Scala analysis: 353_C29
Chromatic tetrachord 65/63 * 189/169 * 52/45
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 65/63 54.105467 2: 15/13 247.741053 tridecimal 5/4-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 52/45 250.3039 1: 65/63 54.1055 2: 189/169 193.6356 3: 52/45 250.3039
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 65/63 54.105 cents 1: 1 189/169 193.636 cents 1: 1 52/45 250.304 cents 2: 1 15/13 247.741 cents tridecimal 5/4-tone 2: 1 676/567 304.409 cents 2: 1 84/65 443.940 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 : 54.1 247.7 498.0 54.1 : 193.6 443.9 498.0 247.7: 250.3 304.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 54.1055 .. 250.3039 cents 28/25, 196.1985 cents 65/63, 54.1055 cents 2: 247.7411 .. 443.9395 cents 28/25, 196.1985 cents 675/676,-2.5629 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 65/63, 54.1055 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 52/45, 250.3039 cents Average / Smallest step : 3.068359 Largest / Average step : 1.507719 Largest / Smallest step : 4.626223 Median interval of one step : 189/169, 193.6356 cents, amount: 1 Least squares average step : 145.98018 cents, oct.: 437.94055 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1749-tone equal temperament with octave 4/3 degrees: 190 870 1749 Least number of segments generator : 875 of 249.165 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1069 of 304.408 cents and inv. generated superset size: 28 = 25 more = 933.333% 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 2.56289 cents Scale diversity : 0.791166 Lumma stability : 0.217271 Lumma impropriety factor : 0.005146 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 : 676/675, 2.5629 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 13 Odd number limit : 567 (O: 189 U: 567) Highest odd numerator or denominator: 65 Scale harmonicity : 0.014086 Average absolute harmonicity : 0.089651 Specific harmonicity : 0.072056 Fundamental : 1/819, -9.6777 octaves, 0.3194 Hz. Guide tone : 780, 9.6073 octaves, 204067.941 Hz. Exponens Consonantiae : 6.388200E+05, 19.28505 octaves Euler's gradus suavitatis : 43 Sum of Mann's harmonic distance : 81.5, average 27.16667 Mersenne's string divisions : 896 Sum of van Prooijen's expressibility: 3.46613, average 1.15538 Sum of Tenney's harmonic distance : 6.98147, average 2.32716 Vogel's harmonic complexity : 25.66667 Wille's k value : 472 Wilson's harmonic complexity : 47 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 16.34623, average 2.72437 Lattice compactness (without 2's) : 13.56895, average 2.26149 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 0.66667 2 3: -2 .. 1 -0.66667 4 1 5: 0 .. 1 0.66667 2 7: -1 .. 0 -0.33333 1 13: -1 .. 1 0.00000 2 2 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <6 10 15 19 27| Scale is weakly epimorphic with val: <6 10 15 22 30| Scale is weakly epimorphic with val: <6 10 16 18 25| Scale is weakly epimorphic with val: <6 10 16 21 28| Scale is weakly epimorphic with val: <6 10 17 20 26| Scale is weakly epimorphic with val: <6 10 18 19 25| Scale is weakly epimorphic with val: <6 10 18 22 25| Scale is weakly epimorphic with val: <6 10 18 22 27| Scale is weakly epimorphic with val: <6 10 19 21 25| Scale is weakly epimorphic with val: <6 10 19 21 26| Scale is weakly epimorphic with val: <6 11 15 20 30| Scale is weakly epimorphic with val: <6 11 16 19 28| Scale