Scala analysis: 130_E16
Enharmonic tetrachord 42/41 * 22/21 * 41/33
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 42/41 41.718502 2: 44/41 122.255537 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 41/33 375.7895 1: 42/41 41.7185 2: 22/21 80.5370 undecimal minor semitone 3: 41/33 375.7895
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 42/41 41.719 cents 1: 1 22/21 80.537 cents undecimal minor semitone 1: 1 41/33 375.789 cents 2: 1 44/41 122.256 cents 2: 1 14/11 417.508 cents undecimal diminished fourth or major third 2: 1 82/63 456.326 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 : 41.7 122.3 498.0 41.7 : 80.5 456.3 498.0 122.3: 375.8 417.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 41.7185 .. 375.7895 cents 1681/1386, 334.0710 cents 42/41, 41.7185 cents 2: 122.2555 .. 456.3265 cents 1681/1386, 334.0710 cents 1452/1681,-253.5339 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 42/41, 41.7185 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 41/33, 375.7895 cents Average / Smallest step : 3.979409 Largest / Average step : 2.263587 Largest / Smallest step : 9.007741 Median interval of one step : 22/21, 80.5370 cents, amount: 1 Least squares average step : 127.16890 cents, oct.: 381.50669 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1707-tone equal temperament with octave 4/3 degrees: 143 419 1707 Least number of segments generator : 854 of 249.168 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1615 of 471.203 cents and inv. generated superset size: 18 = 15 more = 600.000% 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 41.71850 cents Scale diversity : 0.554931 Lumma stability : 0.167529 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 : 451/441, 38.8185 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% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 41 Odd number limit : 63 (O: 41 U: 63) Highest odd numerator or denominator: 41 Scale harmonicity : 0.027932 Fundamental : 1/123, -6.9425 octaves, 2.1270 Hz. Guide tone : 924, 9.8517 octaves, 241742.022 Hz. Exponens Consonantiae : 1.136520E+05, 16.79426 octaves Euler's gradus suavitatis : 63 Sum of Mann's harmonic distance : 87.5, average 29.16667 Mersenne's string divisions : 49385 Sum of van Prooijen's expressibility: 3.70269, average 1.23423 Sum of Tenney's harmonic distance : 7.57145, average 2.52382 Vogel's harmonic complexity : 24.33333 Wille's k value : 31 Wilson's harmonic complexity : 65 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 12.06789, average 2.01132 Lattice compactness (without 2's) : 8.79655, average 1.46609 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -1 .. 1 0.00000 2 1 7: 0 .. 1 0.33333 1 11: 0 .. 1 0.33333 1 41: -1 .. 