Scala analysis: xen12-wilson-08-4C1-tetrany-02
1-3-7-15 4C1 Tetrany, Figure 8
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 3/2 701.955001 perfect fifth 2: 7/4 968.825906 harmonic seventh 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: 3/2 701.9550 perfect fifth 2: 7/6 266.8709 septimal minor third 3: 15/14 119.4428 major diatonic semitone 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 : 702.0 968.8 1088.3 1200.0 702.0 : 266.9 386.3 498.0 1200.0 968.8 : 119.4 231.2 933.1 1200.0 1088.3: 111.7 813.7 1080.6 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 : 356.81377 cents, oct.: 1427.25506 cents Scale is not proper Step pattern alph. order: ABCD Step pattern size order : DCBA 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) Steps are strictly decreasing Length of longest harmonic part : 2 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 -- 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 : 0.359248 Specific harmonicity : 0.243325 Fundamental : 1/8, -3.0000 octaves, 32.7032 Hz. Guide tone : 210, 7.7142 octaves, 54941.369 Hz. Exponens Consonantiae : 1.680000E+03, 10.71425 octaves Euler's gradus suavitatis : 17 Sum of Mann's harmonic distance : 21.0, average 5.25000 Mersenne's string divisions : 3795 Sum of van Prooijen's expressibility: 2.49831, average 0.62458 Sum of Tenney's harmonic distance : 4.60552, average 1.15138 Vogel's harmonic complexity : 6.25000 Wille's k value : 7 Wilson's harmonic complexity : 15 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 23.57601, average 2.35760 Lattice compactness (without 2's) : 10.97469, average 1.09747 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 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 JI-epimorphic with val: <4 5 10 10| Scale is weakly epimorphic with val: <4 7 10 10|
FIT/MODE
4: 2 1 0 1 N D3 SD: 112.4466 c. M: 188.2687 c. 5: 3 1 1 0 N G SD: 56.7613 c. M:-111.7313 c. 7: 4 2 0 1 N SD: 43.0031 c. M:-59.7455 c. 9: 5 2 1 1 N SD: 27.2564 c. M: 35.4926 c. 10: 6 2 1 1 N SD: 10.8615 c. M:-18.0450 c. 21: 12 5 2 2 N SD: 8.3226 c. M: 16.2407 c. 22: 13 5 2 2 N SD: 7.5281 c. M:-12.9923 c. 31: 18 7 3 3 N SD: 3.4408 c. M: 5.1808 c. 41: 24 9 4 4 N SD: 3.0661 c. M: 5.3419 c. 53: 31 12 5 5 N SD: 2.4916 c. M:-4.7590 c. 63: 37 14 6 6 N SD: 2.3010 c. M:-2.8069 c. 77: 45 17 8 7 N SD: 1.8789 c. M:-2.6404 c. 84: 49 19 8 8 N SD: 2.0689 c. M:-2.6027 c. 87: 51 19 9 8 N SD: 1.9429 c. M: 3.3087 c. 94: 55 21 9 9 N SD: 1.7287 c. M: 3.1623 c. 99: 58 22 10 9 N SD: 1.4905 c. M:-2.6404 c. 108: 63 24 11 10 N SD: 1.4890 c. M: 2.1592 c. 118: 69 26 12 11 N SD: 1.3699 c. M: 2.7242 c. 120: 70 27 12 11 N SD: 1.4316 c. M: 1.9550 c. 130: 76 29 13 12 N SD: 0.5619 c. M:-0.9621 c. 140: 82 31 14 13 N SD: 0.4925 c. M:-0.9021 c. 171: 100 38 17 16 N SD: 0.3557 c. M: 0.5494 c. 270: 158 60 27 25 N SD: 0.3391 c. M:-0.6202 c. 301: 176 67 30 28 N SD: 0.1582 c. M: 0.2939 c. 441: 258 98 44 41 N SD: 0.1109 c. M:-0.1667 c. 612: 358 136 61 57 N SD: 0.1007 c. M: 0.1985 c. 742: 434 165 74 69 N SD: 0.0910 c. M:-0.1410 c. 913: 534 203 91 85 N SD: 0.0890 c. M: 0.1512 c. 935: 547 208 93 87 N SD: 0.0953 c. M:-0.1581 c. 966: 565 215 96 90 N SD: 0.0826 c. M:-0.1182 c. 1106: 647 246 110 103 N SD: 0.0410 c. M:-0.0710 c. 1407: 823 313 140 131 N SD: 0.0285 c. M:-0.0440 c. 1547: 905 344 154 144 N SD: 0.0302 c. M:-0.0489 c. 1718: 1005 382 171 160 N SD: 0.0218 c. M: 0.0266 c. 2019: 1181 449 201 188 N SD: 0.0191 c. M: 0.0295 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2:3 x x 4 S SD: 0.0000 cents 3 x 5 x 6 SD: 42.2336 cents 4:6:7 x 8 S SD: 0.0000 cents 5:8:9 x 10 SD: 40.6372 cents 6:9 x 11:12 SD: 12.9686 cents 8:12:14:15:16 S SD: 0.0000 cents