Scala analysis: xen09-wilson-marwa-12-07
Marwa permutation 7 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: 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: 16/15 111.7313 minor diatonic semitone 4: 75/64 274.5824 classic augmented second 5: 16/15 111.7313 minor diatonic semitone 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: 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 32/27 294.135 cents Pythagorean minor third 2: 3 6/5 315.641 cents minor third 2: 3 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: 3 8/5 813.686 cents minor sixth 5: 3 5/3 884.359 cents major sixth, BP sixth 5: 1 27/16 905.865 cents Pythagorean major 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 1088.3 1200.0 182.4 : 203.9 315.6 590.2 702.0 905.9 1017.6 1200.0 386.3 : 111.7 386.3 498.0 702.0 813.7 996.1 1200.0 498.0 : 274.6 386.3 590.2 702.0 884.4 1088.3 1200.0 772.6 : 111.7 315.6 427.4 609.8 813.7 925.4 1200.0 884.4 : 203.9 315.6 498.0 702.0 813.7 1088.3 1200.0 1088.3: 111.7 294.1 498.0 609.8 884.4 996.1 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: 294.1350 .. 386.3137 cents 135/128, 92.1787 cents 2048/2025, 19.5526 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 .. 905.8650 cents 135/128, 92.1787 cents 128/125, 41.0589 cents 6: 925.4176 .. 1088.2687 cents 1125/1024, 162.8511 cents 2048/2025, 19.5526 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 : 177.79344 cents, oct.: 1244.55409 cents Scale is strictly proper Step pattern alph. order: ABCDCBC Step pattern size order : BCADACA Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.434704 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.303532 Rothenberg efficiency : 0.466667 redundancy: 0.533333 Efficiency x scale size : 3.266667 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 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 Best fifths form a closed circle Scale is fully connected 5-limit major-minor triadic 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% 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 Scale is differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 5 Odd number limit : 75 (O: 75 U: 75) Highest odd numerator or denominator: 25 Scale harmonicity : 0.037313 Average absolute harmonicity : 0.237794 Specific harmonicity : 0.221351 Fundamental : 1/144, -7.1699 octaves, 1.8168 Hz. Guide tone : 300, 8.2288 octaves, 78487.670 Hz. Exponens Consonantiae : 4.320000E+04, 15.39874 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 55.0, average 7.85714 Mersenne's string divisions : 9030168 Sum of van Prooijen's expressibility: 5.40334, average 0.77191 Sum of Tenney's harmonic distance : 10.49282, average 1.49897 Vogel's harmonic complexity : 12.28571 Wille's k value : 112 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 86.35171, average 3.08399 Lattice compactness (without 2's) : 42.49405, average 1.51764 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -0.71429 13 1 3: -2 .. 1 -0.42857 5 1 5: 0 .. 2 0.85714 6 5 Average exponent except 2's : 3 / 7 = 0.42857 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 1 1 1 1 SP B ME I SD: 44.9302 c. M: 86.9131 c. Lebeng 8: 1 1 1 2 1 1 1 P M ME I SD: 43.1435 c. M: 86.3137 c. 9: 1 2 1 2 1 1 1 N D3 S SD: 32.6341 c. M: 49.0704 c. 10: 1 2 1 2 1 2 1 P M ME I SD: 37.2596 c. M: 62.4037 c. 11: 2 2 1 2 1 2 1 P M ME S SD: 29.8947 c. M:-50.0499 c. 12: 2 2 1 3 1 2 1 P D3 SD: 15.2704 c. M:-27.3726 c. Ionian Augmented, Ionian sharp 5 19: 3 3 2 4 2 3 2 SP D3 SD: 9.1506 c. M: 14.7327 c. 22: 3 4 2 5 2 4 2 P SD: 9.6099 c. M: 18.7673 c. 31: 5 5 3 7 3 5 3 SP D3 SD: 5.4644 c. M:-11.1447 c. 34: 5 6 3 8 3 6 3 P SD: 3.9156 c. M: 5.9331 c. 53: 8 9 5 12 5 9 5 SP SD: 1.4885 c. M: 2.8161 c. 65: 10 11 6 15 6 11 6 SP SD: 1.6351 c. M:-2.7572 c. 87: 13 15 8 20 8 15 8 SP SD: 1.5278 c. M: 3.0934 c. 118: 18 20 11 27 11 20 11 SP SD: 0.3239 c. M:-0.6471 c. 289: 44 49 27 66 27 49 27 SP SD: 0.2409 c. M: 0.3794 c. 323: 49 55 30 74 30 55 30 SP SD: 0.2048 c. M: 0.3604 c. 441: 67 75 41 101 41 75 41 SP SD: 0.1043 c. M:-0.1667 c. 494: 75 84 46 113 46 84 46 SP SD: 0.1226 c. M: 0.2175 c. 559: 85 95 52 128 52 95 52 SP SD: 0.0942 c. M:-0.1812 c. 612: 93 104 57 140 57 104 57 SP SD: 0.0438 c. M: 0.0784 c. 730: 111 124 68 167 68 124 68 SP SD: 0.0360 c. M:-0.0620 c. 1171: 178 199 109 268 109 199 109 SP SD: 0.0236 c. M:-0.0455 c. 1783: 271 303 166 408 166 303 166 SP SD: 0.0077 c. M: 0.0145 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 6:7 x 8 S SD: 27.5333 cents 5 x 6:7:8 x 9:10 S SD: 27.4297 cents 6:7 x 8:9:10:11:12 S SD: 19.4672 cents 7:8:9 x 11:12:13:14 SD: 14.4409 cents 8:9:10:11 x 13:15:16 SD: 12.0435 cents 9:10:11:12:14:15:17:18 SD: 5.9528 cents 10:11 x 13:16:17:19:20 SD: 12.4843 cents 11:12:14:15:17:18:21:22 SD: 10.9159 cents 12:13:15:16:19:20:23:24 SD: 8.9155 cents 15:17:19:20:23:25:28:30 SD: 7.5927 cents 16:18:20:21:25:27:30:32 SD: 5.8351 cents 21:23:26:28:33:35:39:42 SD: 5.0845 cents 24:27:30:32:38:40:45:48 SD: 4.4911 cents 25:28:31:33:39:42:47:50 SD: 4.2991 cents 27:30:34:36:42:45:51:54 SD: 2.8065 cents 36:40:45:48:56:60:68:72 SD: 2.1319 cents 45:50:56:60:70:75:84:90 SD: 1.9081 cents 48:53:60:64:75:80:90:96 SD: 1.5506 cents 63:70:79:84:98:105:118:126 SD: 1.3772 cents 64:71:80:85:100:107:120:128 SD: 1.2969 cents 72:80:90:96:113:120:135:144 SD: 1.0968 cents 80:89:100:107:125:133:150:160 SD: 1.0364 cents 96:107:120:128:150:160:180:192 SD: 0.7717 cents 108:120:135:144:169:180:203:216 SD: 0.7114 cents 117:130:146:156:183:195:219:234 SD: 0.6499 cents 135:150:169:180:211:225:253:270 SD: 0.3929 cents 144:160:180:192:225:240:270:288 SD: 0.0000 cents