Scala analysis: xen12-wilson-08-4C1-tetrany-01
1-3-7-11 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: 7/4 968.825906 harmonic seventh 4: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 11/8 551.3179 undecimal semi-augmented fourth 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 7/6 266.8709 septimal minor third 4: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 8/7 231.174 cents septimal whole tone 1: 1 7/6 266.871 cents septimal minor third 1: 1 11/8 551.318 cents undecimal semi-augmented fourth 2: 1 14/11 417.508 cents undecimal diminished fourth or major third 2: 1 4/3 498.045 cents perfect fourth 2: 1 3/2 701.955 cents perfect fifth 2: 1 11/7 782.492 cents undecimal augmented fifth 3: 1 16/11 648.682 cents undecimal semi-diminished fifth 3: 1 12/7 933.129 cents septimal major sixth 3: 1 7/4 968.826 cents harmonic 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 : 551.3 702.0 968.8 1200.0 551.3 : 150.6 417.5 648.7 1200.0 702.0 : 266.9 498.0 1049.4 1200.0 968.8 : 231.2 782.5 933.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.6371 .. 551.3179 cents 121/96, 400.6809 cents 12/11, 150.6371 cents 2: 417.5080 .. 782.4920 cents 121/98, 364.9841 cents 112/121,-133.8100 cents 3: 648.6821 .. 1049.3629 cents 121/96, 400.6809 cents 112/121,-133.8100 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 : 11/8, 551.3179 cents Average / Smallest step : 1.991542 Largest / Average step : 1.837726 Largest / Smallest step : 3.659909 Median interval of one step : 249.02250 cents, amount: 0 Least squares average step : 322.05686 cents, oct.: 1288.22742 cents Scale is not 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 53.27294 cents Scale diversity : 1.710650 Lumma stability : 0.251062 Lumma impropriety factor : 0.223017 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 : 49/48, 35.6968 cents Number of recognisable fifths : 1, average 701.9550 cents Length of longest harmonic part : 2 at degree 2 Formal octave complements present : 1 = 25.0000% Scale is differentially coherent in interval class 1 Scale is 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 : 0.028462 Average absolute harmonicity : 0.350333 Specific harmonicity : 0.172966 Fundamental : 1/8, -3.0000 octaves, 32.7032 Hz. Guide tone : 462, 8.8517 octaves, 120871.011 Hz. Exponens Consonantiae : 3.696000E+03, 11.85175 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 19.0, average 4.75000 Mersenne's string divisions : 3135 Sum of van Prooijen's expressibility: 2.36361, average 0.59090 Sum of Tenney's harmonic distance : 4.47082, average 1.11771 Vogel's harmonic complexity : 7.00000 Wille's k value : 5 Wilson's harmonic complexity : 21 Rectangular lattice diameter : 3 Triangular lattice diameter : 1 Lattice compactness : 23.24760, average 2.32476 Lattice compactness (without 2's) : 10.24264, average 1.02426 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -1.25000 7 1 3: 0 .. 1 0.25000 1 1 7: 0 .. 1 0.25000 1 1 11: 0 .. 1 0.25000 1 1 Average exponent except 2's : 3 / 4 = 0.75000 Average absolute exponent except 2's: 3 / 4 = 0.75000 Scale is weakly epimorphic with val: <4 5 10 15| Scale is weakly epimorphic with val: <4 5 11 14| Scale is JI-epimorphic with val: <4 6 11 13| Scale is weakly epimorphic with val: <4 7 10 13|
FIT/MODE
4: 2 0 1 1 N T3 SD: 66.1471 c. M: 101.9550 c. 5: 2 1 1 1 P M ME SD: 37.0465 c. M: 71.3179 c. 7: 3 1 2 1 P G D3 SD: 36.0717 c. M:-59.7455 c. 9: 4 1 2 2 N SD: 26.5915 c. M: 35.4926 c. 10: 5 1 2 2 N SD: 26.3318 c. M:-48.6821 c. 11: 5 1 3 2 N SD: 24.7530 c. M: 47.4095 c. 14: 6 2 3 3 N SD: 24.0288 c. M: 37.0322 c. 15: 7 2 3 3 N SD: 10.9419 c. M:-18.0450 c. 17: 8 2 4 3 N SD: 11.9518 c. M:-19.4094 c. 20: 9 3 4 4 N SD: 11.5284 c. M:-18.0450 c. 22: 10 3 5 4 N SD: 7.9703 c. M:-12.9923 c. 26: 12 3 6 5 N SD: 4.9906 c. M: 9.6473 c. 31: 14 4 7 6 N SD: 5.3862 c. M: 9.3825 c. 41: 19 5 9 8 N SD: 2.8246 c. M:-4.7796 c. 46: 21 6 10 9 N SD: 2.7812 c. M: 3.6085 c. 63: 29 8 14 12 N SD: 1.9864 c. M:-2.8069 c. 72: 33 9 16 14 N SD: 1.5985 c. M: 2.1592 c. 89: 41 11 20 17 N SD: 1.2999 c. M:-1.9606 c. 120: 55 15 27 23 N SD: 1.3170 c. M: 1.9550 c. 130: 60 16 29 25 N SD: 1.2970 c. M:-2.5282 c. 135: 62 17 30 26 N SD: 0.1719 c. M:-0.2672 c. 431: 198 54 96 83 N SD: 0.1719 c. M: 0.3309 c. 566: 260 71 126 109 N SD: 0.1098 c. M: 0.1882 c. 701: 322 88 156 135 N SD: 0.0821 c. M: 0.1054 c. 836: 384 105 186 161 N SD: 0.0741 c. M: 0.1218 c. 877: 403 110 195 169 N SD: 0.0643 c. M:-0.1074 c. 1012: 465 127 225 195 N SD: 0.0429 c. M:-0.0655 c. 1147: 527 144 255 221 N SD: 0.0356 c. M:-0.0502 c. 1578: 725 198 351 304 N SD: 0.0278 c. M: 0.0539 c. 1713: 787 215 381 330 N SD: 0.0145 c. M: 0.0286 c. 1848: 849 232 411 356 N SD: 0.0106 c. M: 0.0192 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 x 5:6 S SD: 33.2878 cents 4 x 6:7:8 S SD: 0.0000 cents