Scala analysis: xen09-wilson-marwa-12-02
Marwa permutation 2 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: 75/64 274.582429 classic augmented second 2: 5/4 386.313714 major third 3: 45/32 590.223716 diatonic tritone 4: 25/16 772.627428 classic augmented fifth 5: 225/128 976.537429 augmented 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: 75/64 274.5824 classic augmented second 2: 16/15 111.7313 minor diatonic semitone 3: 9/8 203.9100 major whole tone 4: 10/9 182.4037 minor whole tone 5: 9/8 203.9100 major whole tone 6: 16/15 111.7313 minor diatonic semitone 7: 16/15 111.7313 minor diatonic semitone
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 : 274.6 386.3 590.2 772.6 976.5 1088.3 1200.0 274.6 : 111.7 315.6 498.0 702.0 813.7 925.4 1200.0 386.3 : 203.9 386.3 590.2 702.0 813.7 1088.3 1200.0 590.2 : 182.4 386.3 498.0 609.8 884.4 996.1 1200.0 772.6 : 203.9 315.6 427.4 702.0 813.7 1017.6 1200.0 976.5 : 111.7 223.5 498.0 609.8 813.7 996.1 1200.0 1088.3: 111.7 386.3 498.0 702.0 884.4 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 : 183.71922 cents, oct.: 1286.03451 cents Scale is not proper Step pattern alph. order: ABCDCBB Step pattern size order : DACBCAA 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 0.0 701.955 813.686 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 2 Length of longest subharmonic part : 2 at degree 3 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: 225 Scale harmonicity : 0.038265 Average absolute harmonicity : 0.201082 Specific harmonicity : 0.186335 Fundamental : 1/128, -7.0000 octaves, 2.0439 Hz. Guide tone : 450, 8.8138 octaves, 117731.504 Hz. Exponens Consonantiae : 5.760000E+04, 15.81378 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 322.5, average 46.07143 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.15346, average 1.30764 Sum of Tenney's harmonic distance : 17.58230, average 2.51176 Vogel's harmonic complexity : 12.28571 Wille's k value : 112 Wilson's harmonic complexity : 16 Rectangular lattice diameter : 4 Triangular lattice diameter : 4 Lattice compactness : 107.50415, average 3.83943 Lattice compactness (without 2's) : 44.55854, average 1.59138 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -7 .. 1 -3.71429 28 1 3: 0 .. 2 0.85714 6 5: 0 .. 2 1.28571 9 6 Average exponent except 2's : 15 / 7 = 2.14286 Average absolute exponent except 2's: 15 / 7 = 2.14286 Scale is JI-epimorphic with val: <7 11 16| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 78.9833 c. M: 119.3946 c. Lebeng 8: 2 1 1 1 2 0 1 N D3 SD: 41.6976 c. M:-73.4626 c. 9: 2 1 1 2 1 1 1 P M ME S SD: 30.6338 c. M: 56.8904 c. 10: 2 1 2 1 2 1 1 P M ME S SD: 26.9800 c. M: 52.6274 c. 12: 3 1 2 2 2 1 1 N T3 SD: 18.3860 c. M:-27.3726 c. 18: 4 2 3 3 3 1 2 N SD: 17.3697 c. M:-27.3726 c. 19: 4 2 3 3 3 2 2 P T3 SD: 18.0952 c. M: 29.1690 c. 21: 5 2 3 4 3 2 2 N SD: 14.3744 c. M:-27.3726 c. 22: 5 2 4 3 4 2 2 N SD: 5.7932 c. M:-9.7763 c. 31: 7 3 5 5 5 3 3 N T3 SD: 5.4061 c. M: 9.5786 c. 43: 10 4 7 7 7 4 4 N T3 SD: 4.3709 c. M:-8.7679 c. 53: 12 5 9 8 9 5 5 N SD: 2.1218 c. M: 2.9525 c. 65: 15 6 11 10 11 6 6 N SD: 1.6864 c. M:-2.7572 c. 87: 20 8 15 13 15 8 8 N SD: 1.6733 c. M:-2.8797 c. 96: 22 9 16 15 16 9 9 N SD: 1.5849 c. M: 2.7237 c. 118: 27 11 20 18 20 11 11 N SD: 0.2151 c. M: 0.3932 c. 376: 86 35 64 57 64 35 35 N SD: 0.1517 c. M: 0.2870 c. 494: 113 46 84 75 84 46 46 N SD: 0.0784 c. M: 0.1578 c. 612: 140 57 104 93 104 57 57 N SD: 0.0525 c. M: 0.0784 c. 1171: 268 109 199 178 199 109 109 N SD: 0.0420 c. M:-0.0638 c. 1289: 295 120 219 196 219 120 120 N SD: 0.0359 c. M:-0.0646 c. 1665: 381 155 283 253 283 155 155 N SD: 0.0254 c. M:-0.0466 c. 1783: 408 166 303 271 303 166 166 N SD: 0.0112 c. M:-0.0189 c. 1901: 435 177 323 289 323 177 177 N SD: 0.0092 c. M:-0.0185 c. 2395: 548 223 407 364 407 223 223 N SD: 0.0089 c. M: 0.0178 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: 43.4535 cents 4 x 5 x 6:7 x 8 S SD: 17.7730 cents 5:6 x 7:8:9 x 10 S SD: 14.3066 cents 6:7 x 8:9 x 11:12 SD: 24.5476 cents 7:8:9:10:11:12:13:14 H SD: 12.1741 cents 9 x 11:13:14:16:17:18 SD: 10.8922 cents 12:14:15:17:19:21:23:24 SD: 6.7851 cents 16:19:20:23:25:28:30:32 SD: 6.4415 cents 17:20:21:24:27:30:32:34 SD: 5.3515 cents 23:27:29:32:36:40:43:46 SD: 4.4087 cents 24:28:30:34:38:42:45:48 SD: 4.0607 cents 25:29:31:35:39:44:47:50 SD: 3.4914 cents 29:34:36:41:45:51:54:58 SD: 3.2503 cents 36:42:45:51:56:63:68:72 SD: 3.2100 cents 37:43:46:52:58:65:69:74 SD: 2.9183 cents 39:46:49:55:61:69:73:78 SD: 2.7326 cents 40:47:50:56:63:70:75:80 SD: 2.5970 cents 41:48:51:58:64:72:77:82 SD: 1.9900 cents 52:61:65:73:81:91:98:104 SD: 1.9074 cents 57:67:71:80:89:100:107:114 SD: 1.3781 cents 64:75:80:90:100:113:120:128 SD: 1.0968 cents 87:102:109:122:136:153:163:174 SD: 0.9389 cents 103:121:129:145:161:181:193:206 SD: 0.8431 cents 111:130:139:156:173:195:208:222 SD: 0.8226 cents 116:136:145:163:181:204:218:232 SD: 0.7077 cents 121:142:151:170:189:213:227:242 SD: 0.7035 cents 128:150:160:180:200:225:240:256 SD: 0.0000 cents