Scala analysis: 137_C2
Chromatic tetrachord 42/41 * 41/39 * 26/21
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 42/41 41.718502 2: 14/13 128.298245 2/3-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 26/21 369.7468 1: 42/41 41.7185 2: 41/39 86.5797 3: 26/21 369.7468
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 42/41 41.719 cents 1: 1 41/39 86.580 cents 1: 1 26/21 369.747 cents 2: 1 14/13 128.298 cents 2/3-tone 2: 1 52/41 411.465 cents 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 : 41.7 128.3 498.0 41.7 : 86.6 456.3 498.0 128.3: 369.7 411.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 41.7185 .. 369.7468 cents 533/441, 328.0283 cents 42/41, 41.7185 cents 2: 128.2982 .. 456.3265 cents 533/441, 328.0283 cents 147/169,-241.4485 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 : 26/21, 369.7468 cents Average / Smallest step : 3.979409 Largest / Average step : 2.227189 Largest / Smallest step : 8.862896 Median interval of one step : 41/39, 86.5797 cents, amount: 1 Least squares average step : 128.03214 cents, oct.: 384.09643 cents Scale is not proper Scale has trivalence property Scale is a mode of a 788-tone equal temperament with octave 4/3 degrees: 66 203 788 Least number of segments generator : 395 of 249.655 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 637 of 402.607 cents and inv. generated superset size: 28 = 25 more = 933.333% 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 : 0.589124 Lumma stability : 0.167529 Lumma impropriety factor : 0.484793 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 : 42/41, 41.7185 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 : 41 Odd number limit : 63 (O: 41 U: 63) Highest odd numerator or denominator: 41 Scale harmonicity : 0.025143 Fundamental : 1/1599, -10.6430 octaves, 0.1636 Hz. Guide tone : 84, 6.3923 octaves, 21976.547 Hz. Exponens Consonantiae : 1.343160E+05, 17.03527 octaves Euler's gradus suavitatis : 65 Sum of Mann's harmonic distance : 58.5, average 19.50000 Mersenne's string divisions : 15687 Sum of van Prooijen's expressibility: 3.20385, average 1.06795 Sum of Tenney's harmonic distance : 6.57529, average 2.19176 Vogel's harmonic complexity : 45.00000 Wille's k value : 430 Wilson's harmonic complexity : 67 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 11.56387, average 1.92731 Lattice compactness (without 2's) : 9.21076, average 1.53513 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.33333 4 3: -1 .. 1 0.00000 2 1 7: 0 .. 1 0.66667 2 13: -1 .. 0 -0.33333 1 1 41: -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 22 25 37| Scale is weakly epimorphic with val: <6 10 22 25 40| Scale is weakly epimorphic with val: <6 11 22 25 37| Scale is weakly epimorphic with val: <6 11 22 25 40| Scale is weakly epimorphic with val: <6 11 22 26 36| Scale is weakly epimorphic with val: <6 11 22 29 36| Scale is weakly epimorphic with val: <7 10 21 25 36| Scale is weakly epimorphic with val: <7 10 21 25 39| Scale is weakly epimorphic with val: <7 10 21 25 42| Scale is weakly epimorphic with val: <7 10 22 26 37| Scale is weakly epimorphic with val: <7 10 22 26 40| Scale is weakly epimorphic with val: <7 10 22 27 36| Scale is weakly epimorphic with val: <7 10 22 30 36| 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 weakly epimorphic with val: <7 11 18 29 38| Scale is weakly epimorphic with val: <7 11 18 29 41| Scale is weakly epimorphic with val: <7 11 18 30 37| Scale is weakly epimorphic with val: <7 11 18 30 40| 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 19 28 38| Scale is weakly epimorphic with val: <7 11 19 28 41| Scale is weakly epimorphic with val: <7 11 19 30 36| Scale is weakly epimorphic with val: <7 11 19 30 39| Scale is weakly epimorphic with val: <7 11 19 30 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 20 28 37| Scale is weakly epimorphic with val: <7 11 20 28 40| Scale is weakly epimorphic with val: <7 11 20 29 36| Scale is weakly epimorphic with val: <7 11 20 29 39| Scale is weakly epimorphic with val: <7 11 20 29 42| 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 21 29 38| Scale is weakly epimorphic with val: <7 11 21 29 41| Scale is weakly epimorphic with val: <7 11 21 30 37| Scale is weakly epimorphic with val: <7 11 21 30 40| 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 