Scala analysis: xen12-wilson-09-4C2-hexany-02
1-3-7-15 4C2 Hexany, Figure 9
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 35/32 155.139620 septimal neutral second 2: 7/6 266.870906 septimal minor third 3: 5/4 386.313714 major third 4: 7/4 968.825906 harmonic seventh 5: 15/8 1088.268715 classic major seventh 6: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 35/32 155.1396 septimal neutral second 2: 16/15 111.7313 minor diatonic semitone 3: 15/14 119.4428 major diatonic semitone 4: 7/5 582.5122 septimal or Huygens' tritone, BP fourth 5: 15/14 119.4428 major diatonic semitone 6: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 16/15 111.731 cents minor diatonic semitone 1: 2 15/14 119.443 cents major diatonic semitone 1: 1 35/32 155.140 cents septimal neutral second 1: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 2: 2 8/7 231.174 cents septimal whole tone 2: 2 7/6 266.871 cents septimal minor third 2: 2 3/2 701.955 cents perfect fifth 3: 1 56/45 378.602 cents septimal narrow major third 3: 2 5/4 386.314 cents major third 3: 2 8/5 813.686 cents minor sixth 3: 1 45/28 821.398 cents septimale wide minor sixth 4: 2 4/3 498.045 cents perfect fourth 4: 2 12/7 933.129 cents septimal major sixth 4: 2 7/4 968.826 cents harmonic seventh 5: 1 10/7 617.488 cents Euler's tritone 5: 1 64/35 1044.860 cents septimal neutral seventh 5: 2 28/15 1080.557 cents grave major seventh 5: 2 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: 3.60000 = 18/5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 0.0 : 155.1 266.9 386.3 968.8 1088.3 1200.0 155.1 : 111.7 231.2 813.7 933.1 1044.9 1200.0 266.9 : 119.4 702.0 821.4 933.1 1088.3 1200.0 386.3 : 582.5 702.0 813.7 968.8 1080.6 1200.0 968.8 : 119.4 231.2 386.3 498.0 617.5 1200.0 1088.3: 111.7 266.9 378.6 498.0 1080.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 582.5122 cents 21/16, 470.7809 cents 16/15, 111.7313 cents 2: 231.1741 .. 701.9550 cents 21/16, 470.7809 cents 40/49,-351.3381 cents 3: 378.6022 .. 821.3978 cents 2025/1568, 442.7956 cents 112/135,-323.3528 cents 4: 498.0450 .. 968.8259 cents 21/16, 470.7809 cents 112/135,-323.3528 cents 5: 617.4878 .. 1088.2687 cents 21/16, 470.7809 cents 40/49,-351.3381 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 7/5, 582.5122 cents Average / Smallest step : 1.790009 Largest / Average step : 2.912561 Largest / Smallest step : 5.213510 Median interval of one step : 15/14, 119.4428 cents, amount: 2 Least squares average step : 201.80736 cents, oct.: 1210.84416 cents Scale is not proper Step pattern alph. order: ABCDCB Step pattern size order : CABDBA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 34.97561 cents Scale diversity : 1.449319 Lumma stability : 0.186219 Lumma impropriety factor : 0.614710 Rothenberg efficiency : 0.466667 redundancy: 0.533333 Efficiency x scale size : 2.800000 Number of different interval sizes : 18 = 3.60000 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.60000 = 18/5 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 225/224, 7.7115 cents Number of recognisable fifths : 2, average 701.9550 cents Length of longest harmonic part : 2 at degree 4 Length of longest subharmonic part : 2 at degree 1 Formal octave complements present : 1 = 16.6667% Scale is n-1 differentially coherent in interval class 1 Scale is differentially coherent in interval class 2 Limited inverse transpositions : 1 Inversional symmetry on intervals : 0-1 3-4 -- Rational properties -- Prime limit : 7 Odd number