Scala analysis: xen12-wilson-38-4C3-tetrany-12
3-5-9-11 4C3 Tetrany, Figure 38
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/10 165.004228 Ptolemy's second, 4/5-tone 2: 11/9 347.407941 undecimal neutral 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: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 10/9 182.4037 minor whole tone 3: 3/2 701.9550 perfect fifth 4: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 10/9 182.404 cents minor whole tone 1: 1 3/2 701.955 cents perfect fifth 2: 1 6/5 315.641 cents minor third 2: 1 11/9 347.408 cents undecimal neutral third 2: 1 18/11 852.592 cents undecimal neutral sixth 2: 1 5/3 884.359 cents major sixth, BP sixth 3: 1 4/3 498.045 cents perfect fourth 3: 1 9/5 1017.596 cents just minor seventh, BP seventh 3: 1 20/11 1034.996 cents large minor seventh 3: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 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 : 165.0 347.4 1049.4 1200.0 165.0 : 182.4 884.4 1035.0 1200.0 347.4 : 702.0 852.6 1017.6 1200.0 1049.4: 150.6 315.6 498.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.6371 .. 701.9550 cents 11/8, 551.3179 cents 12/11, 150.6371 cents 2: 315.6413 .. 884.3587 cents 25/18, 568.7174 cents 4/5,-386.3137 cents 3: 498.0450 .. 1049.3629 cents 11/8, 551.3179 cents 4/5,-386.3137 cents
SHOW DATA
Number of notes : 4 -- Interval properties -- Smallest interval : 12/11, 150.6371 cents, class 1 Average step (divided formal octave): 300.0000 cents Largest one step interval : 3/2, 701.9550 cents Average / Smallest step : 1.991542 Largest / Average step : 2.339850 Largest / Smallest step : 4.659909 Median interval of one step : 173.70397 cents, amount: 0 Least squares average step : 293.59696 cents, oct.: 1174.38786 cents Scale is not proper Step pattern alph. order: ABCD Step pattern size order : BCDA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 133.23757 cents Scale diversity : 1.537479 Lumma stability : 0.251062 Lumma impropriety factor : 0.473931 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 : 121/120, 14.3672 cents Number of recognisable fifths : 1, average 701.9550 cents All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 3 at degree 3 Formal octave complements present : 1 = 25.0000% Scale is differentially coherent in interval class 1 Limited inverse transpositions with margin 551.3179 cents: 1 -- Rational properties -- Prime limit : 11 Odd number limit : 11 (O: 11 U: 11) Highest odd numerator or denominator: 11 Scale harmonicity : 0.031333 Average absolute harmonicity : 0.281846 Specific harmonicity : 0.145893 Fundamental : 1/90, -6.4919 octaves, 2.9070 Hz. Guide tone : 22, 4.4594 octaves, 5755.762 Hz. Exponens Consonantiae : 1.980000E+03, 10.95128 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 30.5, average 7.62500 Mersenne's string divisions : 7140 Sum of van Prooijen's expressibility: 3.12418, average 0.78104 Sum of Tenney's harmonic distance : 6.15760, average 1.53940 Vogel's harmonic complexity : 16.50000 Wille's k value : 82 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 19.32656, average 1.93266 Lattice compactness (without 2's) : 14.77927, average 1.47793 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 1 -0.25000 3 1 3: -2 .. 0 -0.75000 3 5: -1 .. 0 -0.25000 1 11: 0 .. 1 0.75000 3 3 Average exponent except 2's :-1 / 4 =-0.25000 Average absolute exponent except 2's: 7 / 4 = 1.75000 Scale is weakly epimorphic with val: <4 5 8 15| Scale is weakly epimorphic with val: <4 6 9 15| Scale is weakly epimorphic with val: <4 7 8 13|
FIT/MODE
4: 0 1 2 1 N D3 SD: 113.7796 c. M: 165.0042 c. 5: 1 0 3 1 N G SD: 79.2883 c. M: 107.4079 c. 6: 1 1 3 1 N M DE SD: 40.0853 c. M:-52.5921 c. 7: 1 1 4 1 N M DE SD: 11.1161 c. M: 20.7915 c. 22: 3 3 13 3 N M DE SD: 12.0029 c. M: 20.1352 c. 23: 3 4 13 3 N SD: 10.2927 c. M:-17.8095 c. 24: 3 4 14 3 N SD: 7.6199 c. M: 15.0042 c. 30: 4 5 17 4 N SD: 8.2351 c. M:-12.5921 c. 31: 4 5 18 4 N SD: 5.5216 c. M: 10.1655 c. 38: 5 6 22 5 N SD: 5.0799 c. M: 7.2577 c. 49: 7 7 29 6 N SD: 4.3491 c. M:-6.4243 c. 56: 8 8 33 7 N SD: 3.9493 c. M:-6.4243 c. 58: 8 9 34 7 N SD: 3.6278 c. M:-5.8095 c. 65: 9 10 38 8 N SD: 2.3071 c. M:-3.3613 c. 72: 10 11 42 9 N SD: 1.5723 c. M:-2.5921 c. 79: 11 12 46 10 N SD: 1.5632 c. M:-2.0844 c. 80: 11 12 47 10 N SD: 1.2454 c. M: 2.4079 c. 145: 20 22 85 18 N SD: 0.8788 c. M:-1.6715 c. 152: 21 23 89 19 N SD: 0.5060 c. M:-0.7852 c. 255: 35 39 149 32 N SD: 0.4404 c. M:-0.8274 c. 262: 36 40 153 33 N SD: 0.4300 c. M:-0.6837 c. 263: 36 40 154 33 N SD: 0.4924 c. M: 0.7457 c. 270: 37 41 158 34 N SD: 0.5214 c. M: 0.7413 c. 311: 43 47 182 39 N SD: 0.4679 c. M:-0.9122 c. 328: 45 50 192 41 N SD: 0.3762 c. M:-0.6371 c. 335: 46 51 196 42 N SD: 0.1507 c. M: 0.2281 c. 342: 47 52 200 43 N SD: 0.1301 c. M: 0.2401 c. 494: 68 75 289 62 N SD: 0.0924 c. M:-0.1780 c. 677: 93 103 396 85 N SD: 0.0809 c. M: 0.1593 c. 829: 114 126 485 104 N SD: 0.0476 c. M:-0.0942 c. 836: 115 127 489 105 N SD: 0.0562 c. M: 0.0806 c. 1171: 161 178 685 147 N SD: 0.0107 c. M: 0.0170 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x x x 4 S SD: 0.0000 cents 3 x 4 x 6 S SD: 75.3185 cents 4 x 5:7:8 SD: 29.8140 cents 5 x 6:9:10 S SD: 14.9749 cents 6 x 7:11:12 SD: 26.8457 cents 8:9:10:15:16 S SD: 16.8467 cents 9:10:11:17:18 SD: 13.6332 cents 10:11:12:18:20 S SD: 11.2312 cents 13:14:16:24:26 S SD: 10.1194 cents 17:19:21:31:34 SD: 8.6044 cents 18:20:22:33:36 S SD: 4.3499 cents 30:33:37:55:60 SD: 3.9168 cents 31:34:38:57:62 SD: 2.1973 cents 41:45:50:75:82 SD: 1.6640 cents 49:54:60:90:98 SD: 1.3895 cents 59:65:72:108:118 SD: 1.1554 cents 72:79:88:132:144 SD: 1.0943 cents 89:98:109:163:178 SD: 1.0822 cents 90:99:110:165:180 S SD: 0.0000 cents