Scala analysis: xen12-wilson-08-4C1-tetrany-05
1-3-11-15 4C1 Tetrany, Figure 8
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/8 551.317942 undecimal semi-augmented fourth 2: 3/2 701.955001 perfect fifth 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: 11/8 551.3179 undecimal semi-augmented fourth 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 5/4 386.3137 major third 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 : 551.3 702.0 1088.3 1200.0 551.3 : 150.6 537.0 648.7 1200.0 702.0 : 386.3 498.0 1049.4 1200.0 1088.3: 111.7 663.0 813.7 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 : 334.00114 cents, oct.: 1336.00455 cents Scale is not proper Step pattern alph. order: ABCD Step pattern size order : DBCA 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 Best minor thirds form a closed circle 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 Limited inverse transpositions with margin 400.6809 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 : 0.350702 Specific harmonicity : 0.183382 Fundamental : 1/8, -3.0000 octaves, 32.7032 Hz. Guide tone : 330, 8.3663 octaves, 86336.437 Hz. Exponens Consonantiae : 2.640000E+03, 11.36632 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 25.0, average 6.25000 Mersenne's string divisions : 6555 Sum of van Prooijen's expressibility: 2.69461, average 0.67365 Sum of Tenney's harmonic distance : 5.10285, average 1.27571 Vogel's harmonic complexity : 7.00000 Wille's k value : 7 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 25.91254, average 2.59125 Lattice compactness (without 2's) : 10.97469, average 1.09747 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -1.50000 8 1 3: 0 .. 1 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 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: 2 0 2 0 P B DE SD: 79.4491 c. M:-111.7313 c. 5: 2 1 2 0 P D3 SD: 66.8875 c. M:-111.7313 c. 7: 3 1 2 1 P G D3 SD: 36.0517 c. M: 59.6973 c. 8: 4 1 2 1 N D3 SD: 39.1879 c. M:-48.6821 c. 9: 4 1 3 1 P G D3 SD: 22.5575 c. M: 35.2883 c. 13: 6 2 4 1 N SD: 20.7147 c. M:-36.5065 c. 15: 7 2 5 1 N SD: 18.7608 c. M:-31.7313 c. 17: 8 2 5 2 N D3 SD: 16.2917 c. M: 29.4452 c. 19: 9 2 6 2 N D3 SD: 11.8039 c. M:-17.1031 c. 20: 9 3 6 2 N SD: 11.4246 c. M:-18.0450 c. 22: 10 3 7 2 N SD: 4.8029 c. M:-7.1359 c. 41: 19 5 13 4 N SD: 3.5922 c. M: 5.3419 c. 53: 24 7 17 5 N SD: 4.0292 c. M: 7.9217 c. 55: 25 7 18 5 N SD: 3.7279 c. M: 5.8634 c. 63: 29 8 20 6 N SD: 1.9706 c. M:-2.8069 c. 65: 30 8 21 6 N SD: 1.3685 c. M:-2.5282 c. 87: 40 11 28 8 N SD: 1.0389 c. M:-1.4933 c. 152: 70 19 49 14 N SD: 0.9533 c. M:-1.3136 c. 159: 73 20 51 15 N SD: 0.7623 c. M: 1.4763 c. 161: 74 20 52 15 N SD: 0.6781 c. M: 1.3339 c. 181: 83 23 58 17 N SD: 0.8200 c. M: 1.0417 c. 183: 84 23 59 17 N SD: 0.3215 c. M: 0.4983 c. 246: 113 31 79 23 N SD: 0.3388 c. M:-0.4840 c. 248: 114 31 80 23 N SD: 0.3156 c. M:-0.4410 c. 311: 143 39 100 29 N SD: 0.2820 c. M:-0.4505 c. 407: 187 51 131 38 N SD: 0.1945 c. M: 0.3080 c. 429: 197 54 138 40 N SD: 0.1713 c. M: 0.2690 c. 494: 227 62 159 46 N SD: 0.0606 c. M:-0.0991 c. 677: 311 85 218 63 N SD: 0.0473 c. M: 0.0624 c. 1171: 538 147 377 109 N SD: 0.0168 c. M:-0.0319 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x 3 x 4 S SD: 0.0000 cents 3:4:5 x 6 S SD: 63.3413 cents 4 x 6 x 8 S SD: 0.0000 cents