Scala analysis: xen12-wilson-38-4C1-tetrany-08
1-5-9-11 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: 11/8 551.317942 undecimal semi-augmented fourth 4: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/11 648.6821 undecimal semi-diminished fifth 1: 9/8 203.9100 major whole tone 2: 10/9 182.4037 minor whole tone 3: 11/10 165.0042 Ptolemy's second, 4/5-tone 4: 16/11 648.6821 undecimal semi-diminished fifth
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 10/9 182.404 cents minor whole tone 1: 1 9/8 203.910 cents major whole tone 1: 1 16/11 648.682 cents undecimal semi-diminished fifth 2: 1 11/9 347.408 cents undecimal neutral third 2: 1 5/4 386.314 cents major third 2: 1 8/5 813.686 cents minor sixth 2: 1 18/11 852.592 cents undecimal neutral sixth 3: 1 11/8 551.318 cents undecimal semi-augmented fourth 3: 1 16/9 996.090 cents Pythagorean minor seventh 3: 1 9/5 1017.596 cents just minor seventh, BP seventh 3: 1 20/11 1034.996 cents large minor 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 : 203.9 386.3 551.3 1200.0 203.9 : 182.4 347.4 996.1 1200.0 386.3 : 165.0 813.7 1017.6 1200.0 551.3 : 648.7 852.6 1035.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 165.0042 .. 648.6821 cents 160/121, 483.6778 cents 11/10, 165.0042 cents 2: 347.4079 .. 852.5921 cents 162/121, 505.1841 cents 121/144,-301.2741 cents 3: 551.3179 .. 1034.9958 cents 160/121, 483.6778 cents 121/144,-301.2741 cents
SHOW DATA
Number of notes : 4 -- Interval properties -- Smallest interval : 11/10, 165.0042 cents, class 1 Average step (divided formal octave): 300.0000 cents Largest one step interval : 16/11, 648.6821 cents Average / Smallest step : 1.818135 Largest / Average step : 2.162274 Largest / Smallest step : 3.931306 Median interval of one step : 193.15686 cents, amount: 0 Least squares average step : 247.68304 cents, oct.: 990.73217 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 97.36412 cents Scale diversity : 1.566594 Lumma stability : 0.275007 Lumma impropriety factor : 0.420987 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 : 100/99, 17.3995 cents Number of recognisable fifths : 0 Length of longest harmonic part : 3 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 classes 2 and 3 combined Limited inverse transpositions with margin 483.6778 cents: 3 -- Rational properties -- Prime limit : 11 Odd number limit : 11 (O: 11 U: 11) Highest odd numerator or denominator: 11 Scale harmonicity : 0.029485 Average absolute harmonicity : 0.321564 Specific harmonicity : 0.176478 Fundamental : 1/8, -3.0000 octaves, 32.7032 Hz. Guide tone : 990, 9.9513 octaves, 259009.310 Hz. Exponens Consonantiae : 7.920000E+03, 12.95128 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 24.0, average 6.00000 Mersenne's string divisions : 2907 Sum of van Prooijen's expressibility: 2.69461, average 0.67365 Sum of Tenney's harmonic distance : 5.40388, average 1.35097 Vogel's harmonic complexity : 6.75000 Wille's k value : 5 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 28.17902, average 2.81790 Lattice compactness (without 2's) : 13.88635, average 1.38863 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -1.75000 9 1 3: 0 .. 2 0.50000 2 1 5: 0 .. 1 0.25000 1 1 11: 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 5 9 15| Scale is weakly epimorphic with val: <4 7 9 15|
FIT/MODE
4: 1 0 1 2 N D3 SD: 69.0168 c. M:-96.0900 c. 5: 1 1 0 3 N G SD: 61.5749 c. M:-93.6863 c. 6: 1 1 1 3 N M DE SD: 25.3601 c. M:-48.6821 c. 7: 1 1 1 4 N M DE SD: 32.8440 c. M: 43.4566 c. 11: 2 2 1 6 N SD: 26.1871 c. M:-50.0499 c. 13: 2 2 2 7 N M DE SD: 12.9470 c. M: 19.2946 c. 18: 3 3 2 10 N SD: 11.4679 c. M: 17.9846 c. 19: 3 3 3 10 N M DE SD: 11.7812 c. M:-17.1031 c. 22: 4 3 3 12 N SD: 8.0355 c. M:-14.2718 c. 24: 4 4 3 13 N SD: 7.1474 c. M:-13.6863 c. 28: 5 4 4 15 N SD: 5.9570 c. M:-10.3757 c. 31: 5 5 4 17 N SD: 7.0001 c. M: 10.3616 c. 35: 6 5 5 19 N SD: 4.8709 c. M: 9.1709 c. 41: 7 6 6 22 N SD: 3.7988 c. M: 5.8259 c. 46: 8 7 6 25 N SD: 3.8730 c. M:-4.9906 c. 52: 9 8 7 28 N SD: 3.7625 c. M:-5.9940 c. 59: 10 9 8 32 N SD: 1.1153 c. M: 2.1654 c. 124: 21 19 17 67 N SD: 0.5404 c. M:-0.7831 c. 183: 31 28 25 99 N SD: 0.4933 c. M: 0.6313 c. 211: 36 32 29 114 N SD: 0.4943 c. M:-0.8293 c. 224: 38 34 31 121 N SD: 0.4162 c. M: 0.5994 c. 270: 46 41 37 146 N SD: 0.3365 c. M:-0.5344 c. 283: 48 43 39 153 N SD: 0.2954 c. M: 0.4480 c. 342: 58 52 47 185 N SD: 0.3453 c. M: 0.4407 c. 348: 59 53 48 188 N SD: 0.3121 c. M: 0.4617 c. 370: 63 56 51 200 N SD: 0.2775 c. M:-0.4143 c. 394: 67 60 54 213 N SD: 0.2567 c. M:-0.4883 c. 407: 69 62 56 220 N SD: 0.2385 c. M: 0.4702 c. 429: 73 65 59 232 N SD: 0.2469 c. M: 0.2997 c. 435: 74 66 60 235 N SD: 0.2389 c. M:-0.4062 c. 494: 84 75 68 267 N SD: 0.0939 c. M:-0.1386 c. 553: 94 84 76 299 N SD: 0.0840 c. M: 0.1425 c. 618: 105 94 85 334 N SD: 0.0847 c. M:-0.1384 c. 677: 115 103 93 366 N SD: 0.0673 c. M:-0.0969 c. 1047: 178 159 144 566 N SD: 0.0625 c. M:-0.1015 c. 1112: 189 169 153 601 N SD: 0.0654 c. M:-0.1209 c. 1171: 199 178 161 633 N SD: 0.0149 c. M:-0.0228 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x x 3:4 S SD: 75.3185 cents 3 x x 4:6 S SD: 26.6365 cents 4 x 5:6:8 S SD: 50.2124 cents 5 x 6:7:10 SD: 25.7502 cents 6:7 x 8:12 S SD: 27.4916 cents 7:8:9:10:14 SD: 21.6511 cents 8:9:10:11:16 SD: 0.0000 cents