Scala analysis: 274_C19
Chromatic tetrachord 40/39 * 11/10 * 13/11
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: 44/39 208.835280 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 13/11 289.2097 tridecimal minor third 1: 40/39 43.8311 tridecimal minor diesis 2: 11/10 165.0042 Ptolemy's second, 4/5-tone 3: 13/11 289.2097 tridecimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 40/39 43.831 cents tridecimal minor diesis 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 13/11 289.210 cents tridecimal minor third 2: 1 44/39 208.835 cents 2: 1 40/33 333.041 cents 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 : 43.8 208.8 498.0 43.8 : 165.0 454.2 498.0 208.8: 289.2 333.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 289.2097 cents 507/440, 245.3787 cents 40/39, 43.8311 cents 2: 208.8353 .. 454.2139 cents 507/440, 245.3787 cents 484/507,-80.3744 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 : 13/11, 289.2097 cents Average / Smallest step : 3.787612 Largest / Average step : 1.742070 Largest / Smallest step : 6.598284 Median interval of one step : 11/10, 165.0042 cents, amount: 1 Least squares average step : 139.68833 cents, oct.: 419.06499 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 : 0.801342 Lumma stability : 0.176012 Lumma impropriety factor : 0.161380 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 Best minor thirds form a closed circle 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 n-1 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 : 0.019083 Average absolute harmonicity : 0.088576 Specific harmonicity : 0.089205 Fundamental : 1/39, -5.2854 octaves, 6.7083 Hz. Guide tone : 440, 8.7814 octaves, 115115.249 Hz. Exponens Consonantiae : 1.716000E+04, 14.06676 octaves Euler's gradus suavitatis : 32 Sum of Mann's harmonic distance : 84.5, average 28.16667 Mersenne's string divisions : 45899 Sum of van Prooijen's expressibility: 3.65925, average 1.21975 Sum of Tenney's harmonic distance : 7.50682, average 2.50227 Vogel's harmonic complexity : 12.00000 Wille's k value : 6 Wilson's harmonic complexity : 32 Rectangular lattice diameter : 4 Triangular lattice diameter : 1 Lattice compactness : 13.22424, average 2.20404 Lattice compactness (without 2's) : 8.70674, average 1.45112 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -1 ..-1 -1.00000 3 1 5: 0 .. 1 0.33333 1 11: 0 .. 1 0.33333 1 13: -1 .. 0 -0.66667 2 2 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: <7 10 15 26 27| Scale is weakly epimorphic with val: <7 10 16 24 25| Scale is weakly epimorphic with val: <7 10 16 27 28| Scale is weakly epimorphic with val: <7 10 17 23 25| Scale is weakly epimorphic with val: <7 10 17 25 26| Scale is weakly epimorphic with val: <7 10 18 24 26| Scale is weakly epimorphic with val: <7 10 18 26 27| Scale is weakly epimorphic with val: <7 10 19 24 25| Scale is weakly epimorphic with val: <7 10 19 25 27| Scale is weakly epimorphic with val: <7 10 19 27 28| Scale is weakly epimorphic with val: <7 11 15 23 27| Scale is weakly epimorphic with val: <7 11 15 23 30| Scale is weakly epimorphic with val: <7 11 15 24 26| Scale is weakly epimorphic with val: <7 11 15 24 29| Scale is weakly epimorphic with val: <7 11 15 26 27| Scale is weakly epimorphic with val: <7 11 15 26 30| Scale is weakly epimorphic with val: <7 11 15 27 29| Scale is JI-epimorphic with val: <7 11 16 24 25| Scale is weakly epimorphic with val: <7 11 16 24 28| Scale is weakly epimorphic with val: <7 11 16 25 27| Scale is weakly epimorphic with val: <7 11 16 25 30| Scale is weakly epimorphic with val: <7 11 16 27 28| Scale is weakly epimorphic with val: <7 11 17 23 25| Scale is weakly epimorphic with val: <7 11 17 23 28| Scale is JI-epimorphic with val: <7 11 17 25 26| Scale is weakly epimorphic with val: <7 11 17 25 29| Scale is weakly epimorphic with val: <7 11 17 26 28| Scale is weakly