Scala analysis: xen12-wilson-08-4C3-tetrany-00
1-3-7-9 4C3 Tetrany, Figure 8
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: 9/7 435.084095 septimal major third, BP third 3: 3/2 701.955001 perfect fifth 4: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 4/3 498.0450 perfect fourth 1: 9/8 203.9100 major whole tone 2: 8/7 231.1741 septimal whole tone 3: 7/6 266.8709 septimal minor third 4: 4/3 498.0450 perfect fourth
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 9/8 203.910 cents major whole tone 1: 1 8/7 231.174 cents septimal whole tone 1: 1 7/6 266.871 cents septimal minor third 1: 1 4/3 498.045 cents perfect fourth 2: 1 9/7 435.084 cents septimal major third, BP third 2: 1 4/3 498.045 cents perfect fourth 2: 1 3/2 701.955 cents perfect fifth 2: 1 14/9 764.916 cents septimal minor sixth 3: 1 3/2 701.955 cents perfect fifth 3: 1 12/7 933.129 cents septimal major sixth 3: 1 7/4 968.826 cents harmonic seventh 3: 1 16/9 996.090 cents Pythagorean minor 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 : 203.9 435.1 702.0 1200.0 203.9 : 231.2 498.0 996.1 1200.0 435.1 : 266.9 764.9 968.8 1200.0 702.0 : 498.0 702.0 933.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 203.9100 .. 498.0450 cents 32/27, 294.1350 cents 9/8, 203.9100 cents 2: 435.0841 .. 764.9159 cents 98/81, 329.8318 cents 27/28,-62.9609 cents 3: 701.9550 .. 996.0900 cents 32/27, 294.1350 cents 27/28,-62.9609 cents
SHOW DATA
Number of notes : 4 -- Interval properties -- Smallest interval : 9/8, 203.9100 cents, class 1 Average step (divided formal octave): 300.0000 cents Largest one step interval : 4/3, 498.0450 cents Average / Smallest step : 1.471237 Largest / Average step : 1.660150 Largest / Smallest step : 2.442475 Median interval of one step : 249.02250 cents, amount: 0 Least squares average step : 265.99811 cents, oct.: 1063.99243 cents Scale is not proper Scale is a mode of a 1277-tone equal temperament with octave 2/1 degrees: 217 463 747 1277 Least number of segments generator : 639 of 600.470 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 700 of 657.792 cents and inv. generated superset size: 39 = 35 more = 975.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCD Step pattern size order : ABCD Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 1.448605 Lumma stability : 0.339850 Lumma impropriety factor : 0.104935 Rothenberg efficiency : 0.583333 redundancy: 0.416667 Efficiency x scale size : 2.333333 Number of different interval sizes : 10 = 3.33333 / 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 : 64/63, 27.2641 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 2 Most common triad is 0.0 498.045 701.955 cents, amount: 1 Number of recognisable fifths : 2, average 701.9550 cents Best minor thirds form a closed circle All steps are superparticular (epimoric) Steps are strictly increasing Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 3 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 classes 2 and 3 combined -- Rational properties -- Prime limit : 7 Odd number limit : 9 (O: 9 U: 9) Highest odd numerator or denominator: 9 Scale harmonicity : 0.050971 Average absolute harmonicity : 0.364187 Specific harmonicity : 0.274294 Fundamental : 1/56, -5.8074 octaves, 4.6719 Hz. Guide tone : 18, 4.1699 octaves, 4709.260 Hz. Exponens Consonantiae : 1.008000E+03, 9.97728 octaves Euler's gradus suavitatis : 15 Sum of Mann's harmonic distance : 20.5, average 5.12500 Mersenne's string divisions : 4080 Sum of van Prooijen's expressibility: 2.38561, average 0.59640 Sum of Tenney's harmonic distance : 4.73585, average 1.18396 Vogel's harmonic complexity : 11.25000 Wille's k value : 31 Wilson's harmonic complexity : 13 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 24.54392, average 2.45439 Lattice compactness (without 2's) : 13.88635, average 1.38863 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -0.75000 5 1 3: 0 .. 2 1.25000 5 2 7: -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 11|
FIT/MODE
4: 1 0 1 2 N D3 SD: 97.3086 c. M: 135.0841 c. 5: 1 1 1 2 P M ME SD: 30.1892 c. M:-44.9159 c. 11: 2 2 2 5 N M DE SD: 24.7638 c. M: 47.4095 c. 12: 2 2 3 5 N SD: 17.6777 c. M: 35.0841 c. Eskimo tetratonic (Alaska: Bethel) 14: 2 3 3 6 N SD: 18.4474 c. M: 32.4814 c. 16: 3 3 3 7 N M DE SD: 18.6671 c. M: 26.9550 c. 17: 3 3 4 7 N SD: 7.2566 c. M: 11.5547 c. 22: 4 4 5 9 N SD: 8.0038 c. M:-14.2718 c. 24: 4 5 5 10 N SD: 7.7717 c. M:-14.9159 c. 31: 5 6 7 13 N SD: 7.4209 c. M: 10.3616 c. 36: 6 7 8 15 N SD: 2.3545 c. M: 3.9100 c. 41: 7 8 9 17 N SD: 2.0431 c. M:-3.9403 c. 58: 10 11 13 24 N SD: 1.6964 c. M:-2.9865 c. 77: 13 15 17 32 N SD: 0.9735 c. M: 1.3126 c. 94: 16 18 21 39 N SD: 0.5554 c. M: 1.0415 c. 135: 23 26 30 56 N SD: 0.3806 c. M:-0.5344 c. 171: 29 33 38 71 N SD: 0.2243 c. M: 0.4012 c. 265: 45 51 59 110 N SD: 0.1988 c. M: 0.3671 c. 306: 52 59 68 127 N SD: 0.1052 c. M:-0.2100 c. 400: 68 77 89 166 N SD: 0.0656 c. M:-0.0900 c. 571: 97 110 127 237 N SD: 0.0431 c. M: 0.0578 c. 706: 120 136 157 293 N SD: 0.0381 c. M:-0.0560 c. 877: 149 169 195 364 N SD: 0.0257 c. M:-0.0356 c. 1277: 217 246 284 530 N SD: 0.0032 c. M:-0.0054 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x x 3:4 S SD: 0.0000 cents 3 x 4:5:6 S SD: 64.3214 cents 4 x 5:6:8 S SD: 16.2568 cents 5:6 x 8:10 S SD: 52.6706 cents 6:7:8:9:12 S SD: 22.2600 cents 7:8:9:11:14 SD: 21.2567 cents 8:9:10:12:16 S SD: 12.1926 cents 10:11:13:15:20 SD: 10.8386 cents 14:16:18:21:28 S SD: 6.8160 cents 18:20:23:27:36 SD: 6.0075 cents 24:27:31:36:48 SD: 1.9991 cents 32:36:41:48:64 SD: 1.5054 cents 56:63:72:84:112 S SD: 0.0000 cents