Scala analysis: xen12-wilson-38-4C1-tetrany-06
1-5-7-9 4C1 Tetrany, Figure 38
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 5/4 386.313714 major third 3: 7/4 968.825906 harmonic seventh 4: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 9/8 203.9100 major whole tone 2: 10/9 182.4037 minor whole tone 3: 7/5 582.5122 septimal or Huygens' tritone, BP fourth 4: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 10/9 182.404 cents minor whole tone 1: 1 9/8 203.910 cents major whole tone 1: 1 8/7 231.174 cents septimal whole tone 1: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 2: 1 5/4 386.314 cents major third 2: 1 9/7 435.084 cents septimal major third, BP third 2: 1 14/9 764.916 cents septimal minor sixth 2: 1 8/5 813.686 cents minor sixth 3: 1 10/7 617.488 cents Euler's tritone 3: 1 7/4 968.826 cents harmonic seventh 3: 1 16/9 996.090 cents Pythagorean minor seventh 3: 1 9/5 1017.596 cents just minor seventh, BP 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 : 203.9 386.3 968.8 1200.0 203.9 : 182.4 764.9 996.1 1200.0 386.3 : 582.5 813.7 1017.6 1200.0 968.8 : 231.2 435.1 617.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 182.4037 .. 582.5122 cents 63/50, 400.1085 cents 10/9, 182.4037 cents 2: 386.3137 .. 813.6863 cents 32/25, 427.3726 cents 25/28,-196.1985 cents 3: 617.4878 .. 1017.5963 cents 63/50, 400.1085 cents 25/28,-196.1985 cents
SHOW DATA
Number of notes : 4 -- Interval properties -- Smallest interval : 10/9, 182.4037 cents, class 1 Average step (divided formal octave): 300.0000 cents Largest one step interval : 7/5, 582.5122 cents Average / Smallest step : 1.644703 Largest / Average step : 1.941707 Largest / Smallest step : 3.193533 Median interval of one step : 217.54205 cents, amount: 0 Least squares average step : 289.43384 cents, oct.: 1157.73535 cents Scale is not proper Step pattern alph. order: ABCD Step pattern size order : BADC Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 34.97561 cents Scale diversity : 1.556060 Lumma stability : 0.304006 Lumma impropriety factor : 0.326997 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 : 81/80, 21.5063 cents Number of recognisable fifths : 0 Length of longest harmonic part : 3 at degree 3 Length of longest subharmonic part : 1 at degree 0 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 378.6022 cents: 1 -- Rational properties -- Prime limit : 7 Odd number limit : 9 (O: 9 U: 9) Highest odd numerator or denominator: 9 Scale harmonicity : 0.038433 Average absolute harmonicity : 0.330110 Specific harmonicity : 0.231318 Fundamental : 1/8, -3.0000 octaves, 32.7032 Hz. Guide tone : 630, 9.2992 octaves, 164824.106 Hz. Exponens Consonantiae : 5.040000E+03, 12.29921 octaves Euler's gradus suavitatis : 19 Sum of Mann's harmonic distance : 20.0, average 5.00000 Mersenne's string divisions : 1683 Sum of van Prooijen's expressibility: 2.49831, average 0.62458 Sum of Tenney's harmonic distance : 4.90655, average 1.22664 Vogel's harmonic complexity : 6.00000 Wille's k value : 4 Wilson's harmonic complexity : 18 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 26.18757, average 2.61876 Lattice compactness (without 2's) : 13.88635, average 1.38863 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -1.50000 8 1 3: 0 .. 2 0.50000 2 1 5: 0 .. 1 0.25000 1 1 7: 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 11| Scale is weakly epimorphic with val: <4 7 9 11|
FIT/MODE
4: 1 0 2 1 N T3 SD: 73.1785 c. M:-96.0900 c. 5: 1 1 2 1 P M ME SD: 50.3922 c. M:-93.6863 c. 6: 1 1 3 1 N M DE SD: 17.1350 c. M:-31.1741 c. 16: 3 2 8 3 N SD: 12.3583 c. M:-21.0900 c. 19: 3 3 9 4 N SD: 13.4452 c. M: 21.4575 c. 22: 4 3 11 4 N SD: 9.9083 c. M:-14.2718 c. 25: 4 4 12 5 N SD: 7.5016 c. M: 11.9100 c. 31: 5 5 15 6 N SD: 5.2238 c. M: 10.3616 c. 35: 6 5 17 7 N SD: 6.4276 c. M: 9.1709 c. 37: 6 6 18 7 N SD: 5.2972 c. M: 9.3154 c. 40: 7 6 19 8 N SD: 5.6695 c. M: 8.8259 c. 41: 7 6 20 8 N SD: 3.3058 c. M: 5.8259 c. 46: 8 7 22 9 N SD: 3.8997 c. M:-4.9906 c. 47: 8 7 23 9 N SD: 1.8142 c. M: 3.3350 c. 77: 13 12 37 15 N SD: 2.1972 c. M:-3.2967 c. 78: 13 12 38 15 N SD: 2.1410 c. M: 3.9100 c. 93: 16 14 45 18 N SD: 1.4360 c. M:-2.5416 c. 99: 17 15 48 19 N SD: 1.3994 c. M:-2.1506 c. 118: 20 18 57 23 N SD: 1.3882 c. M: 2.7242 c. 124: 21 19 60 24 N SD: 0.7510 c. M: 1.0840 c. 165: 28 25 80 32 N SD: 0.8980 c. M: 1.5532 c. 171: 29 26 83 33 N SD: 0.3341 c. M: 0.4049 c. 270: 46 41 131 52 N SD: 0.3218 c. M:-0.5344 c. 317: 54 48 154 61 N SD: 0.3005 c. M:-0.5064 c. 348: 59 53 169 67 N SD: 0.2470 c. M: 0.4617 c. 441: 75 67 214 85 N SD: 0.1118 c. M:-0.1716 c. 612: 104 93 297 118 N SD: 0.1013 c. M: 0.1985 c. 618: 105 94 300 119 N SD: 0.0721 c. M:-0.1061 c. 789: 134 120 383 152 N SD: 0.0539 c. M: 0.1077 c. 1059: 180 161 514 204 N SD: 0.0528 c. M:-0.0886 c. 1106: 188 168 537 213 N SD: 0.0569 c. M:-0.0710 c. 1230: 209 187 597 237 N SD: 0.0269 c. M: 0.0454 c. 1848: 314 281 897 356 N SD: 0.0260 c. M:-0.0499 c. 1895: 322 288 920 365 N SD: 0.0262 c. M:-0.0395 c. 2336: 397 355 1134 450 N SD: 0.0162 c. M:-0.0284 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x x x 4 S SD: 0.0000 cents 3 x 4:5:6 S SD: 46.6888 cents 4 x 5:7:8 SD: 0.0000 cents 5 x 6:9:10 S SD: 28.6223 cents 7:8:9:12:14 S SD: 16.5759 cents 8:9:10:14:16 SD: 0.0000 cents