Scala analysis: xen09-wilson-marwa-12-03
Marwa permutation 3 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: 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: 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: 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 : 274.6 386.3 590.2 772.6 884.4 1088.3 1200.0 274.6 : 111.7 315.6 498.0 609.8 813.7 925.4 1200.0 386.3 : 203.9 386.3 498.0 702.0 813.7 1088.3 1200.0 590.2 : 182.4 294.1 498.0 609.8 884.4 996.1 1200.0 772.6 : 111.7 315.6 427.4 702.0 813.7 1017.6 1200.0 884.4 : 203.9 315.6 590.2 702.0 905.9 1088.3 1200.0 1088.3: 111.7 386.3 498.0 702.0 884.4 996.1 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 : 180.42712 cents, oct.: 1262.98983 cents Scale is strictly proper Step pattern alph. order: ABCDBCB Step pattern size order : DACBACA Scale is sum-free (all different intervals) 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 : 2 at degree 2 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 n-1 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: 75 Scale harmonicity : 0.035971 Average absolute harmonicity : 0.211154 Specific harmonicity : 0.201300 Fundamental : 1/192, -7.5850 octaves, 1.3626 Hz. Guide tone : 450, 8.8138 octaves, 117731.504 Hz. Exponens Consonantiae : 8.640000E+04, 16.39874 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 150.0, average 21.42857 Mersenne's string divisions : 726690888 Sum of van Prooijen's expressibility: 7.50025, average 1.07146 Sum of Tenney's harmonic distance : 14.29900, average 2.04271 Vogel's harmonic complexity : 13.28571 Wille's k value : 112 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 99.95793, average 3.56993 Lattice compactness (without 2's) : 43.73012, average 1.56179 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -6 .. 1 -2.71429 21 1 3: -1 .. 2 0.42857 5 5: 0 .. 2 1.14286 8 6 Average exponent except 2's : 11 / 7 = 1.57143 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 1 1 1 1 SP B ME I SD: 65.6333 c. M: 103.1539 c. Lebeng 8: 2 1 1 1 1 1 1 P M ME S SD: 31.6650 c. M:-63.6863 c. 9: 2 1 1 2 1 1 1 P M ME S SD: 31.8499 c. M: 56.8904 c. 10: 2 1 2 1 1 2 1 P M ME S SD: 31.1440 c. M: 52.6274 c. 12: 3 1 2 2 1 2 1 P D3 SD: 17.1567 c. M:-27.3726 c. Aeolian flat 1 18: 4 2 3 3 1 3 2 P SD: 16.3640 c. M:-27.3726 c. 19: 4 2 3 3 2 3 2 SP D3 SD: 14.3489 c. M: 21.9508 c. 22: 5 2 4 3 2 4 2 P SD: 6.9931 c. M: 11.6314 c. 31: 7 3 5 5 3 5 3 SP D3 SD: 4.8224 c. M: 9.5786 c. 34: 8 3 6 5 3 6 3 P SD: 5.5117 c. M:-9.7763 c. 43: 10 4 7 7 4 7 4 SP D3 SD: 5.4611 c. M:-8.7679 c. 53: 12 5 9 8 5 9 5 SP SD: 1.8743 c. M: 2.8843 c. 65: 15 6 11 10 6 11 6 SP SD: 1.6659 c. M:-2.7572 c. 87: 20 8 15 13 8 15 8 SP SD: 1.4378 c. M:-2.8797 c. 118: 27 11 20 18 11 20 11 SP SD: 0.2399 c. M: 0.3932 c. 323: 74 30 55 49 30 55 30 SP SD: 0.2599 c. M:-0.4884 c. 376: 86 35 64 57 35 64 35 SP SD: 0.1918 c. M: 0.3162 c. 441: 101 41 75 67 41 75 41 SP SD: 0.1628 c. M:-0.2525 c. 494: 113 46 84 75 46 84 46 SP SD: 0.0960 c. M: 0.1578 c. 612: 140 57 104 93 57 104 57 SP SD: 0.0491 c. M: 0.0784 c. 730: 167 68 124 111 68 124 68 SP SD: 0.0466 c. M: 0.0867 c. 1171: 268 109 199 178 109 199 109 SP SD: 0.0348 c. M:-0.0546 c. 1665: 381 155 283 253 155 283 155 SP SD: 0.0244 c. M:-0.0466 c. 1783: 408 166 303 271 166 303 166 SP SD: 0.0090 c. M:-0.0175 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: 30.7262 cents 4 x 5 x 6:7 x 8 S SD: 27.5333 cents 5:6 x 7:8 x 9:10 S SD: 18.3583 cents 6:7 x 8:9:10:11:12 S SD: 20.4563 cents 7:8:9:10:11:12:13:14 H SD: 12.5816 cents 8:9:10:11 x 13:15:16 SD: 15.3020 cents 9 x 11:13:14:15:17:18 SD: 10.3933 cents 12:14:15:17:19:20:23:24 SD: 6.6951 cents 17:20:21:24:27:28:32:34 SD: 6.0223 cents 23:27:29:32:36:38:43:46 SD: 4.1375 cents 24:28:30:34:38:40:45:48 SD: 3.9085 cents 29:34:36:41:45:48:54:58 SD: 3.6717 cents 32:38:40:45:50:53:60:64 SD: 3.6243 cents 35:41:44:49:55:58:66:70 SD: 3.0313 cents 36:42:45:51:56:60:68:72 SD: 3.0150 cents 39:46:49:55:61:65:73:78 SD: 2.2143 cents 47:55:59:66:73:78:88:94 SD: 2.1838 cents 48:56:60:68:75:80:90:96 SD: 2.1319 cents 52:61:65:73:81:87:98:104 SD: 1.8237 cents 57:67:71:80:89:95:107:114 SD: 1.2908 cents 64:75:80:90:100:107:120:128 SD: 0.7717 cents 121:142:151:170:189:202:227:242 SD: 0.7324 cents 123:144:154:173:192:205:231:246 SD: 0.6644 cents 128:150:160:180:200:213:240:256 SD: 0.3867 cents 192:225:240:270:300:320:360:384 SD: 0.0000 cents