0 -0.66667 2 2 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 18 27 36| Scale is weakly epimorphic with val: <6 10 21 27 36| Scale is weakly epimorphic with val: <6 11 18 27 36| Scale is weakly epimorphic with val: <6 11 21 27 36| Scale is weakly epimorphic with val: <6 11 22 23 36| Scale is weakly epimorphic with val: <6 11 22 26 36| Scale is weakly epimorphic with val: <7 10 18 25 36| Scale is weakly epimorphic with val: <7 10 19 26 37| Scale is weakly epimorphic with val: <7 10 20 27 38| Scale is weakly epimorphic with val: <7 10 21 25 36| Scale is weakly epimorphic with val: <7 10 22 24 36| Scale is weakly epimorphic with val: <7 10 22 26 37| Scale is weakly epimorphic with val: <7 10 22 27 36| Scale is weakly epimorphic with val: <7 11 18 23 38| Scale is weakly epimorphic with val: <7 11 18 23 41| Scale is weakly epimorphic with val: <7 11 18 24 37| Scale is weakly epimorphic with val: <7 11 18 24 40| Scale is weakly epimorphic with val: <7 11 18 26 38| Scale is weakly epimorphic with val: <7 11 18 26 41| Scale is weakly epimorphic with val: <7 11 18 27 37| Scale is weakly epimorphic with val: <7 11 18 27 40| Scale is JI-epimorphic with val: <7 11 19 24 36| Scale is weakly epimorphic with val: <7 11 19 24 39| Scale is weakly epimorphic with val: <7 11 19 24 42| Scale is weakly epimorphic with val: <7 11 19 25 38| Scale is weakly epimorphic with val: <7 11 19 25 41| Scale is weakly epimorphic with val: <7 11 19 27 36| Scale is weakly epimorphic with val: <7 11 19 27 39| Scale is weakly epimorphic with val: <7 11 19 27 42| Scale is weakly epimorphic with val: <7 11 20 23 36| Scale is weakly epimorphic with val: <7 11 20 23 39| Scale is weakly epimorphic with val: <7 11 20 23 42| Scale is JI-epimorphic with val: <7 11 20 25 37| Scale is weakly epimorphic with val: <7 11 20 25 40| Scale is weakly epimorphic with val: <7 11 20 26 36| Scale is weakly epimorphic with val: <7 11 20 26 39| Scale is weakly epimorphic with val: <7 11 20 26 42| Scale is weakly epimorphic with val: <7 11 21 23 38| Scale is weakly epimorphic with val: <7 11 21 23 41| Scale is weakly epimorphic with val: <7 11 21 24 37| Scale is weakly epimorphic with val: <7 11 21 24 40| Scale is JI-epimorphic with val: <7 11 21 26 38| Scale is weakly epimorphic with val: <7 11 21 26 41| Scale is weakly epimorphic with val: <7 11 21 27 37| Scale is weakly epimorphic with val: <7 11 21 27 40| Scale is weakly epimorphic with val: <7 11 22 24 36| Scale is weakly epimorphic with val: <7 11 22 24 39| Scale is weakly epimorphic with val: <7 11 22 24 42| Scale is weakly epimorphic with val: <7 11 22 25 38| Scale is weakly epimorphic with val: <7 11 22 25 41| Scale is weakly epimorphic with val: <7 11 22 27 36| Scale is JI-epimorphic with val: <7 11 22 27 39| Scale is weakly epimorphic with val: <7 11 22 27 42| Scale is weakly epimorphic with val: <7 12 18 25 36| Scale is weakly epimorphic with val: <7 12 19 26 37| Scale is weakly epimorphic with val: <7 12 20 23 36| Scale is weakly epimorphic with val: <7 12 20 26 36| Scale is weakly epimorphic with val: <7 12 20 27 38| Scale is weakly epimorphic with val: <7 12 21 24 37| Scale is weakly epimorphic with val: <7 12 21 25 36| Scale is weakly epimorphic with val: <7 12 21 27 37| Scale is weakly epimorphic with val: <7 12 22 25 38| Scale is weakly epimorphic with val: <7 12 22 26 37| Scale is weakly epimorphic with val: <8 11 18 23 36| Scale is weakly epimorphic with val: <8 11 18 26 39| Scale is weakly epimorphic with val: <8 11 19 24 37| Scale is weakly epimorphic with