Scala analysis: xen09-wilson-marwa-11b-04
Marwa permutation 4 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: 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: 10/9 182.4037 minor whole tone 2: 9/8 203.9100 major whole tone 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: 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 : 182.4 386.3 590.2 792.2 884.4 1088.3 1200.0 182.4 : 203.9 407.8 609.8 702.0 905.9 1017.6 1200.0 386.3 : 203.9 405.9 498.0 702.0 813.7 996.1 1200.0 590.2 : 202.0 294.1 498.0 609.8 792.2 996.1 1200.0 792.2 : 92.2 296.1 407.8 590.2 794.1 998.0 1200.0 884.4 : 203.9 315.6 498.0 702.0 905.9 1107.8 1200.0 1088.3: 111.7 294.1 498.0 702.0 903.9 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 92.1787 .. 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 : 180.32734 cents, oct.: 1262.29141 cents Scale is not proper Step pattern alph. order: ABBCDBE Step pattern size order : CEEDAEB 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 : 1 at degree 0 Length of longest subharmonic part : 2 at degree 0 Formal octave complements present : 1 = 14.2857% Limited inverse transpositions with margin 201.9563 cents: 4 -- 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 : 0.215301 Specific harmonicity : 0.173441 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 : 174.0, average 24.85714 Mersenne's string divisions : 2422728 Sum of van Prooijen's expressibility: 7.08997, average 1.01285 Sum of Tenney's harmonic distance : 13.98563, average 1.99795 Vogel's harmonic complexity : 18.71429 Wille's k value : 1822 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 7 Triangular lattice diameter : 7 Lattice compactness : 133.76478, average 4.77731 Lattice compactness (without 2's) : 65.30436, average 2.33230 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 7 -0.14286 19 1 3: -4 .. 2 -0.57143 10 1 5: 0 .. 1 0.71429 5 5 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: 57.8359 c. M: 106.4657 c. Lebeng 8: 1 2 1 1 1 1 1 P M ME S SD: 35.2335 c. M:-63.6863 c. 10: 1 2 2 1 1 2 1 P D3 S SD: 41.2799 c. M: 72.1800 c. 11: 1 2 2 2 1 2 1 N D3 SD: 41.0955 c. M: 73.3128 c. 12: 2 2 2 2 1 2 1 P D3 S SD: 12.1652 c. M:-17.5963 c. Lydian Augmented, Lydian sharp 5 26: 4 4 5 4 2 5 2 P SD: 11.2255 c. M:-19.4236 c. 29: 4 5 5 5 2 5 3 N SD: 12.0950 c. M: 16.8865 c. 30: 5 5 5 5 2 5 3 P SD: 10.2890 c. M:-17.5963 c. 31: 5 5 5 5 3 5 3 SP D3 S SD: 9.2194 c. M: 17.9864 c. 32: 5 5 6 5 3 5 3 P SD: 8.5915 c. M:-15.6413 c. 33: 5 6 5 6 2 6 3 N SD: 8.1216 c. M:-13.6863 c. 34: 5 6 6 5 3 6 3 P S SD: 7.7413 c. M: 15.7094 c. 35: 5 6 6 6 3 6 3 N SD: 7.5648 c. M: 10.9751 c. 41: 6 7 7 7 3 7 4 N SD: 5.0114 c. M: 6.7940 c. 53: 8 9 9 9 4 9 5 N SD: 1.1973 c. M: 1.5445 c. 118: 18 20 20 20 9 20 11 N SD: 0.5126 c. M:-1.0403 c. 171: 26 29 29 29 13 29 16 N SD: 0.4862 c. M:-0.8025 c. 289: 44 49 49 49 22 49 27 N SD: 0.4527 c. M:-0.8996 c. 323: 49 55 55 54 25 55 30 N SD: 0.4125 c. M: 0.8487 c. 376: 57 64 64 63 29 64 35 N SD: 0.3542 c. M: 0.6906 c. 388: 59 66 66 65 30 66 36 N SD: 0.3164 c. M:-0.4979 c. 429: 65 73 73 72 33 73 40 N SD: 0.3742 c. M: 0.5855 c. 441: 67 75 75 74 34 75 41 N SD: 0.1789 c. M: 0.3433 c. 494: 75 84 84 83 38 84 46 N SD: 0.1493 c. M: 0.2772 c. 559: 85 95 95 94 43 95 52 N SD: 0.0804 c. M:-0.1162 c. 612: 93 104 104 103 47 104 57 N SD: 0.0350 c. M: 0.0508 c. 1171: 178 199 199 197 90 199 109 N SD: 0.0261 c. M:-0.0410 c. 1783: 271 303 303 300 137 303 166 N SD: 0.0154 c. M: 0.0319 c. 1901: 289 323 323 320 146 323 177 N SD: 0.0184 c. M:-0.0346 c. 2395: 364 407 407 403 184 407 223 N SD: 0.0162 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 x 6:7:8 x 9:10 S SD: 20.5048 cents 6:7 x 8:9:10:11:12 S SD: 26.5025 cents 7:8:9:10:11:12:13:14 H SD: 12.9735 cents 8:9:10:11 x 13:15:16 SD: 10.4048 cents 9:10:11:13:14:15:17:18 SD: 9.6602 cents 12:13:15:17:19:20:23:24 SD: 8.5041 cents 15:17:19:21:24:25:28:30 SD: 6.8252 cents 17:19:21:24:27:28:32:34 SD: 4.7610 cents 24:27:30:34:38:40:45:48 SD: 3.6060 cents 27:30:34:38:43:45:51:54 SD: 3.2263 cents 35:39:44:49:55:58:66:70 SD: 3.0996 cents 36:40:45:51:57:60:68:72 SD: 2.6260 cents 44:49:55:62:70:73:83:88 SD: 2.6140 cents 45:50:56:63:71:75:84:90 SD: 1.9469 cents 55:61:69:77:87:92:103:110 SD: 1.7828 cents 57:63:71:80:90:95:107:114 SD: 1.6784 cents 64:71:80:90:101:107:120:128 SD: 0.9249 cents 72:80:90:101:114:120:135:144 SD: 0.7789 cents 81:90:101:114:128:135:152:162 SD: 0.6757 cents 128:142:160:180:202:213:240:256 SD: 0.6400 cents 135:150:169:190:213:225:253:270 SD: 0.5830 cents 136:151:170:191:215:227:255:272 SD: 0.5289 cents 152:169:190:214:240:253:285:304 SD: 0.5074 cents 153:170:191:215:242:255:287:306 SD: 0.4474 cents 200:222:250:281:316:333:375:400 SD: 0.4151 cents 207:230:259:291:327:345:388:414 SD: 0.2771 cents 224:249:280:315:354:373:420:448 SD: 0.2476 cents 288:320:360:405:455:480:540:576 SD: 0.0604 cents