Scala analysis: xen12-wilson-38-4C1-tetrany-01
1-3-5-9 4C1 Tetrany, Figure 38
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 5/4 386.313714 major third 3: 3/2 701.955001 perfect fifth 4: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 4/3 498.0450 perfect fourth 1: 9/8 203.9100 major whole tone 2: 10/9 182.4037 minor whole tone 3: 6/5 315.6413 minor third 4: 4/3 498.0450 perfect fourth
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 10/9 182.404 cents minor whole tone 1: 1 9/8 203.910 cents major whole tone 1: 1 6/5 315.641 cents minor third 1: 1 4/3 498.045 cents perfect fourth 2: 1 5/4 386.314 cents major third 2: 1 4/3 498.045 cents perfect fourth 2: 1 3/2 701.955 cents perfect fifth 2: 1 8/5 813.686 cents minor sixth 3: 1 3/2 701.955 cents perfect fifth 3: 1 5/3 884.359 cents major sixth, BP sixth 3: 1 16/9 996.090 cents Pythagorean minor seventh 3: 1 9/5 1017.596 cents just minor seventh, BP seventh 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 : 203.9 386.3 702.0 1200.0 203.9 : 182.4 498.0 996.1 1200.0 386.3 : 315.6 813.7 1017.6 1200.0 702.0 : 498.0 702.0 884.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 182.4037 .. 498.0450 cents 6/5, 315.6413 cents 10/9, 182.4037 cents 2: 386.3137 .. 813.6863 cents 32/25, 427.3726 cents 15/16,-111.7313 cents 3: 701.9550 .. 1017.5963 cents 6/5, 315.6413 cents 15/16,-111.7313 cents
SHOW DATA
Number of notes : 4 -- Interval properties -- Smallest interval : 10/9, 182.4037 cents, class 1 Average step (divided formal octave): 300.0000 cents Largest one step interval : 4/3, 498.0450 cents Average / Smallest step : 1.644703 Largest / Average step : 1.660150 Largest / Smallest step : 2.730454 Median interval of one step : 259.77564 cents, amount: 0 Least squares average step : 262.74675 cents, oct.: 1050.98699 cents Scale is not proper Step pattern alph. order: ABCD Step pattern size order : BACD Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 1.545610 Lumma stability : 0.304006 Lumma impropriety factor : 0.186219 Rothenberg efficiency : 0.583333 redundancy: 0.416667 Efficiency x scale size : 2.333333 Number of different interval sizes : 10 = 3.33333 / 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 : 81/80, 21.5063 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 2 Most common triad is 0.0 498.045 701.955 cents, amount: 1 Number of recognisable fifths : 2, average 701.9550 cents All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 0 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 : 5 Odd number limit : 9 (O: 9 U: 9) Highest odd numerator or denominator: 9 Scale harmonicity : 0.063559 Average absolute harmonicity : 0.377943 Specific harmonicity : 0.345941 Fundamental : 1/8, -3.0000 octaves, 32.7032 Hz. Guide tone : 90, 6.4919 octaves, 23546.301 Hz. Exponens Consonantiae : 7.200000E+02, 9.49185 octaves Euler's gradus suavitatis : 13 Sum of Mann's harmonic distance : 17.0, average 4.25000 Mersenne's string divisions : 765 Sum of van Prooijen's expressibility: 2.13033, average 0.53258 Sum of Tenney's harmonic distance : 4.23754, average 1.05939 Vogel's harmonic complexity : 5.25000 Wille's k value : 4 Wilson's harmonic complexity : 11 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 24.54392, average 2.45439 Lattice compactness (without 2's) : 12.65028, average 1.26503 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -1.25000 7 1 3: 0 .. 2 0.75000 3 2 5: 0 .. 1 0.25000 1 1 Average exponent except 2's : 4 / 4 = 1.00000 Average absolute exponent except 2's: 4 / 4 = 1.00000 Scale is weakly epimorphic with val: <4 7 9|
FIT/MODE
4: 0 1 1 2 N T3 SD: 121.8854 c. M: 203.9100 c. 5: 1 1 1 2 P M ME SD: 51.0030 c. M:-93.6863 c. 6: 1 1 2 2 P D3 S SD: 49.5364 c. M:-98.0450 c. 7: 1 1 2 3 N SD: 28.3164 c. M: 43.4566 c. 10: 2 1 3 4 N SD: 24.0859 c. M:-36.0900 c. 12: 2 2 3 5 N SD: 7.1837 c. M:-13.6863 c. Eskimo tetratonic (Alaska: Bethel) 29: 5 4 8 12 N SD: 7.1477 c. M: 13.8999 c. 31: 5 5 8 13 N SD: 5.8055 c. M: 10.3616 c. 34: 6 5 9 14 N SD: 4.4948 c. M:-7.8547 c. 41: 7 6 11 17 N SD: 2.9628 c. M: 5.8259 c. 46: 8 7 12 19 N SD: 3.6584 c. M:-4.9906 c. 53: 9 8 14 22 N SD: 0.7081 c. M: 1.4081 c. 65: 11 10 17 27 N SD: 0.8319 c. M:-1.3786 c. 118: 20 18 31 49 N SD: 0.2976 c. M: 0.5202 c. 171: 29 26 45 71 N SD: 0.2841 c. M: 0.4012 c. 289: 49 44 76 120 N SD: 0.2630 c. M: 0.4498 c. 323: 55 49 85 134 N SD: 0.2394 c. M:-0.4244 c. 376: 64 57 99 156 N SD: 0.2059 c. M:-0.3453 c. 388: 66 59 102 161 N SD: 0.1857 c. M:-0.2842 c. 441: 75 67 116 183 N SD: 0.1041 c. M:-0.1716 c. 494: 84 75 130 205 N SD: 0.0869 c. M:-0.1386 c. 559: 95 85 147 232 N SD: 0.0475 c. M:-0.0906 c. 612: 104 93 161 254 N SD: 0.0206 c. M: 0.0392 c. 1171: 199 178 308 486 N SD: 0.0153 c. M:-0.0228 c. 1783: 303 271 469 740 N SD: 0.0090 c. M:-0.0160 c. 2395: 407 364 630 994 N SD: 0.0094 c. M:-0.0148 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: 71.3014 cents 4 x 5:6:8 S SD: 0.0000 cents 5 x 6:8:10 S SD: 44.0687 cents 6:7:8:9:12 S SD: 32.0624 cents 7:8:9:11:14 SD: 24.5052 cents 8:9:10:12:16 S SD: 0.0000 cents