Scala analysis: xen12-wilson-08-4C1-tetrany-10
3-7-9-11 4C1 Tetrany, Figure 8
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: 3/2 701.955001 perfect fifth 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: 9/7 435.0841 septimal major third, BP third 3: 11/9 347.4079 undecimal neutral third 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 7/6 266.871 cents septimal minor third 1: 1 11/9 347.408 cents undecimal neutral third 1: 1 9/7 435.084 cents septimal major third, BP third 2: 1 14/11 417.508 cents undecimal diminished fourth or major third 2: 1 4/3 498.045 cents perfect fourth 2: 1 3/2 701.955 cents perfect fifth 2: 1 11/7 782.492 cents undecimal augmented fifth 3: 1 14/9 764.916 cents septimal minor sixth 3: 1 18/11 852.592 cents undecimal neutral sixth 3: 1 12/7 933.129 cents septimal major sixth 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 : 266.9 702.0 1049.4 1200.0 266.9 : 435.1 782.5 933.1 1200.0 702.0 : 347.4 498.0 764.9 1200.0 1049.4: 150.6 417.5 852.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.6371 .. 435.0841 cents 33/28, 284.4470 cents 12/11, 150.6371 cents 2: 417.5080 .. 782.4920 cents 121/98, 364.9841 cents 98/99,-17.5761 cents 3: 764.9159 .. 1049.3629 cents 33/28, 284.4470 cents 98/99,-17.5761 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 : 9/7, 435.0841 cents Average / Smallest step : 1.991542 Largest / Average step : 1.450280 Largest / Smallest step : 2.888294 Median interval of one step : 307.13942 cents, amount: 0 Least squares average step : 320.62899 cents, oct.: 1282.51596 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 17.57613 cents Scale diversity : 1.654335 Lumma stability : 0.251062 Lumma impropriety factor : 0.029294 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 : 99/98, 17.5761 cents Number of recognisable fifths : 1, average 701.9550 cents 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 n-1 differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval class 2 -- Rational properties -- Prime limit : 11 Odd number limit : 11 (O: 11 U: 11) Highest odd numerator or denominator: 11 Scale harmonicity : 0.027932 Average absolute harmonicity : 0.347542 Specific harmonicity : 0.166072 Fundamental : 1/6, -2.5850 octaves, 43.6043 Hz. Guide tone : 462, 8.8517 octaves, 120871.011 Hz. Exponens Consonantiae : 2.772000E+03, 11.43671 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 19.0, average 4.75000 Mersenne's string divisions : 3315 Sum of van Prooijen's expressibility: 2.36361, average 0.59090 Sum of Tenney's harmonic distance : 4.52197, average 1.13049 Vogel's harmonic complexity : 7.25000 Wille's k value : 5 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 18.89971, average 1.88997 Lattice compactness (without 2's) : 13.54320, average 1.35432 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 1 -0.50000 4 1 3: -1 .. 1 -0.25000 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: 5 / 4 = 1.25000 Scale is weakly epimorphic with val: <4 5 12 15| Scale is JI-epimorphic with val: <4 6 11 13| Scale is weakly epimorphic with val: <4 7 12 13|
FIT/MODE
4: 1 1 1 1 SP B ME I SD: 91.9261 c. M: 149.3629 c. 5: 1 2 1 1 P M ME SD: 47.5221 c. M: 89.3629 c. 8: 2 3 2 1 P G D3 SD: 29.1816 c. M:-48.0450 c. 9: 2 3 3 1 P SD: 19.6515 c. M: 35.2883 c. 10: 2 4 3 1 N SD: 22.2839 c. M:-30.6371 c. 14: 3 5 4 2 P SD: 14.0595 c. M: 20.7915 c. 17: 4 6 5 2 P SD: 9.2820 c. M:-15.4820 c. 22: 5 8 6 3 P SD: 7.9718 c. M: 12.9993 c. 26: 6 9 8 3 P SD: 9.2515 c. M:-12.1755 c. 31: 7 11 9 4 P SD: 3.9140 c. M: 5.1808 c. 41: 9 15 12 5 N SD: 2.7673 c. M:-4.2956 c. 63: 14 23 18 8 N SD: 1.6554 c. M:-2.8069 c. 72: 16 26 21 9 N SD: 1.0331 c. M: 1.9550 c. 104: 23 38 30 13 N SD: 1.2441 c. M:-1.8912 c. 135: 30 49 39 17 N SD: 0.2906 c. M: 0.4741 c. 207: 46 75 60 26 N SD: 0.2762 c. M: 0.5057 c. 342: 76 124 99 43 N SD: 0.1868 c. M: 0.2401 c. 494: 110 179 143 62 N SD: 0.1720 c. M:-0.3356 c. 566: 126 205 164 71 N SD: 0.1718 c. M:-0.2669 c. 629: 140 228 182 79 N SD: 0.1293 c. M:-0.2197 c. 670: 149 243 194 84 N SD: 0.1162 c. M:-0.1893 c. 701: 156 254 203 88 N SD: 0.1014 c. M:-0.1762 c. 764: 170 277 221 96 N SD: 0.1248 c. M: 0.1483 c. 805: 179 292 233 101 N SD: 0.0897 c. M:-0.1568 c. 836: 186 303 242 105 N SD: 0.0731 c. M:-0.1147 c. 877: 195 318 254 110 N SD: 0.0678 c. M:-0.1239 c. 1012: 225 367 293 127 N SD: 0.0438 c. M: 0.0725 c. 1506: 335 546 436 189 N SD: 0.0409 c. M:-0.0614 c. 1641: 365 595 475 206 N SD: 0.0343 c. M:-0.0560 c. 1713: 381 621 496 215 N SD: 0.0237 c. M:-0.0293 c. 1848: 411 670 535 232 N SD: 0.0093 c. M: 0.0123 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x 3 x 4 S SD: 0.0000 cents 3 x x x 6 S SD: 0.0000 cents