Scala analysis: xen12-wilson-08-4C3-tetrany-12
3-7-11-15 4C3 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: 5/4 386.313714 major third 3: 15/11 536.950772 undecimal augmented fourth 4: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 22/15 663.0492 undecimal diminished fifth 1: 15/14 119.4428 major diatonic semitone 2: 7/6 266.8709 septimal minor third 3: 12/11 150.6371 undecimal neutral second, 3/4-tone 4: 22/15 663.0492 undecimal diminished fifth
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 : 119.4 386.3 537.0 1200.0 119.4 : 266.9 417.5 1080.6 1200.0 386.3 : 150.6 813.7 933.1 1200.0 537.0 : 663.0 782.5 1049.4 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 : 243.43075 cents, oct.: 973.72301 cents Scale is not proper Step pattern alph. order: ABCD Step pattern size order : ACBD 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 n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 512.4122 cents: 3 -- Rational properties -- Prime limit : 11 Odd number limit : 15 (O: 15 U: 15) Highest odd numerator or denominator: 15 Scale harmonicity : 0.024671 Average absolute harmonicity : 0.301220 Specific harmonicity : 0.137159 Fundamental : 1/308, -8.2668 octaves, 0.8494 Hz. Guide tone : 30, 4.9069 octaves, 7848.767 Hz. Exponens Consonantiae : 9.240000E+03, 13.17368 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 33.5, average 8.37500 Mersenne's string divisions : 6786 Sum of van Prooijen's expressibility: 3.05115, average 0.76279 Sum of Tenney's harmonic distance : 6.14176, average 1.53544 Vogel's harmonic complexity : 20.25000 Wille's k value : 192 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 20.68974, average 2.06897 Lattice compactness (without 2's) : 13.17084, average 1.31708 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 1 -0.50000 4 1 3: 0 .. 1 0.50000 2 5: 0 .. 1 0.75000 3 1 7: -1 .. 0 -0.25000 1 1 11: -1 .. 0 -0.25000 1 1 Average exponent except 2's : 3 / 4 = 0.75000 Average absolute exponent except 2's: 7 / 4 = 1.75000 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: 0 1 1 2 N T3 SD: 80.1434 c. M: 119.4428 c. 6: 1 1 1 3 N M DE SD: 51.6042 c. M:-80.5572 c. 7: 1 1 1 4 N M DE SD: 35.7236 c. M:-51.9858 c. 9: 1 2 1 5 N D3 SD: 9.9165 c. M:-13.8905 c. 22: 2 5 3 12 N SD: 7.0655 c. M: 10.3519 c. 31: 3 7 4 17 N SD: 3.0183 c. M:-4.9847 c. 40: 4 9 5 22 N SD: 2.4082 c. M:-3.6863 c. 71: 7 16 9 39 N SD: 2.3611 c. M:-3.8943 c. 72: 7 16 9 40 N SD: 2.7238 c. M: 3.6174 c. 78: 8 17 10 43 N SD: 2.1432 c. M:-3.6341 c. 81: 8 18 10 45 N SD: 1.9502 c. M: 3.6174 c. 90: 9 20 11 50 N SD: 1.8385 c. M: 3.6174 c. 100: 10 22 13 55 N SD: 1.9340 c. M:-3.0492 c. 103: 10 23 13 57 N SD: 1.8099 c. M: 2.9380 c. 109: 11 24 14 60 N SD: 1.5794 c. M:-2.4988 c. 112: 11 25 14 62 N SD: 1.0491 c. M: 1.5857 c. 121: 12 27 15 67 N SD: 0.7748 c. M: 1.4136 c. 152: 15 34 19 84 N SD: 0.5777 c. M: 1.0218 c. 221: 22 49 28 122 N SD: 0.4991 c. M: 0.7934 c. 230: 23 51 29 127 N SD: 0.3728 c. M:-0.5572 c. 342: 34 76 43 189 N SD: 0.1964 c. M: 0.3488 c. 351: 35 78 44 194 N SD: 0.1466 c. M:-0.2153 c. 382: 38 85 48 211 N SD: 0.1222 c. M:-0.2220 c. 503: 50 112 63 278 N SD: 0.1437 c. M: 0.1714 c. 693: 69 154 87 383 N SD: 0.1150 c. M: 0.1665 c. 724: 72 161 91 400 N SD: 0.0886 c. M: 0.1259 c. 733: 73 163 92 405 N SD: 0.0409 c. M:-0.0661 c. 1426: 142 317 179 788 N SD: 0.0507 c. M: 0.0644 c. 1457: 145 324 183 805 N SD: 0.0311 c. M:-0.0431 c. 1808: 180 402 227 999 N SD: 0.0202 c. M: 0.0305 c. 2190: 218 487 275 1210 N SD: 0.0194 c. M:-0.0355 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x x 3:4 S SD: 82.5021 cents 3 x x 4:6 S SD: 19.4529 cents 4 x 5 x 8 SD: 0.0000 cents 5 x 6:7:10 SD: 28.0286 cents 6 x x 8:12 S SD: 19.4529 cents 11:12:14:15:22 SD: 11.0288 cents 12:13:15:16:24 SD: 10.8386 cents 13:14:16:18:26 SD: 9.6744 cents 16:17:20:22:32 SD: 5.1009 cents 25:27:31:34:50 SD: 5.0313 cents 27:29:34:37:54 SD: 3.9859 cents 28:30:35:38:56 SD: 2.0659 cents 44:47:55:60:88 SD: 1.3135 cents 72:77:90:98:144 SD: 1.1345 cents 85:91:106:116:170 SD: 1.1269 cents 96:103:120:131:192 SD: 0.6717 cents 124:133:155:169:248 SD: 0.5201 cents 140:150:175:191:280 SD: 0.2061 cents 168:180:210:229:336 SD: 0.1718 cents 308:330:385:420:616 SD: 0.0000 cents