Scala analysis: xen09-wilson-marwa-12-10
Marwa permutation 10 from Figure 12, Helmholtz 16/15 16/15 75/64
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: 32/27 294.134997 Pythagorean minor third 3: 4/3 498.044999 perfect fourth 4: 25/16 772.627428 classic augmented fifth 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: 16/15 111.7313 minor diatonic semitone 3: 9/8 203.9100 major whole tone 4: 75/64 274.5824 classic augmented second 5: 16/15 111.7313 minor diatonic semitone 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: 3 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 75/64 274.582 cents classic augmented second 2: 1 256/225 223.463 cents Neapolitan diminished third 2: 1 32/27 294.135 cents Pythagorean minor third 2: 2 6/5 315.641 cents minor third 2: 2 5/4 386.314 cents major third 2: 1 675/512 478.492 cents wide augmented third 3: 1 32/25 427.373 cents classic diminished fourth 3: 4 4/3 498.045 cents perfect fourth 3: 2 45/32 590.224 cents diatonic tritone 4: 2 64/45 609.776 cents 2nd tritone 4: 4 3/2 701.955 cents perfect fifth 4: 1 25/16 772.627 cents classic augmented fifth 5: 1 1024/675 721.508 cents narrow diminished sixth 5: 2 8/5 813.686 cents minor sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 1 225/128 976.537 cents augmented sixth 6: 1 128/75 925.418 cents diminished seventh 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 3 15/8 1088.269 cents classic major seventh Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 182.4 294.1 498.0 772.6 884.4 996.1 1200.0 182.4 : 111.7 315.6 590.2 702.0 813.7 1017.6 1200.0 294.1 : 203.9 478.5 590.2 702.0 905.9 1088.3 1200.0 498.0 : 274.6 386.3 498.0 702.0 884.4 996.1 1200.0 772.6 : 111.7 223.5 427.4 609.8 721.5 925.4 1200.0 884.4 : 111.7 315.6 498.0 609.8 813.7 1088.3 1200.0 996.1 : 203.9 386.3 498.0 702.0 976.5 1088.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 274.5824 cents 1125/1024, 162.8511 cents 16/15, 111.7313 cents 2: 223.4626 .. 478.4924 cents 151875/131072, 255.0299 cents 16384/16875,-51.1199 cents 3: 427.3726 .. 590.2237 cents 1125/1024, 162.8511 cents 16384/16875,-51.1199 cents 4: 609.7763 .. 772.6274 cents 1125/1024, 162.8511 cents 2048/2025, 19.5526 cents 5: 721.5076 .. 976.5374 cents 151875/131072, 255.0299 cents 16384/16875,-51.1199 cents 6: 925.4176 .. 1088.2687 cents 1125/1024, 162.8511 cents 16384/16875,-51.1199 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 75/64, 274.5824 cents Average / Smallest step : 1.534293 Largest / Average step : 1.601731 Largest / Smallest step : 2.457525 Median interval of one step : 10/9, 182.4037 cents, amount: 1 Most common interval of one step : 16/15, 111.7313 cents, amount: 3 Least squares average step : 172.52609 cents, oct.: 1207.68260 cents Scale is not proper Step pattern alph. order: ABCDBBC Step pattern size order : BACDAAC Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.483493 Lumma stability : 0.202513 Lumma impropriety factor : 0.170400 Rothenberg efficiency : 0.436735 redundancy: 0.563265 Efficiency x scale size : 3.057143 Number of different interval sizes : 24 = 4.00000 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.00000 = 4 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 2048/2025, 19.5526 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 : 1 at degree 0 Formal octave complements present : 1 = 14.2857% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 5 Odd number limit : 675 (O: 675 U: 