Scala analysis: xen12-wilson-08-4C1-tetrany-06
1-7-9-11 4C1 Tetrany, Figure 8
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 11/8 551.317942 undecimal semi-augmented fourth 3: 7/4 968.825906 harmonic seventh 4: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 9/8 203.9100 major whole tone 2: 11/9 347.4079 undecimal neutral third 3: 14/11 417.5080 undecimal diminished fourth or major third 4: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 9/8 203.910 cents major whole tone 1: 1 8/7 231.174 cents septimal whole tone 1: 1 11/9 347.408 cents undecimal neutral third 1: 1 14/11 417.508 cents undecimal diminished fourth or major third 2: 1 9/7 435.084 cents septimal major third, BP 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 14/9 764.916 cents septimal minor sixth 3: 1 11/7 782.492 cents undecimal augmented fifth 3: 1 18/11 852.592 cents undecimal neutral sixth 3: 1 7/4 968.826 cents harmonic seventh 3: 1 16/9 996.090 cents Pythagorean 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 : 203.9 551.3 968.8 1200.0 203.9 : 347.4 764.9 996.1 1200.0 551.3 : 417.5 648.7 852.6 1200.0 968.8 : 231.2 435.1 782.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 203.9100 .. 417.5080 cents 112/99, 213.5980 cents 9/8, 203.9100 cents 2: 435.0841 .. 764.9159 cents 98/81, 329.8318 cents 99/98, 17.5761 cents 3: 782.4920 .. 996.0900 cents 112/99, 213.5980 cents 99/98, 17.5761 cents
SHOW DATA
Number of notes : 4 -- Interval properties -- Smallest interval : 9/8, 203.9100 cents, class 1 Average step (divided formal octave): 300.0000 cents Largest one step interval : 14/11, 417.5080 cents Average / Smallest step : 1.471237 Largest / Average step : 1.391693 Largest / Smallest step : 2.047511 Median interval of one step : 289.29102 cents, amount: 0 Least squares average step : 300.43412 cents, oct.: 1201.73648 cents Scale is strictly 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 17.57613 cents Scale diversity : 1.591247 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.369144 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 : 0 Best minor thirds form a closed circle 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 class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval class 3 -- Rational properties -- Prime limit : 11 Odd number limit : 11 (O: 11 U: 11) Highest odd numerator or denominator: 11 Scale harmonicity : 0.026454 Average absolute harmonicity : 0.312151 Specific harmonicity : 0.159029 Fundamental : 1/8, -3.0000 octaves, 32.7032 Hz. Guide tone : 1386, 10.4367 octaves, 362613.034 Hz. Exponens Consonantiae : 1.108800E+04, 13.43671 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 25.0, average 6.25000 Mersenne's string divisions : 10659 Sum of van Prooijen's expressibility: 2.84073, average 0.71018 Sum of Tenney's harmonic distance : 5.55000, average 1.38750 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 : 28.17902, average 2.81790 Lattice compactness (without 2's) : 13.88635, average 1.38863 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -1.75000 9 1 3: 0 .. 2 0.50000 2 1 7: 0 .. 1 0.25000 1 1 11: 0 .. 1 0.25000 1 1 Average exponent except 2's : 4 / 4 = 1.00000 Average absolute exponent except 2's: 4 / 4 = 1.00000 Scale is weakly epimorphic with val: <4 5 11 13| Scale is weakly epimorphic with val: <4 7 11 13|
FIT/MODE
4: 1 1 1 1 SP B ME I SD: 63.9145 c. M:-96.0900 c. 5: 1 1 2 1 P M ME SD: 40.2077 c. M: 71.3179 c. 6: 1 2 2 1 P D3 I SD: 28.9700 c. M:-48.6821 c. 11: 2 3 4 2 P SD: 10.0854 c. M:-14.2718 c. 24: 4 7 8 5 SP SD: 9.6364 c. M: 18.8259 c. 28: 5 8 10 5 P SD: 10.3296 c. M:-16.8884 c. 30: 5 9 10 6 SP SD: 6.4916 c. M: 8.8259 c. 31: 5 9 11 6 P SD: 7.0101 c. M: 10.3616 c. 35: 6 10 12 7 SP SD: 4.7089 c. M: 8.8259 c. 41: 7 12 14 8 SP SD: 2.8555 c. M:-4.7796 c. 52: 9 15 18 10 SP SD: 2.2837 c. M:-3.7823 c. 72: 12 21 25 14 SP SD: 2.3285 c. M: 3.9100 c. 83: 14 24 29 16 SP SD: 1.2208 c. M: 1.9204 c. 124: 21 36 43 24 SP SD: 0.6577 c. M: 1.0840 c. 135: 23 39 47 26 SP SD: 0.2883 c. M:-0.5344 c. 259: 44 75 90 50 SP SD: 0.2449 c. M: 0.4861 c. 342: 58 99 119 66 SP SD: 0.3603 c. M: 0.4407 c. 348: 59 101 121 67 SP SD: 0.3153 c. M: 0.4617 c. 353: 60 102 123 68 SP SD: 0.3062 c. M: 0.6097 c. 359: 61 104 125 69 SP SD: 0.2874 c. M:-0.5334 c. 394: 67 114 137 76 SP SD: 0.1688 c. M: 0.2980 c. 483: 82 140 168 93 SP SD: 0.1603 c. M:-0.2349 c. 618: 105 179 215 119 SP SD: 0.0882 c. M:-0.1384 c. 753: 128 218 262 145 SP SD: 0.0725 c. M:-0.0984 c. 877: 149 254 305 169 SP SD: 0.0659 c. M:-0.1074 c. 1012: 172 293 352 195 SP SD: 0.0467 c. M:-0.0655 c. 1589: 270 460 553 306 SP SD: 0.0451 c. M:-0.0854 c. 1713: 291 496 596 330 SP SD: 0.0286 c. M: 0.0571 c. 1848: 314 535 643 356 SP SD: 0.0122 c. M: 0.0192 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 4:5:6 S SD: 33.2878 cents 4 x 6:7:8 S SD: 50.2124 cents 5:6:7:9:10 SD: 31.4598 cents 6:7:8:11:12 SD: 28.8187 cents 7:8:10:12:14 S SD: 19.9938 cents 8:9:11:14:16 SD: 0.0000 cents