Scala analysis: xen12-wilson-08-4C3-tetrany-05
1-3-11-15 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: 15/8 1088.268715 classic major seventh 4: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 5/4 386.3137 major third 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 11/8 551.3179 undecimal semi-augmented fourth 4: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 5/4 386.314 cents major third 1: 1 11/8 551.318 cents undecimal semi-augmented fourth 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 16/11 648.682 cents undecimal semi-diminished fifth 3: 1 8/5 813.686 cents minor sixth 3: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 3: 1 15/8 1088.269 cents classic major 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 : 386.3 537.0 1088.3 1200.0 386.3 : 150.6 702.0 813.7 1200.0 537.0 : 551.3 663.0 1049.4 1200.0 1088.3: 111.7 498.0 648.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 551.3179 cents 165/128, 439.5867 cents 16/15, 111.7313 cents 2: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 32/33,-53.2729 cents 3: 648.6821 .. 1088.2687 cents 165/128, 439.5867 cents 32/33,-53.2729 cents
SHOW DATA
Number of notes : 4 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 300.0000 cents Largest one step interval : 11/8, 551.3179 cents Average / Smallest step : 2.685013 Largest / Average step : 1.837726 Largest / Smallest step : 4.934320 Median interval of one step : 268.47539 cents, amount: 0 Least squares average step : 317.50071 cents, oct.: 1270.00285 cents Scale is not proper Step pattern alph. order: ABCD Step pattern size order : CBDA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 14.36717 cents Scale diversity : 1.512247 Lumma stability : 0.186219 Lumma impropriety factor : 0.088788 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 : 121/120, 14.3672 cents Number of recognisable fifths : 1, average 701.9550 cents 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 n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 439.5867 cents: 1 -- Rational properties -- Prime limit : 11 Odd number limit : 15 (O: 15 U: 15) Highest odd numerator or denominator: 15 Scale harmonicity : 0.032002 Average absolute harmonicity : 0.309655 Specific harmonicity : 0.169920 Fundamental : 1/88, -6.4594 octaves, 2.9730 Hz. Guide tone : 30, 4.9069 octaves, 7848.767 Hz. Exponens Consonantiae : 2.640000E+03, 11.36632 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 30.5, average 7.62500 Mersenne's string divisions : 5382 Sum of van Prooijen's expressibility: 3.05115, average 0.76279 Sum of Tenney's harmonic distance : 5.89873, average 1.47468 Vogel's harmonic complexity : 15.50000 Wille's k value : 82 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 24.71564, average 2.47156 Lattice compactness (without 2's) : 11.70674, average 1.17067 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -1.00000 6 1 3: 0 .. 1 0.50000 2 5: 0 .. 1 0.75000 3 2 11: -1 .. 0 -0.25000 1 1 Average exponent except 2's : 4 / 4 = 1.00000 Average absolute exponent except 2's: 6 / 4 = 1.50000 Scale is weakly epimorphic with val: <4 5 9 15| Scale is weakly epimorphic with val: <4 5 10 14| Scale is JI-epimorphic with val: <4 6 9 13| Scale is weakly epimorphic with val: <4 7 10 14|
FIT/MODE
4: 1 1 2 0 N T3 SD: 77.3129 c. M:-111.7313 c. 6: 2 1 2 1 SP B ME SD: 54.6669 c. M: 88.2687 c. Messiaen truncated mode 6 inverse 7: 2 1 3 1 P G D3 SD: 38.6198 c. M: 59.6973 c. 9: 3 1 4 1 P G D3 SD: 12.9136 c. M: 21.6020 c. 13: 4 2 6 1 N SD: 15.4480 c. M:-19.4236 c. 19: 6 2 9 2 N D3 SD: 17.8261 c. M: 31.6876 c. 20: 6 3 9 2 N SD: 13.8752 c. M: 26.3137 c. 21: 7 2 10 2 N D3 SD: 13.2999 c. M: 22.6651 c. 22: 7 3 10 2 N SD: 4.9874 c. M:-8.5038 c. 31: 10 4 14 3 N SD: 3.3467 c. M:-4.9847 c. 53: 17 7 24 5 N SD: 3.3803 c. M:-6.4455 c. 56: 18 7 26 5 N SD: 2.3949 c. M:-4.5884 c. 65: 21 8 30 6 N SD: 1.1488 c. M: 1.5662 c. 87: 28 11 40 8 N SD: 0.8507 c. M:-1.3865 c. 96: 31 12 44 9 N SD: 0.7583 c. M:-1.1863 c. 152: 49 19 70 14 N SD: 0.6601 c. M:-1.2050 c. 161: 52 20 74 15 N SD: 0.6510 c. M:-1.2639 c. 183: 59 23 84 17 N SD: 0.4901 c. M:-0.7541 c. 248: 80 31 114 23 N SD: 0.4552 c. M:-0.7831 c. 311: 100 39 143 29 N SD: 0.3939 c. M: 0.6164 c. 333: 107 42 153 31 N SD: 0.3643 c. M: 0.7281 c. 342: 110 43 157 32 N SD: 0.3299 c. M: 0.5494 c. 398: 128 50 183 37 N SD: 0.2495 c. M: 0.3841 c. 407: 131 51 187 38 N SD: 0.2328 c. M: 0.3414 c. 429: 138 54 197 40 N SD: 0.1782 c. M: 0.2997 c. 494: 159 62 227 46 N SD: 0.0673 c. M: 0.1087 c. 1075: 346 135 494 100 N SD: 0.0665 c. M:-0.1034 c. 1084: 349 136 498 101 N SD: 0.0488 c. M: 0.0768 c. 1171: 377 147 538 109 N SD: 0.0236 c. M:-0.0319 c. 1665: 536 209 765 155 N SD: 0.0125 c. M:-0.0196 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 x 6 S SD: 19.4529 cents 4:5 x x 8 SD: 0.0000 cents 6 x 8:11:12 SD: 18.3404 cents 8:10:11:15:16 SD: 3.5918 cents 33:41:45:62:66 SD: 2.7723 cents 39:49:53:73:78 SD: 2.7652 cents 41:51:56:77:82 SD: 2.3384 cents 47:59:64:88:94 SD: 2.0328 cents 55:69:75:103:110 SD: 1.6564 cents 63:79:86:118:126 SD: 1.5170 cents 64:80:87:120:128 SD: 1.3546 cents 72:90:98:135:144 SD: 0.8022 cents 80:100:109:150:160 SD: 0.3608 cents 88:110:120:165:176 SD: 0.0000 cents