Scala analysis: 239_C16
Chromatic tetrachord 192/185 * 185/171 * 19/16
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 192/185 64.297248 2: 64/57 200.531983 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 19/16 297.5130 19th harmonic 1: 192/185 64.2972 2: 185/171 136.2347 3: 19/16 297.5130 19th harmonic
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 192/185 64.297 cents 1: 1 185/171 136.235 cents 1: 1 19/16 297.513 cents 19th harmonic 2: 1 64/57 200.532 cents 2: 1 228/185 361.810 cents 2: 1 185/144 433.748 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 : 64.3 200.5 498.0 64.3 : 136.2 433.7 498.0 200.5: 297.5 361.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 64.2972 .. 297.5130 cents 3515/3072, 233.2158 cents 192/185, 64.2972 cents 2: 200.5320 .. 433.7478 cents 3515/3072, 233.2158 cents 1024/1083,-96.9810 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 192/185, 64.2972 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 19/16, 297.5130 cents Average / Smallest step : 2.581992 Largest / Average step : 1.792085 Largest / Smallest step : 4.627150 Median interval of one step : 185/171, 136.2347 cents, amount: 1 Least squares average step : 139.96402 cents, oct.: 419.89205 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1890-tone equal temperament with octave 4/3 degrees: 244 761 1890 Least number of segments generator : 947 of 249.550 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1067 of 281.171 cents and inv. generated superset size: 20 = 17 more = 666.667% 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 64.29725 cents Scale diversity : 0.988817 Lumma stability : 0.258199 Lumma impropriety factor : 0.194723 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 : 192/185, 64.2972 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 37 Odd number limit : 185 (O: 185 U: 185) Highest odd numerator or denominator: 185 Scale harmonicity : 0.019291 Fundamental : 1/10545, -13.3643 octaves, 0.0248 Hz. Guide tone : 192, 7.5850 octaves, 50232.109 Hz. Exponens Consonantiae : 2.024640E+06, 20.94923 octaves Euler's gradus suavitatis : 69 Sum of Mann's harmonic distance : 252.5, average 84.16667 Mersenne's string divisions : 319319 Sum of van Prooijen's expressibility: 4.50017, average 1.50006 Sum of Tenney's harmonic distance : 9.19171, average 3.06390 Vogel's harmonic complexity : 47.33333 Wille's k value : 1757 Wilson's harmonic complexity : 67 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 25.72007, average 4.28668 Lattice compactness (without 2's) : 9.51398, average 1.58566 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 6 4.66667 14 3: -1 .. 1 -0.33333 3 1 5: -1 .. 0 -0.33333 1 19: -1 .. 0 -0.33333 1 1 37: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <7 10 15 29 35| Scale is weakly epimorphic with val: <7 10 15 29 38| Scale is weakly epimorphic with val: <7 10 15 29 41| Scale is weakly epimorphic with val: <7 10 16 29 37| Scale is weakly epimorphic with val: <7 10 16 29 40| Scale is weakly epimorphic with val: <7 10 17 29 36| Scale is weakly epimorphic with val: <7 10 17 29 39| Scale is weakly epimorphic with val: <7 10 18 29 35| Scale is weakly epimorphic with val: <7 10 18 29 38| Scale is weakly epimorphic with val: <7 10 18 29 41| Scale is weakly epimorphic with val: <7 10 19 29 37| Scale is weakly epimorphic with val: <7 10 19 29 40| Scale is