Scala analysis: 336_C27
Chromatic tetrachord 46/43 * 43/40 * 80/69
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 46/43 116.756642 2: 23/20 241.960633 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 80/69 256.0844 1: 46/43 116.7566 2: 43/40 125.2040 3: 80/69 256.0844
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 46/43 116.757 cents 1: 1 43/40 125.204 cents 1: 1 80/69 256.084 cents 2: 1 23/20 241.961 cents 2: 1 160/129 372.841 cents 2: 1 86/69 381.288 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 : 116.8 242.0 498.0 116.8: 125.2 381.3 498.0 242.0: 256.1 372.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 116.7566 .. 256.0844 cents 1720/1587, 139.3277 cents 46/43, 116.7566 cents 2: 241.9606 .. 381.2884 cents 1720/1587, 139.3277 cents 1587/1600,-14.1237 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 46/43, 116.7566 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 80/69, 256.0844 cents Average / Smallest step : 1.421889 Largest / Average step : 1.542538 Largest / Smallest step : 2.193317 Median interval of one step : 43/40, 125.2040 cents, amount: 1 Least squares average step : 149.62949 cents, oct.: 448.88848 cents Scale is not proper Scale has trivalence property 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 14.12373 cents Scale diversity : 1.129513 Lumma stability : 0.468860 Lumma impropriety factor : 0.028358 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 : 1849/1840, 8.4474 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 130.8804 cents: 2 -- Rational properties -- Prime limit : 43 Odd number limit : 129 (O: 43 U: 129) Highest odd numerator or denominator: 43 Scale harmonicity : 0.018131 Fundamental : 1/2580, -11.3332 octaves, 0.1014 Hz. Guide tone : 92, 6.5236 octaves, 24069.552 Hz. Exponens Consonantiae : 2.373600E+05, 17.85672 octaves Euler's gradus suavitatis : 75 Sum of Mann's harmonic distance : 69.5, average 23.16667 Mersenne's string divisions : 26789 Sum of van Prooijen's expressibility: 3.47232, average 1.15744 Sum of Tenney's harmonic distance : 7.03817, average 2.34606 Vogel's harmonic complexity : 51.66667 Wille's k value : 1483 Wilson's harmonic complexity : 74 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 15.35300, average 2.55883 Lattice compactness (without 2's) : 7.56048, average 1.26008 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.33333 5 3: -1 .. 0 -0.33333 1 1 5: -1 .. 0 -0.33333 1 23: 0 .. 1 0.66667 2 1 43: -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 15 30 38| Scale is weakly epimorphic with val: <6 10 15 30 41| Scale is weakly epimorphic with val: <6 10 15 34 37| Scale is weakly epimorphic with val: <6 10 16 31 36| Scale is weakly epimorphic with val: <6 10 16 31 39| Scale is weakly epimorphic with val: <6 10 16 31 42| Scale is weakly epimorphic with val: <6 10 16 35 38| Scale is weakly epimorphic with val: <6 10 17 32 37| Scale is weakly epimorphic with val: <6 10 17 32 40| Scale is weakly epimorphic with val: <6 10 17 33 36| Scale is weakly epimorphic with val: <6 10 17 36 39| Scale is weakly epimorphic with val: <6 10 18 33 38| Scale is weakly epimorphic with val: <6 10 18 33 41| Scale is weakly epimorphic with val: <6 10 18 34 37| Scale is weakly epimorphic