Scala analysis: xen12-wilson-08-4C1-tetrany-14
7-9-11-15 4C1 Tetrany, Figure 8
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 15/14 119.442808 major diatonic semitone 2: 9/7 435.084095 septimal major third, BP third 3: 11/7 782.492036 undecimal augmented fifth 4: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 14/11 417.5080 undecimal diminished fourth or major third 1: 15/14 119.4428 major diatonic semitone 2: 6/5 315.6413 minor third 3: 11/9 347.4079 undecimal neutral third 4: 14/11 417.5080 undecimal diminished fourth or major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 15/14 119.443 cents major diatonic semitone 1: 1 6/5 315.641 cents minor third 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 15/11 536.951 cents undecimal augmented fourth 2: 1 22/15 663.049 cents undecimal 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 5/3 884.359 cents major sixth, BP sixth 3: 1 28/15 1080.557 cents grave 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 : 119.4 435.1 782.5 1200.0 119.4 : 315.6 663.0 1080.6 1200.0 435.1 : 347.4 764.9 884.4 1200.0 782.5 : 417.5 537.0 852.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 119.4428 .. 417.5080 cents 196/165, 298.0652 cents 15/14, 119.4428 cents 2: 435.0841 .. 764.9159 cents 98/81, 329.8318 cents 99/98, 17.5761 cents 3: 782.4920 .. 1080.5572 cents 196/165, 298.0652 cents 99/98, 17.5761 cents
SHOW DATA
Number of notes : 4 -- Interval properties -- Smallest interval : 15/14, 119.4428 cents, class 1 Average step (divided formal octave): 300.0000 cents Largest one step interval : 14/11, 417.5080 cents Average / Smallest step : 2.511662 Largest / Average step : 1.391693 Largest / Smallest step : 3.495463 Median interval of one step : 331.52461 cents, amount: 0 Least squares average step : 271.23624 cents, oct.: 1084.94495 cents Scale is strictly proper Step pattern alph. order: ABCD Step pattern size order : ABCD Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.609544 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.228365 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 Steps are strictly increasing 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% -- Rational properties -- Prime limit : 11 Odd number limit : 15 (O: 15 U: 15) Highest odd numerator or denominator: 15 Scale harmonicity : 0.023696 Average absolute harmonicity : 0.287071 Specific harmonicity : 0.128397 Fundamental : 1/14, -3.8074 octaves, 18.6875 Hz. Guide tone : 990, 9.9513 octaves, 259009.310 Hz. Exponens Consonantiae : 1.386000E+04, 13.75864 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 33.0, average 8.25000 Mersenne's string divisions : 4176 Sum of van Prooijen's expressibility: 3.17173, average 0.79293 Sum of Tenney's harmonic distance : 6.30908, average 1.57727 Vogel's harmonic complexity : 9.00000 Wille's k value : 7 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 19.44569, average 1.94457 Lattice compactness (without 2's) : 16.14700, average 1.61470 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 1 0.00000 2 1 3: 0 .. 2 0.75000 3 5: 0 .. 1 0.25000 1 7: -1 .. 0 -0.75000 3 2 11: 0 .. 1 0.25000 1 1 Average exponent except 2's : 2 / 4 = 0.50000 Average absolute exponent except 2's: 8 / 4 = 2.00000 Scale is weakly epimorphic with val: <4 5 8 12 15| Scale is weakly epimorphic with val: <4 5 10 12 13| Scale is weakly epimorphic with val: <4 6 8 11 13| Scale is JI-epimorphic with val: <4 6 9 10 13| Scale is weakly epimorphic with val: <4 7 8 12 13| Scale is weakly epimorphic with val: <4 7 9 11 13| Scale is JI-epimorphic with val: <4 7 10 12 15|
FIT/MODE
4: 0 1 1 2 N T3 SD: 128.2747 c. M: 182.4920 c. 5: 0 2 1 2 P D3 SD: 71.0445 c. M: 119.4428 c. 6: 1 1 2 2 P D3 S SD: 44.7964 c. M:-80.5572 c. 8: 1 2 2 3 P T3 SD: 23.5157 c. M: 32.4920 c. 9: 1 2 3 3 P SD: 20.7989 c. M: 35.0841 c. 11: 1 3 3 4 P SD: 10.7742 c. M: 18.8557 c. 20: 2 5 6 7 P SD: 7.6494 c. M: 15.0841 c. 28: 3 7 8 10 P SD: 7.8763 c. M: 11.0635 c. 31: 3 8 9 11 P SD: 6.4405 c. M: 9.2776 c. 38: 4 10 11 13 SP SD: 6.0266 c. M:-7.0212 c. 41: 4 11 12 14 SP SD: 4.5065 c. M:-7.7519 c. 49: 5 13 14 17 SP SD: 3.2898 c. M:-5.7322 c. 52: 5 14 15 18 SP SD: 2.8454 c. M: 4.0582 c. 60: 6 16 17 21 SP SD: 2.7698 c. M:-4.9159 c. 61: 6 16 18 21 SP SD: 2.5771 c. M:-4.3932 c. 69: 7 18 20 24 SP SD: 1.1595 c. M:-2.2963 c. 121: 12 32 35 42 SP SD: 0.8344 c. M:-1.2795 c. 141: 14 37 41 49 SP SD: 0.5933 c. M: 1.0415 c. 152: 15 40 44 53 SP SD: 0.8125 c. M: 1.0218 c. 190: 19 50 55 66 SP SD: 0.5593 c. M:-0.7054 c. 201: 20 53 58 70 SP SD: 0.4203 c. M:-0.7368 c. 221: 22 58 64 77 SP SD: 0.4564 c. M: 0.6950 c. 262: 26 69 76 91 SP SD: 0.3999 c. M:-0.7141 c. 270: 27 71 78 94 SP SD: 0.3891 c. M:-0.5572 c. 273: 27 72 79 95 SP SD: 0.3847 c. M: 0.7615 c. 331: 33 87 96 115 SP SD: 0.3110 c. M:-0.5895 c. 342: 34 90 99 119 SP SD: 0.0745 c. M: 0.1446 c. 753: 75 198 218 262 SP SD: 0.0428 c. M:-0.0791 c. 1095: 109 288 317 381 SP SD: 0.0160 c. M: 0.0263 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x x 3:4 S SD: 40.2685 cents 3 x 4:5:6 S SD: 39.9178 cents 4 x 5:6:8 S SD: 31.3843 cents 5 x 6:8:10 S SD: 41.1497 cents 7:8:9:11:14 SD: 27.9328 cents 9:10:12:14:18 SD: 22.6896 cents 10:11:13:16:20 SD: 14.6092 cents 11:12:14:17:22 SD: 11.4962 cents 14:15:18:22:28 SD: 0.0000 cents