Scala analysis: xen12-wilson-08-4C3-tetrany-13
3-9-11-15 4C3 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: 15/11 536.950772 undecimal augmented fourth 3: 5/3 884.358713 major sixth, BP sixth 4: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 6/5 315.6413 minor third 1: 5/4 386.3137 major third 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 11/9 347.4079 undecimal neutral third 4: 6/5 315.6413 minor third
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 : 386.3 537.0 884.4 1200.0 386.3 : 150.6 498.0 813.7 1200.0 537.0 : 347.4 663.0 1049.4 1200.0 884.4 : 315.6 702.0 852.6 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 : 297.10971 cents, oct.: 1188.43885 cents Scale is strictly proper Step pattern alph. order: ABCD Step pattern size order : DACB 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 : 1 at degree 0 Length of longest subharmonic part : 2 at degree 3 Formal octave complements present : 1 = 25.0000% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 235.6767 cents: 3 -- Rational properties -- Prime limit : 11 Odd number limit : 15 (O: 15 U: 15) Highest odd numerator or denominator: 15 Scale harmonicity : 0.030381 Average absolute harmonicity : 0.316510 Specific harmonicity : 0.173057 Fundamental : 1/132, -7.0444 octaves, 1.9820 Hz. Guide tone : 30, 4.9069 octaves, 7848.767 Hz. Exponens Consonantiae : 3.960000E+03, 11.95128 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 23.0, average 5.75000 Mersenne's string divisions : 936 Sum of van Prooijen's expressibility: 2.57403, average 0.64351 Sum of Tenney's harmonic distance : 4.99564, average 1.24891 Vogel's harmonic complexity : 16.75000 Wille's k value : 82 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) : 12.94281, average 1.29428 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 1 -0.25000 3 1 3: -1 .. 1 0.00000 2 5: 0 .. 1 0.75000 3 2 11: -1 .. 0 -0.25000 1 1 Average exponent except 2's : 2 / 4 = 0.50000 Average absolute exponent except 2's: 6 / 4 = 1.50000 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: 54.0137 c. M: 86.3137 c. 6: 2 1 1 2 P D3 I SD: 53.1011 c. M: 84.3587 c. 7: 2 1 2 2 SP M ME SD: 28.0307 c. M: 43.4566 c. 9: 3 1 3 2 SP D3 SD: 25.4898 c. M:-48.9746 c. 12: 4 1 4 3 SP D3 SD: 21.1974 c. M: 36.9508 c. 15: 5 2 4 4 SP SD: 13.5792 c. M:-23.0492 c. 16: 5 2 5 4 SP D3 SD: 11.3520 c. M:-15.6413 c. 18: 6 2 5 5 SP SD: 11.3293 c. M: 17.6920 c. 22: 7 3 6 6 SP SD: 7.5468 c. M: 11.6314 c. 27: 9 3 8 7 SP SD: 7.4317 c. M:-13.6863 c. 31: 10 4 9 8 SP SD: 3.9060 c. M:-5.9639 c. 38: 12 5 11 10 SP SD: 3.6843 c. M: 7.3663 c. 49: 16 6 14 13 SP SD: 3.2119 c. M:-5.5230 c. 56: 18 7 16 15 SP SD: 2.9741 c. M: 5.7873 c. 65: 21 8 19 17 SP SD: 1.3762 c. M:-1.7951 c. 87: 28 11 25 23 SP SD: 0.9398 c. M: 1.6001 c. 118: 38 15 34 31 SP SD: 1.0363 c. M:-2.0323 c. 152: 49 19 44 40 SP SD: 0.2797 c. M:-0.5284 c. 255: 82 32 74 67 SP SD: 0.3665 c. M: 0.4802 c. 335: 108 42 97 88 SP SD: 0.3906 c. M:-0.5520 c. 342: 110 43 99 90 SP SD: 0.1971 c. M: 0.3488 c. 407: 131 51 118 107 SP SD: 0.1925 c. M: 0.3414 c. 494: 159 62 143 130 SP SD: 0.1000 c. M: 0.1482 c. 646: 208 81 187 170 SP SD: 0.0973 c. M: 0.1482 c. 677: 218 85 196 178 SP SD: 0.1028 c. M:-0.1317 c. 867: 279 109 251 228 SP SD: 0.0925 c. M: 0.1545 c. 1019: 328 128 295 268 SP SD: 0.0398 c. M: 0.0527 c. 1171: 377 147 339 308 SP SD: 0.0186 c. M:-0.0262 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x 3 x 4 S SD: 82.5021 cents 3 x 4:5:6 S SD: 12.9686 cents 4:5 x 7:8 SD: 28.1557 cents 5:6:7:8:10 S SD: 27.4602 cents 6 x 8:10:12 S SD: 12.9686 cents 8:10:11:13:16 SD: 11.5314 cents 11:14:15:18:22 SD: 11.1305 cents 12:15:16:20:24 S SD: 9.7264 cents 16:20:22:27:32 SD: 6.4659 cents 20:25:27:33:40 SD: 6.1516 cents 24:30:33:40:48 SD: 3.5918 cents 33:41:45:55:66 SD: 2.6311 cents 36:45:49:60:72 SD: 0.8022 cents 96:120:131:160:192 SD: 0.3005 cents 132:165:180:220:264 SD: 0.0000 cents