Scala analysis: 347_C29
Chromatic tetrachord 45/41 * 41/39 * 52/45
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 45/41 161.161310 2: 15/13 247.741053 tridecimal 5/4-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 52/45 250.3039 1: 45/41 161.1613 2: 41/39 86.5797 3: 52/45 250.3039
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 41/39 86.580 cents 1: 1 45/41 161.161 cents 1: 1 52/45 250.304 cents 2: 1 15/13 247.741 cents tridecimal 5/4-tone 2: 1 164/135 336.884 cents 2: 1 52/41 411.465 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 : 161.2 247.7 498.0 161.2: 86.6 336.9 498.0 247.7: 250.3 411.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 86.5797 .. 250.3039 cents 676/615, 163.7242 cents 41/39, 86.5797 cents 2: 247.7411 .. 411.4653 cents 676/615, 163.7242 cents 675/676,-2.5629 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 41/39, 86.5797 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 52/45, 250.3039 cents Average / Smallest step : 1.917481 Largest / Average step : 1.507719 Largest / Smallest step : 2.891022 Median interval of one step : 45/41, 161.1613 cents, amount: 1 Least squares average step : 153.62703 cents, oct.: 460.88109 cents Scale is not proper Scale has trivalence property Scale is a mode of a 581-tone equal temperament with octave 4/3 degrees: 188 289 581 Least number of segments generator : 291 of 249.451 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 334 of 286.312 cents and inv. generated superset size: 21 = 18 more = 700.000% 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 2.56289 cents Scale diversity : 1.082177 Lumma stability : 0.347678 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 Best fifths form a closed circle Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 41 Odd number limit : 135 (O: 45 U: 135) Highest odd numerator or denominator: 45 Scale harmonicity : 0.025938 Fundamental : 1/1599, -10.6430 octaves, 0.1636 Hz. Guide tone : 180, 7.4919 octaves, 47092.602 Hz. Exponens Consonantiae : 2.878200E+05, 18.13481 octaves Euler's gradus suavitatis : 65 Sum of Mann's harmonic distance : 60.5, average 20.16667 Mersenne's string divisions : 1204 Sum of van Prooijen's expressibility: 3.30643, average 1.10214 Sum of Tenney's harmonic distance : 6.63521, average 2.21174 Vogel's harmonic complexity : 45.00000 Wille's k value : 922 Wilson's harmonic complexity : 68 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 14.52234, average 2.42039 Lattice compactness (without 2's) : 11.99410, average 1.99902 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 0.66667 2 3: -1 .. 2 0.66667 4 1 5: 0 .. 1 0.66667 2 13: -1 .. 0 -0.33333 1 1 41: -1 .. 0 -0.33333 1 1 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: <6 10 18 25 37| Scale is weakly epimorphic with val: <6 10 18 25 40| Scale is weakly epimorphic with val: <6 10 19 25 36| Scale is weakly epimorphic with val: <6 10 19 26 38| Scale is weakly epimorphic with val: <6 10 19 26 41| Scale is weakly epimorphic with val: <6 10 19 28 36| Scale is weakly epimorphic with val: <6 11 17 25 37| Scale is weakly epimorphic with val: <6 11 17 25 40| Scale is weakly epimorphic with val: <6 11 17 26 36| Scale is weakly epimorphic with val: <6 11 17 29 36| Scale is weakly epimorphic with val: <6 11 18 26 38| Scale is weakly epimorphic with val: <6 11 18 26 41| Scale is weakly epimorphic with val: <6 11 18 27 37| Scale is weakly epimorphic with val: <6 11 18 30 37| Scale is weakly epimorphic with val: <6 11 19 25 38| Scale is weakly