675) Highest odd numerator or denominator: 27 Scale harmonicity : 0.033557 Average absolute harmonicity : 0.235243 Specific harmonicity : 0.194844 Fundamental : 1/432, -8.7549 octaves, 0.6056 Hz. Guide tone : 800, 9.6439 octaves, 209300.452 Hz. Exponens Consonantiae : 3.456000E+05, 18.39874 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 81.0, average 11.57143 Mersenne's string divisions : 193036200 Sum of van Prooijen's expressibility: 5.91388, average 0.84484 Sum of Tenney's harmonic distance : 12.20748, average 1.74393 Vogel's harmonic complexity : 13.28571 Wille's k value : 337 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 5 Lattice compactness : 105.31462, average 3.76124 Lattice compactness (without 2's) : 49.09960, average 1.75356 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 5 1.28571 17 1 3: -3 .. 0 -1.28571 9 3 5: 0 .. 2 0.57143 4 3 Average exponent except 2's :-5 / 7 =-0.71429 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is JI-epimorphic with val: <7 11 16| = patent
FIT/MODE
7: 1 1 1 2 0 1 1 N T3 SD: 40.8773 c. M:-84.5154 c. 8: 1 1 1 2 1 1 1 P M ME I SD: 31.7482 c. M:-53.9100 c. 11: 2 1 2 2 1 1 2 P D3 S SD: 26.8479 c. M:-47.4095 c. 12: 2 1 2 3 1 1 2 N SD: 13.9235 c. M:-27.3726 c. 19: 3 2 3 4 2 2 3 P SD: 11.9313 c. M:-21.6545 c. 22: 3 2 4 5 2 2 4 N SD: 13.5290 c. M: 21.4077 c. 25: 4 2 4 6 2 3 4 N SD: 12.1484 c. M: 20.3587 c. 26: 4 2 5 6 2 3 4 N SD: 11.7443 c. M:-19.2946 c. 28: 4 3 5 6 3 2 5 N SD: 10.5041 c. M:-16.2407 c. 29: 4 3 5 7 2 3 5 N SD: 10.2659 c. M: 16.8865 c. 31: 5 3 5 7 3 3 5 N SD: 8.7668 c. M:-15.5424 c. 33: 5 3 6 7 3 3 6 N SD: 8.8848 c. M: 14.2718 c. 34: 5 3 6 8 3 3 6 N SD: 6.2098 c. M: 11.7821 c. 41: 6 4 7 9 4 4 7 N SD: 5.6697 c. M: 11.6518 c. 45: 7 4 8 10 4 4 8 N SD: 5.3645 c. M: 9.4233 c. 46: 7 4 8 11 4 4 8 N SD: 5.1627 c. M:-9.9813 c. 48: 7 5 8 11 4 5 8 N SD: 5.3657 c. M: 9.3587 c. 53: 8 5 9 12 5 5 9 N SD: 1.2766 c. M: 2.8161 c. 65: 10 6 11 15 6 6 11 N SD: 1.6100 c. M:-2.7572 c. 118: 18 11 20 27 11 11 20 N SD: 0.4751 c. M:-0.7803 c. 171: 26 16 29 39 16 16 29 N SD: 0.3918 c. M: 0.6976 c. 289: 44 27 49 66 27 27 49 N SD: 0.3577 c. M:-0.6747 c. 323: 49 30 55 74 30 30 55 N SD: 0.3377 c. M: 0.6365 c. 376: 57 35 64 86 35 35 64 N SD: 0.3461 c. M: 0.5180 c. 388: 59 36 66 89 36 36 66 N SD: 0.2724 c. M:-0.5684 c. 441: 67 41 75 101 41 41 75 N SD: 0.1402 c. M: 0.2574 c. 494: 75 46 84 113 46 46 84 N SD: 0.1518 c. M: 0.2175 c. 559: 85 52 95 128 52 52 95 N SD: 0.0805 c. M:-0.1812 c. 612: 93 57 104 140 57 57 104 N SD: 0.0400 c. M: 0.0784 c. 1171: 178 109 199 268 109 109 199 N SD: 0.0222 c. M:-0.0455 c. 1783: 271 166 303 408 166 166 303 N SD: 0.0128 c. M: 0.0239 c. 2395: 364 223 407 548 223 223 407 N SD: 0.0166 c. M: 0.0238 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: 35.3362 cents 3 x x 4 x 5 x 6 S SD: 0.0000 cents 4 x 5 x 6 x 7:8 S SD: 29.8275 cents 5 x 6:7:8 x 9:10 S SD: 19.7439 cents 6 x 7:8:9:10:11:12 S SD: 15.4344 cents 7:8 x 9:11:12 x 14 SD: 18.7814 cents 8:9 x 11 x 13:14:16 SD: 15.4467 cents 9:10:11:12:14:15:16:18 S SD: 7.6897 cents 16:18:19:21:25:27:28:32 SD: 7.0322 cents 17:19:20:23:27:28:30:34 SD: 6.8333 cents 18:20:21:24:28:30:32:36 S SD: 4.0477 cents 27:30:32:36:42:45:48:54 S SD: 1.1016 cents 81:90:96:108:127:135:144:162 SD: 0.8535 cents 108:120:128:144:169:180:192:216 SD: 0.3661 cents 135:150:160:180:211:225:240:270 SD: 0.0733 cents 297:330:352:396:464:495:528:594 SD: 0.0333 cents 432:480:512:576:675:720:768:864 SD: 0.0000 cents