Scala analysis: 236_C15
Chromatic tetrachord 40/39 * 273/250 * 25/21
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: 28/25 196.198479 middle second 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 25/21 301.8465 BP second, quasi-equal minor third 1: 40/39 43.8311 tridecimal minor diesis 2: 273/250 152.3674 3: 25/21 301.8465 BP second, quasi-equal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 40/39 43.831 cents tridecimal minor diesis 1: 1 273/250 152.367 cents 1: 1 25/21 301.847 cents BP second, quasi-equal minor third 2: 1 28/25 196.198 cents middle second 2: 1 1000/819 345.678 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 : 43.8 196.2 498.0 43.8 : 152.4 454.2 498.0 196.2: 301.8 345.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 301.8465 cents 65/56, 258.0155 cents 40/39, 43.8311 cents 2: 196.1985 .. 454.2139 cents 65/56, 258.0155 cents 588/625,-105.6480 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 : 25/21, 301.8465 cents Average / Smallest step : 3.787612 Largest / Average step : 1.818188 Largest / Smallest step : 6.886591 Median interval of one step : 273/250, 152.3674 cents, amount: 1 Least squares average step : 137.88307 cents, oct.: 413.64922 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1716-tone equal temperament with octave 4/3 degrees: 151 676 1716 Least number of segments generator : 859 of 249.313 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1109 of 321.872 cents and inv. generated superset size: 53 = 50 more = 1766.667% Number of contiguous 1-step segments: 0 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 : 0.811167 Lumma stability : 0.176012 Lumma impropriety factor : 0.212125 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 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% -- Rational properties -- Prime limit : 13 Odd number limit : 819 (O: 273 U: 819) Highest odd numerator or denominator: 39 Scale harmonicity : 0.017450 Average absolute harmonicity : 0.094457 Specific harmonicity : 0.091645 Fundamental : 1/975, -9.9293 octaves, 0.2683 Hz. Guide tone : 280, 8.1293 octaves, 73255.158 Hz. Exponens Consonantiae : 2.730000E+05, 18.05854 octaves Euler's gradus suavitatis : 36 Sum of Mann's harmonic distance : 69.5, average 23.16667 Mersenne's string divisions : 29309 Sum of van Prooijen's expressibility: 3.46613, average 1.15538 Sum of Tenney's harmonic distance : 7.11740, average 2.37247 Vogel's harmonic complexity : 22.66667 Wille's k value : 162 Wilson's harmonic complexity : 38 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 16.48726, average 2.74788 Lattice compactness (without 2's) : 12.29592, average 2.04932 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -1 .. 0 -0.66667 2 1 5: -2 .. 1 -0.33333 3 7: 0 .. 1 0.33333 1 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 15 21 25| Scale is weakly epimorphic with val: <6 10 15 21 28| Scale is weakly epimorphic with val: <6 11 15 21 26| Scale is weakly epimorphic with val: <6 11 15 21 29| Scale is weakly epimorphic with val: <7 10 15 19 27| Scale is weakly epimorphic with val: <7 10 15 19 30| Scale is weakly epimorphic with val: <7 10 16 21 25| Scale is weakly epimorphic with val: <7 10 16 21 28| Scale is weakly epimorphic with val: <7 10 17 19 25| Scale is weakly epimorphic with val: <7 10 17 22 25| Scale is weakly epimorphic with val: <7 10 18 18 26| Scale is weakly epimorphic with val: <7 10 18 21 26| Scale is weakly epimorphic with val: <7 10 19 20 27| Scale is weakly epimorphic with val: <7 11 15 18 27| Scale is weakly epimorphic with val: <7 11 15 18 30| Scale is weakly epimorphic with val: <7 11 15 20 26| Scale is weakly epimorphic with val: <7 11 15 20 29| Scale is weakly epimorphic with val: <7 11 15 21 27| Scale is weakly epimorphic with val: <7 11 15 21 30| Scale is weakly epimorphic with val: <7 11 16 19 27| Scale is weakly epimorphic with val: <7 11 16 19 30| Scale is JI-epimorphic with val: <7 11 16 20 25| Scale is weakly epimorphic with val: <7 11 16 20 28| Scale is weakly epimorphic with val: <7 11 16 22 27| Scale is weakly epimorphic with val: <7 11 16 22 30| Scale is weakly epimorphic with val: <7 11 17 18 25| Scale is weakly epimorphic with val: <7 11 17 18 28| Scale is weakly