Scala analysis: xen12-wilson-08-4C3-tetrany-07
1-7-9-15 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: 5/3 884.358713 major sixth, BP sixth 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: 14/9 764.9159 septimal minor sixth 3: 9/8 203.9100 major whole tone 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 : 119.4 884.4 1088.3 1200.0 119.4 : 764.9 968.8 1080.6 1200.0 884.4 : 203.9 315.6 435.1 1200.0 1088.3: 111.7 231.2 996.1 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 : 331.76555 cents, oct.: 1327.06218 cents Scale is not proper Step pattern alph. order: ABCD Step pattern size order : BDCA 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 : 1 at degree 0 Length of longest subharmonic part : 2 at degree 3 Formal octave complements present : 1 = 25.0000% Scale is n-1 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 : 0.038433 Average absolute harmonicity : 0.310575 Specific harmonicity : 0.201272 Fundamental : 1/168, -7.3923 octaves, 1.5573 Hz. Guide tone : 30, 4.9069 octaves, 7848.767 Hz. Exponens Consonantiae : 5.040000E+03, 12.29921 octaves Euler's gradus suavitatis : 19 Sum of Mann's harmonic distance : 31.5, average 7.87500 Mersenne's string divisions : 16008 Sum of van Prooijen's expressibility: 3.05115, average 0.76279 Sum of Tenney's harmonic distance : 5.87852, average 1.46963 Vogel's harmonic complexity : 15.00000 Wille's k value : 157 Wilson's harmonic complexity : 18 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 24.64239, average 2.46424 Lattice compactness (without 2's) : 14.35702, average 1.43570 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -0.75000 5 1 3: -1 .. 1 0.25000 3 5: 0 .. 1 0.75000 3 2 7: -1 .. 0 -0.25000 1 1 Average exponent except 2's : 3 / 4 = 0.75000 Average absolute exponent except 2's: 7 / 4 = 1.75000 Scale is weakly epimorphic with val: <4 5 8 11| Scale is weakly epimorphic with val: <4 7 10 11|
FIT/MODE
4: 0 3 1 0 N SD: 82.1510 c. M: 119.4428 c. 6: 0 4 1 1 N G SD: 85.4025 c. M: 119.4428 c. 7: 1 4 1 1 N M DE SD: 41.8539 c. M: 59.6973 c. 8: 1 5 1 1 N M DE SD: 25.7045 c. M: 38.2687 c. 10: 1 6 2 1 N SD: 22.5631 c. M: 44.3587 c. 11: 1 7 2 1 N SD: 7.8966 c. M: 11.6314 c. 30: 3 19 5 3 N SD: 4.6819 c. M: 8.2687 c. 31: 3 20 5 3 N SD: 4.0586 c. M:-5.9639 c. 41: 4 26 7 4 N SD: 4.3002 c. M: 6.3099 c. 42: 4 27 7 4 N SD: 2.9563 c. M: 5.1571 c. 53: 5 34 9 5 N SD: 3.2731 c. M: 6.2353 c. 61: 6 39 10 6 N SD: 3.2590 c. M: 6.3015 c. 72: 7 46 12 7 N SD: 2.8773 c. M: 4.9354 c. 73: 7 47 12 7 N SD: 3.2111 c. M: 4.3743 c. 83: 8 53 14 8 N SD: 2.9856 c. M: 3.9314 c. 87: 9 55 15 8 N SD: 2.5752 c. M:-4.6951 c. 88: 9 56 15 8 N SD: 2.3334 c. M:-3.2845 c. 98: 10 62 17 9 N SD: 2.1680 c. M:-3.0062 c. 99: 10 63 17 9 N SD: 1.6079 c. M:-2.6404 c. 110: 11 70 19 10 N SD: 1.3968 c. M:-2.6404 c. 118: 12 75 20 11 N SD: 1.3116 c. M:-2.5911 c. 129: 13 82 22 12 N SD: 0.8108 c. M:-1.4874 c. 141: 14 90 24 13 N SD: 0.6782 c. M:-1.0930 c. 160: 16 102 27 15 N SD: 0.5729 c. M: 0.7687 c. 171: 17 109 29 16 N SD: 0.2936 c. M: 0.5494 c. 312: 31 199 53 29 N SD: 0.1924 c. M:-0.2567 c. 441: 44 281 75 41 N SD: 0.1651 c. M:-0.2851 c. 483: 48 308 82 45 N SD: 0.1153 c. M: 0.1881 c. 612: 61 390 104 57 N SD: 0.0871 c. M:-0.1650 c. 783: 78 499 133 73 N SD: 0.0941 c. M: 0.1461 c. 924: 92 589 157 86 N SD: 0.0403 c. M:-0.0569 c. 1095: 109 698 186 102 N SD: 0.0281 c. M: 0.0495 c. 2019: 201 1287 343 188 N SD: 0.0230 c. M:-0.0395 c. 2030: 202 1294 345 189 N SD: 0.0210 c. M: 0.0339 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x 3 x 4 S SD: 91.2019 cents 3:4:5 x 6 S SD: 126.2007 cents 4:5:7 x 8 SD: 93.3064 cents 5:6:8:9:10 S SD: 55.0472 cents 6:7:10:11:12 SD: 38.1188 cents 7:8:12:13:14 S SD: 30.7580 cents 8:9:13:15:16 SD: 23.7906 cents 9:10:15:17:18 SD: 16.0611 cents 10:11:17:19:20 SD: 15.3643 cents 11:12:18:21:22 S SD: 13.5906 cents 12:13:20:23:24 SD: 10.6472 cents 13:14:22:24:26 SD: 9.6744 cents 14:15:23:26:28 SD: 7.4791 cents 15:16:25:28:30 SD: 2.7264 cents 39:42:65:73:78 SD: 2.3344 cents 42:45:70:79:84 SD: 1.3718 cents 57:61:95:107:114 SD: 0.7159 cents 96:103:160:180:192 SD: 0.6007 cents 111:119:185:208:222 SD: 0.3676 cents 153:164:255:287:306 SD: 0.2666 cents 168:180:280:315:336 SD: 0.0000 cents