is weakly epimorphic with val: <6 11 17 18 25| Scale is weakly epimorphic with val: <6 11 17 18 26| Scale is weakly epimorphic with val: <6 11 17 21 25| Scale is weakly epimorphic with val: <6 11 17 21 29| Scale is weakly epimorphic with val: <6 11 18 20 26| Scale is weakly epimorphic with val: <6 11 18 20 27| Scale is weakly epimorphic with val: <6 11 19 19 25| Scale is weakly epimorphic with val: <6 11 19 19 27| Scale is weakly epimorphic with val: <6 11 19 22 27| Scale is weakly epimorphic with val: <6 11 19 22 28| Scale is weakly epimorphic with val: <7 10 15 18 26| Scale is weakly epimorphic with val: <7 10 15 21 29| Scale is weakly epimorphic with val: <7 10 16 20 27| Scale is weakly epimorphic with val: <7 10 17 19 25| Scale is weakly epimorphic with val: <7 10 17 22 28| Scale is weakly epimorphic with val: <7 10 18 18 25| Scale is weakly epimorphic with val: <7 10 18 21 25| Scale is weakly epimorphic with val: <7 10 18 21 26| Scale is weakly epimorphic with val: <7 10 19 20 26| Scale is weakly epimorphic with val: <7 11 15 19 25| Scale is weakly epimorphic with val: <7 11 15 19 27| Scale is weakly epimorphic with val: <7 11 15 19 28| Scale is weakly epimorphic with val: <7 11 15 19 30| Scale is weakly epimorphic with val: <7 11 15 22 25| Scale is weakly epimorphic with val: <7 11 15 22 27| Scale is weakly epimorphic with val: <7 11 15 22 28| Scale is weakly epimorphic with val: <7 11 15 22 30| Scale is JI-epimorphic with val: <7 11 16 18 25| Scale is weakly epimorphic with val: <7 11 16 18 26| Scale is weakly epimorphic with val: <7 11 16 18 28| Scale is weakly epimorphic with val: <7 11 16 18 29| Scale is weakly epimorphic with val: <7 11 16 21 25| Scale is weakly epimorphic with val: <7 11 16 21 26| Scale is weakly epimorphic with val: <7 11 16 21 28| Scale is weakly epimorphic with val: <7 11 16 21 29| Scale is JI-epimorphic with val: <7 11 17 20 26| Scale is weakly epimorphic with val: <7 11 17 20 27| = patent Scale is weakly epimorphic with val: <7 11 17 20 29| Scale is weakly epimorphic with val: <7 11 17 20 30| Scale is weakly epimorphic with val: <7 11 18 19 25| Scale is weakly epimorphic with val: <7 11 18 19 27| Scale is weakly epimorphic with val: <7 11 18 19 28| Scale is weakly epimorphic with val: <7 11 18 19 30| Scale is weakly epimorphic with val: <7 11 18 22 25| Scale is JI-epimorphic with val: <7 11 18 22 27| Scale is weakly epimorphic with val: <7 11 18 22 28| Scale is weakly epimorphic with val: <7 11 18 22 30| Scale is weakly epimorphic with val: <7 11 19 21 25| Scale is weakly epimorphic with val: <7 11 19 21 26| Scale is weakly epimorphic with val: <7 11 19 21 28| Scale is weakly epimorphic with val: <7 11 19 21 29| Scale is weakly epimorphic with val: <7 12 16 19 25| Scale is weakly epimorphic with val: <7 12 16 19 30| Scale is weakly epimorphic with val: <7 12 16 22 25| Scale is weakly epimorphic with val: <7 12 17 18 26| Scale is weakly epimorphic with val: <7 12 17 18 28| Scale is weakly epimorphic with val: <7 12 17 21 26| Scale is weakly epimorphic with val: <7 12 18 20 27| Scale is weakly epimorphic with val: <7 12 18 20 29| Scale is weakly epimorphic with val: <7 12 19 19 27| Scale is weakly epimorphic with val: <7 12 19 19 28| Scale is weakly epimorphic with val: <7 12 19 22 28| Scale is weakly epimorphic with val: <7 12 19 22 30| Scale is weakly epimorphic with val: <8 11 15 18 28| Scale is weakly epimorphic with