epimorphic with val: <7 11 18 23 27| Scale is weakly epimorphic with val: <7 11 18 23 30| Scale is weakly epimorphic with val: <7 11 18 24 26| Scale is weakly epimorphic with val: <7 11 18 24 29| Scale is JI-epimorphic with val: <7 11 18 26 27| Scale is weakly epimorphic with val: <7 11 18 26 30| Scale is weakly epimorphic with val: <7 11 18 27 29| Scale is weakly epimorphic with val: <7 11 19 24 25| Scale is weakly epimorphic with val: <7 11 19 24 28| Scale is weakly epimorphic with val: <7 11 19 25 27| Scale is weakly epimorphic with val: <7 11 19 25 30| Scale is JI-epimorphic with val: <7 11 19 27 28| Scale is weakly epimorphic with val: <7 12 19 24 25| Scale is weakly epimorphic with val: <8 11 15 24 25| Scale is weakly epimorphic with val: <8 11 15 25 27| Scale is weakly epimorphic with val: <8 11 16 23 25| Scale is weakly epimorphic with val: <8 11 16 25 26| Scale is weakly epimorphic with val: <8 11 16 26 28| Scale is weakly epimorphic with val: <8 11 17 23 27| Scale is weakly epimorphic with val: <8 11 17 24 26| Scale is weakly epimorphic with val: <8 11 17 26 27| Scale is weakly epimorphic with val: <8 11 17 27 29| Scale is weakly epimorphic with val: <8 11 18 24 28| Scale is weakly epimorphic with val: <8 11 18 25 27| Scale is weakly epimorphic with val: <8 11 18 27 28| Scale is weakly epimorphic with val: <8 11 19 23 25| Scale is weakly epimorphic with val: <8 11 19 25 29| Scale is weakly epimorphic with val: <8 11 19 26 28| Scale is weakly epimorphic with val: <8 12 15 24 25| Scale is weakly epimorphic with val: <8 12 15 27 28| Scale is weakly epimorphic with val: <8 12 16 23 25| Scale is weakly epimorphic with val: <8 12 16 25 26| Scale is weakly epimorphic with val: <8 12 17 24 26| Scale is weakly epimorphic with val: <8 12 17 26 27| Scale is weakly epimorphic with val: <8 12 18 24 25| Scale is weakly epimorphic with val: <8 12 18 25 27| Scale is weakly epimorphic with val: <8 12 18 27 28| Scale is weakly epimorphic with val: <8 12 19 23 28| Scale is weakly epimorphic with val: <8 12 19 25 26| Scale is weakly epimorphic with val: <8 12 19 26 28|
FIT/MODE
3: 0 1 2 N G T3 SD: 35.3777 c. M: 43.8311 c. 4: 0 2 2 P M DE S SD: 34.3326 c. M: 43.8311 c. 5: 0 2 3 N G T3 SD: 25.9079 c. M: 43.8311 c. 7: 1 2 4 N T3 SD: 15.9954 c. M:-27.3182 c. 8: 1 2 5 N T3 SD: 16.5980 c. M: 22.0684 c. 9: 1 3 5 N T3 SD: 9.8170 c. M:-12.5181 c. 10: 1 3 6 N T3 SD: 6.5364 c. M: 9.6173 c. 12: 1 4 7 N T3 SD: 1.5438 c. M: 2.3273 c. 43: 4 14 25 N T3 SD: 1.4568 c. M:-2.4987 c. 45: 4 15 26 N T3 SD: 0.8750 c. M:-1.4504 c. 55: 5 18 32 N T3 SD: 0.8955 c. M:-1.4458 c. 57: 5 19 33 N T3 SD: 0.5078 c. M:-0.8679 c. 67: 6 22 39 N T3 SD: 0.5997 c. M:-0.7700 c. 69: 6 23 40 N T3 SD: 0.4129 c. M: 0.5228 c. 112: 10 37 65 N T3 SD: 0.3802 c. M:-0.6373 c. 124: 11 41 72 N T3 SD: 0.2027 c. M:-0.3504 c. 136: 12 45 79 N T3 SD: 0.0860 c. M:-0.1141 c. 205: 18 68 119 N T3 SD: 0.0820 c. M:-0.1007 c. 284: 25 94 165 N T3 SD: 0.0853 c. M: 0.1474 c. 329: 29 109 191 N T3 SD: 0.0574 c. M:-0.0711 c. 341: 30 113 198 N T3 SD: 0.0154 c. M:-0.0223 c. 477: 42 158 277 N T3 SD: 0.0143 c. M:-0.0220 c. 818: 72 271 475 N T3 SD: 0.0041 c. M:-0.0067 c. 1977: 174 655 1148 N T3 SD: 0.0039 c. M:-0.0060 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: 68.0849 cents 6 x 7:8 S SD: 29.0178 cents 7 x 8:9 S SD: 33.4032 cents 8 x 9:11 SD: 26.7501 cents 9 x 10:12 S SD: 13.2158 cents 10 x 11:13 SD: 30.9932 cents 11 x 12:15 S SD: 35.0025 cents 12 x 14:16 S SD: 29.0178 cents 13 x 15:17 SD: 25.7088 cents 15:16:17:20 SD: 22.7842 cents 16:17:18:21 S SD: 22.3701 cents 17:18:19:23 SD: 20.9294 cents 18:19:20:24 S SD: 18.7850 cents 21:22:24:28 S SD: 14.3231 cents 22:23:25:29 SD: 13.5169 cents 23:24:26:31 SD: 11.7991 cents 24:25:27:32 SD: 9.0965 cents 29:30:33:39 SD: 8.5797 cents 30:31:34:40 SD: 5.0440 cents 33:34:37:44 SD: 4.4411 cents 38:39:43:51 SD: 4.1753 cents 39:40:44:52 SD: 0.0000 cents