Scala analysis: xen12-wilson-38-4C1-tetrany-14
5-7-9-11 4C1 Tetrany, Figure 38
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/10 165.004228 Ptolemy's second, 4/5-tone 2: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 3: 9/5 1017.596288 just minor seventh, BP seventh 4: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 14/11 417.5080 undecimal diminished fourth or major third 3: 9/7 435.0841 septimal major third, BP third 4: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 10/9 182.404 cents minor whole tone 1: 1 14/11 417.508 cents undecimal diminished fourth or major third 1: 1 9/7 435.084 cents septimal major third, BP third 2: 1 11/9 347.408 cents undecimal neutral third 2: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 2: 1 10/7 617.488 cents Euler's tritone 2: 1 18/11 852.592 cents undecimal neutral sixth 3: 1 14/9 764.916 cents septimal minor sixth 3: 1 11/7 782.492 cents undecimal augmented fifth 3: 1 9/5 1017.596 cents just minor seventh, BP seventh 3: 1 20/11 1034.996 cents large minor 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 : 165.0 582.5 1017.6 1200.0 165.0 : 417.5 852.6 1035.0 1200.0 582.5 : 435.1 617.5 782.5 1200.0 1017.6: 182.4 347.4 764.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 165.0042 .. 435.0841 cents 90/77, 270.0799 cents 11/10, 165.0042 cents 2: 347.4079 .. 852.5921 cents 162/121, 505.1841 cents 77/81,-87.6762 cents 3: 764.9159 .. 1034.9958 cents 90/77, 270.0799 cents 77/81,-87.6762 cents
SHOW DATA
Number of notes : 4 -- Interval properties -- Smallest interval : 11/10, 165.0042 cents, class 1 Average step (divided formal octave): 300.0000 cents Largest one step interval : 9/7, 435.0841 cents Average / Smallest step : 1.818135 Largest / Average step : 1.450280 Largest / Smallest step : 2.636806 Median interval of one step : 299.95584 cents, amount: 0 Least squares average step : 306.09392 cents, oct.: 1224.37566 cents Scale is not proper Step pattern alph. order: ABCD Step pattern size order : ACDB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 70.10002 cents Scale diversity : 1.564296 Lumma stability : 0.275007 Lumma impropriety factor : 0.146127 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 : 100/99, 17.3995 cents Number of recognisable fifths : 0 Length of longest harmonic part : 2 at degree 3 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 25.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined -- Rational properties -- Prime limit : 11 Odd number limit : 11 (O: 11 U: 11) Highest odd numerator or denominator: 11 Scale harmonicity : 0.023696 Average absolute harmonicity : 0.296062 Specific harmonicity : 0.137662 Fundamental : 1/10, -3.3219 octaves, 26.1626 Hz. Guide tone : 1386, 10.4367 octaves, 362613.034 Hz. Exponens Consonantiae : 1.386000E+04, 13.75864 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 25.0, average 6.25000 Mersenne's string divisions : 84 Sum of van Prooijen's expressibility: 2.84073, average 0.71018 Sum of Tenney's harmonic distance : 5.53970, average 1.38493 Vogel's harmonic complexity : 8.25000 Wille's k value : 5 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 19.43097, average 1.94310 Lattice compactness (without 2's) : 16.01534, average 1.60153 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 1 0.00000 2 1 3: 0 .. 2 0.50000 2 5: -1 .. 0 -0.75000 3 1 7: 0 .. 1 0.25000 1 1 11: 0 .. 1 0.25000 1 1 Average exponent except 2's : 1 / 4 = 0.25000 Average absolute exponent except 2's: 7 / 4 = 1.75000 Scale is weakly epimorphic with val: <4 5 8 11 13| Scale is weakly epimorphic with val: <4 5 9 12 15| Scale is weakly epimorphic with val: <4 6 9 10 15| Scale is JI-epimorphic with val: <4 6 9 11 14| = patent Scale is weakly epimorphic with val: <4 6 10 11 13| Scale is weakly epimorphic with val: <4 7 8 11 13| Scale is weakly epimorphic with val: <4 7 9 12 15|
FIT/MODE
4: 0 2 1 1 N T3 SD: 101.6871 c. M: 165.0042 c. 5: 0 2 2 1 N G SD: 101.3071 c. M: 165.0042 c. 6: 1 2 2 1 P D3 I SD: 21.4485 c. M:-34.9958 c. 8: 1 3 3 1 N D3 I SD: 19.8806 c. M:-32.4037 c. 13: 2 4 5 2 N SD: 17.4014 c. M: 28.6660 c. 14: 2 5 5 2 N D3 I SD: 10.8114 c. M:-17.4878 c. 21: 3 7 8 3 N SD: 8.4346 c. M: 11.0836 c. 27: 4 9 10 4 N SD: 7.1934 c. M:-12.7735 c. 31: 4 11 11 5 N SD: 7.5998 c. M: 11.1447 c. 35: 5 12 13 5 N SD: 6.3609 c. M:-10.9751 c. 37: 5 13 13 6 N SD: 6.2911 c. M: 12.1909 c. 39: 5 14 14 6 N SD: 5.7840 c. M: 11.1581 c. 41: 6 14 15 6 N SD: 6.4571 c. M:-10.6055 c. 44: 6 15 16 7 N SD: 6.5184 c. M: 9.7849 c. 45: 6 16 16 7 N SD: 3.8883 c. M: 5.0042 c. 52: 7 18 19 8 N SD: 3.4692 c. M: 5.5891 c. 58: 8 20 21 9 N SD: 2.4990 c. M: 3.8032 c. 66: 9 23 24 10 N SD: 0.8209 c. M: 1.3679 c. 138: 19 48 50 21 N SD: 0.1555 c. M:-0.2132 c. 204: 28 71 74 31 N SD: 0.1710 c. M: 0.2983 c. 342: 47 119 124 52 N SD: 0.0599 c. M: 0.0919 c. 480: 66 167 174 73 N SD: 0.0486 c. M: 0.0963 c. 822: 113 286 298 125 N SD: 0.0466 c. M: 0.0780 c. 1164: 160 405 422 177 N SD: 0.0488 c. M: 0.0705 c. 1302: 179 453 472 198 N SD: 0.0461 c. M: 0.0848 c. 1506: 207 524 546 229 N SD: 0.0507 c. M: 0.0664 c. 1782: 245 620 646 271 N SD: 0.0463 c. M: 0.0879 c. 1862: 256 648 675 283 N SD: 0.0458 c. M:-0.0872 c. 2000: 275 696 725 304 N SD: 0.0440 c. M:-0.0878 c. 2066: 284 719 749 314 N SD: 0.0410 c. M:-0.0628 c. 2204: 303 767 799 335 N SD: 0.0363 c. M:-0.0649 c. 2342: 322 815 849 356 N SD: 0.0345 c. M:-0.0668 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x 3 x 4 S SD: 59.7214 cents 3 x 4:5:6 S SD: 52.5853 cents 4 x 6:7:8 S SD: 43.0053 cents 5:6:7:9:10 SD: 37.6593 cents 6:7:8:11:12 SD: 34.0226 cents 7:8:10:13:14 SD: 23.0883 cents 8:9:11:14:16 SD: 17.4379 cents 9:10:13:16:18 SD: 15.1918 cents 10:11:14:18:20 SD: 0.0000 cents