val: <8 11 16 20 29| Scale is weakly epimorphic with val: <8 11 17 19 25| Scale is weakly epimorphic with val: <8 11 17 19 27| Scale is weakly epimorphic with val: <8 11 17 22 25| Scale is weakly epimorphic with val: <8 11 17 22 30| Scale is weakly epimorphic with val: <8 11 18 18 25| Scale is weakly epimorphic with val: <8 11 18 18 26| Scale is weakly epimorphic with val: <8 11 18 21 26| Scale is weakly epimorphic with val: <8 11 18 21 28| Scale is weakly epimorphic with val: <8 11 19 20 26| Scale is weakly epimorphic with val: <8 11 19 20 27| Scale is weakly epimorphic with val: <8 12 16 18 25| Scale is weakly epimorphic with val: <8 12 16 18 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 20 30| Scale is weakly epimorphic with val: <8 12 18 19 27| Scale is weakly epimorphic with val: <8 12 18 19 28| Scale is weakly epimorphic with val: <8 12 18 22 27| Scale is weakly epimorphic with val: <8 12 19 21 28| Scale is weakly epimorphic with val: <8 12 19 21 29|
FIT/MODE
3: 0 1 2 N G T3 SD: 56.5878 c. M: 81.7261 c. 4: 0 2 2 P M DE S SD: 31.2466 c. M: 54.1055 c. 6: 1 2 3 P T3 SD: 16.7030 c. M:-28.9020 c. 8: 1 3 4 P T3 SD: 4.7633 c. M:-8.1502 c. 10: 1 4 5 P T3 SD: 2.5910 c. M: 4.3010 c. 18: 2 7 9 P T3 SD: 1.0267 c. M:-1.2814 c. 28: 3 11 14 P T3 SD: 0.8554 c. M:-1.2814 c. 46: 5 18 23 P T3 SD: 0.7400 c. M:-1.2814 c. 64: 7 25 32 P T3 SD: 0.7698 c. M:-1.2814 c. 74: 8 29 37 P T3 SD: 0.7552 c. M:-1.2814 c. 82: 9 32 41 P T3 SD: 0.8069 c. M:-1.2814 c. 99: 11 38 50 N T3 SD: 1.0071 c. M: 1.2339 c. 100: 11 39 50 P T3 SD: 0.8374 c. M:-1.2814 c. 101: 11 39 51 N T3 SD: 0.6882 c. M: 1.1841 c. 103: 11 40 52 N T3 SD: 0.8427 c. M: 1.1362 c. 109: 12 42 55 N T3 SD: 0.7147 c. M: 1.0032 c. 111: 12 43 56 N T3 SD: 0.5758 c. M: 0.9620 c. 119: 13 46 60 N T3 SD: 0.4999 c. M: 0.8112 c. 121: 13 47 61 N T3 SD: 0.5654 c. M: 0.7766 c. 129: 14 50 65 N T3 SD: 0.3760 c. M: 0.6490 c. 137: 15 53 69 N T3 SD: 0.3950 c. M: 0.5362 c. 139: 15 54 70 N T3 SD: 0.3603 c. M: 0.5101 c. 147: 16 57 74 N T3 SD: 0.2456 c. M: 0.4126 c. 157: 17 61 79 N T3 SD: 0.2034 c. M: 0.3047 c. 165: 18 64 83 N T3 SD: 0.1855 c. M: 0.2278 c. 175: 19 68 88 N T3 SD: 0.0838 c. M: 0.1415 c. 193: 21 75 97 N T3 SD: 0.0499 c. M:-0.0860 c. 368: 40 143 185 N T3 SD: 0.0450 c. M: 0.0719 c. 378: 41 147 190 N T3 SD: 0.0532 c. M: 0.0847 c. 396: 43 154 199 N T3 SD: 0.0198 c. M: 0.0248 c. 571: 62 222 287 N T3 SD: 0.0220 c. M: 0.0270 c. 589: 64 229 296 N T3 SD: 0.0100 c. M:-0.0131 c. 1160: 126 451 583 N T3 SD: 0.0058 c. M: 0.0075 c. 1353: 147 526 680 N T3 SD: 0.0052 c. M: 0.0069 c. 1749: 190 680 879 N T3 SD: 0.0006 c. M: 0.0011 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: 54.1875 cents 6 x 7:8 S SD: 9.5649 cents 7 x 8:9 S SD: 32.5520 cents 8 x 9:11 SD: 34.4934 cents 9 x 10:12 S SD: 32.6687 cents 10 x 12:13 S SD: 40.4092 cents 11:12:13:15 SD: 37.3447 cents 12:13:14:16 S SD: 28.8688 cents 13:14:15:17 SD: 27.1512 cents 14:15:16:19 SD: 24.6810 cents 15:16:17:20 SD: 21.8202 cents 17:18:20:23 SD: 20.4948 cents 18:19:21:24 SD: 14.6288 cents 19:20:22:25 SD: 14.0093 cents 20:21:23:27 SD: 12.5511 cents 21:22:24:28 S SD: 10.3981 cents 24:25:28:32 SD: 8.4355 cents 25:26:29:33 SD: 8.0128 cents 26:27:30:35 S SD: 6.6718 cents 27:28:31:36 SD: 4.1079 cents 33:34:38:44 SD: 1.4192 cents 90:93:104:120 SD: 1.2316 cents 123:127:142:164 SD: 0.5340 cents 156:161:180:208 SD: 0.1707 cents 345:356:398:460 SD: 0.1356 cents 474:489:547:632 SD: 0.0987 cents