Scala analysis: 162_C6
Chromatic tetrachord 39/37 * 37/36 * 16/13
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 39/37 91.138624 2: 13/12 138.572661 tridecimal 2/3-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 16/13 359.4723 tridecimal neutral third 1: 39/37 91.1386 2: 37/36 47.4340 3: 16/13 359.4723 tridecimal neutral third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 37/36 47.434 cents 1: 1 39/37 91.139 cents 1: 1 16/13 359.472 cents tridecimal neutral third 2: 1 13/12 138.573 cents tridecimal 2/3-tone 2: 1 148/117 406.906 cents 2: 1 48/37 450.611 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 : 91.1 138.6 498.0 91.1 : 47.4 406.9 498.0 138.6: 359.5 450.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 47.4340 .. 359.4723 cents 576/481, 312.0383 cents 37/36, 47.4340 cents 2: 138.5727 .. 450.6110 cents 576/481, 312.0383 cents 169/192,-220.8997 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 37/36, 47.4340 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 16/13, 359.4723 cents Average / Smallest step : 3.499913 Largest / Average step : 2.165300 Largest / Smallest step : 7.578363 Median interval of one step : 39/37, 91.1386 cents, amount: 1 Least squares average step : 133.02992 cents, oct.: 399.08977 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1470-tone equal temperament with octave 4/3 degrees: 269 409 1470 Least number of segments generator : 737 of 249.700 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 947 of 320.849 cents and inv. generated superset size: 71 = 68 more = 2366.667% 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 47.43404 cents Scale diversity : 0.669676 Lumma stability : 0.190481 Lumma impropriety factor : 0.443534 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 : 1404/1369, 43.7046 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% Scale is n-1 differentially coherent in interval classes 1 and 2 combined -- Rational properties -- Prime limit : 37 Odd number limit : 117 (O: 39 U: 117) Highest odd numerator or denominator: 39 Scale harmonicity : 0.031759 Fundamental : 1/444, -8.7944 octaves, 0.5892 Hz. Guide tone : 156, 7.2854 octaves, 40813.588 Hz. Exponens Consonantiae : 6.926400E+04, 16.07982 octaves Euler's gradus suavitatis : 57 Sum of Mann's harmonic distance : 54.0, average 18.00000 Mersenne's string divisions : 13300 Sum of van Prooijen's expressibility: 3.18213, average 1.06071 Sum of Tenney's harmonic distance : 6.43157, average 2.14386 Vogel's harmonic complexity : 37.33333 Wille's k value : 240 Wilson's harmonic complexity : 56 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 16.05130, average 2.67522 Lattice compactness (without 2's) : 9.06450, average 1.51075 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.00000 4 3: -1 .. 1 -0.33333 3 1 13: 0 .. 