Scala analysis: xen09-wilson-marwa-11b-09
Marwa permutation 9 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: 16/9 996.089998 Pythagorean minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 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: 16/15 111.7313 minor diatonic semitone 7: 9/8 203.9100 major whole tone
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 9/8 203.910 cents major whole tone 2: 2 6/5 315.641 cents minor third 2: 3 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: 3 8/5 813.686 cents minor sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 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 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: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 182.4 386.3 498.0 792.2 884.4 996.1 1200.0 182.4 : 203.9 315.6 609.8 702.0 813.7 1017.6 1200.0 386.3 : 111.7 405.9 498.0 609.8 813.7 996.1 1200.0 498.0 : 294.1 386.3 498.0 702.0 884.4 1088.3 1200.0 792.2 : 92.2 203.9 407.8 590.2 794.1 905.9 1200.0 884.4 : 111.7 315.6 498.0 702.0 813.7 1107.8 1200.0 996.1 : 203.9 386.3 590.2 702.0 996.1 1088.3 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 : 10/9, 182.4037 cents, amount: 1 Least squares average step : 174.40157 cents, oct.: 1220.81098 cents Scale is not proper Step pattern alph. order: ABCDECB Step pattern size order : CDBEABD Scale is not a Constant Structure Scale diversity : 1.423133 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 Length of longest harmonic part : 2 at degree 6 Length of longest subharmonic part : 2 at degree 0 Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 5 Odd number limit : 405 (O: 405 U: 405) Highest odd numerator or denominator: 81 Scale harmonicity : 0.038363 Average absolute harmonicity : 0.240844 Specific harmonicity : 0.211686 Fundamental : 1/324, -8.3399 octaves, 0.8075 Hz. Guide tone : 640, 9.3219 octaves, 167440.362 Hz. Exponens Consonantiae : 2.073600E+05, 17.66178 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 140.0, average 20.00000 Mersenne's string divisions : 2633400 Sum of van Prooijen's expressibility: 5.69203, average 0.81315 Sum of Tenney's harmonic distance : 11.98563, average 1.71223 Vogel's harmonic complexity : 13.71429 Wille's k value : 202 Wilson's harmonic complexity : 17 Rectangular lattice diameter : 5 Triangular lattice diameter : 5 Lattice compactness : 106.16247, average 3.79152 Lattice compactness (without 2's) : 51.30072, average 1.83217 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 7 1.85714 17 1 3: -4 .. 0 -1.42857 10 3 5: 0 .. 1 0.42857 3 3 Average exponent except 2's :-7 / 7 =-1.00000 Average absolute exponent except 2's: 13 / 7 = 1.85714
FIT/MODE
7: 1 1 1 2 0 1 1 N T3 SD: 34.4106 c. M:-64.9629 c. 9: 1 2 1 2 1 0 2 N T3 SD: 38.2446 c. M: 62.7567 c. 10: 1 2 1 2 1 1 2 P M ME S SD: 43.7401 c. M: 72.1800 c. 12: 2 2 1 3 1 1 2 N T3 SD: 10.8355 c. M:-17.5963 c. 27: 4 5 2 7 2 2 5 N SD: 10.0681 c. M: 18.3122 c. 29: 4 5 3 7 2 3 5 N SD: 10.4344 c. M: 16.8865 c. 31: 5 5 3 8 2 3 5 N SD: 10.1703 c. M:-20.7232 c. 33: 5 6 3 8 2 3 6 N SD: 10.0697 c. M: 14.2718 c. 34: 5 6 3 8 3 3 6 N SD: 7.2390 c. M: 15.7094 c. 37: 6 6 3 9 3 4 6 N SD: 9.5853 c. M: 13.8016 c. 38: 6 6 4 9 3 4 6 N SD: 7.2909 c. M:-14.4363 c. 39: 6 7 3 10 3 3 7 N SD: 8.2905 c. M:-13.6863 c. 41: 6 7 4 10 3 4 7 N SD: 4.2230 c. M: 6.7940 c. 53: 8 9 5 13 4 5 9 N SD: 0.8858 c. M: 1.4081 c. 118: 18 20 11 29 9 11 20 N SD: 0.5352 c. M:-1.0403 c. 171: 26 29 16 42 13 16 29 N SD: 0.3764 c. M:-0.8025 c. 224: 34 38 21 55 17 21 38 N SD: 0.4165 c. M:-0.6771 c. 289: 44 49 27 71 22 27 49 N SD: 0.4103 c. M:-0.8996 c. 323: 49 55 30 79 25 30 55 N SD: 0.3967 c. M: 0.8487 c. 335: 51 57 31 82 26 31 57 N SD: 0.3663 c. M:-0.5520 c. 376: 57 64 35 92 29 35 64 N SD: 0.3752 c. M: 0.6906 c. 388: 59 66 36 95 30 36 66 N SD: 0.2258 c. M: 0.4274 c. 441: 67 75 41 108 34 41 75 N SD: 0.1556 c. M: 0.3433 c. 494: 75 84 46 121 38 46 84 N SD: 0.1587 c. M: 0.2772 c. 506: 77 86 47 124 39 47 86 N SD: 0.1531 c. M:-0.2476 c. 559: 85 95 52 137 43 52 95 N SD: 0.0560 c. M:-0.0906 c. 612: 93 104 57 150 47 57 104 N SD: 0.0313 c. M: 0.0508 c. 1171: 178 199 109 287 90 109 199 N SD: 0.0188 c. M: 0.0365 c. 1783: 271 303 166 437 137 166 303 N SD: 0.0151 c. M: 0.0319 c. 2395: 364 407 223 587 184 223 407 N SD: 0.0172 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 x 7:8 S SD: 23.5636 cents 5 x 6:7:8 x 9:10 S SD: 22.8511 cents 6:7 x 8:9:10:11:12 S SD: 22.4309 cents 7:8:9 x 11:12 x 14 SD: 17.0053 cents 8:9:10:11 x 13:14:16 SD: 12.8723 cents 9:10:11:12:14:15:16:18 S SD: 6.7868 cents 10:11 x 13:16:17:18:20 SD: 10.9599 cents 12:13:15:16:19:20:21:24 SD: 7.3899 cents 15:17:19:20:24:25:27:30 SD: 7.3209 cents 17:19:21:23:27:28:30:34 SD: 6.0959 cents 19:21:24:25:30:32:34:38 SD: 5.3404 cents 21:23:26:28:33:35:37:42 SD: 5.0100 cents 24:27:30:32:38:40:43:48 SD: 3.6574 cents 27:30:34:36:43:45:48:54 SD: 2.6525 cents 36:40:45:48:57:60:64:72 SD: 0.4826 cents 117:130:146:156:185:195:208:234 SD: 0.4485 cents 153:170:191:204:242:255:272:306 SD: 0.3953 cents 171:190:214:228:270:285:304:342 SD: 0.3535 cents 207:230:259:276:327:345:368:414 SD: 0.2532 cents 216:240:270:288:341:360:384:432 SD: 0.2416 cents 243:270:304:324:384:405:432:486 SD: 0.2035 cents 252:280:315:336:398:420:448:504 SD: 0.1381 cents 288:320:360:384:455:480:512:576 SD: 0.0604 cents 324:360:405:432:512:540:576:648 SD: 0.0000 cents