Scala analysis: xen12-wilson-08-4C1-tetrany-13
3-9-11-15 4C1 Tetrany, Figure 8
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: 3/2 701.955001 perfect fifth 3: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 4: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 5/4 386.3137 major third 2: 6/5 315.6413 minor third 3: 11/9 347.4079 undecimal neutral third 4: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 6/5 315.641 cents minor third 1: 1 11/9 347.408 cents undecimal neutral third 1: 1 5/4 386.314 cents major third 2: 1 4/3 498.045 cents perfect fourth 2: 1 15/11 536.951 cents undecimal augmented fourth 2: 1 22/15 663.049 cents undecimal diminished fifth 2: 1 3/2 701.955 cents perfect fifth 3: 1 8/5 813.686 cents minor sixth 3: 1 18/11 852.592 cents undecimal neutral sixth 3: 1 5/3 884.359 cents major sixth, BP sixth 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 : 386.3 702.0 1049.4 1200.0 386.3 : 315.6 663.0 813.7 1200.0 702.0 : 347.4 498.0 884.4 1200.0 1049.4: 150.6 537.0 852.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.6371 .. 386.3137 cents 55/48, 235.6767 cents 12/11, 150.6371 cents 2: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 16/15, 111.7313 cents 3: 813.6863 .. 1049.3629 cents 55/48, 235.6767 cents 16/15, 111.7313 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 : 5/4, 386.3137 cents Average / Smallest step : 1.991542 Largest / Average step : 1.287712 Largest / Smallest step : 2.564533 Median interval of one step : 331.52461 cents, amount: 0 Least squares average step : 324.61042 cents, oct.: 1298.44167 cents Scale is strictly proper Step pattern alph. order: ABCD Step pattern size order : DBCA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 111.73129 cents Scale diversity : 1.637421 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.437281 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 : 55/54, 31.7667 cents Number of recognisable fifths : 1, average 701.9550 cents Best minor thirds form a closed circle 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 n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Limited inverse transpositions with margin 196.7709 cents: 3 -- Rational properties -- Prime limit : 11 Odd number limit : 15 (O: 15 U: 15) Highest odd numerator or denominator: 11 Scale harmonicity : 0.030381 Average absolute harmonicity : 0.359386 Specific harmonicity : 0.187040 Fundamental : 1/12, -3.5850 octaves, 21.8021 Hz. Guide tone : 330, 8.3663 octaves, 86336.437 Hz. Exponens Consonantiae : 3.960000E+03, 11.95128 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 17.0, average 4.25000 Mersenne's string divisions : 765 Sum of van Prooijen's expressibility: 2.21748, average 0.55437 Sum of Tenney's harmonic distance : 4.19976, average 1.04994 Vogel's harmonic complexity : 8.25000 Wille's k value : 7 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 20.19829, average 2.01983 Lattice compactness (without 2's) : 12.21076, average 1.22108 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 1 -0.75000 5 1 3: -1 .. 1 0.00000 2 1 5: 0 .. 1 0.25000 1 1 11: 0 .. 1 0.25000 1 1 Average exponent except 2's : 2 / 4 = 0.50000 Average absolute exponent except 2's: 4 / 4 = 1.00000 Scale is JI-epimorphic with val: <4 6 9 13| Scale is weakly epimorphic with val: <4 7 9 13|
FIT/MODE
4: 1 1 1 1 SP B ME I SD: 100.1925 c. M: 149.3629 c. 5: 2 1 1 1 P M ME SD: 65.3615 c. M:-93.6863 c. 6: 2 1 2 1 SP B ME SD: 57.0501 c. M: 101.9550 c. Messiaen truncated mode 6 inverse 7: 2 2 2 1 SP M ME SD: 25.4191 c. M: 43.4566 c. 9: 3 2 3 1 SP D3 SD: 20.8087 c. M: 35.2883 c. 10: 3 3 3 1 SP M DE SD: 22.1171 c. M:-30.6371 c. 15: 5 4 4 2 SP SD: 12.2536 c. M:-18.0450 c. 22: 7 6 6 3 SP SD: 7.7478 c. M: 12.9993 c. 24: 8 6 7 3 SP SD: 6.9199 c. M:-13.6863 c. 31: 10 8 9 4 SP SD: 3.3581 c. M: 5.1808 c. 56: 18 15 16 7 SP SD: 2.6305 c. M:-5.1879 c. 65: 21 17 19 8 SP SD: 1.6390 c. M:-2.9448 c. 87: 28 23 25 11 SP SD: 0.9251 c. M:-1.4933 c. 118: 38 31 34 15 SP SD: 0.9636 c. M: 1.9053 c. 152: 49 40 44 19 SP SD: 0.5345 c. M:-0.6766 c. 183: 59 48 53 23 SP SD: 0.3390 c. M:-0.5715 c. 270: 87 71 78 34 SP SD: 0.3243 c. M: 0.4741 c. 311: 100 82 90 39 SP SD: 0.2848 c. M: 0.4616 c. 335: 108 88 97 42 SP SD: 0.2994 c. M:-0.5520 c. 342: 110 90 99 43 SP SD: 0.2343 c. M: 0.3488 c. 407: 131 107 118 51 SP SD: 0.1821 c. M:-0.2685 c. 494: 159 130 143 62 SP SD: 0.0546 c. M: 0.0789 c. 677: 218 178 196 85 SP SD: 0.0533 c. M:-0.0969 c. 1171: 377 308 339 147 SP SD: 0.0124 c. M:-0.0228 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x 3 x 4 S SD: 0.0000 cents 3:4 x x 6 S SD: 55.8656 cents 4:5:6:7:8 H SD: 20.1343 cents 8:10:12:15:16 S SD: 9.7264 cents 12:15:18:22:24 SD: 0.0000 cents