Scala analysis: 280_C20
Chromatic tetrachord 168/155 * 310/297 * 33/28
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 168/155 139.431621 2: 112/99 213.597962 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 33/28 284.4470 undecimal minor third 1: 168/155 139.4316 2: 310/297 74.1663 3: 33/28 284.4470 undecimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 310/297 74.166 cents 1: 1 168/155 139.432 cents 1: 1 33/28 284.447 cents undecimal minor third 2: 1 112/99 213.598 cents 2: 1 155/126 358.613 cents 2: 1 198/155 423.879 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 : 139.4 213.6 498.0 139.4: 74.2 358.6 498.0 213.6: 284.4 423.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 74.1663 .. 284.4470 cents 9801/8680, 210.2807 cents 310/297, 74.1663 cents 2: 213.5980 .. 423.8787 cents 9801/8680, 210.2807 cents 3136/3267,-70.8491 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 310/297, 74.1663 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 33/28, 284.4470 cents Average / Smallest step : 2.238414 Largest / Average step : 1.713382 Largest / Smallest step : 3.835258 Median interval of one step : 168/155, 139.4316 cents, amount: 1 Least squares average step : 147.19732 cents, oct.: 441.59197 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1961-tone equal temperament with octave 4/3 degrees: 549 841 1961 Least number of segments generator : 981 of 249.149 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1486 of 377.407 cents and inv. generated superset size: 37 = 34 more = 1233.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 70.84907 cents Scale diversity : 1.062408 Lumma stability : 0.297830 Lumma impropriety factor : 0.142254 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 : 24948/24025, 65.2653 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 31 Odd number limit : 297 (O: 155 U: 297) Highest odd numerator or denominator: 155 Scale harmonicity : 0.021337 Fundamental : 1/15345, -13.9055 octaves, 0.0170 Hz. Guide tone : 336, 8.3923 octaves, 87906.190 Hz. Exponens Consonantiae : 5.155920E+06, 22.29780 octaves Euler's gradus suavitatis : 61 Sum of Mann's harmonic distance : 270.5, average 90.16667 Mersenne's string divisions : 477071 Sum of van Prooijen's expressibility: 4.66309, average 1.55436 Sum of Tenney's harmonic distance : 9.53968, average 3.17989 Vogel's harmonic complexity : 43.00000 Wille's k value : 2557 Wilson's harmonic complexity : 63 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 19.14619, average 3.19103 Lattice compactness (without 2's) : 12.67971, average 2.11328 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 3.00000 9 3: -2 .. 1 -0.66667 4 1 5: -1 .. 0 -0.33333 1 7: 0 .. 1 0.66667 2 11: -1 .. 0 -0.33333 1 1 31: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <7 11 16 19 24 36| Scale is weakly epimorphic with val: <7 11 16 19 26 34| Scale is weakly epimorphic with val: <7 11 16 19 26 37| Scale is JI-epimorphic with val: <7 11 16 20 24 35| Scale is weakly epimorphic with val: <7 11 16 20 24 38| Scale is weakly epimorphic with val: <7 11 16 20 25 34| Scale is weakly epimorphic with val: <7 11 16 20 25 37| Scale is JI-epimorphic with val: <7 11 16 21 25 36| Scale is weakly epimorphic with val: <7 11 16 21 26 35| Scale is weakly epimorphic with val: <7 11 16 21 26 38| Scale is weakly epimorphic with val: <7 11 17 19 24 35| Scale is weakly epimorphic with val: <7 11 17 19 24 38| Scale is weakly epimorphic with val: <7 11 