Scala analysis: 232_C15
Chromatic tetrachord 56/53 * 53/50 * 25/21
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 56/53 95.321361 2: 28/25 196.198479 middle second 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 25/21 301.8465 BP second, quasi-equal minor third 1: 56/53 95.3214 2: 53/50 100.8771 3: 25/21 301.8465 BP second, quasi-equal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 56/53 95.321 cents 1: 1 53/50 100.877 cents 1: 1 25/21 301.847 cents BP second, quasi-equal minor third 2: 1 28/25 196.198 cents middle second 2: 1 200/159 397.168 cents 2: 1 53/42 402.724 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 : 95.3 196.2 498.0 95.3 : 100.9 402.7 498.0 196.2: 301.8 397.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 95.3214 .. 301.8465 cents 1325/1176, 206.5252 cents 56/53, 95.3214 cents 2: 196.1985 .. 402.7236 cents 1325/1176, 206.5252 cents 588/625,-105.6480 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 56/53, 95.3214 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 25/21, 301.8465 cents Average / Smallest step : 1.741635 Largest / Average step : 1.818188 Largest / Smallest step : 3.166620 Median interval of one step : 53/50, 100.8771 cents, amount: 1 Least squares average step : 141.56095 cents, oct.: 424.68285 cents Scale is not proper Scale has trivalence property Scale is a mode of a 627-tone equal temperament with octave 4/3 degrees: 120 247 627 Least number of segments generator : 314 of 249.420 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 607 of 482.158 cents and inv. generated superset size: 26 = 23 more = 866.667% 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 95.32136 cents Scale diversity : 1.065950 Lumma stability : 0.382782 Lumma impropriety factor : 0.212125 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 : 2809/2800, 5.5558 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% Limited inverse transpositions with margin 200.9694 cents: 2 -- Rational properties -- Prime limit : 53 Odd number limit : 159 (O: 53 U: 159) Highest odd numerator or denominator: 53 Scale harmonicity : 0.034780 Fundamental : 1/3975, -11.9567 octaves, 0.0658 Hz. Guide tone : 56, 5.8074 octaves, 14651.032 Hz. Exponens Consonantiae : 2.226000E+05, 17.76409 octaves Euler's gradus suavitatis : 72 Sum of Mann's harmonic distance : 84.5, average 28.16667 Mersenne's string divisions : 40439 Sum of van Prooijen's expressibility: 3.59934, average 1.19978 Sum of Tenney's harmonic distance : 7.39674, average 2.46558 Vogel's harmonic complexity : 51.00000 Wille's k value : 662 Wilson's harmonic complexity : 73 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 14.81595, average 2.46933 Lattice compactness (without 2's) : 10.09977, average 1.68330 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -1 .. 0 -0.33333 1 1 5: -2 .. 0 -0.66667 2 7: 0 .. 1 0.66667 2 1 53: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 15 21 41| Scale is weakly epimorphic with val: <6 11 15 21 40| Scale is weakly epimorphic with val: <7 10 15 19 41| Scale is weakly epimorphic with val: <7 10 16 21 40| Scale is weakly epimorphic with val: <7 10 17 22 40| Scale is weakly epimorphic with val: <7 11 15 18 41| Scale is weakly epimorphic with val: <7 11 15 20 42| Scale is weakly epimorphic with val: <7 11 15 21 41| Scale is weakly epimorphic with val: <7 11 16 19 41| Scale is JI-epimorphic with val: <7 11 16 20 40| Scale is weakly epimorphic with val: <7 11 16 22 41| Scale is weakly