Scala analysis: xen12-wilson-08-4C1-tetrany-07
1-7-9-15 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: 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: 9/8 203.9100 major whole tone 2: 14/9 764.9159 septimal minor sixth 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 9/8 203.910 cents major whole tone 1: 1 14/9 764.916 cents septimal minor sixth 2: 1 8/7 231.174 cents septimal whole tone 2: 1 6/5 315.641 cents minor third 2: 1 5/3 884.359 cents major sixth, BP sixth 2: 1 7/4 968.826 cents harmonic seventh 3: 1 9/7 435.084 cents septimal major third, BP third 3: 1 16/9 996.090 cents Pythagorean minor seventh 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 : 203.9 968.8 1088.3 1200.0 203.9 : 764.9 884.4 996.1 1200.0 968.8 : 119.4 231.2 435.1 1200.0 1088.3: 111.7 315.6 1080.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 764.9159 cents 35/24, 653.1846 cents 16/15, 111.7313 cents 2: 231.1741 .. 968.8259 cents 49/32, 737.6518 cents 36/49,-533.7418 cents 3: 435.0841 .. 1088.2687 cents 35/24, 653.1846 cents 36/49,-533.7418 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 : 14/9, 764.9159 cents Average / Smallest step : 2.685013 Largest / Average step : 2.549720 Largest / Smallest step : 6.846032 Median interval of one step : 161.67640 cents, amount: 0 Least squares average step : 340.21227 cents, oct.: 1360.84906 cents Scale is not proper Step pattern alph. order: ABCD Step pattern size order : CDBA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 27.26409 cents Scale diversity : 1.451815 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 : 0 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 n-1 differentially coherent in interval class 1 Scale is differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval class 3 -- Rational properties -- Prime limit : 7 Odd number limit : 15 (O: 15 U: 15) Highest odd numerator or denominator: 15 Scale harmonicity : 0.038433 Average absolute harmonicity : 0.321067 Specific harmonicity : 0.216619 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 : 27.0, average 6.75000 Mersenne's string divisions : 12903 Sum of van Prooijen's expressibility: 2.97543, average 0.74386 Sum of Tenney's harmonic distance : 5.68470, average 1.42118 Vogel's harmonic complexity : 6.50000 Wille's k value : 7 Wilson's harmonic complexity : 18 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 27.89900, average 2.78990 Lattice compactness (without 2's) : 14.21076, average 1.42108 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -1.75000 9 1 3: 0 .. 2 0.75000 3 1 5: 0 .. 1 0.25000 1 1 7: 0 .. 1 0.25000 1 1 Average exponent except 2's : 5 / 4 = 1.25000 Average absolute exponent except 2's: 5 / 4 = 1.25000 Scale is weakly epimorphic with val: <4 5 8 11| Scale is weakly epimorphic with val: <4 7 10 11|
FIT/MODE
4: 1 2 1 0 N D3 SD: 81.3237 c. M:-111.7313 c. 5: 1 3 1 0 N D3 SD: 58.8733 c. M:-111.7313 c. 6: 1 4 0 1 N G SD: 46.8468 c. M: 88.2687 c. 8: 1 5 1 1 N M DE SD: 47.7174 c. M: 68.8259 c. 9: 1 6 1 1 N M DE SD: 40.9495 c. M: 70.5767 c. 10: 2 6 1 1 N SD: 19.0313 c. M:-36.0900 c. 11: 2 7 1 1 N SD: 9.7398 c. M:-14.2718 c. 30: 5 19 3 3 N SD: 6.3552 c. M: 8.8259 c. 31: 5 20 3 3 N SD: 5.6542 c. M: 10.3616 c. 41: 7 26 4 4 N SD: 3.0946 c. M: 5.3419 c. 42: 7 27 4 4 N SD: 2.6733 c. M: 3.9100 c. 52: 9 33 5 5 N SD: 2.6371 c. M:-3.7823 c. 53: 9 34 5 5 N SD: 2.4923 c. M:-4.7590 c. 77: 13 49 8 7 N SD: 1.9630 c. M:-2.6404 c. 83: 14 53 8 8 N SD: 2.1053 c. M: 3.9314 c. 88: 15 56 9 8 N SD: 1.3955 c. M:-2.6404 c. 105: 18 67 10 10 N SD: 2.0344 c. M:-2.6027 c. 118: 20 75 12 11 N SD: 1.3883 c. M: 2.7242 c. 119: 20 76 12 11 N SD: 1.2447 c. M: 2.2293 c. 129: 22 82 13 12 N SD: 0.7867 c. M: 1.3840 c. 130: 22 83 13 12 N SD: 0.6677 c. M:-0.9621 c. 171: 29 109 17 16 N SD: 0.3958 c. M: 0.5494 c. 182: 31 116 18 17 N SD: 0.3629 c. M:-0.4856 c. 259: 44 165 26 24 N SD: 0.3620 c. M:-0.5344 c. 301: 51 192 30 28 N SD: 0.2997 c. M: 0.5877 c. 312: 53 199 31 29 N SD: 0.2265 c. M:-0.4049 c. 441: 75 281 44 41 N SD: 0.1335 c. M:-0.1716 c. 483: 82 308 48 45 N SD: 0.1145 c. M: 0.1833 c. 612: 104 390 61 57 N SD: 0.1008 c. M: 0.1985 c. 742: 126 473 74 69 N SD: 0.1085 c. M:-0.1410 c. 753: 128 480 75 70 N SD: 0.1080 c. M:-0.1775 c. 794: 135 506 79 74 N SD: 0.0861 c. M:-0.1202 c. 924: 157 589 92 86 N SD: 0.0227 c. M:-0.0430 c. 2030: 345 1294 202 189 N SD: 0.0259 c. M:-0.0411 c. 2201: 374 1403 219 205 N SD: 0.0184 c. M: 0.0361 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x x x 4 S SD: 0.0000 cents 3:4:5 x 6 S SD: 102.0077 cents 4:5:7 x 8 SD: 60.8012 cents 5:6:9 x 10 S SD: 40.6372 cents 6:7 x 11:12 SD: 24.6706 cents 7:8:12:13:14 S SD: 11.9689 cents 8:9:14:15:16 SD: 0.0000 cents