Scala analysis: xen12-wilson-08-4C1-tetrany-08
1-7-11-15 4C1 Tetrany, Figure 8
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/8 551.317942 undecimal semi-augmented fourth 2: 7/4 968.825906 harmonic seventh 3: 15/8 1088.268715 classic major seventh 4: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 11/8 551.3179 undecimal semi-augmented fourth 2: 14/11 417.5080 undecimal diminished fourth or major third 3: 15/14 119.4428 major diatonic semitone 4: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 15/14 119.443 cents major diatonic semitone 1: 1 14/11 417.508 cents undecimal diminished fourth or major third 1: 1 11/8 551.318 cents undecimal semi-augmented fourth 2: 1 8/7 231.174 cents septimal whole tone 2: 1 15/11 536.951 cents undecimal augmented fourth 2: 1 22/15 663.049 cents undecimal diminished fifth 2: 1 7/4 968.826 cents harmonic seventh 3: 1 16/11 648.682 cents undecimal semi-diminished fifth 3: 1 11/7 782.492 cents undecimal augmented fifth 3: 1 28/15 1080.557 cents grave major seventh 3: 1 15/8 1088.269 cents classic 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 : 551.3 968.8 1088.3 1200.0 551.3 : 417.5 537.0 648.7 1200.0 968.8 : 119.4 231.2 782.5 1200.0 1088.3: 111.7 663.0 1080.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 551.3179 cents 165/128, 439.5867 cents 16/15, 111.7313 cents 2: 231.1741 .. 968.8259 cents 49/32, 737.6518 cents 64/77,-320.1438 cents 3: 648.6821 .. 1088.2687 cents 165/128, 439.5867 cents 64/77,-320.1438 cents
SHOW DATA
Number of notes : 4 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 300.0000 cents Largest one step interval : 11/8, 551.3179 cents Average / Smallest step : 2.685013 Largest / Average step : 1.837726 Largest / Smallest step : 4.934320 Median interval of one step : 268.47539 cents, amount: 0 Least squares average step : 351.79253 cents, oct.: 1407.17012 cents Scale is not proper Step pattern alph. order: ABCD Step pattern size order : DCBA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 14.36717 cents Scale diversity : 1.594398 Lumma stability : 0.186219 Lumma impropriety factor : 0.533573 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 : 225/224, 7.7115 cents Number of recognisable fifths : 0 Steps are strictly decreasing Length of longest harmonic part : 2 at degree 2 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 : 15 (O: 15 U: 15) Highest odd numerator or denominator: 15 Scale harmonicity : 0.024077 Average absolute harmonicity : 0.302869 Specific harmonicity : 0.145233 Fundamental : 1/8, -3.0000 octaves, 32.7032 Hz. Guide tone : 2310, 11.1737 octaves, 604355.056 Hz. Exponens Consonantiae : 1.848000E+04, 14.17368 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 28.0, average 7.00000 Mersenne's string divisions : 14421 Sum of van Prooijen's expressibility: 3.06258, average 0.76565 Sum of Tenney's harmonic distance : 5.77185, average 1.44296 Vogel's harmonic complexity : 7.75000 Wille's k value : 7 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 26.70710, average 2.67071 Lattice compactness (without 2's) : 11.70674, average 1.17067 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -1.75000 9 1 3: 0 .. 1 0.25000 1 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 : 4 / 4 = 1.00000 Average absolute exponent except 2's: 4 / 4 = 1.00000 Scale is weakly epimorphic with val: <4 5 8 10 15| Scale is weakly epimorphic with val: <4 5 8 11 14| Scale is weakly epimorphic with val: <4 5 9 11 13| Scale is JI-epimorphic with val: <4 5 10 10 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 JI-epimorphic with val: <4 7 8 10 13| Scale is weakly epimorphic with val: <4 7 10 10 15| Scale is weakly epimorphic with val: <4 7 10 11 14|
FIT/MODE
4: 2 1 1 0 N T3 SD: 69.9836 c. M:-111.7313 c. 5: 2 2 0 1 N G SD: 73.5136 c. M: 128.2687 c. 6: 3 2 0 1 N SD: 52.7568 c. M: 88.2687 c. 9: 4 3 1 1 N SD: 22.6375 c. M: 35.4926 c. 11: 5 4 1 1 N SD: 7.2483 c. M:-12.9923 c. 20: 9 7 2 2 N SD: 8.2820 c. M: 11.3179 c. 30: 14 10 3 3 N SD: 7.4439 c. M: 8.8259 c. 31: 14 11 3 3 N SD: 5.2093 c. M: 9.3825 c. 41: 19 14 4 4 N SD: 3.8799 c. M: 5.3419 c. 52: 24 18 5 5 N SD: 2.2306 c. M: 3.6533 c. 63: 29 22 6 6 N SD: 1.8993 c. M:-2.6027 c. 83: 38 29 8 8 N SD: 2.1890 c. M: 3.9314 c. 87: 40 30 9 8 N SD: 1.8052 c. M: 3.3087 c. 98: 45 34 10 9 N SD: 1.0733 c. M:-1.5272 c. 109: 50 38 11 10 N SD: 0.9256 c. M:-1.6395 c. 150: 69 52 15 14 N SD: 0.5522 c. M: 0.8259 c. 161: 74 56 16 15 N SD: 0.1360 c. M:-0.2349 c. 581: 267 202 58 54 N SD: 0.1446 c. M:-0.1994 c. 592: 272 206 59 55 N SD: 0.1320 c. M:-0.2448 c. 742: 341 258 74 69 N SD: 0.1178 c. M:-0.1645 c. 753: 346 262 75 70 N SD: 0.1084 c. M:-0.1775 c. 903: 415 314 90 84 N SD: 0.1062 c. M:-0.1771 c. 914: 420 318 91 85 N SD: 0.0990 c. M:-0.1339 c. 934: 429 325 93 87 N SD: 0.0862 c. M: 0.1402 c. 1075: 494 374 107 100 N SD: 0.0961 c. M:-0.1239 c. 1095: 503 381 109 102 N SD: 0.0573 c. M: 0.0851 c. 1256: 577 437 125 117 N SD: 0.0386 c. M: 0.0522 c. 1417: 651 493 141 132 N SD: 0.0293 c. M: 0.0542 c. 1578: 725 549 157 147 N SD: 0.0287 c. M: 0.0558 c. 1848: 849 643 184 172 N SD: 0.0237 c. M:-0.0430 c. 2009: 923 699 200 187 N SD: 0.0184 c. M:-0.0339 c. 2170: 997 755 216 202 N SD: 0.0194 c. M:-0.0262 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2:3 x x 4 S SD: 75.3185 cents 3:4:5 x 6 S SD: 33.2878 cents 4:6:7 x 8 S SD: 50.2124 cents 5:7:9 x 10 SD: 19.2978 cents 6:8 x 11:12 SD: 21.9891 cents 7:10:12:13:14 SD: 19.2470 cents 8:11:14:15:16 SD: 0.0000 cents