Scala analysis: xen09-wilson-marwa-12-09
Marwa permutation 9 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: 5/4 386.313714 major 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: 9/8 203.9100 major whole tone 3: 16/15 111.7313 minor diatonic semitone 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: 2 6/5 315.641 cents minor third 2: 4 5/4 386.314 cents major 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: 4 8/5 813.686 cents minor sixth 5: 2 5/3 884.359 cents major sixth, BP 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: 4 Average number of different intervals per interval class: 3.33333 = 10/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 182.4 386.3 498.0 772.6 884.4 996.1 1200.0 182.4 : 203.9 315.6 590.2 702.0 813.7 1017.6 1200.0 386.3 : 111.7 386.3 498.0 609.8 813.7 996.1 1200.0 498.0 : 274.6 386.3 498.0 702.0 884.4 1088.3 1200.0 772.6 : 111.7 223.5 427.4 609.8 813.7 925.4 1200.0 884.4 : 111.7 315.6 498.0 702.0 813.7 1088.3 1200.0 996.1 : 203.9 386.3 590.2 702.0 976.5 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 .. 386.3137 cents 1125/1024, 162.8511 cents 16384/16875,-51.1199 cents 3: 427.3726 .. 590.2237 cents 1125/1024, 162.8511 cents 128/125, 41.0589 cents 4: 609.7763 .. 772.6274 cents 1125/1024, 162.8511 cents 2048/2025, 19.5526 cents 5: 813.6863 .. 976.5374 cents 1125/1024, 162.8511 cents 128/125, 41.0589 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 : 173.84292 cents, oct.: 1216.90047 cents Scale is not proper Step pattern alph. order: ABCDCCB Step pattern size order : BCADAAC Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.448366 Lumma stability : 0.270944 Lumma impropriety factor : 0.085200 Rothenberg efficiency : 0.478912 redundancy: 0.521088 Efficiency x scale size : 3.352381 Number of different interval sizes : 20 = 3.33333 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.33333 = 10/3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 2048/2025, 19.5526 cents Most common triad is 0.0 386.314 498.045 cents, amount: 3 Number of recognisable fifths : 4, average 701.9550 cents Best fifths form a closed circle 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 n-1 differentially coherent in interval class 1 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 : 225 (O: 225 U: 225) Highest odd numerator or denominator: 25 Scale harmonicity : 0.038265 Average absolute harmonicity : 0.241261 Specific harmonicity : 0.212014 Fundamental : 1/144, -7.1699 octaves, 1.8168 Hz. Guide tone : 400, 8.6439 octaves, 104650.226 Hz. Exponens Consonantiae : 5.760000E+04, 15.81378 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 56.0, average 8.00000 Mersenne's string divisions : 9815400 Sum of van Prooijen's expressibility: 5.18149, average 0.74021 Sum of Tenney's harmonic distance : 10.57200, average 1.51029 Vogel's harmonic complexity : 11.28571 Wille's k value : 112 Wilson's harmonic complexity : 16 Rectangular lattice diameter : 4 Triangular lattice diameter : 4 Lattice compactness : 94.17048, average 3.36323 Lattice compactness (without 2's) : 42.49405, average 1.51764 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 4 0.28571 14 1 3: -2 .. 0 -0.85714 6 2 5: 0 .. 2 0.71429 5 4 Average exponent except 2's :-1 / 7 =-0.14286 Average absolute exponent except 2's: 11 / 7 = 1.57143 Scale is JI-epimorphic with val: <7 11 16| = patent
FIT/MODE
7: 1 1 1 2 0 1 1 N T3 SD: 40.0202 c. M:-84.5154 c. 8: 1 2 0 2 1 1 1 P D3 S SD: 39.7801 c. M:-63.6863 c. 10: 1 2 1 2 1 1 2 P M ME S SD: 39.5548 c. M: 62.4037 c. 12: 2 2 1 3 1 1 2 N T3 SD: 14.6870 c. M:-27.3726 c. 19: 3 3 2 4 2 2 3 P T3 SD: 9.1169 c. M: 14.7327 c. 31: 5 5 3 7 3 3 5 N T3 SD: 6.5142 c. M:-11.1447 c. 34: 5 6 3 8 3 3 6 N SD: 4.3884 c. M: 7.8547 c. 53: 8 9 5 12 5 5 9 N SD: 1.3809 c. M: 2.8161 c. 65: 10 11 6 15 6 6 11 N SD: 1.6250 c. M:-2.7572 c. 118: 18 20 11 27 11 11 20 N SD: 0.3756 c. M:-0.6471 c. 171: 26 29 16 39 16 16 29 N SD: 0.3452 c. M: 0.6976 c. 289: 44 49 27 66 27 27 49 N SD: 0.2576 c. M:-0.4498 c. 323: 49 55 30 74 30 30 55 N SD: 0.2383 c. M: 0.4244 c. 441: 67 75 41 101 41 41 75 N SD: 0.1054 c. M: 0.1716 c. 559: 85 95 52 128 52 52 95 N SD: 0.0863 c. M:-0.1812 c. 612: 93 104 57 140 57 57 104 N SD: 0.0422 c. M: 0.0784 c. 730: 111 124 68 167 68 68 124 N SD: 0.0417 c. M:-0.0744 c. 1171: 178 199 109 268 109 109 199 N SD: 0.0214 c. M:-0.0455 c. 1783: 271 303 166 408 166 166 303 N SD: 0.0091 c. M: 0.0160 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: 18.9373 cents 5 x 6:7:8 x 9:10 S SD: 23.8978 cents 6:7 x 8:9:10:11:12 S SD: 20.3902 cents 7:8:9 x 11:12 x 14 SD: 17.0094 cents 8:9:10:11 x 13:14:16 SD: 12.8723 cents 9:10:11:12:14:15:16:18 S SD: 5.6661 cents 10:11 x 13:16:17:18:20 SD: 12.4137 cents 11:12:14:15:17:18:20:22 SD: 11.4100 cents 12:13:15:16:19:20:21:24 SD: 8.0690 cents 16:18:20:21:25:27:28:32 SD: 7.0156 cents 18:20:23:24:28:30:32:36 SD: 5.5463 cents 21:23:26:28:33:35:37:42 SD: 5.0171 cents 24:27:30:32:38:40:43:48 SD: 4.8861 cents 27:30:34:36:42:45:48:54 SD: 2.1319 cents 36:40:45:48:56:60:64:72 S SD: 1.1016 cents 72:80:90:96:113:120:128:144 SD: 1.0968 cents 81:90:101:108:127:135:144:162 SD: 1.0499 cents 96:107:120:128:150:160:171:192 SD: 0.9101 cents 99:110:124:132:155:165:176:198 SD: 0.7059 cents 108:120:135:144:169:180:192:216 SD: 0.3661 cents 144:160:180:192:225:240:256:288 SD: 0.0000 cents