JI-epimorphic with val: <7 11 15 29 37| Scale is weakly epimorphic with val: <7 11 15 29 40| Scale is weakly epimorphic with val: <7 11 15 30 36| Scale is weakly epimorphic with val: <7 11 15 30 39| Scale is weakly epimorphic with val: <7 11 15 32 37| Scale is weakly epimorphic with val: <7 11 15 32 40| Scale is weakly epimorphic with val: <7 11 15 33 36| Scale is weakly epimorphic with val: <7 11 15 33 39| Scale is JI-epimorphic with val: <7 11 16 29 36| Scale is weakly epimorphic with val: <7 11 16 29 39| Scale is weakly epimorphic with val: <7 11 16 30 35| Scale is weakly epimorphic with val: <7 11 16 30 38| Scale is weakly epimorphic with val: <7 11 16 30 41| Scale is weakly epimorphic with val: <7 11 16 32 36| Scale is weakly epimorphic with val: <7 11 16 32 39| Scale is weakly epimorphic with val: <7 11 16 33 35| Scale is weakly epimorphic with val: <7 11 16 33 38| Scale is weakly epimorphic with val: <7 11 16 33 41| Scale is JI-epimorphic with val: <7 11 17 29 35| Scale is weakly epimorphic with val: <7 11 17 29 38| Scale is weakly epimorphic with val: <7 11 17 29 41| Scale is weakly epimorphic with val: <7 11 17 30 37| Scale is weakly epimorphic with val: <7 11 17 30 40| Scale is weakly epimorphic with val: <7 11 17 32 35| Scale is weakly epimorphic with val: <7 11 17 32 38| Scale is weakly epimorphic with val: <7 11 17 32 41| Scale is weakly epimorphic with val: <7 11 17 33 37| Scale is weakly epimorphic with val: <7 11 17 33 40| Scale is weakly epimorphic with val: <7 11 18 29 37| Scale is weakly epimorphic with val: <7 11 18 29 40| Scale is weakly epimorphic with val: <7 11 18 30 36| Scale is weakly epimorphic with val: <7 11 18 30 39| Scale is weakly epimorphic with val: <7 11 18 32 37| Scale is weakly epimorphic with val: <7 11 18 32 40| Scale is weakly epimorphic with val: <7 11 18 33 36| Scale is weakly epimorphic with val: <7 11 18 33 39| Scale is weakly epimorphic with val: <7 11 19 29 36| Scale is weakly epimorphic with val: <7 11 19 29 39| Scale is weakly epimorphic with val: <7 11 19 30 35| Scale is weakly epimorphic with val: <7 11 19 30 38| Scale is weakly epimorphic with val: <7 11 19 30 41| Scale is weakly epimorphic with val: <7 11 19 32 36| Scale is weakly epimorphic with val: <7 11 19 32 39| Scale is weakly epimorphic with val: <7 11 19 33 35| Scale is weakly epimorphic with val: <7 11 19 33 38| Scale is weakly epimorphic with val: <7 11 19 33 41| Scale is weakly epimorphic with val: <7 12 15 29 36| Scale is weakly epimorphic with val: <7 12 15 32 36| Scale is weakly epimorphic with val: <7 12 16 29 35| Scale is weakly epimorphic with val: <7 12 16 32 35| Scale is weakly epimorphic with val: <8 11 15 30 41| Scale is weakly epimorphic with val: <8 11 15 33 41| Scale is weakly epimorphic with val: <8 11 15 34 37| Scale is weakly epimorphic with val: <8 11 15 34 40| Scale is weakly epimorphic with val: <8 11 16 30 40| Scale is weakly epimorphic with val: <8 11 16 33 40| Scale is weakly epimorphic with val: <8 11 16 34 36| Scale is weakly epimorphic with val: <8 11 16 34 39| Scale is weakly epimorphic with val: <8 11 17 30 39| Scale is weakly epimorphic with val: <8 11 17 33 39| Scale is weakly epimorphic with val: <8 11 17 34 35| Scale is weakly epimorphic with val: <8 11 17 34 38| Scale is weakly epimorphic with val: <8 11 17 34 41| Scale is weakly epimorphic with val: <8 11 18 30 38| Scale is weakly