with val: <6 10 19 34 36| Scale is weakly epimorphic with val: <6 10 19 34 39| Scale is weakly epimorphic with val: <6 10 19 34 42| Scale is weakly epimorphic with val: <6 10 19 35 38| Scale is weakly epimorphic with val: <6 11 15 30 37| Scale is weakly epimorphic with val: <6 11 15 30 40| Scale is weakly epimorphic with val: <6 11 15 35 38| Scale is weakly epimorphic with val: <6 11 16 31 38| Scale is weakly epimorphic with val: <6 11 16 31 41| Scale is weakly epimorphic with val: <6 11 16 33 36| Scale is weakly epimorphic with val: <6 11 16 36 39| Scale is weakly epimorphic with val: <6 11 17 32 36| Scale is weakly epimorphic with val: <6 11 17 32 39| Scale is weakly epimorphic with val: <6 11 17 32 42| Scale is weakly epimorphic with val: <6 11 17 34 37| Scale is weakly epimorphic with val: <6 11 18 33 37| Scale is weakly epimorphic with val: <6 11 18 33 40| Scale is weakly epimorphic with val: <6 11 18 35 38| Scale is weakly epimorphic with val: <6 11 19 33 36| Scale is weakly epimorphic with val: <6 11 19 34 38| Scale is weakly epimorphic with val: <6 11 19 34 41| Scale is weakly epimorphic with val: <6 11 19 36 39| Scale is weakly epimorphic with val: <7 10 15 32 37| Scale is weakly epimorphic with val: <7 10 15 32 40| Scale is weakly epimorphic with val: <7 10 15 34 38| Scale is weakly epimorphic with val: <7 10 16 32 36| Scale is weakly epimorphic with val: <7 10 16 33 38| Scale is weakly epimorphic with val: <7 10 16 33 41| Scale is weakly epimorphic with val: <7 10 16 35 39| Scale is weakly epimorphic with val: <7 10 17 33 37| Scale is weakly epimorphic with val: <7 10 17 34 36| Scale is weakly epimorphic with val: <7 10 17 34 39| Scale is weakly epimorphic with val: <7 10 17 34 42| Scale is weakly epimorphic with val: <7 10 17 36 40| Scale is weakly epimorphic with val: <7 10 18 34 38| Scale is weakly epimorphic with val: <7 10 18 35 37| Scale is weakly epimorphic with val: <7 10 18 35 40| Scale is weakly epimorphic with val: <7 10 19 32 36| Scale is weakly epimorphic with val: <7 10 19 35 39| Scale is weakly epimorphic with val: <7 10 19 36 38| Scale is weakly epimorphic with val: <7 10 19 36 41| Scale is weakly epimorphic with val: <7 11 15 30 38| Scale is weakly epimorphic with val: <7 11 15 30 41| Scale is JI-epimorphic with val: <7 11 15 31 37| Scale is weakly epimorphic with val: <7 11 15 31 40| Scale is weakly epimorphic with val: <7 11 15 33 38| Scale is weakly epimorphic with val: <7 11 15 33 41| Scale is weakly epimorphic with val: <7 11 15 34 37| Scale is weakly epimorphic with val: <7 11 15 34 40| Scale is weakly epimorphic with val: <7 11 15 36 38| Scale is weakly epimorphic with val: <7 11 15 36 41| Scale is weakly epimorphic with val: <7 11 16 31 36| Scale is weakly epimorphic with val: <7 11 16 31 39| Scale is weakly epimorphic with val: <7 11 16 31 42| Scale is JI-epimorphic with val: <7 11 16 32 38| Scale is weakly epimorphic with val: <7 11 16 32 41| Scale is weakly epimorphic with val: <7 11 16 34 36| Scale is weakly epimorphic with val: <7 11 16 34 39| Scale is weakly epimorphic with val: <7 11 16 34 42| Scale is weakly epimorphic with val: <7 11 16 35 38| Scale is weakly epimorphic with val: <7 11 16 35 41| Scale is weakly epimorphic with val: <7 