Scala analysis: 285_C21
Chromatic tetrachord 51/47 * 47/45 * 20/17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 51/47 141.403788 2: 17/15 216.686695 septendecimal whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 20/17 281.3583 septendecimal augmented second 1: 51/47 141.4038 2: 47/45 75.2829 3: 20/17 281.3583 septendecimal augmented second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 47/45 75.283 cents 1: 1 51/47 141.404 cents 1: 1 20/17 281.358 cents septendecimal augmented second 2: 1 17/15 216.687 cents septendecimal whole tone 2: 1 188/153 356.641 cents 2: 1 60/47 422.762 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 : 141.4 216.7 498.0 141.4: 75.3 356.6 498.0 216.7: 281.4 422.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 75.2829 .. 281.3583 cents 900/799, 206.0754 cents 47/45, 75.2829 cents 2: 216.6867 .. 422.7621 cents 900/799, 206.0754 cents 289/300,-64.6716 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 47/45, 75.2829 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 20/17, 281.3583 cents Average / Smallest step : 2.205215 Largest / Average step : 1.694776 Largest / Smallest step : 3.737346 Median interval of one step : 51/47, 141.4038 cents, amount: 1 Least squares average step : 147.77944 cents, oct.: 443.33832 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1032-tone equal temperament with octave 4/3 degrees: 293 449 1032 Least number of segments generator : 517 of 249.505 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 979 of 472.467 cents and inv. generated superset size: 37 = 34 more = 1233.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 64.67161 cents Scale diversity : 1.069455 Lumma stability : 0.302314 Lumma impropriety factor : 0.129851 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 : 300/289, 64.6716 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 47 Odd number limit : 153 (O: 51 U: 153) Highest odd numerator or denominator: 51 Scale harmonicity : 0.022805 Fundamental : 1/705, -9.4615 octaves, 0.3711 Hz. Guide tone : 204, 7.6724 octaves, 53371.615 Hz. Exponens Consonantiae : 1.438200E+05, 17.13390 octaves Euler's gradus suavitatis : 73 Sum of Mann's harmonic distance : 68.5, average 22.83333 Mersenne's string divisions : 1568 Sum of van Prooijen's expressibility: 3.41514, average 1.13838 Sum of Tenney's harmonic distance : 6.86539, average 2.28846 Vogel's harmonic complexity : 48.66667 Wille's k value : 399 Wilson's harmonic complexity : 75 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 13.06789, average 2.17798 Lattice compactness (without 2's) : 10.03261, average 1.67210 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 0.66667 2 3: -1 .. 1 -0.33333 3 1 5: -1 .. 0 -0.33333 1 17: 0 .. 1 0.66667 2 1 47: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 15 28 37| Scale is weakly epimorphic with val: <6 10 15 28 40| Scale is weakly epimorphic with val: <6 10 15 28 43| Scale is weakly epimorphic with val: <6 10 15 32 39| Scale is weakly epimorphic with val: <6 10 16 29 38| Scale is weakly epimorphic with val: <6 10 16 29 41| Scale is weakly epimorphic with val: <6 10 16 30 37| Scale is weakly epimorphic with val: <6 10 16 33 40| Scale is weakly epimorphic with val: <6 10 17 30 39| Scale is weakly epimorphic with val: <6 10 17 30 42| Scale is weakly epimorphic with val: <6 10 17 31 38| Scale is weakly epimorphic with val: <6 10 18 31 37| Scale is weakly epimorphic with val: <6 10 18 31 40| Scale is