Scala analysis: xen12-wilson-38-4C1-tetrany-02
1-3-5-11 4C1 Tetrany, Figure 38
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 5/4 386.313714 major third 2: 11/8 551.317942 undecimal semi-augmented fourth 3: 3/2 701.955001 perfect fifth 4: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 4/3 498.0450 perfect fourth 1: 5/4 386.3137 major third 2: 11/10 165.0042 Ptolemy's second, 4/5-tone 3: 12/11 150.6371 undecimal neutral second, 3/4-tone 4: 4/3 498.0450 perfect fourth
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 5/4 386.314 cents major third 1: 1 4/3 498.045 cents perfect fourth 2: 1 6/5 315.641 cents minor third 2: 1 11/8 551.318 cents undecimal semi-augmented fourth 2: 1 16/11 648.682 cents undecimal semi-diminished fifth 2: 1 5/3 884.359 cents major sixth, BP sixth 3: 1 3/2 701.955 cents perfect fifth 3: 1 8/5 813.686 cents minor sixth 3: 1 20/11 1034.996 cents large minor seventh 3: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 0.0 : 386.3 551.3 702.0 1200.0 386.3 : 165.0 315.6 813.7 1200.0 551.3 : 150.6 648.7 1035.0 1200.0 702.0 : 498.0 884.4 1049.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.6371 .. 498.0450 cents 11/9, 347.4079 cents 12/11, 150.6371 cents 2: 315.6413 .. 884.3587 cents 25/18, 568.7174 cents 9/10,-182.4037 cents 3: 701.9550 .. 1049.3629 cents 11/9, 347.4079 cents 9/10,-182.4037 cents
SHOW DATA
Number of notes : 4 -- Interval properties -- Smallest interval : 12/11, 150.6371 cents, class 1 Average step (divided formal octave): 300.0000 cents Largest one step interval : 4/3, 498.0450 cents Average / Smallest step : 1.991542 Largest / Average step : 1.660150 Largest / Smallest step : 3.306258 Median interval of one step : 275.65897 cents, amount: 0 Least squares average step : 279.82715 cents, oct.: 1119.30861 cents Scale is not proper Step pattern alph. order: ABCD Step pattern size order : CBAD Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 53.27294 cents Scale diversity : 1.674660 Lumma stability : 0.251062 Lumma impropriety factor : 0.304006 Rothenberg efficiency : 0.500000 redundancy: 0.500000 Efficiency x scale size : 2.000000 Number of different interval sizes : 12 = 4.00000 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 4.00000 = 4 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 121/120, 14.3672 cents Number of recognisable fifths : 1, average 701.9550 cents All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 1 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 25.0000% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval class 3 -- Rational properties -- Prime limit : 11 Odd number limit : 11 (O: 11 U: 11) Highest odd numerator or denominator: 11 Scale harmonicity : 0.032002 Average absolute harmonicity : 0.359746 Specific harmonicity : 0.193807 Fundamental : 1/8, -3.0000 octaves, 32.7032 Hz. Guide tone : 330, 8.3663 octaves, 86336.437 Hz. Exponens Consonantiae : 2.640000E+03, 11.36632 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 18.0, average 4.50000 Mersenne's string divisions : 855 Sum of van Prooijen's expressibility: 2.21748, average 0.55437 Sum of Tenney's harmonic distance : 4.32469, average 1.08117 Vogel's harmonic complexity : 6.50000 Wille's k value : 5 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 3 Triangular lattice diameter : 1 Lattice compactness : 23.24760, average 2.32476 Lattice compactness (without 2's) : 10.24264, average 1.02426 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -1.25000 7 1 3: 0 .. 1 0.25000 1 1 5: 0 .. 1 0.25000 1 1 11: 0 .. 1 0.25000 1 1 Average exponent except 2's : 3 / 4 = 0.75000 Average absolute exponent except 2's: 3 / 4 = 0.75000 Scale is weakly epimorphic with val: <4 5 10 15| Scale is weakly epimorphic with val: <4 6 9 15| Scale is JI-epimorphic with val: <4 7 9 14| Scale is weakly epimorphic with val: <4 7 10 13|
FIT/MODE
4: 1 1 0 2 N T3 SD: 71.0894 c. M: 101.9550 c. 5: 2 0 1 2 N G SD: 59.5588 c. M:-93.6863 c. 6: 2 1 1 2 P D3 I SD: 55.1590 c. M:-98.0450 c. 7: 2 1 1 3 N SD: 29.6800 c. M: 43.4566 c. 9: 3 1 1 4 N SD: 20.9525 c. M: 35.2883 c. 13: 4 2 2 5 N SD: 20.1925 c. M:-36.5065 c. 15: 5 2 2 6 N SD: 12.1276 c. M:-18.0450 c. 19: 6 3 2 8 N SD: 9.9860 c. M:-17.1031 c. 22: 7 3 3 9 N SD: 5.1359 c. M:-7.1359 c. 31: 10 4 4 13 N SD: 5.3732 c. M: 9.3825 c. 41: 13 6 5 17 N SD: 3.7756 c. M: 5.8259 c. 46: 15 6 6 19 N SD: 3.2720 c. M:-4.9906 c. 50: 16 7 6 21 N SD: 3.2125 c. M: 5.9550 c. 63: 20 9 8 26 N SD: 3.0722 c. M: 5.3613 c. 65: 21 9 8 27 N SD: 1.4548 c. M:-2.5282 c. 87: 28 12 11 36 N SD: 0.7756 c. M:-1.4933 c. 137: 44 19 17 57 N SD: 0.8047 c. M: 1.2251 c. 152: 49 21 19 63 N SD: 0.7846 c. M:-1.3136 c. 159: 51 22 20 66 N SD: 0.7293 c. M: 1.4081 c. 183: 59 25 23 76 N SD: 0.4107 c. M:-0.5715 c. 224: 72 31 28 93 N SD: 0.3895 c. M: 0.5994 c. 270: 87 37 34 112 N SD: 0.2443 c. M:-0.3530 c. 407: 131 56 51 169 N SD: 0.1242 c. M: 0.2351 c. 494: 159 68 62 205 N SD: 0.0722 c. M:-0.0991 c. 677: 218 93 85 281 N SD: 0.0602 c. M:-0.0969 c. 901: 290 124 113 374 N SD: 0.0618 c. M: 0.0762 c. 1084: 349 149 136 450 N SD: 0.0589 c. M: 0.1100 c. 1171: 377 161 147 486 N SD: 0.0126 c. M:-0.0228 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x x 3:4 S SD: 0.0000 cents 3 x 4:5:6 S SD: 63.3413 cents 4:5 x 6:8 S SD: 0.0000 cents 6 x 8:9:12 S SD: 17.7576 cents 8:10:11:12:16 S SD: 0.0000 cents