17 19 26 36| Scale is JI-epimorphic with val: <7 11 17 20 24 34| Scale is weakly epimorphic with val: <7 11 17 20 24 37| Scale is weakly epimorphic with val: <7 11 17 20 25 36| = patent Scale is JI-epimorphic with val: <7 11 17 21 25 35| Scale is weakly epimorphic with val: <7 11 17 21 25 38| Scale is weakly epimorphic with val: <7 11 17 21 26 34| Scale is weakly epimorphic with val: <7 11 17 21 26 37| Scale is weakly epimorphic with val: <7 11 18 19 24 34| Scale is weakly epimorphic with val: <7 11 18 19 24 37| Scale is weakly epimorphic with val: <7 11 18 19 26 35| Scale is weakly epimorphic with val: <7 11 18 19 26 38| Scale is weakly epimorphic with val: <7 11 18 20 24 36| Scale is weakly epimorphic with val: <7 11 18 20 25 35| Scale is weakly epimorphic with val: <7 11 18 20 25 38| Scale is JI-epimorphic with val: <7 11 18 21 25 34| Scale is weakly epimorphic with val: <7 11 18 21 25 37| Scale is weakly epimorphic with val: <7 11 18 21 26 36| Scale is weakly epimorphic with val: <7 12 16 20 26 34| Scale is weakly epimorphic with val: <7 12 16 21 24 35| Scale is weakly epimorphic with val: <7 12 17 21 24 34|
FIT/MODE
3: 1 0 2 N G T3 SD: 31.4686 c. M: 47.5830 c. 4: 1 1 2 P M ME S SD: 22.1925 c. M:-35.4245 c. 5: 1 1 3 N M DE S SD: 24.4447 c. M: 39.8226 c. 7: 2 1 4 N T3 SD: 1.6575 c. M:-2.8670 c. 40: 11 6 23 N T3 SD: 1.8090 c. M: 2.4692 c. 47: 13 7 27 N T3 SD: 1.3629 c. M: 1.6745 c. 54: 15 8 31 N T3 SD: 1.0540 c. M: 1.4677 c. 61: 17 9 35 N T3 SD: 0.8432 c. M: 1.3165 c. 68: 19 10 39 N T3 SD: 0.7084 c. M: 1.1964 c. 72: 20 11 41 N T3 SD: 0.7919 c. M: 1.0858 c. 75: 21 11 43 N T3 SD: 0.6345 c. M: 1.0988 c. 79: 22 12 45 N T3 SD: 0.6067 c. M:-0.7505 c. 86: 24 13 49 N T3 SD: 0.4670 c. M:-0.6772 c. 93: 26 14 53 N T3 SD: 0.3722 c. M:-0.6149 c. 100: 28 15 57 N T3 SD: 0.3243 c. M:-0.5614 c. 107: 30 16 61 N T3 SD: 0.3204 c. M:-0.5148 c. 114: 32 17 65 N T3 SD: 0.3473 c. M:-0.4740 c. 147: 41 22 84 N T3 SD: 0.3131 c. M: 0.5211 c. 154: 43 23 88 N T3 SD: 0.2290 c. M: 0.3671 c. 161: 45 24 92 N T3 SD: 0.1569 c. M: 0.2265 c. 168: 47 25 96 N T3 SD: 0.1034 c. M: 0.1501 c. 175: 49 26 100 N T3 SD: 0.0875 c. M: 0.1501 c. 261: 73 39 149 N T3 SD: 0.1038 c. M: 0.1317 c. 268: 75 40 153 N T3 SD: 0.0734 c. M:-0.1154 c. 275: 77 41 157 N T3 SD: 0.0639 c. M:-0.1086 c. 282: 79 42 161 N T3 SD: 0.0792 c. M:-0.1022 c. 429: 120 64 245 N T3 SD: 0.0689 c. M: 0.1183 c. 436: 122 65 249 N T3 SD: 0.0413 c. M: 0.0704 c. 443: 124 66 253 N T3 SD: 0.0151 c. M: 0.0240 c. 450: 126 67 257 N T3 SD: 0.0130 c. M:-0.0210 c. 893: 250 133 510 N T3 SD: 0.0054 c. M:-0.0092 c. 1343: 376 200 767 N T3 SD: 0.0062 c. M:-0.0088 c. 1511: 423 225 863 N T3 SD: 0.0060 c. M: 0.0088 c. 1961: 549 292 1120 N T3 SD: 0.0029 c. M: 0.0050 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: 66.2336 cents 6 x 7:8 S SD: 26.6365 cents 7 x 8:9 S SD: 32.6841 cents 8 x 9:11 SD: 27.0733 cents 9 x 10:12 S SD: 15.5971 cents 10:11 x 13 SD: 25.3728 cents 11:12 x 15 S SD: 20.2436 cents 12:13:14:16 S SD: 17.7600 cents 13:14:15:17 SD: 16.3972 cents 14:15:16:19 SD: 13.5294 cents 15:16:17:20 SD: 9.2907 cents 18 x 20:24 S SD: 15.5971 cents 20:22:23:27 SD: 14.6094 cents 21:23:24:28 SD: 8.4007 cents 22:24:25:29 SD: 8.0035 cents 23:25:26:31 SD: 6.4664 cents 24:26:27:32 SD: 3.2420 cents 45:49:51:60 SD: 2.8574 cents 60:65:68:80 SD: 1.0686 cents 84:91:95:112 SD: 0.3404 cents 228:247:258:304 SD: 0.3168 cents 297:322:336:396 SD: 0.1619 cents 381:413:431:508 SD: 0.0750 cents 465:504:526:620 SD: 0.0665 cents