Scala analysis: xen12-wilson-08-4C3-tetrany-03
1-3-9-11 4C3 Tetrany, Figure 8
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/9 347.407941 undecimal neutral third 2: 11/8 551.317942 undecimal semi-augmented fourth 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: 11/9 347.4079 undecimal neutral third 2: 9/8 203.9100 major whole tone 3: 4/3 498.0450 perfect fourth 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 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 : 347.4 551.3 1049.4 1200.0 347.4 : 203.9 702.0 852.6 1200.0 551.3 : 498.0 648.7 996.1 1200.0 1049.4: 150.6 498.0 702.0 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 : 313.27109 cents, oct.: 1253.08435 cents Scale is proper Step pattern alph. order: ABCD Step pattern size order : CBDA 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 Formal octave complements present : 1 = 25.0000% Scale is n-1 differentially coherent in interval class 1 -- 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 : 0.283876 Specific harmonicity : 0.162593 Fundamental : 1/72, -6.1699 octaves, 3.6337 Hz. Guide tone : 22, 4.4594 octaves, 5755.762 Hz. Exponens Consonantiae : 1.584000E+03, 10.62936 octaves Euler's gradus suavitatis : 19 Sum of Mann's harmonic distance : 29.5, average 7.37500 Mersenne's string divisions : 19380 Sum of van Prooijen's expressibility: 3.12418, average 0.78104 Sum of Tenney's harmonic distance : 6.06069, average 1.51517 Vogel's harmonic complexity : 14.25000 Wille's k value : 49 Wilson's harmonic complexity : 17 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 24.40831, average 2.44083 Lattice compactness (without 2's) : 13.30056, average 1.33006 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -0.75000 5 1 3: -2 .. 0 -0.75000 3 11: 0 .. 1 0.75000 3 3 Average exponent except 2's : 0 / 4 = 0.00000 Average absolute exponent except 2's: 6 / 4 = 1.50000 Scale is weakly epimorphic with val: <4 5 15| Scale is weakly epimorphic with val: <4 7 13|
FIT/MODE
4: 1 1 1 1 SP B ME I SD: 82.0469 c. M: 149.3629 c. 5: 1 1 2 1 P M ME SD: 78.4354 c. M: 107.4079 c. 6: 2 1 2 1 SP B ME SD: 43.5103 c. M:-52.5921 c. Messiaen truncated mode 6 inverse 7: 2 1 3 1 P G D3 SD: 21.3564 c. M: 37.0322 c. 13: 4 2 5 2 SP D3 SD: 20.2309 c. M: 33.9783 c. 15: 4 3 6 2 P SD: 15.1182 c. M: 27.4079 c. 17: 5 3 7 2 P SD: 8.6510 c. M:-13.3879 c. 24: 7 4 10 3 P SD: 1.4884 c. M:-2.5921 c. 87: 25 15 36 11 P SD: 1.4147 c. M: 2.5804 c. 104: 30 18 43 13 P SD: 1.4466 c. M:-2.5282 c. 111: 32 19 46 14 P SD: 0.8138 c. M: 1.4620 c. 135: 39 23 56 17 P SD: 0.4519 c. M: 0.7413 c. 159: 46 27 66 20 P SD: 0.2696 c. M: 0.3745 c. 311: 90 53 129 39 P SD: 0.2484 c. M:-0.4505 c. 335: 97 57 139 42 P SD: 0.1895 c. M:-0.3238 c. 359: 104 61 149 45 P SD: 0.1899 c. M:-0.2244 c. 470: 136 80 195 59 P SD: 0.1221 c. M: 0.1739 c. 494: 143 84 205 62 P SD: 0.0554 c. M:-0.0991 c. 518: 150 88 215 65 P SD: 0.0531 c. M:-0.0824 c. 653: 189 111 271 82 P SD: 0.0517 c. M: 0.0879 c. 677: 196 115 281 85 P SD: 0.0343 c. M: 0.0624 c. 1012: 293 172 420 127 P SD: 0.0411 c. M:-0.0655 c. 1147: 332 195 476 144 P SD: 0.0384 c. M: 0.0671 c. 1171: 339 199 486 147 P SD: 0.0071 c. M: 0.0126 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x 3 x 4 S SD: 75.3185 cents 3 x 4 x 6 S SD: 26.6365 cents 5:6:7:9:10 SD: 13.6732 cents 13:16:18:24:26 SD: 5.2240 cents 18:22:25:33:36 SD: 4.3499 cents 31:38:43:57:62 SD: 4.1934 cents 32:39:44:59:64 SD: 2.7440 cents 37:45:51:68:74 SD: 2.6080 cents 40:49:55:73:80 SD: 2.2030 cents 53:65:73:97:106 SD: 1.8164 cents 54:66:74:99:108 SD: 1.4597 cents 59:72:81:108:118 SD: 1.1560 cents 67:82:92:123:134 SD: 1.0169 cents 72:88:99:132:144 SD: 0.0000 cents