Scala analysis: 131_E16
Enharmonic tetrachord 44/43 * 43/41 * 41/33
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 44/43 39.800237 2: 44/41 122.255537 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 41/33 375.7895 1: 44/43 39.8002 2: 43/41 82.4553 3: 41/33 375.7895
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 44/43 39.800 cents 1: 1 43/41 82.455 cents 1: 1 41/33 375.789 cents 2: 1 44/41 122.256 cents 2: 1 164/129 415.590 cents 2: 1 43/33 458.245 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 : 39.8 122.3 498.0 39.8 : 82.5 458.2 498.0 122.3: 375.8 415.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 39.8002 .. 375.7895 cents 1763/1452, 335.9892 cents 44/43, 39.8002 cents 2: 122.2555 .. 458.2448 cents 1763/1452, 335.9892 cents 1452/1681,-253.5339 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 44/43, 39.8002 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 41/33, 375.7895 cents Average / Smallest step : 4.171206 Largest / Average step : 2.263587 Largest / Smallest step : 9.441890 Median interval of one step : 43/41, 82.4553 cents, amount: 1 Least squares average step : 127.03188 cents, oct.: 381.09564 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1051-tone equal temperament with octave 4/3 degrees: 84 258 1051 Least number of segments generator : 526 of 249.259 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 619 of 293.330 cents and inv. generated superset size: 30 = 27 more = 1000.000% 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 39.80024 cents Scale diversity : 0.547418 Lumma stability : 0.159826 Lumma impropriety factor : 0.509058 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 : 44/43, 39.8002 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 43 Odd number limit : 129 (O: 43 U: 129) Highest odd numerator or denominator: 43 Scale harmonicity : 0.043767 Fundamental : 1/5289, -12.3688 octaves, 0.0495 Hz. Guide tone : 44, 5.4594 octaves, 11511.525 Hz. Exponens Consonantiae : 2.327160E+05, 17.82821 octaves Euler's gradus suavitatis : 97 Sum of Mann's harmonic distance : 89.5, average 29.83333 Mersenne's string divisions : 51765 Sum of van Prooijen's expressibility: 3.72337, average 1.24112 Sum of Tenney's harmonic distance : 7.61234, average 2.53745 Vogel's harmonic complexity : 67.33333 Wille's k value : 881 Wilson's harmonic complexity : 98 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 9.53663, average 1.58944 Lattice compactness (without 2's) : 5.82843, average 0.97140 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 2 2.00000 6 3: -1 .. 0 -0.33333 1 1 11: 0 .. 1 0.66667 2 41: -1 .. 0 -0.33333 1 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 27 36 38| Scale is weakly epimorphic with val: <6 10 27 36 41| Scale is weakly epimorphic with val: <6 11 27 36 37| Scale is weakly epimorphic with val: <6 11 27 36 40| Scale is weakly epimorphic with val: <7 10 25 36 37| Scale is weakly epimorphic with val: <7 10 25 36 40| Scale is weakly epimorphic with val: <7 10 26 37 38| Scale is weakly epimorphic with val: <7 10 26 37 41| Scale is weakly epimorphic with val: <7 10 27 36 38| Scale is weakly epimorphic with val: <7 10 27 38 39| Scale is weakly epimorphic with val: <7 10 27 38 42| Scale is weakly epimorphic with val: <7 11 23 36 38| Scale is weakly epimorphic with val: <7 11 23 36 41| Scale is weakly epimorphic with val: <7 11 23 38 39| Scale is weakly epimorphic with val: <7 11 23 38 42| Scale is weakly epimorphic with val: <7 11 23 39 41| Scale is weakly epimorphic with val: <7 11 23 41 42| Scale is JI-epimorphic with val: <7 11 24 36 37| Scale is weakly epimorphic with val: <7 11 24 36 40| Scale is weakly epimorphic with val: <7 11 24 37 39| Scale is weakly epimorphic with val: <7 11 24 37 42| Scale is weakly epimorphic with val: <7 11 24 39 40| Scale is weakly epimorphic with val: <7 11 24 40 42| Scale is JI-epimorphic with val: <7 11 25 37 38| Scale is weakly epimorphic with val: <7 11 25 37 41| Scale is weakly epimorphic with val: <7 11 25 38 40| Scale is weakly epimorphic with val: <7 11 25 40 41| Scale is weakly epimorphic with val: <7 11 26 36 38| Scale is weakly epimorphic with val: <7 11 26 36 41| Scale is JI-epimorphic with val: <7 11 26 38 39| Scale is weakly epimorphic with val: <7 11 26 38 42| Scale is weakly epimorphic with val: <7 11 26 39 