11 17 30 36| Scale is weakly epimorphic with val: <7 11 17 30 39| Scale is weakly epimorphic with val: <7 11 17 30 42| Scale is weakly epimorphic with val: <7 11 17 32 37| Scale is weakly epimorphic with val: <7 11 17 32 40| Scale is weakly epimorphic with val: <7 11 17 33 36| Scale is JI-epimorphic with val: <7 11 17 33 39| = patent Scale is weakly epimorphic with val: <7 11 17 33 42| Scale is weakly epimorphic with val: <7 11 17 35 37| Scale is weakly epimorphic with val: <7 11 17 35 40| Scale is weakly epimorphic with val: <7 11 17 36 36| Scale is weakly epimorphic with val: <7 11 17 36 39| Scale is weakly epimorphic with val: <7 11 17 36 42| Scale is weakly epimorphic with val: <7 11 18 30 38| Scale is weakly epimorphic with val: <7 11 18 30 41| Scale is weakly epimorphic with val: <7 11 18 31 37| Scale is weakly epimorphic with val: <7 11 18 31 40| Scale is weakly epimorphic with val: <7 11 18 33 38| Scale is weakly epimorphic with val: <7 11 18 33 41| Scale is weakly epimorphic with val: <7 11 18 34 37| Scale is JI-epimorphic with val: <7 11 18 34 40| Scale is weakly epimorphic with val: <7 11 18 36 38| Scale is weakly epimorphic with val: <7 11 18 36 41| Scale is weakly epimorphic with val: <7 11 19 31 36| Scale is weakly epimorphic with val: <7 11 19 31 39| Scale is weakly epimorphic with val: <7 11 19 31 42| Scale is weakly epimorphic with val: <7 11 19 32 38| Scale is weakly epimorphic with val: <7 11 19 32 41| Scale is weakly epimorphic with val: <7 11 19 34 36| Scale is weakly epimorphic with val: <7 11 19 34 39| Scale is weakly epimorphic with val: <7 11 19 34 42| Scale is weakly epimorphic with val: <7 11 19 35 38| Scale is JI-epimorphic with val: <7 11 19 35 41| Scale is weakly epimorphic with val: <7 12 15 32 38| Scale is weakly epimorphic with val: <7 12 15 32 41| Scale is weakly epimorphic with val: <7 12 15 33 37| Scale is weakly epimorphic with val: <7 12 15 36 40| Scale is weakly epimorphic with val: <7 12 16 33 36| Scale is weakly epimorphic with val: <7 12 16 33 39| Scale is weakly epimorphic with val: <7 12 16 33 42| Scale is weakly epimorphic with val: <7 12 16 34 38| Scale is weakly epimorphic with val: <7 12 17 32 36| Scale is weakly epimorphic with val: <7 12 17 34 37| Scale is weakly epimorphic with val: <7 12 17 34 40| Scale is weakly epimorphic with val: <7 12 17 35 39| Scale is weakly epimorphic with val: <7 12 18 33 37| Scale is weakly epimorphic with val: <7 12 18 35 38| Scale is weakly epimorphic with val: <7 12 18 35 41| Scale is weakly epimorphic with val: <7 12 18 36 40| Scale is weakly epimorphic with val: <7 12 19 34 38| Scale is weakly epimorphic with val: <7 12 19 36 36| Scale is weakly epimorphic with val: <7 12 19 36 39| Scale is weakly epimorphic with val: <7 12 19 36 42| Scale is weakly epimorphic with val: <8 11 15 32 37| Scale is weakly epimorphic with val: <8 11 15 34 38| Scale is weakly epimorphic with val: <8 11 15 34 41| Scale is weakly epimorphic with val: <8 11 15 35 40| Scale is weakly epimorphic with val: <8 11 16 33 38| Scale is weakly epimorphic with val: <8 11 16 35 36| Scale is weakly epimorphic with val: <8 11 16 35 39| Scale is weakly epimorphic with val: <8 11 16 35 42| Scale is weakly epimorphic with val: <8 11 16 