Scala analysis: 202_C11
Chromatic tetrachord 17/14 * 56/53 * 53/51
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 17/14 336.129503 supraminor third 2: 68/53 431.450864 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 53/51 66.5941 1: 17/14 336.1295 supraminor third 2: 56/53 95.3214 3: 53/51 66.5941
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 53/51 66.594 cents 1: 1 56/53 95.321 cents 1: 1 17/14 336.130 cents supraminor third 2: 1 56/51 161.915 cents 2: 1 53/42 402.724 cents 2: 1 68/53 431.451 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 : 336.1 431.5 498.0 336.1: 95.3 161.9 498.0 431.5: 66.6 402.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 66.5941 .. 336.1295 cents 867/742, 269.5354 cents 53/51, 66.5941 cents 2: 161.9155 .. 431.4509 cents 867/742, 269.5354 cents 784/867,-174.2140 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 53/51, 66.5941 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 17/14, 336.1295 cents Average / Smallest step : 2.492937 Largest / Average step : 2.024694 Largest / Smallest step : 5.047434 Median interval of one step : 56/53, 95.3214 cents, amount: 1 Least squares average step : 192.36902 cents, oct.: 577.10705 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1092-tone equal temperament with octave 4/3 degrees: 737 946 1092 Least number of segments generator : 547 of 249.479 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 779 of 355.290 cents and inv. generated superset size: 54 = 51 more = 1800.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : LMS Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 66.59414 cents Scale diversity : 0.865825 Lumma stability : 0.267422 Lumma impropriety factor : 0.349796 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 : 2856/2809, 28.7272 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly decreasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 53 Odd number limit : 53 (O: 53 U: 53) Highest odd numerator or denominator: 53 Scale harmonicity : 0.021706 Fundamental : 1/2226, -11.1202 octaves, 0.1175 Hz. Guide tone : 68, 6.0875 octaves, 17790.538 Hz. Exponens Consonantiae : 1.513680E+05, 17.20770 octaves Euler's gradus suavitatis : 80 Sum of Mann's harmonic distance : 79.5, average 26.50000 Mersenne's string divisions : 26257 Sum of van Prooijen's expressibility: 3.43185, average 1.14395 Sum of Tenney's harmonic distance : 7.01254, average 2.33751 Vogel's harmonic complexity : 55.33333 Wille's k value : 1351 Wilson's harmonic complexity : 80 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 14.24478, average 2.37413 Lattice compactness (without 2's) : 7.56048, average 1.26008 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 1.00000 5 3: -1 .. 0 -0.33333 1 1 7: -1 .. 0 -0.33333 1 17: 0 .. 1 0.66667 2 1 53: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <6 10 18 27 41| Scale is weakly epimorphic with val: <6 10 18 31 40| Scale is weakly epimorphic with val: <6 10 19 28 42| Scale is weakly epimorphic with val: <6 10 19 32 41| Scale is weakly epimorphic with val: <6 10 20 29 40| Scale is weakly epimorphic with val: <6 10 20 33 42| Scale is weakly epimorphic with val: <6 10 21 30 41| Scale is weakly epimorphic with val: <6 10 21 31 40| Scale is weakly epimorphic with val: <6 10 22 31 42| Scale is weakly epimorphic with val: <6 10 22 32 41| Scale is weakly epimorphic with val: <6 11 18 27 40| Scale is weakly epimorphic with val: <6 11 18 32 41| Scale is weakly epimorphic with val: <6 11 19 28 41| Scale is weakly epimorphic with val: <6 11 19 33 42| Scale is weakly epimorphic with val: <6 11 20 29 42| Scale is weakly epimorphic with val: <6 11 20 31 40| Scale is weakly epimorphic with val: <6 11 21 30 40| Scale is weakly epimorphic with val: <6 11 21 32 41| Scale is weakly epimorphic with val: <6 11 22 31 41| Scale is weakly epimorphic with val: <6 11 22 33 42| Scale is weakly epimorphic with val: <7 10 18 28 40| Scale is weakly epimorphic with val: <7 10 18 30 41| Scale is weakly epimorphic with val: <7 10 19 29 41| Scale is weakly epimorphic with val: <7 10 19 31 42| Scale is weakly epimorphic with val: <7 10 20 29 40| Scale is weakly epimorphic with val: <7 10 20 30 42| Scale is weakly epimorphic with val: <7 10 21 30 41| Scale is weakly epimorphic with val: <7 10 21 31 40| Scale is weakly epimorphic with val: <7 10 22 31 42| Scale is weakly epimorphic with val: <7 10 22 32 41| Scale is weakly epimorphic with val: <7 11 18 27 40| Scale is weakly epimorphic with val: <7 11 18 29 41| Scale is weakly