41| Scale is weakly epimorphic with val: <7 11 26 41 42| Scale is weakly epimorphic with val: <7 11 27 36 37| Scale is weakly epimorphic with val: <7 11 27 36 40| Scale is weakly epimorphic with val: <7 11 27 37 39| Scale is weakly epimorphic with val: <7 11 27 37 42| Scale is JI-epimorphic with val: <7 11 27 39 40| Scale is weakly epimorphic with val: <7 11 27 40 42| Scale is weakly epimorphic with val: <7 12 25 36 38| Scale is weakly epimorphic with val: <7 12 25 36 41| Scale is weakly epimorphic with val: <7 12 26 36 37| Scale is weakly epimorphic with val: <7 12 26 37 39| Scale is weakly epimorphic with val: <7 12 26 37 42| Scale is weakly epimorphic with val: <7 12 27 37 38| Scale is weakly epimorphic with val: <7 12 27 38 40| Scale is weakly epimorphic with val: <8 11 23 36 38| Scale is weakly epimorphic with val: <8 11 23 36 41| Scale is weakly epimorphic with val: <8 11 24 36 37| Scale is weakly epimorphic with val: <8 11 24 37 39| Scale is weakly epimorphic with val: <8 11 24 37 42| Scale is weakly epimorphic with val: <8 11 25 37 38| Scale is weakly epimorphic with val: <8 11 25 38 40| Scale is weakly epimorphic with val: <8 11 26 38 39| Scale is weakly epimorphic with val: <8 11 26 39 41| Scale is weakly epimorphic with val: <8 11 27 36 40| Scale is weakly epimorphic with val: <8 11 27 39 40| Scale is weakly epimorphic with val: <8 11 27 40 42| Scale is weakly epimorphic with val: <8 12 23 36 37| Scale is weakly epimorphic with val: <8 12 23 36 40| Scale is weakly epimorphic with val: <8 12 24 37 38| Scale is weakly epimorphic with val: <8 12 24 37 41| Scale is weakly epimorphic with val: <8 12 25 36 38| Scale is weakly epimorphic with val: <8 12 25 38 39| Scale is weakly epimorphic with val: <8 12 25 38 42| Scale is weakly epimorphic with val: <8 12 26 37 39| Scale is weakly epimorphic with val: <8 12 26 39 40| Scale is weakly epimorphic with val: <8 12 27 38 40| Scale is weakly epimorphic with val: <8 12 27 40 41|
FIT/MODE
3: 0 1 2 N G T3 SD: 34.1514 c. M:-43.7595 c. 4: 0 1 3 N G T3 SD: 23.0156 c. M: 39.8002 c. 5: 0 1 4 N G T3 SD: 26.4381 c. M: 39.8002 c. 7: 1 1 5 N M DE S SD: 21.4824 c. M:-31.3490 c. 8: 1 1 6 N M DE S SD: 13.0299 c. M:-22.4554 c. 9: 1 1 7 N M DE S SD: 11.1878 c. M:-15.5381 c. 11: 1 2 8 N T3 SD: 8.4513 c. M:-13.5749 c. 12: 1 2 9 N T3 SD: 1.6320 c. M:-2.2557 c. 25: 2 4 19 N T3 SD: 1.5733 c. M: 2.7247 c. 37: 3 6 28 N T3 SD: 0.7233 c. M: 1.1095 c. 49: 4 8 37 N T3 SD: 0.5212 c. M:-0.8565 c. 61: 5 10 46 N T3 SD: 0.6035 c. M:-1.0231 c. 86: 7 14 65 N T3 SD: 0.5641 c. M:-0.7383 c. 102: 8 17 77 N T3 SD: 0.4393 c. M: 0.7379 c. 114: 9 19 86 N T3 SD: 0.2807 c. M: 0.4809 c. 126: 10 21 95 N T3 SD: 0.2255 c. M:-0.2793 c. 151: 12 25 114 N T3 SD: 0.1790 c. M: 0.2205 c. 163: 13 27 123 N T3 SD: 0.0500 c. M: 0.0789 c. 338: 27 56 255 N T3 SD: 0.0277 c. M:-0.0455 c. 501: 40 83 378 N T3 SD: 0.0236 c. M: 0.0362 c. 550: 44 91 415 N T3 SD: 0.0255 c. M:-0.0434 c. 713: 57 118 538 N T3 SD: 0.0122 c. M:-0.0154 c. 876: 70 145 661 N T3 SD: 0.0107 c. M: 0.0185 c. 1051: 84 174 793 N T3 SD: 0.0042 c. M:-0.0055 c. 1214: 97 201 916 N T3 SD: 0.0034 c. M: 0.0059 c. 2265: 181 375 1709 N T3 SD: 0.0011 c. M:-0.0019 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 x 7 SD: 84.4672 cents 6 x 7:8 S SD: 72.3077 cents 7 x 8:9 S SD: 62.9034 cents 8 x 9:11 SD: 48.7480 cents 9 x 10:12 S SD: 30.0741 cents 10 x 11:13 SD: 30.6130 cents 11 x 12:15 S SD: 24.0789 cents 12 x 13:16 SD: 8.1586 cents 13 x 14:17 SD: 17.0780 cents 14 x 15:19 SD: 15.3855 cents 15 x 16:20 S SD: 5.2621 cents 16 x 17:21 SD: 16.1449 cents 17 x 18:23 SD: 17.1880 cents 18 x 19:24 SD: 14.3263 cents 19 x 20:25 S SD: 20.2795 cents 20 x 21:27 SD: 21.7398 cents 21:22:23:28 SD: 17.9543 cents 22:23:24:29 SD: 16.9232 cents 23:24:25:31 SD: 14.8567 cents 24:25:26:32 SD: 11.6397 cents 25:26:27:33 SD: 11.6092 cents 26:27:28:35 S SD: 10.3447 cents 27:28:29:36 SD: 7.7355 cents 30:31:32:40 S SD: 6.6552 cents 36:37:39:48 SD: 6.0048 cents 38:39:41:51 SD: 5.1852 cents 39:40:42:52 SD: 2.4212 cents 42:43:45:56 SD: 0.9882 cents 81:83:87:108 SD: 0.9435 cents 123:126:132:164 SD: 0.6394 cents 165:169:177:220 SD: 0.6051 cents 177:181:190:236 SD: 0.3991 cents 219:224:235:292 SD: 0.2470 cents 300:307:322:400 SD: 0.0977 cents 342:350:367:456 SD: 0.0857 cents 519:531:557:692 SD: 0.0799 cents 561:574:602:748 SD: 0.0661 cents