weakly epimorphic with val: <6 10 18 31 43| Scale is weakly epimorphic with val: <6 10 18 32 39| Scale is weakly epimorphic with val: <6 10 19 30 37| Scale is weakly epimorphic with val: <6 10 19 32 38| Scale is weakly epimorphic with val: <6 10 19 32 41| Scale is weakly epimorphic with val: <6 10 19 33 40| Scale is weakly epimorphic with val: <6 11 15 29 38| Scale is weakly epimorphic with val: <6 11 15 29 41| Scale is weakly epimorphic with val: <6 11 15 31 39| Scale is weakly epimorphic with val: <6 11 16 29 37| Scale is weakly epimorphic with val: <6 11 16 30 39| Scale is weakly epimorphic with val: <6 11 16 30 42| Scale is weakly epimorphic with val: <6 11 16 32 40| Scale is weakly epimorphic with val: <6 11 17 30 38| Scale is weakly epimorphic with val: <6 11 17 31 37| Scale is weakly epimorphic with val: <6 11 17 31 40| Scale is weakly epimorphic with val: <6 11 17 31 43| Scale is weakly epimorphic with val: <6 11 17 33 41| Scale is weakly epimorphic with val: <6 11 18 31 39| Scale is weakly epimorphic with val: <6 11 18 32 38| Scale is weakly epimorphic with val: <6 11 18 32 41| Scale is weakly epimorphic with val: <6 11 19 29 37| Scale is weakly epimorphic with val: <6 11 19 32 40| Scale is weakly epimorphic with val: <6 11 19 33 39| Scale is weakly epimorphic with val: <6 11 19 33 42| Scale is weakly epimorphic with val: <7 10 15 28 39| Scale is weakly epimorphic with val: <7 10 15 28 42| Scale is weakly epimorphic with val: <7 10 15 30 37| Scale is weakly epimorphic with val: <7 10 15 33 40| Scale is weakly epimorphic with val: <7 10 16 29 37| Scale is weakly epimorphic with val: <7 10 16 29 40| Scale is weakly epimorphic with val: <7 10 16 29 43| Scale is weakly epimorphic with val: <7 10 16 31 38| Scale is weakly epimorphic with val: <7 10 17 30 38| Scale is weakly epimorphic with val: <7 10 17 30 41| Scale is weakly epimorphic with val: <7 10 17 32 39| Scale is weakly epimorphic with val: <7 10 18 30 37| Scale is weakly epimorphic with val: <7 10 18 31 39| Scale is weakly epimorphic with val: <7 10 18 31 42| Scale is weakly epimorphic with val: <7 10 18 33 40| Scale is weakly epimorphic with val: <7 10 19 31 38| Scale is weakly epimorphic with val: <7 10 19 32 37| Scale is weakly epimorphic with val: <7 10 19 32 40| Scale is weakly epimorphic with val: <7 10 19 32 43| Scale is weakly epimorphic with val: <7 11 15 27 39| Scale is weakly epimorphic with val: <7 11 15 27 42| Scale is JI-epimorphic with val: <7 11 15 28 38| Scale is weakly epimorphic with val: <7 11 15 28 41| Scale is weakly epimorphic with val: <7 11 15 30 39| Scale is weakly epimorphic with val: <7 11 15 30 42| Scale is weakly epimorphic with val: <7 11 15 31 38| Scale is weakly epimorphic with val: <7 11 15 31 41| Scale is weakly epimorphic with val: <7 11 15 33 39| Scale is weakly epimorphic with val: <7 11 15 33 42| Scale is weakly epimorphic with val: <7 11 16 28 37| Scale is weakly epimorphic with val: <7 11 16 28 40| Scale is weakly epimorphic with val: <7 11 16 28 43| Scale is JI-epimorphic with val: <7 11 16 29 39| Scale is weakly epimorphic with val: <7 11 16 29 42| Scale is weakly epimorphic with val: <7 11 16 31 37| Scale is weakly epimorphic with val: <7 11 16 31 40| Scale is weakly epimorphic with val: <7 11 16 31 43| Scale is weakly epimorphic with val: <7 11 16 32 39| Scale is weakly epimorphic with val: <7 11 16 32 42| Scale is weakly epimorphic with val: <7 11 17 27 37| Scale is weakly epimorphic with val: <7 11 