Scala analysis: xen12-wilson-38-4C1-tetrany-11
3-5-7-11 4C1 Tetrany, Figure 38
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 7/6 266.870906 septimal minor third 2: 5/3 884.358713 major sixth, BP sixth 3: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 4: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 7/6 266.8709 septimal minor third 2: 10/7 617.4878 Euler's tritone 3: 11/10 165.0042 Ptolemy's second, 4/5-tone 4: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 7/6 266.871 cents septimal minor third 1: 1 10/7 617.488 cents Euler's tritone 2: 1 6/5 315.641 cents minor third 2: 1 14/11 417.508 cents undecimal diminished fourth or major third 2: 1 11/7 782.492 cents undecimal augmented fifth 2: 1 5/3 884.359 cents major sixth, BP sixth 3: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 3: 1 12/7 933.129 cents septimal major sixth 3: 1 20/11 1034.996 cents large minor seventh 3: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 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 : 266.9 884.4 1049.4 1200.0 266.9 : 617.5 782.5 933.1 1200.0 884.4 : 165.0 315.6 582.5 1200.0 1049.4: 150.6 417.5 1035.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.6371 .. 617.4878 cents 55/42, 466.8507 cents 12/11, 150.6371 cents 2: 315.6413 .. 884.3587 cents 25/18, 568.7174 cents 21/25,-301.8465 cents 3: 582.5122 .. 1049.3629 cents 55/42, 466.8507 cents 21/25,-301.8465 cents
SHOW DATA
Number of notes : 4 -- Interval properties -- Smallest interval : 12/11, 150.6371 cents, class 1 Average step (divided formal octave): 300.0000 cents Largest one step interval : 10/7, 617.4878 cents Average / Smallest step : 1.991542 Largest / Average step : 2.058293 Largest / Smallest step : 4.099176 Median interval of one step : 215.93757 cents, amount: 0 Least squares average step : 332.78924 cents, oct.: 1331.15695 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 34.97561 cents Scale diversity : 1.642486 Lumma stability : 0.251062 Lumma impropriety factor : 0.473931 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 : 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 differentially coherent in interval classes 2 and 3 combined -- Rational properties -- Prime limit : 11 Odd number limit : 11 (O: 11 U: 11) Highest odd numerator or denominator: 11 Scale harmonicity : 0.025295 Average absolute harmonicity : 0.306934 Specific harmonicity : 0.151084 Fundamental : 1/6, -2.5850 octaves, 43.6043 Hz. Guide tone : 770, 9.5887 octaves, 201451.685 Hz. Exponens Consonantiae : 4.620000E+03, 12.17368 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 20.5, average 5.12500 Mersenne's string divisions : 5304 Sum of van Prooijen's expressibility: 2.58546, average 0.64637 Sum of Tenney's harmonic distance : 4.91991, average 1.22998 Vogel's harmonic complexity : 7.25000 Wille's k value : 5 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 4 Triangular lattice diameter : 1 Lattice compactness : 17.38766, average 1.73877 Lattice compactness (without 2's) : 12.72792, average 1.27279 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 1 -0.25000 3 1 3: -1 .. 0 -0.75000 3 5: 0 .. 1 0.25000 1 1 7: 0 .. 1 0.25000 1 1 11: 0 .. 1 0.25000 1 1 Average exponent except 2's : 0 / 4 = 0.00000 Average absolute exponent except 2's: 6 / 4 = 1.50000 Scale is weakly epimorphic with val: <4 5 8 10 15| Scale is weakly epimorphic with val: <4 5 8 11 14| Scale is weakly epimorphic with val: <4 5 10 12 15| Scale is JI-epimorphic with val: <4 6 8 11 13| Scale is weakly epimorphic with val: <4 6 9 12 15| Scale is weakly epimorphic with val: <4 7 8 10 13| Scale is JI-epimorphic with val: <4 7 9 12 14| Scale is weakly epimorphic with val: <4 7 10 12 13|
FIT/MODE
4: 1 2 0 1 N T3 SD: 76.8952 c. M: 149.3629 c. 5: 1 3 0 1 N G SD: 60.0612 c. M: 89.3629 c. 6: 1 3 1 1 N M DE SD: 59.2132 c. M: 84.3587 c. 7: 1 4 1 1 N M DE SD: 50.7007 c. M: 95.4423 c. 8: 2 4 1 1 N SD: 18.3207 c. M:-33.1291 c. 14: 3 7 2 2 N SD: 17.8019 c. M: 27.2159 c. 15: 3 8 2 2 N SD: 14.3936 c. M: 26.8709 c. 18: 4 9 3 2 N SD: 12.3741 c. M: 17.6920 c. 22: 5 11 3 3 N SD: 9.2001 c. M: 12.9993 c. 23: 5 12 3 3 N SD: 4.3987 c. M: 6.0013 c. 31: 7 16 4 4 N SD: 4.1835 c. M:-5.9639 c. 49: 11 25 7 6 N SD: 2.6193 c. M:-3.6983 c. 64: 14 33 9 8 N SD: 2.7007 c. M: 4.3709 c. 72: 16 37 10 9 N SD: 0.6122 c. M: 1.0254 c. 167: 37 86 23 21 N SD: 0.5811 c. M: 1.0026 c. 175: 39 90 24 22 N SD: 0.3181 c. M:-0.5577 c. 247: 55 127 34 31 N SD: 0.1840 c. M:-0.3356 c. 342: 76 176 47 43 N SD: 0.1742 c. M: 0.2401 c. 517: 115 266 71 65 N SD: 0.1204 c. M: 0.2333 c. 589: 131 303 81 74 N SD: 0.0982 c. M: 0.1482 c. 931: 207 479 128 117 N SD: 0.1163 c. M: 0.1685 c. 1083: 241 557 149 136 N SD: 0.1143 c. M:-0.1651 c. 1084: 241 558 149 136 N SD: 0.0923 c. M:-0.1431 c. 1156: 257 595 159 145 N SD: 0.0818 c. M:-0.1180 c. 1259: 280 648 173 158 N SD: 0.0792 c. M:-0.1528 c. 1331: 296 685 183 167 N SD: 0.0578 c. M:-0.0891 c. 1403: 312 722 193 176 N SD: 0.0541 c. M:-0.1025 c. 1506: 335 775 207 189 N SD: 0.0633 c. M:-0.1034 c. 1578: 351 812 217 198 N SD: 0.0489 c. M:-0.0667 c. 1673: 372 861 230 210 N SD: 0.0306 c. M: 0.0448 c. 1848: 411 951 254 232 N SD: 0.0297 c. M:-0.0569 c. 1920: 427 988 264 241 N SD: 0.0103 c. M:-0.0163 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: 77.0580 cents 4:5 x 7:8 SD: 48.0194 cents 5:6:8:9:10 S SD: 22.8887 cents 6:7:10:11:12 SD: 0.0000 cents