Scala analysis: xen12-wilson-38-4C3-tetrany-01
1-3-5-9 4C3 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: 3/2 701.955001 perfect fifth 3: 9/5 1017.596288 just minor seventh, BP seventh 4: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 9/8 203.9100 major whole tone 2: 4/3 498.0450 perfect fourth 3: 6/5 315.6413 minor third 4: 10/9 182.4037 minor whole tone
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 : 203.9 702.0 1017.6 1200.0 203.9 : 498.0 813.7 996.1 1200.0 702.0 : 315.6 498.0 702.0 1200.0 1017.6: 182.4 386.3 884.4 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 : 315.35363 cents, oct.: 1261.41452 cents Scale is not proper Step pattern alph. order: ABCD Step pattern size order : BDCA 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 Number of recognisable fifths : 2, average 701.9550 cents All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 3 Formal octave complements present : 1 = 25.0000% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 -- 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 : 0.369488 Specific harmonicity : 0.330687 Fundamental : 1/40, -5.3219 octaves, 6.5406 Hz. Guide tone : 18, 4.1699 octaves, 4709.260 Hz. Exponens Consonantiae : 7.200000E+02, 9.49185 octaves Euler's gradus suavitatis : 13 Sum of Mann's harmonic distance : 19.5, average 4.87500 Mersenne's string divisions : 3570 Sum of van Prooijen's expressibility: 2.38561, average 0.59640 Sum of Tenney's harmonic distance : 4.58973, average 1.14743 Vogel's harmonic complexity : 9.75000 Wille's k value : 22 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) : 13.88635, average 1.38863 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -0.75000 5 1 3: 0 .. 2 1.25000 5 2 5: -1 .. 0 -0.25000 1 1 Average exponent except 2's : 4 / 4 = 1.00000 Average absolute exponent except 2's: 6 / 4 = 1.50000 Scale is weakly epimorphic with val: <4 7 9|
FIT/MODE
4: 0 2 1 1 N T3 SD: 128.2605 c. M: 203.9100 c. 5: 1 2 1 1 P M ME SD: 35.1619 c. M: 57.5963 c. 7: 1 3 2 1 N SD: 18.9688 c. M: 32.4814 c. 12: 2 5 3 2 N SD: 9.0656 c. M: 17.5963 c. 19: 3 8 5 3 N SD: 8.8104 c. M: 14.4363 c. 29: 5 12 8 4 N SD: 8.6067 c. M:-16.8865 c. 31: 5 13 8 5 N SD: 8.0375 c. M: 11.1447 c. 34: 6 14 9 5 N SD: 5.2991 c. M:-7.8547 c. 41: 7 17 11 6 N SD: 3.4398 c. M:-6.7940 c. 46: 8 19 12 7 N SD: 2.6772 c. M:-4.7857 c. 53: 9 22 14 8 N SD: 0.6404 c. M:-1.2716 c. 118: 20 49 31 18 N SD: 0.4350 c. M: 0.6471 c. 171: 29 71 45 26 N SD: 0.2258 c. M: 0.4012 c. 224: 38 93 59 34 N SD: 0.2299 c. M: 0.3386 c. 335: 57 139 88 51 N SD: 0.2065 c. M: 0.2829 c. 388: 66 161 102 59 N SD: 0.1246 c. M:-0.2137 c. 441: 75 183 116 67 N SD: 0.1061 c. M:-0.1716 c. 506: 86 210 133 77 N SD: 0.1052 c. M: 0.2050 c. 559: 95 232 147 85 N SD: 0.0355 c. M: 0.0650 c. 612: 104 254 161 93 N SD: 0.0262 c. M:-0.0508 c. 1171: 199 486 308 178 N SD: 0.0105 c. M:-0.0183 c. 1783: 303 740 469 271 N SD: 0.0115 c. M:-0.0160 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x 3 x 4 S SD: 0.0000 cents 3 x x 5:6 SD: 66.6188 cents 4:5:6:7:8 H SD: 47.2028 cents 5:6:8:9:10 S SD: 39.5030 cents 6:7:9:11:12 SD: 17.6302 cents 8:9:12:14:16 S SD: 12.1926 cents 10:11:15:18:20 SD: 9.7264 cents 14:16:21:25:28 SD: 7.6388 cents 16:18:24:29:32 SD: 2.9952 cents 24:27:36:43:48 SD: 2.0084 cents 40:45:60:72:80 S SD: 0.0000 cents