36 41| Scale is weakly epimorphic with val: <8 11 17 31 36| Scale is weakly epimorphic with val: <8 11 17 34 39| Scale is weakly epimorphic with val: <8 11 17 36 37| Scale is weakly epimorphic with val: <8 11 17 36 40| Scale is weakly epimorphic with val: <8 11 18 32 37| Scale is weakly epimorphic with val: <8 11 18 35 40| Scale is weakly epimorphic with val: <8 11 19 33 38| Scale is weakly epimorphic with val: <8 11 19 36 41| Scale is weakly epimorphic with val: <8 12 15 33 38| Scale is weakly epimorphic with val: <8 12 15 34 37| Scale is weakly epimorphic with val: <8 12 15 34 40| Scale is weakly epimorphic with val: <8 12 15 36 41| Scale is weakly epimorphic with val: <8 12 16 31 36| Scale is weakly epimorphic with val: <8 12 16 34 39| Scale is weakly epimorphic with val: <8 12 16 35 38| Scale is weakly epimorphic with val: <8 12 16 35 41| Scale is weakly epimorphic with val: <8 12 17 32 37| Scale is weakly epimorphic with val: <8 12 17 35 40| Scale is weakly epimorphic with val: <8 12 17 36 36| Scale is weakly epimorphic with val: <8 12 17 36 39| Scale is weakly epimorphic with val: <8 12 17 36 42| Scale is weakly epimorphic with val: <8 12 18 33 38| Scale is weakly epimorphic with val: <8 12 18 36 41| Scale is weakly epimorphic with val: <8 12 19 31 36| Scale is weakly epimorphic with val: <8 12 19 34 39|
FIT/MODE
3: 1 0 2 N G T3 SD: 52.2626 c. M: 75.9456 c. 4: 1 1 2 P M ME S SD: 6.0554 c. M:-7.7546 c. 17: 4 4 9 N M DE S SD: 4.3871 c. M: 7.5865 c. 18: 4 5 9 P T3 SD: 5.3801 c. M:-7.0619 c. 21: 5 5 11 N M DE S SD: 2.9630 c. M: 4.7963 c. 25: 6 6 13 N M DE S SD: 2.3166 c. M: 2.8990 c. 29: 7 7 15 N M DE S SD: 2.1837 c. M:-3.4611 c. 31: 7 8 16 N T3 SD: 2.5422 c. M: 4.2949 c. 33: 8 8 17 N M DE S SD: 2.3157 c. M:-3.9815 c. 35: 8 9 18 N T3 SD: 1.6849 c. M: 2.9178 c. 39: 9 10 20 N T3 SD: 1.1228 c. M: 1.8232 c. 43: 10 11 22 N T3 SD: 0.9099 c. M:-1.2706 c. 47: 11 12 24 N T3 SD: 1.0242 c. M:-1.7635 c. 60: 14 15 31 N T3 SD: 0.7817 c. M: 1.2389 c. 64: 15 16 33 N T3 SD: 0.4160 c. M: 0.7201 c. 68: 16 17 35 N T3 SD: 0.2910 c. M:-0.4304 c. 107: 25 27 55 N T3 SD: 0.2304 c. M: 0.3910 c. 111: 26 28 57 N T3 SD: 0.1995 c. M:-0.3315 c. 171: 40 43 88 N T3 SD: 0.1942 c. M: 0.2549 c. 175: 41 44 90 N T3 SD: 0.0516 c. M: 0.0718 c. 354: 83 89 182 N T3 SD: 0.0185 c. M:-0.0273 c. 529: 124 133 272 N T3 SD: 0.0073 c. M: 0.0126 c. 883: 207 222 454 N T3 SD: 0.0066 c. M:-0.0114 c. 1412: 331 355 726 N T3 SD: 0.0053 c. M:-0.0074 c. 1941: 455 488 998 N T3 SD: 0.0053 c. M: 0.0073 c. 2009: 471 505 1033 N T3 SD: 0.0048 c. M:-0.0075 c. 2184: 512 549 1123 N T3 SD: 0.0044 c. M: 0.0075 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: 56.0436 cents 6 x 7:8 S SD: 12.4551 cents 7 x 8:9 S SD: 31.9391 cents 8 x 9:11 SD: 32.7332 cents 9 x 10:12 S SD: 29.7785 cents 11:12:13:15 SD: 23.3191 cents 12:13:14:16 S SD: 11.0376 cents 14:15:16:19 SD: 10.8654 cents 15:16:17:20 SD: 8.5896 cents 26:28:30:35 S SD: 7.0007 cents 27:29:31:36 SD: 2.4981 cents 60:64:69:80 SD: 1.6751 cents 72:77:83:96 SD: 1.4031 cents 87:93:100:116 SD: 0.5201 cents 114:122:131:152 SD: 0.4923 cents 186:199:214:248 SD: 0.2780 cents 273:292:314:364 SD: 0.1300 cents 300:321:345:400 SD: 0.1254 cents 387:414:445:516 SD: 0.0648 cents 573:613:659:764 SD: 0.0490 cents