1 0.66667 2 1 37: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 25 37| Scale is weakly epimorphic with val: <6 10 25 40| Scale is weakly epimorphic with val: <6 10 29 36| Scale is weakly epimorphic with val: <6 11 26 35| Scale is weakly epimorphic with val: <6 11 26 38| Scale is weakly epimorphic with val: <6 11 26 41| Scale is weakly epimorphic with val: <6 11 28 36| Scale is weakly epimorphic with val: <7 10 27 35| Scale is weakly epimorphic with val: <7 10 27 38| Scale is weakly epimorphic with val: <7 10 27 41| Scale is weakly epimorphic with val: <7 10 29 36| Scale is weakly epimorphic with val: <7 11 26 35| Scale is weakly epimorphic with val: <7 11 26 38| Scale is weakly epimorphic with val: <7 11 26 41| Scale is JI-epimorphic with val: <7 11 27 37| Scale is weakly epimorphic with val: <7 11 27 40| Scale is weakly epimorphic with val: <7 11 29 35| Scale is weakly epimorphic with val: <7 11 29 38| Scale is weakly epimorphic with val: <7 11 29 41| Scale is weakly epimorphic with val: <7 11 30 37| Scale is weakly epimorphic with val: <7 11 30 40| Scale is weakly epimorphic with val: <7 12 27 36| Scale is weakly epimorphic with val: <7 12 29 37| Scale is weakly epimorphic with val: <7 12 29 40| Scale is weakly epimorphic with val: <7 12 30 39| Scale is weakly epimorphic with val: <8 11 28 36| Scale is weakly epimorphic with val: <8 11 30 37| Scale is weakly epimorphic with val: <8 11 30 40| Scale is weakly epimorphic with val: <8 12 27 36| Scale is weakly epimorphic with val: <8 12 30 39|
FIT/MODE
3: 1 0 2 N G T3 SD: 46.0418 c. M:-74.8764 c. 4: 1 0 3 N G T3 SD: 20.9082 c. M:-33.3726 c. 6: 1 1 4 N M DE S SD: 16.5247 c. M:-27.4423 c. 7: 1 1 5 N M DE S SD: 11.7396 c. M: 19.9893 c. 10: 2 1 7 N T3 SD: 7.9429 c. M:-10.8408 c. 11: 2 1 8 N T3 SD: 1.6188 c. M: 2.7422 c. 32: 6 3 23 N T3 SD: 1.5596 c. M:-2.2448 c. 39: 7 4 28 N T3 SD: 1.4904 c. M:-1.9016 c. 43: 8 4 31 N T3 SD: 0.9105 c. M:-1.5209 c. 50: 9 5 36 N T3 SD: 0.9993 c. M: 1.4905 c. 54: 10 5 39 N T3 SD: 0.6439 c. M:-1.0919 c. 65: 12 6 47 N T3 SD: 0.5997 c. M:-0.8081 c. 72: 13 7 52 N T3 SD: 0.7129 c. M: 1.2138 c. 76: 14 7 55 N T3 SD: 0.6531 c. M: 0.9550 c. 82: 15 8 59 N T3 SD: 0.6486 c. M:-1.1229 c. 83: 15 8 60 N T3 SD: 0.7284 c. M: 1.1305 c. 93: 17 9 67 N T3 SD: 0.3885 c. M:-0.6657 c. 104: 19 10 75 N T3 SD: 0.1963 c. M:-0.3053 c. 115: 21 11 83 N T3 SD: 0.1107 c. M: 0.1913 c. 219: 40 21 158 N T3 SD: 0.1324 c. M: 0.1715 c. 241: 44 23 174 N T3 SD: 0.1370 c. M: 0.2092 c. 262: 48 25 189 N T3 SD: 0.1285 c. M:-0.1956 c. 273: 50 26 197 N T3 SD: 0.0635 c. M:-0.0784 c. 284: 52 27 205 N T3 SD: 0.0356 c. M:-0.0527 c. 388: 71 37 280 N T3 SD: 0.0337 c. M:-0.0584 c. 399: 73 38 288 N T3 SD: 0.0149 c. M: 0.0188 c. 787: 144 75 568 N T3 SD: 0.0125 c. M:-0.0193 c. 1071: 196 102 773 N T3 SD: 0.0051 c. M:-0.0069 c. 1470: 269 140 1061 N T3 SD: 0.0006 c. M: 0.0010 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: 98.0918 cents 6 x 7:8 S SD: 64.1491 cents 7 x 8:9 S SD: 55.9891 cents 8 x 9:11 SD: 42.1514 cents 9 x 10:12 S SD: 21.9155 cents 10 x 11:13 SD: 25.5919 cents 11 x 12:15 S SD: 20.3667 cents 12 x 13:16 SD: 0.0000 cents 13 x 14:17 SD: 17.5761 cents 14 x 15:19 SD: 18.0616 cents 15:16 x 20 S SD: 10.2963 cents 16:17 x 21 SD: 15.2826 cents 17:18 x 23 SD: 13.2274 cents 20:21:22:27 SD: 11.5742 cents 21:22:23:28 SD: 7.2295 cents 24:25:26:32 SD: 6.8221 cents 28 x 30:37 SD: 12.3190 cents 29 x 31:39 SD: 13.7396 cents 30:32:33:40 SD: 11.1688 cents 31:33:34:41 SD: 10.2447 cents 32:34:35:43 SD: 8.4780 cents 33:35:36:44 SD: 5.3815 cents 35:37:38:47 SD: 4.6181 cents 36:38:39:48 SD: 0.8215 cents 132:139:143:176 SD: 0.5608 cents 168:177:182:224 SD: 0.2643 cents 204:215:221:272 SD: 0.0725 cents 240:253:260:320 SD: 0.0617 cents 444:468:481:592 SD: 0.0000 cents