Scala analysis: xen12-wilson-08-4C3-tetrany-09
1-9-11-15 4C3 Tetrany, Figure 8
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 15/11 536.950772 undecimal augmented fourth 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: 15/11 536.9508 undecimal augmented fourth 2: 11/9 347.4079 undecimal neutral third 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 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 : 537.0 884.4 1088.3 1200.0 537.0 : 347.4 551.3 663.0 1200.0 884.4 : 203.9 315.6 852.6 1200.0 1088.3: 111.7 648.7 996.1 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 : 345.68248 cents, oct.: 1382.72991 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 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 Steps are strictly decreasing Formal octave complements present : 1 = 25.0000% -- 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 : 0.307466 Specific harmonicity : 0.162555 Fundamental : 1/264, -8.0444 octaves, 0.9910 Hz. Guide tone : 30, 4.9069 octaves, 7848.767 Hz. Exponens Consonantiae : 7.920000E+03, 12.95128 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 30.0, average 7.50000 Mersenne's string divisions : 7176 Sum of van Prooijen's expressibility: 3.05115, average 0.76279 Sum of Tenney's harmonic distance : 5.77379, average 1.44345 Vogel's harmonic complexity : 18.25000 Wille's k value : 247 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 24.44148, average 2.44415 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 -0.50000 4 1 3: -1 .. 1 0.25000 3 5: 0 .. 1 0.75000 3 2 11: -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 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: 2 1 1 0 N T3 SD: 64.6215 c. M:-111.7313 c. 6: 3 1 1 1 N M DE SD: 68.7076 c. M: 88.2687 c. 7: 3 2 1 1 N SD: 34.7065 c. M: 59.6973 c. 9: 4 3 1 1 N SD: 26.8247 c. M:-48.9746 c. 11: 5 3 2 1 N SD: 7.3242 c. M: 11.6314 c. 31: 14 9 5 3 N SD: 4.4653 c. M:-5.9639 c. 42: 19 12 7 4 N SD: 3.2882 c. M:-5.9064 c. 45: 20 13 8 4 N SD: 3.7992 c. M:-5.0646 c. 53: 24 15 9 5 N SD: 3.3734 c. M:-6.4455 c. 54: 24 16 9 5 N SD: 2.9152 c. M:-4.5302 c. 65: 29 19 11 6 N SD: 1.2846 c. M:-1.7951 c. 76: 34 22 13 7 N SD: 0.6095 c. M:-1.2050 c. 141: 63 41 24 13 N SD: 0.7686 c. M:-1.0930 c. 183: 82 53 31 17 N SD: 0.5961 c. M:-0.8872 c. 235: 105 68 40 22 N SD: 0.6876 c. M: 0.9545 c. 248: 111 72 42 23 N SD: 0.6086 c. M:-1.1252 c. 259: 116 75 44 24 N SD: 0.4682 c. M:-0.5834 c. 331: 148 96 56 31 N SD: 0.4000 c. M: 0.6554 c. 342: 153 99 58 32 N SD: 0.2897 c. M: 0.5494 c. 353: 158 102 60 33 N SD: 0.3479 c. M: 0.5060 c. 407: 182 118 69 38 N SD: 0.2438 c. M: 0.3414 c. 418: 187 121 71 39 N SD: 0.1474 c. M: 0.2304 c. 494: 221 143 84 46 N SD: 0.0920 c. M: 0.1482 c. 677: 303 196 115 63 N SD: 0.0958 c. M:-0.1317 c. 1019: 456 295 173 95 N SD: 0.0775 c. M: 0.1431 c. 1095: 490 317 186 102 N SD: 0.0329 c. M: 0.0495 c. 1171: 524 339 199 109 N SD: 0.0217 c. M:-0.0319 c. 1665: 745 482 283 155 N SD: 0.0210 c. M: 0.0344 c. 2266: 1014 656 385 211 N SD: 0.0184 c. M:-0.0307 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2:3 x x 4 S SD: 82.5021 cents 3:4:5 x 6 S SD: 12.9686 cents 4:5:7 x 8 SD: 57.5676 cents 5:7:8:9:10 SD: 27.4602 cents 6:8:10:11:12 S SD: 13.7553 cents 8:11:13:15:16 SD: 11.5314 cents 9:12:15:17:18 SD: 10.2375 cents 14:19:23:26:28 SD: 7.7592 cents 16:22:27:30:32 SD: 6.4659 cents 17:23:28:32:34 SD: 6.3812 cents 22:30:37:41:44 SD: 4.7185 cents 24:33:40:45:48 SD: 3.5918 cents 30:41:50:56:60 SD: 2.1540 cents 33:45:55:62:66 SD: 0.8735 cents 63:86:105:118:126 SD: 0.6477 cents 96:131:160:180:192 SD: 0.3005 cents 168:229:280:315:336 SD: 0.1718 cents 231:315:385:433:462 SD: 0.1249 cents 264:360:440:495:528 SD: 0.0000 cents