11 22 28 38| Scale is weakly epimorphic with val: <7 11 22 28 41| Scale is weakly epimorphic with val: <7 11 22 30 36| Scale is weakly epimorphic with val: <7 11 22 30 39| Scale is weakly epimorphic with val: <7 11 22 30 42| Scale is weakly epimorphic with val: <7 12 20 26 36| Scale is weakly epimorphic with val: <7 12 20 29 36| Scale is weakly epimorphic with val: <7 12 21 25 36| Scale is weakly epimorphic with val: <7 12 21 25 39| Scale is weakly epimorphic with val: <7 12 21 25 42| Scale is weakly epimorphic with val: <7 12 21 27 37| Scale is weakly epimorphic with val: <7 12 21 30 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: <7 12 22 26 40| Scale is weakly epimorphic with val: <7 12 22 28 38| Scale is weakly epimorphic with val: <8 11 20 25 38| Scale is weakly epimorphic with val: <8 11 20 25 41| Scale is weakly epimorphic with val: <8 11 20 27 36| Scale is weakly epimorphic with val: <8 11 20 30 36| Scale is weakly epimorphic with val: <8 11 21 25 37| Scale is weakly epimorphic with val: <8 11 21 26 36| Scale is weakly epimorphic with val: <8 11 21 26 39| Scale is weakly epimorphic with val: <8 11 21 26 42| Scale is weakly epimorphic with val: <8 11 21 28 37| Scale is weakly epimorphic with val: <8 11 22 26 38| Scale is weakly epimorphic with val: <8 11 22 27 37| Scale is weakly epimorphic with val: <8 11 22 27 40| Scale is weakly epimorphic with val: <8 11 22 29 38| Scale is weakly epimorphic with val: <8 12 19 25 36| Scale is weakly epimorphic with val: <8 12 19 28 36| Scale is weakly epimorphic with val: <8 12 20 25 38| Scale is weakly epimorphic with val: <8 12 20 25 41| Scale is weakly epimorphic with val: <8 12 20 26 37| Scale is weakly epimorphic with val: <8 12 20 29 37| Scale is weakly epimorphic with val: <8 12 21 26 36| Scale is weakly epimorphic with val: <8 12 21 26 39| Scale is weakly epimorphic with val: <8 12 21 26 42| Scale is weakly epimorphic with val: <8 12 21 27 38| Scale is weakly epimorphic with val: <8 12 21 30 38| Scale is weakly epimorphic with val: <8 12 22 25 39| Scale is weakly epimorphic with val: <8 12 22 27 37| Scale is weakly epimorphic with val: <8 12 22 27 40| Scale is weakly epimorphic with val: <8 12 22 28 39|
FIT/MODE
3: 0 1 2 N G T3 SD: 32.4704 c. M: 41.7185 c. 4: 0 1 3 N G T3 SD: 24.1852 c. M: 41.7185 c. 7: 1 1 5 N M DE S SD: 18.8165 c. M:-29.4308 c. 8: 1 1 6 N M DE S SD: 12.0570 c. M:-20.5371 c. 9: 1 1 7 N M DE S SD: 12.8585 c. M: 17.6216 c. 10: 1 2 7 N T3 SD: 13.0542 c. M:-21.1153 c. 11: 1 2 8 N T3 SD: 4.8096 c. M:-7.5322 c. 12: 1 2 9 N T3 SD: 2.1899 c. M: 3.7870 c. 23: 2 4 17 N T3 SD: 1.3131 c. M:-1.6265 c. 35: 3 6 26 N T3 SD: 0.5761 c. M:-0.9711 c. 82: 7 14 61 N T3 SD: 0.6321 c. M:-0.7975 c. 85: 7 15 63 N T3 SD: 0.5364 c. M: 0.7030 c. 97: 8 17 72 N T3 SD: 0.3728 c. M: 0.6426 c. 109: 9 19 81 N T3 SD: 0.4018 c. M: 0.5955 c. 120: 10 21 89 N T3 SD: 0.2437 c. M:-0.3634 c. 132: 11 23 98 N T3 SD: 0.1242 c. M: 0.2148 c. 155: 13 27 115 N T3 SD: 0.1360 c. M:-0.2295 c. 167: 14 29 124 N T3 SD: 0.0393 c. M: 0.0591 c. 454: 38 79 337 N T3 SD: 0.0355 c. M:-0.0526 c. 466: 39 81 346 N T3 SD: 0.0341 c. M: 0.0463 c. 489: 41 85 363 N T3 SD: 0.0297 c. M:-0.0399 c. 621: 52 108 461 N T3 SD: 0.0154 c. M:-0.0225 c. 788: 66 137 585 N T3 SD: 0.0038 c. M:-0.0052 c. 955: 80 166 709 N T3 SD: 0.0038 c. M: 0.0060 c. 1743: 146 303 1294 N T3 SD: 0.0006 c. M: 0.0009 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: 69.2863 cents 7 x 8:9 S SD: 60.3065 cents 8 x 9:11 SD: 46.2470 cents 9 x 10:12 S SD: 27.0527 cents 10 x 11:13 SD: 28.5854 cents 11 x 12:15 S SD: 22.4315 cents 12 x 13:16 SD: 5.1372 cents 13 x 14:17 SD: 16.8086 cents 14 x 15:19 SD: 15.9480 cents 15 x 16:20 S SD: 8.2835 cents 16 x 17:21 SD: 17.9459 cents 17 x 18:23 SD: 19.3638 cents 18 x 19:24 SD: 17.3476 cents 19 x 20:25 S SD: 22.8357 cents 20:21:22:27 SD: 20.1033 cents 21:22:23:28 SD: 16.1907 cents 22:23:24:29 SD: 15.3919 cents 23:24:25:31 SD: 13.4562 cents 24:25:26:32 SD: 10.2409 cents 26:27:28:35 S SD: 9.6166 cents 27:28:29:36 SD: 7.2439 cents 35:36:38:47 SD: 6.6639 cents 36:37:39:48 SD: 3.9191 cents 39:40:42:52 SD: 0.7042 cents 168:172:181:224 SD: 0.4090 cents 207:212:223:276 SD: 0.2393 cents 246:252:265:328 SD: 0.1675 cents 495:507:533:660 SD: 0.1178 cents 534:547:575:712 SD: 0.0814 cents 573:587:617:764 SD: 0.0758 cents