Scala analysis: xen12-wilson-08-4C1-tetrany-09
1-9-11-15 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: 11/8 551.317942 undecimal semi-augmented fourth 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: 11/9 347.4079 undecimal neutral third 3: 15/11 536.9508 undecimal augmented fourth 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 9/8 203.910 cents major whole tone 1: 1 11/9 347.408 cents undecimal neutral third 1: 1 15/11 536.951 cents undecimal augmented fourth 2: 1 6/5 315.641 cents minor third 2: 1 11/8 551.318 cents undecimal semi-augmented fourth 2: 1 16/11 648.682 cents undecimal semi-diminished fifth 2: 1 5/3 884.359 cents major sixth, BP sixth 3: 1 22/15 663.049 cents undecimal diminished fifth 3: 1 18/11 852.592 cents undecimal neutral sixth 3: 1 16/9 996.090 cents Pythagorean minor 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 : 203.9 551.3 1088.3 1200.0 203.9 : 347.4 884.4 996.1 1200.0 551.3 : 537.0 648.7 852.6 1200.0 1088.3: 111.7 315.6 663.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 536.9508 cents 225/176, 425.2195 cents 16/15, 111.7313 cents 2: 315.6413 .. 884.3587 cents 25/18, 568.7174 cents 22/25,-221.3095 cents 3: 663.0492 .. 1088.2687 cents 225/176, 425.2195 cents 22/25,-221.3095 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 : 15/11, 536.9508 cents Average / Smallest step : 2.685013 Largest / Average step : 1.789836 Largest / Smallest step : 4.805733 Median interval of one step : 275.65897 cents, amount: 0 Least squares average step : 312.37840 cents, oct.: 1249.51360 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 14.36717 cents Scale diversity : 1.628191 Lumma stability : 0.186219 Lumma impropriety factor : 0.368849 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 : 121/120, 14.3672 cents Number of recognisable fifths : 0 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 25.0000% Scale is differentially coherent in interval class 1 -- Rational properties -- Prime limit : 11 Odd number limit : 15 (O: 15 U: 15) Highest odd numerator or denominator: 15 Scale harmonicity : 0.029485 Average absolute harmonicity : 0.312520 Specific harmonicity : 0.170075 Fundamental : 1/8, -3.0000 octaves, 32.7032 Hz. Guide tone : 990, 9.9513 octaves, 259009.310 Hz. Exponens Consonantiae : 7.920000E+03, 12.95128 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 31.0, average 7.75000 Mersenne's string divisions : 22287 Sum of van Prooijen's expressibility: 3.17173, average 0.79293 Sum of Tenney's harmonic distance : 6.18203, average 1.54551 Vogel's harmonic complexity : 7.25000 Wille's k value : 7 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 29.30467, average 2.93047 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 -2.00000 10 1 3: 0 .. 2 0.75000 3 1 5: 0 .. 1 0.25000 1 1 11: 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 15| Scale is weakly epimorphic with val: <4 5 10 13| Scale is weakly epimorphic with val: <4 7 8 13| Scale is weakly epimorphic with val: <4 7 10 15|
FIT/MODE
4: 1 1 2 0 N T3 SD: 77.6001 c. M:-111.7313 c. 5: 1 1 3 0 N G SD: 68.6888 c. M:-111.7313 c. 6: 1 2 2 1 P D3 I SD: 50.4396 c. M: 88.2687 c. 7: 1 2 3 1 N SD: 38.6982 c. M: 59.6973 c. 9: 1 3 4 1 N SD: 37.9841 c. M: 70.5767 c. 10: 2 3 4 1 N SD: 30.5810 c. M:-48.6821 c. 11: 2 3 5 1 N SD: 7.8268 c. M:-14.2718 c. 24: 4 7 11 2 N SD: 6.2179 c. M:-11.7313 c. 30: 5 9 13 3 N SD: 6.3055 c. M:-8.6821 c. 31: 5 9 14 3 N SD: 7.3269 c. M: 10.3616 c. 35: 6 10 16 3 N SD: 4.7315 c. M:-8.8741 c. 41: 7 12 18 4 N SD: 3.6165 c. M: 5.3419 c. 52: 9 15 23 5 N SD: 2.9174 c. M:-3.7823 c. 54: 9 16 24 5 N SD: 2.8996 c. M:-4.2376 c. 65: 11 19 29 6 N SD: 1.4152 c. M:-2.5282 c. 76: 13 22 34 7 N SD: 1.1190 c. M:-1.3532 c. 118: 20 34 53 11 N SD: 1.1155 c. M: 2.1654 c. 141: 24 41 63 13 N SD: 1.0982 c. M:-1.8735 c. 148: 25 43 66 14 N SD: 1.0765 c. M: 1.7822 c. 159: 27 46 71 15 N SD: 0.7646 c. M: 1.4763 c. 170: 29 49 76 16 N SD: 0.8108 c. M: 1.2099 c. 172: 29 50 77 16 N SD: 0.7977 c. M: 1.5844 c. 183: 31 53 82 17 N SD: 0.4220 c. M: 0.6313 c. 235: 40 68 105 22 N SD: 0.3604 c. M: 0.6091 c. 259: 44 75 116 24 N SD: 0.2688 c. M:-0.5344 c. 407: 69 118 182 38 N SD: 0.2816 c. M: 0.4702 c. 418: 71 121 187 39 N SD: 0.1367 c. M: 0.2304 c. 494: 84 143 221 46 N SD: 0.0853 c. M:-0.1386 c. 677: 115 196 303 63 N SD: 0.0561 c. M: 0.0695 c. 1095: 186 317 490 102 N SD: 0.0617 c. M: 0.0851 c. 1171: 199 339 524 109 N SD: 0.0186 c. M:-0.0319 c. 2083: 354 603 932 194 N SD: 0.0203 c. M: 0.0306 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x 3 x 4 S SD: 75.3185 cents 3 x 4 x 6 S SD: 26.6365 cents 4 x 6 x 8 S SD: 75.3185 cents 5:6:7:9:10 SD: 33.9591 cents 6:7:8:11:12 SD: 22.7977 cents 7:8:10:13:14 SD: 18.3648 cents 8:9:11:15:16 SD: 0.0000 cents