val: <8 11 19 27 40| Scale is weakly epimorphic with val: <8 11 20 24 36| Scale is weakly epimorphic with val: <8 11 20 25 38| Scale is weakly epimorphic with val: <8 11 20 27 36| Scale is weakly epimorphic with val: <8 11 21 23 36| Scale is weakly epimorphic with val: <8 11 21 25 37| Scale is weakly epimorphic with val: <8 11 21 26 39| Scale is weakly epimorphic with val: <8 11 22 23 38| Scale is weakly epimorphic with val: <8 11 22 24 37| Scale is weakly epimorphic with val: <8 11 22 26 38| Scale is weakly epimorphic with val: <8 11 22 27 40| Scale is weakly epimorphic with val: <8 12 18 23 36| Scale is weakly epimorphic with val: <8 12 18 26 39| Scale is weakly epimorphic with val: <8 12 19 24 37| Scale is weakly epimorphic with val: <8 12 19 25 36| Scale is weakly epimorphic with val: <8 12 19 27 40| Scale is weakly epimorphic with val: <8 12 20 23 37| Scale is weakly epimorphic with val: <8 12 20 25 38| Scale is weakly epimorphic with val: <8 12 20 26 37| Scale is weakly epimorphic with val: <8 12 21 23 36| Scale is weakly epimorphic with val: <8 12 21 24 38| Scale is weakly epimorphic with val: <8 12 21 26 39| Scale is weakly epimorphic with val: <8 12 21 27 38| Scale is weakly epimorphic with val: <8 12 22 24 37| Scale is weakly epimorphic with val: <8 12 22 25 39| Scale is weakly epimorphic with val: <8 12 22 27 40|
FIT/MODE
3: 0 1 2 N G T3 SD: 34.9062 c. M:-43.7595 c. 4: 0 1 3 N G T3 SD: 24.1214 c. M: 41.7185 c. 5: 0 1 4 N G T3 SD: 27.4062 c. M: 41.7185 c. 7: 1 1 5 N M DE S SD: 20.5580 c. M:-29.4308 c. 8: 1 1 6 N M DE S SD: 11.9284 c. M:-20.5371 c. 9: 1 1 7 N M DE S SD: 10.3210 c. M:-13.6198 c. 11: 1 2 8 N T3 SD: 8.1023 c. M:-13.5749 c. 12: 1 2 9 N T3 SD: 1.3082 c. M:-2.2557 c. 37: 3 6 28 N T3 SD: 1.0028 c. M: 1.3365 c. 49: 4 8 37 N T3 SD: 0.6348 c. M: 1.0618 c. 61: 5 10 46 N T3 SD: 0.5314 c. M: 0.8951 c. 73: 6 12 55 N T3 SD: 0.5526 c. M: 0.7833 c. 94: 8 15 71 N T3 SD: 0.4478 c. M:-0.6683 c. 106: 9 17 80 N T3 SD: 0.3325 c. M:-0.5683 c. 118: 10 19 89 N T3 SD: 0.2944 c. M:-0.4887 c. 130: 11 21 98 N T3 SD: 0.3137 c. M:-0.4238 c. 143: 12 23 108 N T3 SD: 0.2103 c. M: 0.3564 c. 155: 13 25 117 N T3 SD: 0.0941 c. M: 0.1542 c. 167: 14 27 126 N T3 SD: 0.0224 c. M:-0.0338 c. 872: 73 141 658 N T3 SD: 0.0218 c. M: 0.0289 c. 884: 74 143 667 N T3 SD: 0.0156 c. M: 0.0270 c. 1039: 87 168 784 N T3 SD: 0.0150 c. M: 0.0212 c. 1051: 88 170 793 N T3 SD: 0.0104 c. M: 0.0173 c. 1206: 101 195 910 N T3 SD: 0.0102 c. M: 0.0156 c. 1218: 102 197 919 N T3 SD: 0.0071 c. M: 0.0103 c. 1373: 115 222 1036 N T3 SD: 0.0068 c. M: 0.0114 c. 1385: 116 224 1045 N T3 SD: 0.0055 c. M:-0.0082 c. 1540: 129 249 1162 N T3 SD: 0.0047 c. M: 0.0081 c. 1707: 143 276 1288 N T3 SD: 0.0039 c. M: 0.0055 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: 17.4757 cents 22:23:24:29 SD: 16.4611 cents 23:24:25:31 SD: 14.3766 cents 24:25:26:32 SD: 11.0784 cents 26:27:28:35 S SD: 9.8253 cents 27:28:29:36 SD: 7.0974 cents 30:31:32:40 S SD: 6.1211 cents 36:37:39:48 SD: 5.7631 cents 38:39:41:51 SD: 5.0091 cents 39:40:42:52 SD: 2.1338 cents 42:43:45:56 SD: 0.9930 cents 81:83:87:108 SD: 0.5143 cents 123:126:132:164 SD: 0.0000 cents