17 27 40| Scale is weakly epimorphic with val: <7 11 17 27 43| Scale is weakly epimorphic with val: <7 11 17 29 38| Scale is weakly epimorphic with val: <7 11 17 29 41| Scale is weakly epimorphic with val: <7 11 17 30 37| Scale is JI-epimorphic with val: <7 11 17 30 40| = patent Scale is weakly epimorphic with val: <7 11 17 30 43| Scale is weakly epimorphic with val: <7 11 17 32 38| Scale is weakly epimorphic with val: <7 11 17 32 41| Scale is weakly epimorphic with val: <7 11 17 33 37| Scale is weakly epimorphic with val: <7 11 17 33 40| Scale is weakly epimorphic with val: <7 11 17 33 43| Scale is weakly epimorphic with val: <7 11 18 27 39| Scale is weakly epimorphic with val: <7 11 18 27 42| Scale is weakly epimorphic with val: <7 11 18 28 38| Scale is weakly epimorphic with val: <7 11 18 28 41| Scale is weakly epimorphic with val: <7 11 18 30 39| Scale is weakly epimorphic with val: <7 11 18 30 42| Scale is weakly epimorphic with val: <7 11 18 31 38| Scale is JI-epimorphic with val: <7 11 18 31 41| Scale is weakly epimorphic with val: <7 11 18 33 39| Scale is weakly epimorphic with val: <7 11 18 33 42| Scale is weakly epimorphic with val: <7 11 19 28 37| Scale is weakly epimorphic with val: <7 11 19 28 40| Scale is weakly epimorphic with val: <7 11 19 28 43| Scale is weakly epimorphic with val: <7 11 19 29 39| Scale is weakly epimorphic with val: <7 11 19 29 42| Scale is weakly epimorphic with val: <7 11 19 31 37| Scale is weakly epimorphic with val: <7 11 19 31 40| Scale is weakly epimorphic with val: <7 11 19 31 43| Scale is weakly epimorphic with val: <7 11 19 32 39| Scale is JI-epimorphic with val: <7 11 19 32 42| Scale is weakly epimorphic with val: <7 12 15 28 37| Scale is weakly epimorphic with val: <7 12 15 30 38| Scale is weakly epimorphic with val: <7 12 15 30 41| Scale is weakly epimorphic with val: <7 12 15 31 40| Scale is weakly epimorphic with val: <7 12 16 29 38| Scale is weakly epimorphic with val: <7 12 16 31 39| Scale is weakly epimorphic with val: <7 12 16 31 42| Scale is weakly epimorphic with val: <7 12 16 32 41| Scale is weakly epimorphic with val: <7 12 17 30 39| Scale is weakly epimorphic with val: <7 12 17 32 37| Scale is weakly epimorphic with val: <7 12 17 32 40| Scale is weakly epimorphic with val: <7 12 17 32 43| Scale is weakly epimorphic with val: <7 12 17 33 42| Scale is weakly epimorphic with val: <7 12 18 28 37| Scale is weakly epimorphic with val: <7 12 18 31 40| Scale is weakly epimorphic with val: <7 12 18 33 38| Scale is weakly epimorphic with val: <7 12 18 33 41| Scale is weakly epimorphic with val: <7 12 19 29 38| Scale is weakly epimorphic with val: <7 12 19 32 41| Scale is weakly epimorphic with val: <8 11 15 29 39| Scale is weakly epimorphic with val: <8 11 15 29 42| Scale is weakly epimorphic with val: <8 11 15 30 38| Scale is weakly epimorphic with val: <8 11 15 33 41| Scale is weakly epimorphic with val: <8 11 16 30 37| Scale is weakly epimorphic with val: <8 11 16 30 40| Scale is weakly epimorphic with val: <8 11 16 30 43| Scale is weakly epimorphic with val: <8 11 16 31 39| Scale is weakly epimorphic with val: <8 11 17 29 37| Scale is weakly epimorphic with val: <8 11 17 31 38| Scale is weakly epimorphic with val: <8 11 17 31 41| Scale is weakly epimorphic with val: <8 11 17 32 40| Scale is weakly epimorphic with val: <8 11 18 30 38| Scale is weakly epimorphic with val: <8 11 18 32 39| Scale is weakly epimorphic with val: <8 11 18 32 42| Scale is weakly