epimorphic with val: <7 11 17 18 40| Scale is weakly epimorphic with val: <7 11 17 19 42| Scale is weakly epimorphic with val: <7 11 17 21 40| Scale is JI-epimorphic with val: <7 11 17 22 42| Scale is weakly epimorphic with val: <7 11 18 18 41| Scale is weakly epimorphic with val: <7 11 18 20 42| Scale is weakly epimorphic with val: <7 11 18 21 41| Scale is weakly epimorphic with val: <7 11 19 19 41| Scale is weakly epimorphic with val: <7 11 19 20 40| Scale is weakly epimorphic with val: <7 11 19 22 41| Scale is weakly epimorphic with val: <7 12 15 19 42| Scale is weakly epimorphic with val: <7 12 16 21 41| Scale is weakly epimorphic with val: <7 12 16 22 40| Scale is weakly epimorphic with val: <7 12 19 22 40| Scale is weakly epimorphic with val: <8 11 15 21 42| Scale is weakly epimorphic with val: <8 11 16 19 42| Scale is weakly epimorphic with val: <8 11 16 20 41| Scale is weakly epimorphic with val: <8 11 17 19 40| Scale is weakly epimorphic with val: <8 11 17 21 41| Scale is weakly epimorphic with val: <8 11 18 21 42| Scale is weakly epimorphic with val: <8 11 19 20 41| Scale is weakly epimorphic with val: <8 12 15 19 40| Scale is weakly epimorphic with val: <8 12 16 19 41| Scale is weakly epimorphic with val: <8 12 16 21 42| Scale is weakly epimorphic with val: <8 12 17 20 41| Scale is weakly epimorphic with val: <8 12 17 21 40| Scale is weakly epimorphic with val: <8 12 18 19 40| Scale is weakly epimorphic with val: <8 12 19 21 42|
FIT/MODE
3: 0 1 2 N G T3 SD: 57.7270 c. M: 95.3214 c. 4: 1 1 2 P M ME S SD: 34.8445 c. M:-52.8240 c. 5: 1 1 3 N M DE S SD: 3.0277 c. M:-4.2876 c. 26: 5 5 16 N M DE S SD: 2.6934 c. M: 4.6427 c. 31: 6 6 19 N M DE S SD: 2.0625 c. M: 3.4069 c. 36: 7 7 22 N M DE S SD: 1.6965 c. M: 2.5143 c. 41: 8 8 25 N M DE S SD: 1.5096 c. M:-1.8582 c. 43: 8 9 26 N T3 SD: 1.5895 c. M: 2.6618 c. 46: 9 9 28 N M DE S SD: 1.4403 c. M:-2.1222 c. 48: 9 10 29 N T3 SD: 1.2446 c. M: 1.9379 c. 53: 10 11 32 N T3 SD: 1.0205 c. M: 1.3506 c. 58: 11 12 35 N T3 SD: 0.9024 c. M:-1.3021 c. 63: 12 13 38 N T3 SD: 0.8711 c. M:-1.4384 c. 68: 13 14 41 N T3 SD: 0.8997 c. M:-1.5547 c. 74: 14 15 45 N T3 SD: 0.8642 c. M: 1.0966 c. 79: 15 16 48 N T3 SD: 0.6201 c. M: 0.7631 c. 84: 16 17 51 N T3 SD: 0.4070 c. M: 0.5379 c. 89: 17 18 54 N T3 SD: 0.2237 c. M: 0.3381 c. 94: 18 19 57 N T3 SD: 0.0963 c. M: 0.1595 c. 193: 37 39 117 N T3 SD: 0.1019 c. M:-0.1588 c. 287: 55 58 174 N T3 SD: 0.0929 c. M:-0.1228 c. 340: 65 69 206 N T3 SD: 0.0806 c. M: 0.1069 c. 345: 66 70 209 N T3 SD: 0.0804 c. M:-0.1323 c. 429: 82 87 260 N T3 SD: 0.0716 c. M: 0.1239 c. 434: 83 88 263 N T3 SD: 0.0470 c. M: 0.0731 c. 439: 84 89 266 N T3 SD: 0.0425 c. M:-0.0698 c. 528: 101 107 320 N T3 SD: 0.0297 c. M: 0.0514 c. 533: 102 108 323 N T3 SD: 0.0181 c. M:-0.0294 c. 627: 120 127 380 N T3 SD: 0.0012 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: 73.1459 cents 6 x 7:8 S SD: 35.3362 cents 7 x 8:9 S SD: 36.0117 cents 8 x 9:11 SD: 26.9141 cents 9 x 10:12 S SD: 6.8974 cents 10 x 11:13 SD: 26.8991 cents 11 x 12:15 S SD: 29.9562 cents 12:13 x 16 SD: 21.6256 cents 14:15:16:19 SD: 17.4613 cents 15:16:17:20 SD: 8.7499 cents 17:18:19:23 SD: 8.5973 cents 18:19:20:24 S SD: 4.6338 cents 33:35:37:44 SD: 2.2693 cents 51:54:57:68 SD: 1.7145 cents 84:89:94:112 SD: 1.6666 cents 90:95:101:120 SD: 1.2793 cents 108:114:121:144 SD: 0.6037 cents 141:149:158:188 SD: 0.3013 cents 159:168:178:212 SD: 0.2593 cents 267:282:299:356 SD: 0.2441 cents 300:317:336:400 SD: 0.0343 cents