Scala analysis: xen12-wilson-08-4C1-tetrany-04
1-3-9-15 4C1 Tetrany, Figure 8
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: 15/8 1088.268715 classic major seventh 4: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 9/8 203.9100 major whole tone 2: 4/3 498.0450 perfect fourth 3: 5/4 386.3137 major third 4: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 9/8 203.910 cents major whole 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 4/3 498.045 cents perfect fourth 2: 1 3/2 701.955 cents perfect 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 16/9 996.090 cents Pythagorean minor seventh 3: 1 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: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 0.0 : 203.9 702.0 1088.3 1200.0 203.9 : 498.0 884.4 996.1 1200.0 702.0 : 386.3 498.0 702.0 1200.0 1088.3: 111.7 315.6 813.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 498.0450 cents 5/4, 386.3137 cents 16/15, 111.7313 cents 2: 315.6413 .. 884.3587 cents 25/18, 568.7174 cents 9/10,-182.4037 cents 3: 701.9550 .. 1088.2687 cents 5/4, 386.3137 cents 9/10,-182.4037 cents
SHOW DATA
Number of notes : 4 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 300.0000 cents Largest one step interval : 4/3, 498.0450 cents Average / Smallest step : 2.685013 Largest / Average step : 1.660150 Largest / Smallest step : 4.457525 Median interval of one step : 295.11186 cents, amount: 0 Least squares average step : 322.42087 cents, oct.: 1289.68349 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 : 1.663646 Lumma stability : 0.186219 Lumma impropriety factor : 0.304006 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 : 25/24, 70.6724 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 : 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 -- Rational properties -- Prime limit : 5 Odd number limit : 15 (O: 15 U: 15) Highest odd numerator or denominator: 15 Scale harmonicity : 0.063559 Average absolute harmonicity : 0.368900 Specific harmonicity : 0.336624 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 : 24.0, average 6.00000 Mersenne's string divisions : 5865 Sum of van Prooijen's expressibility: 2.60746, average 0.65186 Sum of Tenney's harmonic distance : 5.01569, average 1.25392 Vogel's harmonic complexity : 5.75000 Wille's k value : 7 Wilson's harmonic complexity : 11 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 26.17358, average 2.61736 Lattice compactness (without 2's) : 12.24264, average 1.22426 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -1.50000 8 1 3: 0 .. 2 1.00000 4 2 5: 0 .. 1 0.25000 1 1 Average exponent except 2's : 5 / 4 = 1.25000 Average absolute exponent except 2's: 5 / 4 = 1.25000 Scale is weakly epimorphic with val: <4 5 10| Scale is weakly epimorphic with val: <4 7 10|
FIT/MODE
4: 0 2 1 1 N T3 SD: 147.8337 c. M: 203.9100 c. 5: 1 2 2 0 N G SD: 59.3969 c. M:-111.7313 c. 6: 1 2 2 1 P D3 I SD: 67.4564 c. M: 101.9550 c. 7: 1 3 2 1 N SD: 34.9377 c. M: 59.6973 c. 10: 2 4 3 1 N SD: 20.5942 c. M:-36.0900 c. 12: 2 5 4 1 N SD: 6.2597 c. M:-11.7313 c. 31: 5 13 10 3 N SD: 6.1956 c. M: 10.3616 c. 34: 6 14 11 3 N SD: 5.2757 c. M:-7.8547 c. 41: 7 17 13 4 N SD: 2.7252 c. M: 5.3419 c. 53: 9 22 17 5 N SD: 0.7421 c. M: 1.4763 c. 65: 11 27 21 6 N SD: 0.6695 c. M:-0.9621 c. 118: 20 49 38 11 N SD: 0.2983 c. M: 0.5202 c. 289: 49 120 93 27 N SD: 0.3150 c. M: 0.4498 c. 323: 55 134 104 30 N SD: 0.2745 c. M:-0.4244 c. 376: 64 156 121 35 N SD: 0.1936 c. M:-0.3453 c. 429: 73 178 138 40 N SD: 0.1780 c. M:-0.2858 c. 441: 75 183 142 41 N SD: 0.1271 c. M:-0.1716 c. 494: 84 205 159 46 N SD: 0.0776 c. M:-0.1386 c. 559: 95 232 180 52 N SD: 0.0536 c. M:-0.1034 c. 612: 104 254 197 57 N SD: 0.0179 c. M: 0.0334 c. 1171: 199 486 377 109 N SD: 0.0189 c. M:-0.0319 c. 1289: 219 535 415 120 N SD: 0.0193 c. M: 0.0310 c. 1783: 303 740 574 166 N SD: 0.0101 c. M:-0.0160 c. 1901: 323 789 612 177 N SD: 0.0097 c. M: 0.0173 c. 2395: 407 994 771 223 N SD: 0.0083 c. M:-0.0148 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 5 x 6 SD: 91.2019 cents 4:5:6 x 8 S SD: 60.8012 cents 5:6:8:9:10 S SD: 43.2741 cents 6:7:9:11:12 SD: 18.5029 cents 8:9:12:15:16 S SD: 0.0000 cents