epimorphic with val: <7 11 17 19 26| Scale is weakly epimorphic with val: <7 11 17 19 29| Scale is weakly epimorphic with val: <7 11 17 21 25| Scale is weakly epimorphic with val: <7 11 17 21 28| Scale is JI-epimorphic with val: <7 11 17 22 26| Scale is weakly epimorphic with val: <7 11 17 22 29| Scale is weakly epimorphic with val: <7 11 18 18 27| Scale is weakly epimorphic with val: <7 11 18 18 30| Scale is weakly epimorphic with val: <7 11 18 20 26| Scale is weakly epimorphic with val: <7 11 18 20 29| Scale is weakly epimorphic with val: <7 11 18 21 27| Scale is weakly epimorphic with val: <7 11 18 21 30| Scale is weakly epimorphic with val: <7 11 19 19 27| Scale is weakly epimorphic with val: <7 11 19 19 30| Scale is weakly epimorphic with val: <7 11 19 20 25| Scale is weakly epimorphic with val: <7 11 19 20 28| Scale is weakly epimorphic with val: <7 11 19 22 27| Scale is weakly epimorphic with val: <7 11 19 22 30| Scale is weakly epimorphic with val: <7 12 15 19 26| Scale is weakly epimorphic with val: <7 12 15 19 29| Scale is weakly epimorphic with val: <7 12 16 21 27| Scale is weakly epimorphic with val: <7 12 16 21 30| Scale is weakly epimorphic with val: <7 12 19 19 25| Scale is weakly epimorphic with val: <7 12 19 22 25| Scale is weakly epimorphic with val: <8 11 15 18 25| Scale is weakly epimorphic with val: <8 11 15 21 25| Scale is weakly epimorphic with val: <8 11 16 19 25| Scale is weakly epimorphic with val: <8 11 16 19 28| Scale is weakly epimorphic with val: <8 11 16 20 26| Scale is weakly epimorphic with val: <8 11 17 19 27| Scale is weakly epimorphic with val: <8 11 17 21 26| Scale is weakly epimorphic with val: <8 11 17 21 29| Scale is weakly epimorphic with val: <8 11 17 22 27| Scale is weakly epimorphic with val: <8 11 18 18 28| Scale is weakly epimorphic with val: <8 11 18 21 28| Scale is weakly epimorphic with val: <8 11 19 20 29| Scale is weakly epimorphic with val: <8 12 16 18 25| Scale is weakly epimorphic with val: <8 12 16 19 26| Scale is weakly epimorphic with val: <8 12 16 19 29| Scale is weakly epimorphic with val: <8 12 16 21 25| Scale is weakly epimorphic with val: <8 12 17 20 26| Scale is weakly epimorphic with val: <8 12 17 21 27| Scale is weakly epimorphic with val: <8 12 17 21 30| Scale is weakly epimorphic with val: <8 12 18 19 27| Scale is weakly epimorphic with val: <8 12 18 22 27| Scale is weakly epimorphic with val: <8 12 19 21 28|
FIT/MODE
3: 0 1 2 N G T3 SD: 30.7257 c. M: 43.8311 c. 5: 0 2 3 N G T3 SD: 25.3658 c. M: 43.8311 c. 7: 1 2 4 N T3 SD: 18.6532 c. M:-27.3182 c. 8: 1 2 5 N T3 SD: 11.9502 c. M:-18.4246 c. 10: 1 3 6 N T3 SD: 3.8643 c. M:-5.9734 c. 13: 1 4 8 N T3 SD: 4.1643 c. M: 5.5199 c. 23: 2 7 14 N T3 SD: 0.8150 c. M: 1.3113 c. 56: 5 17 34 N T3 SD: 0.4815 c. M:-0.6373 c. 79: 7 24 48 N T3 SD: 0.4733 c. M: 0.7631 c. 91: 8 28 55 N T3 SD: 0.4801 c. M:-0.8303 c. 104: 9 32 63 N T3 SD: 0.4304 c. M: 0.7310 c. 114: 10 35 69 N T3 SD: 0.2443 c. M:-0.3982 c. 137: 12 42 83 N T3 SD: 0.1355 c. M: 0.2067 c. 160: 14 49 97 N T3 SD: 0.1552 c. M: 0.2521 c. 170: 15 52 103 N T3 SD: 0.0838 c. M:-0.1141 c. 193: 17 59 117 N T3 SD: 0.0497 c. M: 0.0771 c. 330: 29 101 200 N T3 SD: 0.0366 c. M: 0.0635 c. 500: 44 153 303 N T3 SD: 0.0181 c. M:-0.0313 c. 523: 46 160 317 N T3 SD: 0.0220 c. M: 0.0278 c. 693: 61 212 420 N T3 SD: 0.0049 c. M:-0.0084 c. 1716: 151 525 1040 N T3 SD: 0.0032 c. M: 0.0054 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: 73.1459 cents 6 x 7:8 S SD: 35.3362 cents 7 x 8:9 S SD: 36.0117 cents 8 x 9:11 SD: 26.9141 cents 9 x 10:12 S SD: 6.8974 cents 10 x 11:13 SD: 26.8991 cents 11 x 12:15 S SD: 29.9562 cents 12 x 13:16 SD: 28.8129 cents 13 x 15:17 SD: 30.7683 cents 14:15:16:19 SD: 29.5886 cents 15:16:17:20 SD: 23.6413 cents 16:17:18:21 S SD: 22.4573 cents 17:18:19:23 SD: 20.2502 cents 18:19:20:24 S SD: 17.2161 cents 21:22:24:28 S SD: 16.9004 cents 22:23:25:29 SD: 15.3454 cents 23:24:26:31 SD: 12.9059 cents 24:25:27:32 SD: 9.3091 cents 27:28:30:36 S SD: 7.8616 cents 31:32:35:41 SD: 7.5559 cents 32:33:36:43 SD: 6.0565 cents 33:34:37:44 SD: 2.6905 cents 42:43:47:56 SD: 1.1423 cents 75:77:84:100 SD: 0.5768 cents 117:120:131:156 SD: 0.1762 cents 507:520:568:676 SD: 0.1626 cents 549:563:615:732 SD: 0.1375 cents