limit : 45 (O: 45 U: 45) Highest odd numerator or denominator: 35 Scale harmonicity : 0.035690 Average absolute harmonicity : 0.233516 Specific harmonicity : 0.173618 Fundamental : 1/96, -6.5850 octaves, 2.7253 Hz. Guide tone : 210, 7.7142 octaves, 54941.369 Hz. Exponens Consonantiae : 2.016000E+04, 14.29921 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 63.0, average 10.50000 Mersenne's string divisions : 1983267 Sum of van Prooijen's expressibility: 5.10933, average 0.85155 Sum of Tenney's harmonic distance : 9.80087, average 1.63348 Vogel's harmonic complexity : 12.00000 Wille's k value : 52 Wilson's harmonic complexity : 18 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 59.31967, average 2.82475 Lattice compactness (without 2's) : 26.64151, average 1.26864 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 1 -2.00000 14 1 3: -1 .. 1 0.00000 2 5: 0 .. 1 0.50000 3 2 7: 0 .. 1 0.50000 3 3 Average exponent except 2's : 6 / 6 = 1.00000 Average absolute exponent except 2's: 8 / 6 = 1.33333 Scale is weakly epimorphic with val: <6 9 14 19| Scale is weakly epimorphic with val: <6 11 14 15| Scale is weakly epimorphic with val: <6 11 15 16|
FIT/MODE
6: 1 0 1 3 0 1 N SD: 50.7193 c. M: 88.2687 c. 7: 1 1 0 4 0 1 N SD: 50.1016 c. M:-75.9862 c. 8: 1 1 0 4 1 1 N SD: 49.6244 c. M: 86.3137 c. 9: 1 1 1 4 1 1 N M DE SD: 19.9551 c. M: 35.4926 c. 10: 1 1 1 5 1 1 N M DE SD: 21.5852 c. M: 35.1396 c. 15: 2 1 2 7 2 1 N SD: 18.3383 c. M:-31.7313 c. 18: 2 2 2 9 1 2 N SD: 18.7143 c. M:-31.1741 c. 19: 2 2 2 9 2 2 N M DE SD: 17.1317 c. M: 28.8238 c. 21: 3 2 2 10 2 2 N D3 SD: 11.6977 c. M:-18.8434 c. 22: 3 2 2 11 2 2 N D3 SD: 7.1001 c. M:-12.9923 c. 31: 4 3 3 15 3 3 N D3 SD: 2.5167 c. M: 4.3977 c. 77: 10 7 8 37 8 7 N SD: 2.1910 c. M:-3.2967 c. 94: 12 9 9 46 9 9 N D3 SD: 2.1724 c. M: 3.3350 c. 99: 13 9 10 48 10 9 N SD: 1.6409 c. M:-2.6404 c. 108: 14 10 11 52 11 10 N SD: 1.4079 c. M:-2.5752 c. 109: 14 10 11 53 11 10 N SD: 1.3978 c. M: 2.6507 c. 130: 17 12 13 63 13 12 N SD: 1.0681 c. M:-1.7835 c. 140: 18 13 14 68 14 13 N SD: 0.6561 c. M: 1.1566 c. 171: 22 16 17 83 17 16 N SD: 0.4467 c. M: 0.7537 c. 270: 35 25 27 131 27 25 N SD: 0.3483 c. M:-0.6202 c. 301: 39 28 30 146 30 28 N SD: 0.2400 c. M:-0.3972 c. 441: 57 41 44 214 44 41 N SD: 0.1235 c. M: 0.2042 c. 472: 61 44 47 229 47 44 N SD: 0.1126 c. M: 0.1818 c. 913: 118 85 91 443 91 85 N SD: 0.0811 c. M: 0.1512 c. 1075: 139 100 107 522 107 100 N SD: 0.0765 c. M:-0.1043 c. 1106: 143 103 110 537 110 103 N SD: 0.0416 c. M:-0.0710 c. 1547: 200 144 154 751 154 144 N SD: 0.0208 c. M: 0.0319 c. 2019: 261 188 201 980 201 188 N SD: 0.0153 c. M: 0.0295 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x x x x 4 S SD: 0.0000 cents 3 x x 4:5 x 6 S SD: 46.6888 cents 4 x x 5:7 x 8 SD: 0.0000 cents 5 x 6 x 9 x 10 S SD: 22.9906 cents 6 x 7:8 x 11:12 SD: 29.5778 cents 7 x 8:9:12:13:14 S SD: 14.4243 cents 8:9 x 10:14:15:16 SD: 9.7541 cents 9:10 x 11:16:17:18 SD: 11.2491 cents 11:12:13:14:19:21:22 SD: 9.0946 cents 12:13:14:15:21:23:24 SD: 6.9168 cents 19:21:22:24:33:36:38 SD: 6.0721 cents 20:22:23:25:35:38:40 SD: 5.8776 cents 23:25:27:29:40:43:46 SD: 4.0741 cents 24:26:28:30:42:45:48 SD: 2.7612 cents 32:35:37:40:56:60:64 SD: 2.5878 cents 41:45:48:51:72:77:82 SD: 2.2874 cents 52:57:61:65:91:98:104 SD: 2.2537 cents 53:58:62:66:93:99:106 SD: 1.9002 cents 55:60:64:69:96:103:110 SD: 1.7055 cents 64:70:75:80:112:120:128 SD: 1.2853 cents 72:79:84:90:126:135:144 SD: 0.9145 cents 96:105:112:120:168:180:192 SD: 0.0000 cents