Scala analysis: xen12-wilson-08-4C3-tetrany-02
1-3-7-15 4C3 Tetrany, Figure 8
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 15/14 119.442808 major diatonic semitone 2: 5/4 386.313714 major third 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: 15/14 119.4428 major diatonic semitone 2: 7/6 266.8709 septimal minor third 3: 3/2 701.9550 perfect fifth 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 15/14 119.443 cents major diatonic semitone 1: 1 7/6 266.871 cents septimal minor third 1: 1 3/2 701.955 cents perfect fifth 2: 1 8/7 231.174 cents septimal whole tone 2: 1 5/4 386.314 cents major third 2: 1 8/5 813.686 cents minor sixth 2: 1 7/4 968.826 cents harmonic seventh 3: 1 4/3 498.045 cents perfect fourth 3: 1 12/7 933.129 cents septimal major sixth 3: 1 28/15 1080.557 cents grave major seventh 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 : 119.4 386.3 1088.3 1200.0 119.4 : 266.9 968.8 1080.6 1200.0 386.3 : 702.0 813.7 933.1 1200.0 1088.3: 111.7 231.2 498.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 701.9550 cents 45/32, 590.2237 cents 16/15, 111.7313 cents 2: 231.1741 .. 968.8259 cents 49/32, 737.6518 cents 16/21,-470.7809 cents 3: 498.0450 .. 1088.2687 cents 45/32, 590.2237 cents 16/21,-470.7809 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 : 3/2, 701.9550 cents Average / Smallest step : 2.685013 Largest / Average step : 2.339850 Largest / Smallest step : 6.282529 Median interval of one step : 193.15686 cents, amount: 0 Least squares average step : 298.56255 cents, oct.: 1194.25018 cents Scale is not proper Step pattern alph. order: ABCD Step pattern size order : BCDA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 1.642746 Lumma stability : 0.186219 Lumma impropriety factor : 0.614710 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 : 225/224, 7.7115 cents Number of recognisable fifths : 1, average 701.9550 cents All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 3 Formal octave complements present : 1 = 25.0000% Scale is differentially coherent in interval class 1 -- Rational properties -- Prime limit : 7 Odd number limit : 15 (O: 15 U: 15) Highest odd numerator or denominator: 15 Scale harmonicity : 0.042822 Average absolute harmonicity : 0.312763 Specific harmonicity : 0.216369 Fundamental : 1/56, -5.8074 octaves, 4.6719 Hz. Guide tone : 30, 4.9069 octaves, 7848.767 Hz. Exponens Consonantiae : 1.680000E+03, 10.71425 octaves Euler's gradus suavitatis : 17 Sum of Mann's harmonic distance : 32.0, average 8.00000 Mersenne's string divisions : 6003 Sum of van Prooijen's expressibility: 3.05115, average 0.76279 Sum of Tenney's harmonic distance : 6.00346, average 1.50087 Vogel's harmonic complexity : 12.25000 Wille's k value : 52 Wilson's harmonic complexity : 15 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 23.98569, average 2.39857 Lattice compactness (without 2's) : 11.70674, average 1.17067 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -1.25000 7 1 3: 0 .. 1 0.50000 2 5: 0 .. 1 0.75000 3 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 9 11| Scale is JI-epimorphic with val: <4 5 10 10| Scale is weakly epimorphic with val: <4 7 10 10|
FIT/MODE
4: 0 1 2 1 N D3 SD: 119.5426 c. M: 188.2687 c. 5: 0 1 3 1 N D3 SD: 114.1569 c. M: 146.3137 c. 6: 1 1 3 1 N M DE SD: 60.1418 c. M: 88.2687 c. 7: 0 2 4 1 N SD: 70.2119 c. M: 119.4428 c. 8: 1 2 4 1 N SD: 40.1690 c. M:-63.6863 c. 9: 1 2 5 1 N SD: 14.5509 c. M: 21.6020 c. 10: 1 2 6 1 N SD: 13.7940 c. M: 26.3137 c. 12: 1 3 7 1 N SD: 13.2567 c. M: 19.4428 c. 19: 2 4 11 2 N SD: 8.8630 c. M: 14.5845 c. 21: 2 5 12 2 N SD: 7.4235 c. M:-13.6863 c. 22: 2 5 13 2 N SD: 5.7953 c. M: 10.3519 c. 31: 3 7 18 3 N SD: 2.7809 c. M: 4.3977 c. 72: 7 16 42 7 N SD: 3.1995 c. M: 4.9354 c. 78: 8 17 46 7 N SD: 2.8462 c. M:-4.0390 c. 87: 9 19 51 8 N SD: 2.4484 c. M:-4.6951 c. 99: 10 22 58 9 N SD: 1.7714 c. M:-2.6404 c. 109: 11 24 64 10 N SD: 1.2672 c. M:-1.6581 c. 130: 13 29 76 12 N SD: 0.8855 c. M:-1.3786 c. 140: 14 31 82 13 N SD: 0.4363 c. M: 0.5994 c. 171: 17 38 100 16 N SD: 0.3333 c. M: 0.5494 c. 301: 30 67 176 28 N SD: 0.2200 c. M:-0.3972 c. 441: 44 98 258 41 N SD: 0.1700 c. M:-0.2851 c. 463: 46 103 271 43 N SD: 0.1923 c. M:-0.2842 c. 472: 47 105 276 44 N SD: 0.0952 c. M: 0.1331 c. 612: 61 136 358 57 N SD: 0.0864 c. M:-0.1650 c. 913: 91 203 534 85 N SD: 0.0970 c. M:-0.1629 c. 935: 93 208 547 87 N SD: 0.0560 c. M: 0.0845 c. 1106: 110 246 647 103 N SD: 0.0560 c. M: 0.0938 c. 1376: 137 306 805 128 N SD: 0.0557 c. M:-0.1034 c. 1407: 140 313 823 131 N SD: 0.0284 c. M:-0.0402 c. 1547: 154 344 905 144 N SD: 0.0193 c. M:-0.0312 c. 2019: 201 449 1181 188 N SD: 0.0142 c. M:-0.0223 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x 3 x 4 S SD: 157.8206 cents 3 x 4 x 6 S SD: 55.8656 cents 4 x 5 x 8 SD: 0.0000 cents 5 x 6:9:10 S SD: 33.3153 cents 6 x 8:11:12 SD: 39.4371 cents 7:8:9:13:14 SD: 30.7580 cents 8:9:10:15:16 S SD: 21.1168 cents 9:10:11:17:18 SD: 18.7766 cents 11:12:14:21:22 S SD: 13.5075 cents 12:13:15:23:24 SD: 10.6472 cents 13:14:16:24:26 S SD: 9.7447 cents 15:16:19:28:30 SD: 6.3480 cents 16:17:20:30:32 SD: 3.6218 cents 39:42:49:73:78 SD: 3.2172 cents 40:43:50:75:80 SD: 1.4403 cents 56:60:70:105:112 S SD: 0.0000 cents