epimorphic with val: <8 11 18 33 38| Scale is weakly epimorphic with val: <8 11 18 34 37| Scale is weakly epimorphic with val: <8 11 18 34 40| Scale is weakly epimorphic with val: <8 11 19 30 37| Scale is weakly epimorphic with val: <8 11 19 33 37| Scale is weakly epimorphic with val: <8 11 19 34 36| Scale is weakly epimorphic with val: <8 11 19 34 39| Scale is weakly epimorphic with val: <8 12 15 33 37| Scale is weakly epimorphic with val: <8 12 15 33 40| Scale is weakly epimorphic with val: <8 12 16 28 41| Scale is weakly epimorphic with val: <8 12 16 31 41| Scale is weakly epimorphic with val: <8 12 16 33 36| Scale is weakly epimorphic with val: <8 12 16 33 39| Scale is weakly epimorphic with val: <8 12 16 34 41| Scale is weakly epimorphic with val: <8 12 17 28 40| Scale is weakly epimorphic with val: <8 12 17 31 40| Scale is weakly epimorphic with val: <8 12 17 33 35| Scale is weakly epimorphic with val: <8 12 17 33 38| Scale is weakly epimorphic with val: <8 12 17 33 41| Scale is weakly epimorphic with val: <8 12 17 34 40| Scale is weakly epimorphic with val: <8 12 18 28 39| Scale is weakly epimorphic with val: <8 12 18 31 39| Scale is weakly epimorphic with val: <8 12 18 33 37| Scale is weakly epimorphic with val: <8 12 18 33 40| Scale is weakly epimorphic with val: <8 12 18 34 39| Scale is weakly epimorphic with val: <8 12 19 28 38| Scale is weakly epimorphic with val: <8 12 19 31 38| Scale is weakly epimorphic with val: <8 12 19 33 36| Scale is weakly epimorphic with val: <8 12 19 33 39| Scale is weakly epimorphic with val: <8 12 19 34 38|
FIT/MODE
3: 0 1 2 N G T3 SD: 42.1330 c. M: 64.2972 c. 5: 1 1 3 N M DE S SD: 20.4014 c. M:-35.3118 c. 6: 1 1 4 N M DE S SD: 22.6679 c. M: 34.5170 c. 7: 1 2 4 N T3 SD: 8.4414 c. M:-12.9159 c. 8: 1 2 5 N T3 SD: 8.0342 c. M: 13.7651 c. 13: 2 3 8 N T3 SD: 8.8030 c. M:-12.3251 c. 15: 2 4 9 N T3 SD: 1.4345 c. M:-2.1088 c. 32: 4 9 19 N T3 SD: 1.5710 c. M: 2.0416 c. 40: 5 11 24 N T3 SD: 1.4018 c. M: 2.0416 c. 47: 6 13 28 N T3 SD: 0.6226 c. M:-0.8054 c. 62: 8 17 37 N T3 SD: 0.1700 c. M:-0.2926 c. 139: 18 38 83 N T3 SD: 0.1333 c. M:-0.1978 c. 201: 26 55 120 N T3 SD: 0.1236 c. M:-0.1727 c. 256: 33 70 153 N T3 SD: 0.1013 c. M: 0.1467 c. 318: 41 87 190 N T3 SD: 0.0599 c. M: 0.0839 c. 380: 49 104 227 N T3 SD: 0.0437 c. M: 0.0757 c. 395: 51 108 236 N T3 SD: 0.0310 c. M: 0.0531 c. 457: 59 125 273 N T3 SD: 0.0037 c. M: 0.0062 c. 1433: 185 392 856 N T3 SD: 0.0039 c. M:-0.0067 c. 1890: 244 517 1129 N T3 SD: 0.0021 c. M:-0.0036 c. 2347: 303 642 1402 N T3 SD: 0.0011 c. M:-0.0017 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: 71.3878 cents 6 x 7:8 S SD: 33.1695 cents 7 x 8:9 S SD: 35.0108 cents 8 x 9:11 SD: 26.6900 cents 9 x 10:12 S SD: 9.0641 cents 10 x 11:13 SD: 28.2107 cents 11 x 12:15 S SD: 31.6353 cents 12 x 13:16 SD: 30.9797 cents 13:14:15:17 SD: 28.7807 cents 14:15:16:19 SD: 23.3783 cents 15:16:17:20 SD: 16.7032 cents 16:17:18:21 S SD: 16.3565 cents 17:18:19:23 SD: 14.5430 cents 18:19:20:24 S SD: 11.4865 cents 22:23:25:29 SD: 10.4533 cents 23:24:26:31 SD: 7.9982 cents 24:25:27:32 SD: 2.4049 cents 57:59:64:76 SD: 1.5312 cents 81:84:91:108 SD: 0.5567 cents 105:109:118:140 SD: 0.5345 cents 186:193:209:248 SD: 0.4506 cents 213:221:239:284 SD: 0.4115 cents 237:246:266:316 SD: 0.2407 cents 318:330:357:424 SD: 0.1022 cents 342:355:384:456 SD: 0.0967 cents 423:439:475:564 SD: 0.0643 cents