epimorphic with val: <8 11 18 33 41| Scale is weakly epimorphic with val: <8 11 19 31 39| Scale is weakly epimorphic with val: <8 11 19 33 37| Scale is weakly epimorphic with val: <8 11 19 33 40| Scale is weakly epimorphic with val: <8 11 19 33 43| Scale is weakly epimorphic with val: <8 12 15 29 38| Scale is weakly epimorphic with val: <8 12 15 30 37| Scale is weakly epimorphic with val: <8 12 15 30 40| Scale is weakly epimorphic with val: <8 12 15 30 43| Scale is weakly epimorphic with val: <8 12 15 32 41| Scale is weakly epimorphic with val: <8 12 16 30 39| Scale is weakly epimorphic with val: <8 12 16 31 38| Scale is weakly epimorphic with val: <8 12 16 31 41| Scale is weakly epimorphic with val: <8 12 16 33 42| Scale is weakly epimorphic with val: <8 12 17 28 37| Scale is weakly epimorphic with val: <8 12 17 31 40| Scale is weakly epimorphic with val: <8 12 17 32 39| Scale is weakly epimorphic with val: <8 12 17 32 42| Scale is weakly epimorphic with val: <8 12 18 29 38| Scale is weakly epimorphic with val: <8 12 18 32 41| Scale is weakly epimorphic with val: <8 12 18 33 37| Scale is weakly epimorphic with val: <8 12 18 33 40| Scale is weakly epimorphic with val: <8 12 18 33 43| Scale is weakly epimorphic with val: <8 12 19 30 39| Scale is weakly epimorphic with val: <8 12 19 33 42|
FIT/MODE
3: 1 0 2 N G T3 SD: 32.5235 c. M: 50.6717 c. 4: 1 1 2 P M ME S SD: 21.0631 c. M:-32.3358 c. 6: 2 1 3 P T3 SD: 23.4614 c. M:-32.3358 c. 7: 2 1 4 N T3 SD: 1.9400 c. M: 3.2388 c. 25: 7 4 14 N T3 SD: 1.8097 c. M:-2.4531 c. 32: 9 5 18 N T3 SD: 1.0367 c. M: 1.3286 c. 39: 11 6 22 N T3 SD: 0.5865 c. M: 0.9296 c. 46: 13 7 26 N T3 SD: 0.3856 c. M: 0.6519 c. 53: 15 8 30 N T3 SD: 0.4112 c. M: 0.5540 c. 99: 28 15 56 N T3 SD: 0.3773 c. M: 0.5426 c. 145: 41 22 82 N T3 SD: 0.3742 c. M: 0.5773 c. 152: 43 23 86 N T3 SD: 0.3850 c. M: 0.5095 c. 172: 49 26 97 N T3 SD: 0.3940 c. M:-0.4841 c. 179: 51 27 101 N T3 SD: 0.3473 c. M:-0.4973 c. 186: 53 28 105 N T3 SD: 0.3183 c. M:-0.5123 c. 193: 55 29 109 N T3 SD: 0.3072 c. M:-0.5261 c. 211: 60 32 119 N T3 SD: 0.2999 c. M:-0.4704 c. 218: 62 33 123 N T3 SD: 0.2463 c. M:-0.3513 c. 225: 64 34 127 N T3 SD: 0.2051 c. M:-0.2623 c. 232: 66 35 131 N T3 SD: 0.1801 c. M:-0.2814 c. 239: 68 36 135 N T3 SD: 0.1741 c. M:-0.2994 c. 264: 75 40 149 N T3 SD: 0.1608 c. M:-0.2647 c. 271: 77 41 153 N T3 SD: 0.1181 c. M:-0.1742 c. 278: 79 42 157 N T3 SD: 0.0893 c. M:-0.1270 c. 285: 81 43 161 N T3 SD: 0.0843 c. M:-0.1458 c. 317: 90 48 179 N T3 SD: 0.0738 c. M:-0.1278 c. 324: 92 49 183 N T3 SD: 0.0332 c. M:-0.0551 c. 331: 94 50 187 N T3 SD: 0.0219 c. M:-0.0350 c. 655: 186 99 370 N T3 SD: 0.0188 c. M:-0.0258 c. 701: 199 106 396 N T3 SD: 0.0120 c. M: 0.0187 c. 1032: 293 156 583 N T3 SD: 0.0012 c. M:-0.0015 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: 65.0514 cents 6 x 7:8 S SD: 25.0921 cents 7 x 8:9 S SD: 32.3031 cents 8 x 9:11 SD: 27.3918 cents 9 x 10:12 S SD: 17.1415 cents 10:11 x 13 SD: 24.8905 cents 11:12 x 15 S SD: 19.9932 cents 12:13:14:16 S SD: 16.7547 cents 13:14:15:17 SD: 15.8684 cents 14:15:16:19 SD: 13.4623 cents 15:16:17:20 SD: 9.8908 cents 18 x 20:24 S SD: 17.1415 cents 20:22:23:27 SD: 13.5740 cents 21:23:24:28 SD: 7.2170 cents 23:25:26:31 SD: 6.4863 cents 24:26:27:32 SD: 4.3622 cents 36:39:41:48 SD: 2.9755 cents 45:49:51:60 SD: 2.0081 cents 60:65:68:80 SD: 0.9437 cents 105:114:119:140 SD: 0.3232 cents 165:179:187:220 SD: 0.1372 cents 270:293:306:360 SD: 0.0419 cents 435:472:493:580 SD: 0.0260 cents