epimorphic with val: <7 11 18 30 40| Scale is weakly epimorphic with val: <7 11 18 32 41| Scale is weakly epimorphic with val: <7 11 18 33 40| Scale is weakly epimorphic with val: <7 11 19 27 42| Scale is weakly epimorphic with val: <7 11 19 28 41| Scale is weakly epimorphic with val: <7 11 19 30 42| Scale is weakly epimorphic with val: <7 11 19 31 41| Scale is weakly epimorphic with val: <7 11 19 33 42| Scale is JI-epimorphic with val: <7 11 20 28 40| Scale is weakly epimorphic with val: <7 11 20 29 42| Scale is weakly epimorphic with val: <7 11 20 31 40| Scale is weakly epimorphic with val: <7 11 20 32 42| Scale is weakly epimorphic with val: <7 11 21 27 40| Scale is JI-epimorphic with val: <7 11 21 29 41| Scale is weakly epimorphic with val: <7 11 21 30 40| Scale is weakly epimorphic with val: <7 11 21 32 41| Scale is weakly epimorphic with val: <7 11 21 33 40| Scale is weakly epimorphic with val: <7 11 22 27 42| Scale is weakly epimorphic with val: <7 11 22 28 41| Scale is JI-epimorphic with val: <7 11 22 30 42| Scale is weakly epimorphic with val: <7 11 22 31 41| Scale is weakly epimorphic with val: <7 11 22 33 42| Scale is weakly epimorphic with val: <7 12 18 28 41| Scale is weakly epimorphic with val: <7 12 18 29 40| Scale is weakly epimorphic with val: <7 12 19 29 42| Scale is weakly epimorphic with val: <7 12 19 30 41| Scale is weakly epimorphic with val: <7 12 20 30 40| Scale is weakly epimorphic with val: <7 12 20 31 42| Scale is weakly epimorphic with val: <7 12 21 29 40| Scale is weakly epimorphic with val: <7 12 21 31 41| Scale is weakly epimorphic with val: <7 12 22 30 41| Scale is weakly epimorphic with val: <7 12 22 32 42| Scale is weakly epimorphic with val: <8 11 18 27 40| Scale is weakly epimorphic with val: <8 11 18 29 41| Scale is weakly epimorphic with val: <8 11 19 28 41| Scale is weakly epimorphic with val: <8 11 19 30 42| Scale is weakly epimorphic with val: <8 11 20 29 42| Scale is weakly epimorphic with val: <8 11 20 31 40| Scale is weakly epimorphic with val: <8 11 21 27 40| Scale is weakly epimorphic with val: <8 11 21 32 41| Scale is weakly epimorphic with val: <8 11 22 28 41| Scale is weakly epimorphic with val: <8 11 22 33 42| Scale is weakly epimorphic with val: <8 12 18 28 41| Scale is weakly epimorphic with val: <8 12 18 29 40| Scale is weakly epimorphic with val: <8 12 19 29 42| Scale is weakly epimorphic with val: <8 12 19 30 41| Scale is weakly epimorphic with val: <8 12 20 27 40| Scale is weakly epimorphic with val: <8 12 20 31 42| Scale is weakly epimorphic with val: <8 12 21 28 41| Scale is weakly epimorphic with val: <8 12 21 32 40| Scale is weakly epimorphic with val: <8 12 22 29 42| Scale is weakly epimorphic with val: <8 12 22 33 41|
FIT/MODE
3: 2 1 0 N G T3 SD: 38.5209 c. M:-66.5941 c. 4: 3 1 0 N G T3 SD: 44.0978 c. M:-66.5941 c. 5: 3 1 1 N M DE S SD: 28.7603 c. M: 37.3025 c. 6: 4 1 1 N M DE S SD: 9.7674 c. M: 16.4134 c. 9: 6 2 1 N T3 SD: 6.9161 c. M:-11.2558 c. 13: 9 2 2 N M DE S SD: 7.6539 c. M: 10.0282 c. 15: 10 3 2 N T3 SD: 2.3693 c. M: 4.0995 c. 22: 15 4 3 N T3 SD: 2.1311 c. M:-3.4466 c. 31: 21 6 4 N T3 SD: 1.5283 c. M:-2.3303 c. 37: 25 7 5 N T3 SD: 0.4666 c. M: 0.7092 c. 83: 56 16 11 N T3 SD: 0.3444 c. M:-0.5882 c. 89: 60 17 12 N T3 SD: 0.3862 c. M: 0.5580 c. 120: 81 23 16 N T3 SD: 0.1125 c. M:-0.1881 c. 157: 106 30 21 N T3 SD: 0.0764 c. M:-0.1302 c. 209: 141 40 28 N T3 SD: 0.1051 c. M: 0.1296 c. 277: 187 53 37 N T3 SD: 0.0679 c. M:-0.0958 c. 329: 222 63 44 N T3 SD: 0.0370 c. M: 0.0627 c. 449: 303 86 60 N T3 SD: 0.0298 c. M:-0.0402 c. 486: 328 93 65 N T3 SD: 0.0097 c. M: 0.0168 c. 935: 631 179 125 N T3 SD: 0.0109 c. M: 0.0157 c. 1092: 737 209 146 N T3 SD: 0.0045 c. M:-0.0057 c. 1578: 1065 302 211 N T3 SD: 0.0022 c. M:-0.0035 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 5 x S SD: 45.1372 cents 5:6 x 7 S SD: 43.4582 cents 6:7 x 8 S SD: 34.6293 cents 7 x 9 x SD: 3.6332 cents 8 x 10:11 S SD: 34.9119 cents 9:11 x 12 SD: 5.6392 cents 10:12:13 x S SD: 15.3128 cents 12 x 15:16 S SD: 22.5686 cents 13:16:17 x SD: 20.2013 cents 14:17:18:19 SD: 10.2856 cents 15:18:19:20 S SD: 10.0714 cents 16:19 x 21 SD: 23.6356 cents 17:21:22:23 SD: 13.9163 cents 18:22:23:24 SD: 4.4400 cents 39:47:50:52 SD: 4.3902 cents 42:51:54:56 SD: 1.2111 cents 60:73:77:80 SD: 1.1392 cents 99:120:127:132 SD: 1.0331 cents 102:124:131:136 SD: 0.8840 cents 117:142:150:156 SD: 0.5232 cents 159:193:204:212 SD: 0.2135 cents 219:266:281:292 SD: 0.1598 cents 336:408:431:448 SD: 0.1263 cents 378:459:485:504 SD: 0.0225 cents