Scala analysis: xen12-wilson-08-4C1-tetrany-12
3-7-11-15 4C1 Tetrany, Figure 8
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 7/6 266.870906 septimal minor third 2: 5/4 386.313714 major third 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: 15/14 119.4428 major diatonic semitone 3: 22/15 663.0492 undecimal diminished fifth 4: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 15/14 119.443 cents major diatonic semitone 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 22/15 663.049 cents undecimal diminished fifth 2: 1 5/4 386.314 cents major 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 8/5 813.686 cents minor sixth 3: 1 15/11 536.951 cents undecimal augmented fourth 3: 1 12/7 933.129 cents septimal major sixth 3: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 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 : 266.9 386.3 1049.4 1200.0 266.9 : 119.4 782.5 933.1 1200.0 386.3 : 663.0 813.7 1080.6 1200.0 1049.4: 150.6 417.5 537.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 119.4428 .. 663.0492 cents 308/225, 543.6064 cents 15/14, 119.4428 cents 2: 386.3137 .. 813.6863 cents 32/25, 427.3726 cents 75/88,-276.7355 cents 3: 536.9508 .. 1080.5572 cents 308/225, 543.6064 cents 75/88,-276.7355 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 : 22/15, 663.0492 cents Average / Smallest step : 2.511662 Largest / Average step : 2.210164 Largest / Smallest step : 5.551186 Median interval of one step : 208.75398 cents, amount: 0 Least squares average step : 299.58624 cents, oct.: 1198.34495 cents Scale is not proper Step pattern alph. order: ABCD Step pattern size order : CADB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 119.44281 cents Scale diversity : 1.721475 Lumma stability : 0.199071 Lumma impropriety factor : 0.356144 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 : 56/55, 31.1943 cents Number of recognisable fifths : 0 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 differentially coherent in interval class 1 Limited inverse transpositions with margin 512.4122 cents: 1 -- Rational properties -- Prime limit : 11 Odd number limit : 15 (O: 15 U: 15) Highest odd numerator or denominator: 11 Scale harmonicity : 0.024671 Average absolute harmonicity : 0.309122 Specific harmonicity : 0.147518 Fundamental : 1/12, -3.5850 octaves, 21.8021 Hz. Guide tone : 770, 9.5887 octaves, 201451.685 Hz. Exponens Consonantiae : 9.240000E+03, 13.17368 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 21.0, average 5.25000 Mersenne's string divisions : 1989 Sum of van Prooijen's expressibility: 2.58546, average 0.64637 Sum of Tenney's harmonic distance : 5.04485, average 1.26121 Vogel's harmonic complexity : 8.50000 Wille's k value : 7 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 20.17564, average 2.01756 Lattice compactness (without 2's) : 12.53517, average 1.25352 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 1 -0.75000 5 1 3: -1 .. 0 -0.50000 2 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 : 1 / 4 = 0.25000 Average absolute exponent except 2's: 5 / 4 = 1.25000 Scale is weakly epimorphic with val: <4 5 9 12 15| Scale is weakly epimorphic with val: <4 5 10 12 14| Scale is weakly epimorphic with val: <4 6 9 12 13| Scale is JI-epimorphic with val: <4 6 10 11 13| Scale is weakly epimorphic with val: <4 7 9 10 13| Scale is JI-epimorphic with val: <4 7 10 12 14|
FIT/MODE
4: 1 0 2 1 N T3 SD: 87.8306 c. M: 149.3629 c. 5: 1 1 2 1 P M ME SD: 66.1152 c. M:-93.6863 c. 6: 1 1 3 1 N M DE SD: 42.1181 c. M: 66.8709 c. 8: 2 1 4 1 N D3 SD: 35.8953 c. M:-63.6863 c. 9: 2 1 5 1 N D3 SD: 11.0315 c. M:-17.3037 c. 22: 5 2 12 3 N SD: 7.4748 c. M: 12.9993 c. 31: 7 3 17 4 N SD: 2.9602 c. M: 4.2017 c. 40: 9 4 22 5 N SD: 2.4385 c. M:-3.6863 c. 71: 16 7 39 9 N SD: 2.2716 c. M:-3.5516 c. 72: 16 7 40 9 N SD: 1.5273 c. M: 2.9804 c. 81: 18 8 45 10 N SD: 1.3702 c. M:-2.4889 c. 103: 23 10 57 13 N SD: 1.1482 c. M: 1.8477 c. 112: 25 11 62 14 N SD: 0.6591 c. M:-0.9862 c. 230: 51 23 127 29 N SD: 0.5271 c. M: 0.7839 c. 239: 53 24 132 30 N SD: 0.4090 c. M: 0.7621 c. 270: 60 27 149 34 N SD: 0.3127 c. M: 0.4741 c. 342: 76 34 189 43 N SD: 0.2351 c. M: 0.3488 c. 351: 78 35 194 44 N SD: 0.1465 c. M:-0.2097 c. 382: 85 38 211 48 N SD: 0.1100 c. M: 0.1483 c. 693: 154 69 383 87 N SD: 0.1319 c. M: 0.2042 c. 724: 161 72 400 91 N SD: 0.1151 c. M: 0.1917 c. 733: 163 73 405 92 N SD: 0.0271 c. M:-0.0437 c. 1848: 411 184 1021 232 N SD: 0.0264 c. M:-0.0499 c. 2190: 487 218 1210 275 N SD: 0.0270 c. M: 0.0479 c. 2302: 512 229 1272 289 N SD: 0.0257 c. M: 0.0409 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x 3 x 4 S SD: 157.8206 cents 3 x 4 x 6 S SD: 55.8656 cents 4 x 5:7:8 SD: 26.8457 cents 5:6 x 9:10 S SD: 19.4012 cents 7:8:9:13:14 SD: 16.1087 cents 9 x 11:17:18 SD: 21.5632 cents 11:13:14:20:22 SD: 10.2424 cents 12:14:15:22:24 SD: 0.0000 cents