Scala analysis: xen12-wilson-08-4C1-tetrany-00
1-3-7-9 4C1 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: 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: 9/8 203.9100 major whole tone 2: 4/3 498.0450 perfect fourth 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 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 : 203.9 702.0 968.8 1200.0 203.9 : 498.0 764.9 996.1 1200.0 702.0 : 266.9 498.0 702.0 1200.0 968.8 : 231.2 435.1 933.1 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 : 310.47659 cents, oct.: 1241.90636 cents Scale is not proper Step pattern alph. order: ABCD Step pattern size order : ADCB 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) Length of longest harmonic part : 3 at degree 2 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 Scale is n-1 differentially coherent in interval class 3 -- 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 : 0.368530 Specific harmonicity : 0.284707 Fundamental : 1/8, -3.0000 octaves, 32.7032 Hz. Guide tone : 126, 6.9773 octaves, 32964.821 Hz. Exponens Consonantiae : 1.008000E+03, 9.97728 octaves Euler's gradus suavitatis : 15 Sum of Mann's harmonic distance : 18.0, average 4.50000 Mersenne's string divisions : 2805 Sum of van Prooijen's expressibility: 2.27646, average 0.56912 Sum of Tenney's harmonic distance : 4.38367, average 1.09592 Vogel's harmonic complexity : 5.75000 Wille's k value : 4 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) : 12.65028, average 1.26503 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -1.25000 7 1 3: 0 .. 2 0.75000 3 2 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 11|
FIT/MODE
4: 0 2 1 1 N T3 SD: 119.0705 c. M: 203.9100 c. 5: 1 2 1 1 P M ME SD: 20.6519 c. M:-36.0900 c. 12: 2 5 3 2 N SD: 15.7396 c. M:-31.1741 c. 16: 3 6 4 3 P SD: 17.3888 c. M: 26.9550 c. 17: 3 7 4 3 N SD: 10.6518 c. M:-19.4094 c. 22: 4 9 5 4 N SD: 10.2884 c. M:-14.2718 c. 24: 4 10 5 5 N SD: 9.6634 c. M: 18.8259 c. 29: 5 12 6 6 N SD: 8.7123 c. M: 17.1018 c. 31: 5 13 7 6 N SD: 5.8176 c. M: 10.3616 c. 36: 6 15 8 7 N SD: 2.4379 c. M: 3.9100 c. 41: 7 17 9 8 N SD: 1.5816 c. M: 2.9722 c. 77: 13 32 17 15 N SD: 1.4894 c. M: 2.5921 c. 89: 15 37 20 17 N SD: 1.3509 c. M:-1.9606 c. 94: 16 39 21 18 N SD: 0.7198 c. M:-1.3869 c. 130: 22 54 29 25 N SD: 0.5078 c. M: 0.8331 c. 135: 23 56 30 26 N SD: 0.3004 c. M:-0.5344 c. 171: 29 71 38 33 N SD: 0.3021 c. M: 0.4049 c. 265: 45 110 59 51 N SD: 0.1383 c. M:-0.2307 c. 306: 52 127 68 59 N SD: 0.0994 c. M: 0.1985 c. 400: 68 166 89 77 N SD: 0.1005 c. M:-0.1741 c. 441: 75 183 98 85 N SD: 0.1127 c. M:-0.1716 c. 571: 97 237 127 110 N SD: 0.0319 c. M: 0.0571 c. 706: 120 293 157 136 N SD: 0.0319 c. M:-0.0560 c. 1012: 172 420 225 195 N SD: 0.0350 c. M: 0.0512 c. 1277: 217 530 284 246 N SD: 0.0047 c. M:-0.0073 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x 3 x 4 S SD: 0.0000 cents 3 x x 5:6 SD: 42.2336 cents 5:6:8:9:10 S SD: 41.3418 cents 6:7:9:11:12 SD: 25.5567 cents 7:8:11:12:14 SD: 23.0540 cents 8:9:12:14:16 S SD: 0.0000 cents