182.4037 cents, amount: 1 Least squares average step : 178.35209 cents, oct.: 1248.46460 cents Scale is not proper Step pattern alph. order: ABCDEBC Step pattern size order : CDBEADB 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 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 0 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 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 : 1215 (O: 1215 U: 1215) Highest odd numerator or denominator: 81 Scale harmonicity : 0.033632 Average absolute harmonicity : 0.237376 Specific harmonicity : 0.195678 Fundamental : 1/648, -9.3399 octaves, 0.4037 Hz. Guide tone : 1920, 10.9069 octaves, 502321.085 Hz. Exponens Consonantiae : 1.244160E+06, 20.24674 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 139.0, average 19.85714 Mersenne's string divisions : 2422728 Sum of van Prooijen's expressibility: 5.91388, average 0.84484 Sum of Tenney's harmonic distance : 11.90645, average 1.70092 Vogel's harmonic complexity : 15.71429 Wille's k value : 607 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 6 Triangular lattice diameter : 6 Lattice compactness : 112.71635, average 4.02558 Lattice compactness (without 2's) : 55.81396, average 1.99336 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 7 0.85714 16 1 3: -4 .. 1 -1.00000 9 2 5: 0 .. 1 0.57143 4 4 Average exponent except 2's :-3 / 7 =-0.42857 Average absolute exponent except 2's: 13 / 7 = 1.85714
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 50.5853 c. M: 106.4657 c. Lebeng 8: 1 1 1 2 1 1 1 P M ME I SD: 45.1927 c. M: 86.3137 c. 9: 1 2 1 2 1 1 1 N D3 S SD: 31.0916 c. M: 49.0704 c. 12: 2 2 1 3 1 2 1 P D3 SD: 11.6140 c. M:-17.5963 c. Ionian Augmented, Ionian sharp 5 26: 4 4 3 6 2 5 2 P SD: 11.2095 c. M:-19.4236 c. 27: 4 5 2 7 2 4 3 N SD: 10.9601 c. M: 21.6020 c. 29: 4 5 3 7 2 5 3 N SD: 11.3838 c. M: 16.8865 c. 31: 5 5 3 7 3 5 3 SP D3 SD: 8.7020 c. M: 17.9864 c. 32: 5 5 3 8 3 5 3 P SD: 8.7204 c. M:-15.6413 c. 33: 5 6 3 8 2 6 3 N SD: 8.5614 c. M:-13.6863 c. 34: 5 6 3 8 3 6 3 P SD: 6.9625 c. M: 15.7094 c. 39: 6 7 3 10 3 6 4 N SD: 8.2651 c. M:-13.6863 c. 41: 6 7 4 10 3 7 4 N SD: 4.6665 c. M: 6.7940 c. 53: 8 9 5 13 4 9 5 N SD: 1.0456 c. M: 1.4763 c. 118: 18 20 11 29 9 20 11 N SD: 0.5003 c. M:-1.0403 c. 171: 26 29 16 42 13 29 16 N SD: 0.4022 c. M:-0.8025 c. 224: 34 38 21 55 17 38 21 N SD: 0.4914 c. M: 0.7687 c. 289: 44 49 27 71 22 49 27 N SD: 0.4000 c. M:-0.8996 c. 323: 49 55 30 79 25 55 30 N SD: 0.3775 c. M: 0.8487 c. 335: 51 57 31 82 26 57 31 N SD: 0.4372 c. M:-0.6865 c. 376: 57 64 35 92 29 64 35 N SD: 0.3520 c. M: 0.6906 c. 388: 59 66 36 95 30 66 36 N SD: 0.2575 c. M: 0.4274 c. 441: 67 75 41 108 34 75 41 N SD: 0.1548 c. M: 0.3433 c. 494: 75 84 46 121 38 84 46 N SD: 0.1499 c. M: 0.2772 c. 506: 77 86 47 124 39 86 47 N SD: 0.1830 c. M:-0.2688 c. 559: 85 95 52 137 43 95 52 N SD: 0.0676 c. M:-0.1034 c. 612: 93 104 57 150 47 104 57 N SD: 0.0334 c. M: 0.0508 c. 1171: 178 199 109 287 90 199 109 N SD: 0.0212 c. M: 0.0365 c. 1783: 271 303 166 437 137 303 166 N SD: 0.0143 c. M: 0.0319 c. 2395: 364 407 223 587 184 407 223 N SD: 0.0163 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: 0.0000 cents 4 x 5 x 6:7 x 8 S SD: 30.8983 cents 5 x 6:7:8 x 9:10 S SD: 26.5228 cents 6:7 x 8:9:10:11:12 S SD: 21.5953 cents 7:8:9 x 11:12:13:14 SD: 14.4376 cents 8:9:10:11 x 13:15:16 SD: 12.0435 cents 9:10:11:12:14:15:17:18 SD: 7.0280 cents 10:11 x 13:16:17:19:20 SD: 11.0398 cents 12:13:15:16:19:20:23:24 SD: 8.3059 cents 15:17:19:20:24:25:28:30 SD: 6.7357 cents 16:18:20:21:25:27:30:32 SD: 6.4692 cents 17:19:21:23:27:28:32:34 SD: 5.8963 cents 19:21:24:25:30:32:36:38 SD: 5.7093 cents 21:23:26:28:33:35:39:42 SD: 5.0776 cents 24:27:30:32:38:40:45:48 SD: 3.1100 cents 33:37:41:44:52:55:62:66 SD: 2.8309 cents 36:40:45:48:57:60:68:72 SD: 1.8880 cents 45:50:56:60:71:75:84:90 SD: 1.6052 cents 63:70:79:84:100:105:118:126 SD: 1.3772 cents 64:71:80:85:101:107:120:128 SD: 1.3388 cents 72:80:90:96:114:120:135:144 SD: 0.4826 cents 153:170:191:204:242:255:287:306 SD: 0.4097 cents 207:230:259:276:327:345:388:414 SD: 0.2654 cents 216:240:270:288:341:360:405:432 SD: 0.2416 cents 279:310:349:372:441:465:523:558 SD: 0.1969 cents 288:320:360:384:455:480:540:576 SD: 0.0604 cents 360:400:450:480:569:600:675:720 SD: 0.0483 cents