Scala analysis: xen12-wilson-08-4C1-tetrany-03
1-3-9-11 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: 11/8 551.317942 undecimal semi-augmented fourth 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: 11/9 347.4079 undecimal neutral third 3: 12/11 150.6371 undecimal neutral second, 3/4-tone 4: 4/3 498.0450 perfect fourth
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 9/8 203.910 cents major whole tone 1: 1 11/9 347.408 cents undecimal neutral third 1: 1 4/3 498.045 cents perfect fourth 2: 1 4/3 498.045 cents perfect fourth 2: 1 11/8 551.318 cents undecimal semi-augmented fourth 2: 1 16/11 648.682 cents undecimal semi-diminished fifth 2: 1 3/2 701.955 cents perfect fifth 3: 1 3/2 701.955 cents perfect fifth 3: 1 18/11 852.592 cents undecimal neutral sixth 3: 1 16/9 996.090 cents Pythagorean minor seventh 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 : 203.9 551.3 702.0 1200.0 203.9 : 347.4 498.0 996.1 1200.0 551.3 : 150.6 648.7 852.6 1200.0 702.0 : 498.0 702.0 1049.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.6371 .. 498.0450 cents 11/9, 347.4079 cents 12/11, 150.6371 cents 2: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 1/1, 0.0000 cents 3: 701.9550 .. 1049.3629 cents 11/9, 347.4079 cents 1/1, 0.0000 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 : 4/3, 498.0450 cents Average / Smallest step : 1.991542 Largest / Average step : 1.660150 Largest / Smallest step : 3.306258 Median interval of one step : 275.65897 cents, amount: 0 Least squares average step : 273.74703 cents, oct.: 1094.98812 cents Scale is proper Step pattern alph. order: ABCD Step pattern size order : BCAD Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 1.618265 Rothenberg stability : 0.666667 = 2/3 Lumma stability : 0.251062 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 : 33/32, 53.2729 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 Best minor thirds form a closed circle Length of longest harmonic part : 1 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 n-1 differentially coherent in interval class 2 -- Rational properties -- Prime limit : 11 Odd number limit : 11 (O: 11 U: 11) Highest odd numerator or denominator: 11 Scale harmonicity : 0.036344 Average absolute harmonicity : 0.359984 Specific harmonicity : 0.205941 Fundamental : 1/8, -3.0000 octaves, 32.7032 Hz. Guide tone : 198, 7.6294 octaves, 51801.862 Hz. Exponens Consonantiae : 1.584000E+03, 10.62936 octaves Euler's gradus suavitatis : 19 Sum of Mann's harmonic distance : 22.0, average 5.50000 Mersenne's string divisions : 4845 Sum of van Prooijen's expressibility: 2.47276, average 0.61819 Sum of Tenney's harmonic distance : 4.88100, average 1.22025 Vogel's harmonic complexity : 6.50000 Wille's k value : 5 Wilson's harmonic complexity : 17 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 26.93498, average 2.69350 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 -1.50000 8 1 3: 0 .. 2 0.75000 3 2 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 15| Scale is weakly epimorphic with val: <4 7 13|
FIT/MODE
4: 1 1 0 2 N T3 SD: 74.1587 c. M: 101.9550 c. 5: 1 1 1 2 P M ME SD: 40.9706 c. M: 71.3179 c. 7: 1 2 1 3 P G D3 SD: 25.9335 c. M: 37.0322 c. 11: 2 3 1 5 N SD: 24.9285 c. M: 47.4095 c. 13: 2 4 2 5 SP D3 SD: 20.6845 c. M:-36.5065 c. 15: 3 4 2 6 P SD: 20.6367 c. M:-36.0900 c. 17: 3 5 2 7 P SD: 8.0056 c. M:-13.3879 c. 24: 4 7 3 10 P SD: 2.2829 c. M: 3.9100 c. 65: 11 19 8 27 P SD: 1.3472 c. M:-2.5282 c. 89: 15 26 11 37 P SD: 1.1916 c. M: 1.6628 c. 94: 16 27 12 39 P SD: 1.2064 c. M: 2.3818 c. 111: 19 32 14 46 P SD: 0.8361 c. M:-1.4954 c. 135: 23 39 17 56 P SD: 0.3162 c. M:-0.5344 c. 159: 27 46 20 66 P SD: 0.2022 c. M: 0.3745 c. 294: 50 85 37 122 P SD: 0.1770 c. M: 0.2975 c. 359: 61 104 45 149 P SD: 0.1072 c. M:-0.2141 c. 494: 84 143 62 205 P SD: 0.0919 c. M:-0.1386 c. 518: 88 150 65 215 P SD: 0.0321 c. M: 0.0490 c. 1171: 199 339 147 486 P SD: 0.0106 c. M:-0.0183 c. 1689: 287 489 212 701 P SD: 0.0072 c. M:-0.0142 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: 63.3413 cents 4 x x 6:8 S SD: 0.0000 cents