Scala analysis: 275_C19
Chromatic tetrachord 66/65 * 10/9 * 13/11, Wilson
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 66/65 26.431568 Winmeanma 2: 44/39 208.835280 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 13/11 289.2097 tridecimal minor third 1: 66/65 26.4316 Winmeanma 2: 10/9 182.4037 minor whole tone 3: 13/11 289.2097 tridecimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 66/65 26.432 cents Winmeanma 1: 1 10/9 182.404 cents minor whole tone 1: 1 13/11 289.210 cents tridecimal minor third 2: 1 44/39 208.835 cents 2: 1 6/5 315.641 cents minor third 2: 1 130/99 471.613 cents 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 : 26.4 208.8 498.0 26.4 : 182.4 471.6 498.0 208.8: 289.2 315.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 26.4316 .. 289.2097 cents 845/726, 262.7782 cents 66/65, 26.4316 cents 2: 208.8353 .. 471.6134 cents 845/726, 262.7782 cents 484/507,-80.3744 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 66/65, 26.4316 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 13/11, 289.2097 cents Average / Smallest step : 6.280937 Largest / Average step : 1.742070 Largest / Smallest step : 10.941830 Median interval of one step : 10/9, 182.4037 cents, amount: 1 Least squares average step : 138.44551 cents, oct.: 415.33653 cents Scale is not proper Scale has trivalence property Scale is a mode of a 942-tone equal temperament with octave 4/3 degrees: 50 395 942 Least number of segments generator : 473 of 250.080 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 799 of 422.439 cents and inv. generated superset size: 27 = 24 more = 900.000% 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 26.43157 cents Scale diversity : 0.606588 Lumma stability : 0.106141 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 : 66/65, 26.4316 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% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 13 Odd number limit : 99 (O: 65 U: 99) Highest odd numerator or denominator: 65 Scale harmonicity : 0.018495 Average absolute harmonicity : 0.085449 Specific harmonicity : 0.077591 Fundamental : 1/195, -7.6073 octaves, 1.3417 Hz. Guide tone : 132, 7.0444 octaves, 34534.575 Hz. Exponens Consonantiae : 2.574000E+04, 14.65172 octaves Euler's gradus suavitatis : 33 Sum of Mann's harmonic distance : 110.5, average 36.83333 Mersenne's string divisions : 76111 Sum of van Prooijen's expressibility: 3.88110, average 1.29370 Sum of Tenney's harmonic distance : 7.94616, average 2.64872 Vogel's harmonic complexity : 18.66667 Wille's k value : 49 Wilson's harmonic complexity : 35 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 13.81002, average 2.30167 Lattice compactness (without 2's) : 11.02808, average 1.83801 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -1 .. 1 -0.33333 3 1 5: -1 .. 0 -0.33333 1 11: 0 .. 1 0.66667 2 13: -1 .. 0 -0.66667 2 2 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <7 10 17 24 25| Scale is weakly epimorphic with val: <7 10 17 25 26| Scale is weakly epimorphic with val: <7 10 17 26 27| Scale is weakly epimorphic with val: <7 10 17 27 28| Scale is weakly epimorphic with val: <7 11 16 23 27| Scale is weakly epimorphic with val: <7 11 16 23 30| Scale is JI-epimorphic with val: <7 11 16 24 25| Scale is weakly epimorphic with val: <7 11 16 24 28| Scale is JI-epimorphic with val: <7 11 16 25 26| Scale is weakly epimorphic with val: <7 11 16 25 29| Scale is JI-epimorphic with val: <7 11 16 26 27| Scale is weakly epimorphic with val: <7 11 16 26 30| Scale is JI-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 weakly epimorphic with val: <7 11 17 24 26| Scale is weakly epimorphic with val: <7 11 17 24 29| Scale is weakly epimorphic with val: <7 11 17 25 27| = patent Scale is weakly epimorphic with val: <7 11 17 25 30| Scale is weakly epimorphic with val: <7 11 17 26 28| Scale is weakly epimorphic with val: <7 11 17 27 29| Scale is weakly epimorphic with val: <7 11 19 23 27| Scale is weakly epimorphic with val: <7 11 19 23 30| 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 26| Scale is weakly epimorphic with val: <7 11 19 25 29| Scale is weakly epimorphic with val: <7 11 19 26 27| Scale is weakly epimorphic with val: <7 11 19 26 30| Scale is weakly epimorphic with val: <7 11 19 27 28| Scale is weakly epimorphic with val: <7 12 15 24 25| Scale is weakly epimorphic with val: <7 12 15 25 26| Scale is weakly epimorphic with val: <7 12 15 26 27| Scale is weakly epimorphic with val: <7 12 15 27 28| Scale is weakly epimorphic with val: <8 11 15 24 25| Scale is weakly epimorphic with val: <8 11 15 25 26| Scale is weakly epimorphic with val: <8 11 15 26 27| Scale is weakly epimorphic with val: <8 11 15 27 28| Scale is weakly epimorphic with val: <8 11 16 23 25| Scale is weakly epimorphic with val: <8 11 16 24 26| Scale is weakly epimorphic with val: <8 11 16 25 27| Scale is weakly epimorphic with val: <8 11 16 26 28| Scale is weakly epimorphic with val: <8 11 16 27 29| Scale is weakly epimorphic with val: <8 11 19 23 25| Scale is weakly epimorphic with val: <8 11 19 24 26| Scale is weakly epimorphic with val: <8 11 19 25 27| Scale is weakly epimorphic with val: <8 11 19 26 28| Scale is weakly epimorphic with val: <8 11 19 27 29| Scale is weakly epimorphic with val: <8 12 15 23 25| Scale is weakly epimorphic with val: <8 12 15 24 26| Scale is weakly epimorphic with val: <8 12 15 25 27| Scale is weakly epimorphic with val: <8 12 15 26 28| Scale is weakly epimorphic with val: <8 12 15 27 29| Scale is weakly epimorphic with val: <8 12 17 24 25| Scale is weakly epimorphic with val: <8 12 17 25 26| Scale is weakly epimorphic with val: <8 12 17 26 27| Scale is weakly epimorphic with val: <8 12 17 27 28|
FIT/MODE
3: 0 1 2 N G T3 SD: 29.0528 c. M: 42.8203 c. 4: 0 2 2 P M DE S SD: 27.7707 c. M:-40.1872 c. 5: 0 2 3 N G T3 SD: 16.2390 c. M: 26.4316 c. 7: 0 3 4 N G T3 SD: 15.4909 c. M: 26.4316 c. 12: 1 4 7 N T3 SD: 8.7351 c. M:-15.0722 c. 14: 1 5 8 N T3 SD: 5.9125 c. M:-9.1431 c. 16: 1 6 9 N T3 SD: 5.8915 c. M:-9.0594 c. 17: 1 6 10 N T3 SD: 2.7283 c. M: 3.7579 c. 19: 1 7 11 N T3 SD: 0.5167 c. M:-0.8679 c. 55: 3 20 32 N T3 SD: 0.5339 c. M:-0.7345 c. 74: 4 27 43 N T3 SD: 0.3043 c. M:-0.4898 c. 93: 5 34 54 N T3 SD: 0.1996 c. M:-0.3450 c. 112: 6 41 65 N T3 SD: 0.1729 c. M:-0.2494 c. 243: 13 89 141 N T3 SD: 0.1770 c. M:-0.2206 c. 265: 14 97 154 N T3 SD: 0.1447 c. M: 0.2202 c. 284: 15 104 165 N T3 SD: 0.1121 c. M: 0.1474 c. 303: 16 111 176 N T3 SD: 0.0903 c. M: 0.1322 c. 322: 17 118 187 N T3 SD: 0.0808 c. M: 0.1373 c. 377: 20 138 219 N T3 SD: 0.0612 c. M: 0.1055 c. 396: 21 145 230 N T3 SD: 0.0359 c. M: 0.0588 c. 415: 22 152 241 N T3 SD: 0.0193 c. M: 0.0292 c. 923: 49 338 536 N T3 SD: 0.0087 c. M: 0.0125 c. 942: 50 345 547 N T3 SD: 0.0038 c. M:-0.0052 c. 1357: 72 497 788 N T3 SD: 0.0037 c. M: 0.0062 c. 2280: 121 835 1324 N T3 SD: 0.0034 c. M: 0.0059 c. 2299: 122 842 1335 N T3 SD: 0.0014 c. M: 0.0020 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 14 x 16:19 SD: 18.9602 cents 22:23:25:29 SD: 18.5587 cents 23:24:26:31 SD: 16.9786 cents 24:25:27:32 SD: 14.8381 cents 28:29:32:37 SD: 14.5981 cents 29:30:33:39 SD: 12.8339 cents 30:31:34:40 SD: 10.4450 cents 32:33:36:43 SD: 10.1447 cents 33:34:37:44 SD: 9.1498 cents 36:37:41:48 SD: 8.8654 cents 37:38:42:49 SD: 8.4309 cents 38:39:43:51 SD: 7.4480 cents 39:40:44:52 SD: 5.7998 cents 45:46:51:60 SD: 4.6744 cents 47:48:53:63 SD: 4.5386 cents 48:49:54:64 SD: 3.4977 cents 54:55:61:72 SD: 1.9217 cents 63:64:71:84 SD: 0.6837 cents 132:134:149:176 SD: 0.3261 cents 195:198:220:260 SD: 0.0000 cents