Scala analysis: 216_C14
Chromatic tetrachord 40/39 * 13/12 * 6/5, Barbour
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 40/39 43.831051 tridecimal minor diesis 2: 10/9 182.403712 minor whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 6/5 315.6413 minor third 1: 40/39 43.8311 tridecimal minor diesis 2: 13/12 138.5727 tridecimal 2/3-tone 3: 6/5 315.6413 minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 40/39 43.831 cents tridecimal minor diesis 1: 1 13/12 138.573 cents tridecimal 2/3-tone 1: 1 6/5 315.641 cents minor third 2: 1 10/9 182.404 cents minor whole tone 2: 1 16/13 359.472 cents tridecimal neutral third 2: 1 13/10 454.214 cents tridecimal semi-diminished fourth Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 43.8 182.4 498.0 43.8 : 138.6 454.2 498.0 182.4: 315.6 359.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 315.6413 cents 117/100, 271.8102 cents 40/39, 43.8311 cents 2: 182.4037 .. 454.2139 cents 117/100, 271.8102 cents 25/27,-133.2376 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 40/39, 43.8311 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 3.787612 Largest / Average step : 1.901282 Largest / Smallest step : 7.201317 Median interval of one step : 13/12, 138.5727 cents, amount: 1 Least squares average step : 135.91239 cents, oct.: 407.73717 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABC Step pattern size order : SML Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 43.83105 cents Scale diversity : 0.802420 Lumma stability : 0.176012 Lumma impropriety factor : 0.267521 Rothenberg efficiency : 0.666667 redundancy: 0.333333 Efficiency x scale size : 2.000000 Number of different interval sizes : 6 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 40/39, 43.8311 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 All steps are superparticular (epimoric) 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 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is differentially coherent in interval class 1 -- Rational properties -- Prime limit : 13 Odd number limit : 39 (O: 13 U: 39) Highest odd numerator or denominator: 39 Scale harmonicity : 0.027110 Average absolute harmonicity : 0.107347 Specific harmonicity : 0.135522 Fundamental : 1/117, -6.8704 octaves, 2.2361 Hz. Guide tone : 40, 5.3219 octaves, 10465.023 Hz. Exponens Consonantiae : 4.680000E+03, 12.19229 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 52.5, average 17.50000 Mersenne's string divisions : 10507 Sum of van Prooijen's expressibility: 3.02243, average 1.00748 Sum of Tenney's harmonic distance : 6.22655, average 2.07552 Vogel's harmonic complexity : 16.00000 Wille's k value : 32 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 4 Triangular lattice diameter : 1 Lattice compactness : 14.06325, average 2.34388 Lattice compactness (without 2's) : 9.21076, average 1.53513 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 3 2.00000 6 3: -2 ..-1 -1.33333 4 1 5: 0 .. 1 0.66667 2 1 13: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 17 27| Scale is weakly epimorphic with val: <6 10 17 30| Scale is weakly epimorphic with val: <6 11 19 27| Scale is weakly epimorphic with val: <6 11 19 30| Scale is weakly epimorphic with val: <7 10 16 25| Scale is weakly epimorphic with val: <7 10 16 28| Scale is weakly epimorphic with val: <7 10 18 26| Scale is weakly epimorphic with val: <7 11 16 27| Scale is weakly epimorphic with val: <7 11 16 30| Scale is JI-epimorphic with val: <7 11 17 26| Scale is weakly epimorphic with val: <7 11 17 29| Scale is weakly epimorphic with val: <7 11 19 27| Scale is weakly epimorphic with val: <7 11 19 30| Scale is weakly epimorphic with val: <8 11 15 25| Scale is weakly epimorphic with val: <8 11 17 26| Scale is weakly epimorphic with val: <8 11 17 29| Scale is weakly epimorphic with val: <8 11 18 28| Scale is weakly epimorphic with val: <8 12 18 27| Scale is weakly epimorphic with val: <8 12 19 26| Scale is weakly epimorphic with val: <8 12 19 29|
FIT/MODE
3: 0 1 2 N G T3 SD: 27.0170 c. M: 43.8311 c. 8: 1 2 5 N T3 SD: 10.9316 c. M:-18.4246 c. 9: 1 2 6 N T3 SD: 11.5615 c. M: 16.3887 c. 10: 1 3 6 N T3 SD: 10.3021 c. M:-16.8143 c. 11: 1 3 7 N T3 SD: 1.1212 c. M:-1.4458 c. 46: 4 13 29 N T3 SD: 1.0028 c. M:-1.6564 c. 57: 5 16 36 N T3 SD: 0.6327 c. M:-1.0866 c. 68: 6 19 43 N T3 SD: 0.4101 c. M:-0.7011 c. 79: 7 22 50 N T3 SD: 0.2992 c. M:-0.4229 c. 90: 8 25 57 N T3 SD: 0.2820 c. M:-0.4396 c. 169: 15 47 107 N T3 SD: 0.2809 c. M:-0.3741 c. 172: 15 48 109 N T3 SD: 0.2294 c. M: 0.3969 c. 183: 16 51 116 N T3 SD: 0.1687 c. M: 0.2861 c. 194: 17 54 123 N T3 SD: 0.1318 c. M: 0.1879 c. 205: 18 57 130 N T3 SD: 0.1251 c. M: 0.1921 c. 251: 22 70 159 N T3 SD: 0.1330 c. M: 0.1777 c. 262: 23 73 166 N T3 SD: 0.0804 c. M: 0.1095 c. 273: 24 76 173 N T3 SD: 0.0322 c. M: 0.0469 c. 284: 25 79 180 N T3 SD: 0.0137 c. M: 0.0210 c. 557: 49 155 353 N T3 SD: 0.0103 c. M: 0.0174 c. 841: 74 234 533 N T3 SD: 0.0052 c. M: 0.0078 c. 1966: 173 547 1246 N T3 SD: 0.0049 c. M: 0.0068 c.
FIT/HARMONIC
1 x x 2 S SD: 701.9550 cents 2 x x 3 S SD: 203.9100 cents 3 x x 4 S SD: 0.0000 cents 4 x x 5 S SD: 111.7313 cents 5 x 6:7 S SD: 78.8780 cents 6 x 7:8 S SD: 42.2336 cents 7 x 8:9 S SD: 39.8203 cents 8 x 9:11 SD: 28.7251 cents 9 x 10:12 S SD: 0.0000 cents 10 x 11:13 SD: 23.5791 cents 11 x 12:15 S SD: 25.1136 cents 12 x 13:16 SD: 21.9155 cents 13 x 14:17 SD: 31.8493 cents 14 x 16:19 SD: 28.7988 cents 15:16:17:20 SD: 25.3547 cents 16:17:18:21 S SD: 23.4332 cents 17:18:19:23 SD: 20.4952 cents 18:19:20:24 S SD: 16.5907 cents 20:21:22:27 SD: 16.3862 cents 21:22:23:28 SD: 14.7868 cents 24:25:27:32 SD: 11.4648 cents 25:26:28:33 SD: 10.9157 cents 26:27:29:35 SD: 9.3164 cents 27:28:30:36 S SD: 6.3766 cents 33:34:37:44 SD: 5.8415 cents 34:35:38:45 SD: 5.8377 cents 35:36:39:47 SD: 4.7214 cents 36:37:40:48 SD: 1.2010 cents 81:83:90:108 SD: 0.5346 cents 117:120:130:156 S SD: 0.0000 cents