epimorphic with val: <6 11 19 27 36| Scale is weakly epimorphic with val: <6 11 19 27 39| Scale is weakly epimorphic with val: <6 11 19 27 42| Scale is weakly epimorphic with val: <6 11 19 28 38| Scale is weakly epimorphic with val: <7 10 18 25 36| Scale is weakly epimorphic with val: <7 10 18 25 39| Scale is weakly epimorphic with val: <7 10 18 25 42| Scale is weakly epimorphic with val: <7 10 19 26 37| Scale is weakly epimorphic with val: <7 10 19 26 40| Scale is weakly epimorphic with val: <7 10 19 27 36| Scale is weakly epimorphic with val: <7 10 19 30 36| Scale is weakly epimorphic with val: <7 11 15 25 38| Scale is weakly epimorphic with val: <7 11 15 25 41| Scale is weakly epimorphic with val: <7 11 15 27 36| Scale is weakly epimorphic with val: <7 11 15 27 39| Scale is weakly epimorphic with val: <7 11 15 27 42| Scale is weakly 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 36| Scale is weakly epimorphic with val: <7 11 15 30 39| Scale is weakly epimorphic with val: <7 11 15 30 42| Scale is JI-epimorphic with val: <7 11 16 25 37| Scale is weakly epimorphic with val: <7 11 16 25 40| Scale is weakly epimorphic with val: <7 11 16 26 36| Scale is weakly epimorphic with val: <7 11 16 26 39| Scale is weakly epimorphic with val: <7 11 16 26 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 29 36| Scale is weakly epimorphic with val: <7 11 16 29 39| Scale is weakly epimorphic with val: <7 11 16 29 42| Scale is JI-epimorphic with val: <7 11 17 26 38| Scale is weakly epimorphic with val: <7 11 17 26 41| 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 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 weakly epimorphic with val: <7 11 17 30 40| Scale is weakly epimorphic with val: <7 11 18 25 38| Scale is weakly epimorphic with val: <7 11 18 25 41| Scale is weakly epimorphic with val: <7 11 18 27 36| Scale is JI-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 36| 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 19 25 37| Scale is weakly epimorphic with val: <7 11 19 25 40| Scale is weakly epimorphic with val: <7 11 19 26 36| Scale is weakly epimorphic with val: <7 11 19 26 39| Scale is weakly epimorphic with val: <7 11 19 26 42| Scale is weakly epimorphic with val: <7 11 19 28 37| Scale is JI-epimorphic with val: <7 11 19 28 40| Scale is weakly epimorphic with val: <7 11 19 29 36| 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 12 15 26 36| Scale is weakly epimorphic with val: <7 12 15 29 36| Scale is weakly epimorphic with val: <7 12 16 25 36| Scale is weakly epimorphic with val: <7 12 16 25 39| Scale is weakly epimorphic with val: <7 12 16 25 42| Scale is weakly epimorphic with val: <7 12 16 27 37| Scale is weakly epimorphic with val: <7 12 16 30 37| Scale is weakly epimorphic with val: <7 12 17 25 38| Scale is weakly epimorphic with val: <7 12 17 26 37| Scale is weakly epimorphic with val: <7 12 17 26 40| Scale is weakly epimorphic with val: <7 12 17 28 38| Scale is weakly epimorphic with val: <7 12 18 26 39| Scale is weakly epimorphic with val: <7 12 18 27 38| Scale is weakly epimorphic with val: <7 12 18 27 41| Scale is weakly epimorphic with val: <7 12 18 29 39| Scale is weakly epimorphic with val: <7 12 19 27 40| Scale is weakly epimorphic with val: <7 12 19 28 36| Scale is weakly epimorphic with val: <7 12 19 28 39| Scale is weakly epimorphic with val: <7 12 19 28 42| Scale is weakly epimorphic with val: <7 12 19 30 40| Scale is weakly epimorphic with val: <8 11 17 25 38| Scale is weakly epimorphic with val: <8 11 17 25 41| Scale is weakly epimorphic with val: <8 11 17 27 36| Scale is weakly epimorphic with val: <8 11 17 30 36| Scale is weakly epimorphic with val: <8 11 18 25 37| Scale is weakly epimorphic with val: <8 11 18 26 36| Scale is weakly epimorphic with val: <8 11 18 26 39| Scale is weakly epimorphic with val: <8 11 18 26 42| Scale is weakly epimorphic with val: <8 11 18 28 37| Scale is weakly epimorphic with val: <8 11 19 26 38| Scale is weakly epimorphic with val: <8 11 19 27 37| Scale is weakly epimorphic with val: <8 11 19 27 40| Scale is weakly epimorphic with val: <8 11 19 29 38| Scale is weakly epimorphic with val: <8 12 15 25 36| Scale is weakly epimorphic with val: <8 12 15 28 36| Scale is weakly epimorphic with val: <8 12 16 25 38| Scale is weakly epimorphic with val: <8 12 16 25 41| Scale is weakly epimorphic with val: <8 12 16 26 37| Scale is weakly epimorphic with val: <8 12 16 29 37| Scale is weakly epimorphic with val: <8 12 17 26 36| Scale is weakly epimorphic with val: <8 12 17 26 39| Scale is weakly epimorphic with val: <8 12 17 26 42| Scale is weakly epimorphic with val: <8 12 17 27 38| Scale is weakly epimorphic with val: <8 12 17 30 38| Scale is weakly epimorphic with val: <8 12 18 25 39| Scale is weakly epimorphic with val: <8 12 18 27 37| Scale is weakly epimorphic with val: <8 12 18 27 40| Scale is weakly epimorphic with val: <8 12 18 28 39| Scale is weakly epimorphic with val: <8 12 19 26 40| Scale is weakly epimorphic with val: <8 12 19 28 38| Scale is weakly epimorphic with val: <8 12 19 28 41| Scale is weakly epimorphic with val: <8 12 19 29 40|
FIT/MODE
3: 1 0 2 N G T3 SD: 47.2677 c. M: 81.7261 c. 4: 1 1 2 P M ME S SD: 21.1729 c. M: 36.6501 c. 6: 2 1 3 P T3 SD: 2.8983 c. M:-4.8537 c. 22: 7 4 11 P T3 SD: 1.7216 c. M: 2.6924 c. 28: 9 5 14 P T3 SD: 0.9659 c. M:-1.2814 c. 34: 11 6 17 P T3 SD: 0.7400 c. M:-1.2814 c. 40: 13 7 20 P T3 SD: 0.8440 c. M:-1.2814 c. 62: 20 11 31 P T3 SD: 0.7945 c. M:-1.2814 c. 74: 24 13 37 P T3 SD: 0.7696 c. M:-1.2814 c. 96: 31 17 48 P T3 SD: 0.7646 c. M:-1.2814 c. 99: 32 17 50 N T3 SD: 0.7197 c. M: 1.2339 c. 105: 34 18 53 N T3 SD: 0.6326 c. M: 1.0902 c. 111: 36 19 56 N T3 SD: 0.5944 c. M: 0.9620 c. 115: 37 20 58 N T3 SD: 0.7369 c. M: 0.9207 c. 117: 38 20 59 N T3 SD: 0.5982 c. M: 0.8470 c. 121: 39 21 61 N T3 SD: 0.5790 c. M: 0.7766 c. 127: 41 22 64 N T3 SD: 0.4481 c. M: 0.6794 c. 133: 43 23 67 N T3 SD: 0.3505 c. M: 0.5909 c. 139: 45 24 70 N T3 SD: 0.2978 c. M: 0.5101 c. 145: 47 25 73 N T3 SD: 0.2973 c. M: 0.4359 c. 155: 50 27 78 N T3 SD: 0.3451 c. M: 0.5016 c. 161: 52 28 81 N T3 SD: 0.2321 c. M: 0.3021 c. 167: 54 29 84 N T3 SD: 0.1386 c. M: 0.2097 c. 173: 56 30 87 N T3 SD: 0.0967 c. M: 0.1580 c. 201: 65 35 101 N T3 SD: 0.0638 c. M: 0.1020 c. 207: 67 36 104 N T3 SD: 0.0513 c. M:-0.0784 c. 374: 121 65 188 N T3 SD: 0.0335 c. M: 0.0502 c. 380: 123 66 191 N T3 SD: 0.0324 c. M:-0.0480 c. 581: 188 101 292 N T3 SD: 0.0034 c. M: 0.0044 c. 1950: 631 339 980 N T3 SD: 0.0026 c. M:-0.0044 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 8:9 x 11 SD: 34.1521 cents 9:10 x 12 S SD: 10.6212 cents 12:13:14:16 S SD: 9.8669 cents 16:18 x 21 S SD: 25.3514 cents 17:19:20:23 SD: 17.4948 cents 18:20:21:24 S SD: 9.5289 cents 19:21:22:25 SD: 8.8766 cents 20:22:23:27 SD: 7.5329 cents 21:23:24:28 SD: 5.6560 cents 32:35:37:43 SD: 5.0636 cents 33:36:38:44 SD: 3.6971 cents 39:43:45:52 SD: 2.6246 cents 51:56:59:68 SD: 1.5276 cents 72:79:83:96 SD: 0.5635 cents 123:135:142:164 SD: 0.3127 cents 195:214:225:260 SD: 0.0658 cents