Scala analysis: 279_C20
Chromatic tetrachord 336/323 * 323/297 * 33/28
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 336/323 68.312482 2: 112/99 213.597962 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 33/28 284.4470 undecimal minor third 1: 336/323 68.3125 2: 323/297 145.2855 3: 33/28 284.4470 undecimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 336/323 68.312 cents 1: 1 323/297 145.285 cents 1: 1 33/28 284.447 cents undecimal minor third 2: 1 112/99 213.598 cents 2: 1 396/323 352.760 cents 2: 1 323/252 429.733 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 : 68.3 213.6 498.0 68.3 : 145.3 429.7 498.0 213.6: 284.4 352.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 68.3125 .. 284.4470 cents 3553/3136, 216.1346 cents 336/323, 68.3125 cents 2: 213.5980 .. 429.7325 cents 3553/3136, 216.1346 cents 3136/3267,-70.8491 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 336/323, 68.3125 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 33/28, 284.4470 cents Average / Smallest step : 2.430229 Largest / Average step : 1.713382 Largest / Smallest step : 4.163910 Median interval of one step : 323/297, 145.2855 cents, amount: 1 Least squares average step : 142.11739 cents, oct.: 426.35216 cents Scale is not proper Scale has trivalence property Scale is a mode of a 977-tone equal temperament with octave 4/3 degrees: 134 419 977 Least number of segments generator : 489 of 249.277 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 843 of 429.736 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 68.31248 cents Scale diversity : 1.023120 Lumma stability : 0.274323 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 : 336/323, 68.3125 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 : 19 Odd number limit : 323 (O: 323 U: 323) Highest odd numerator or denominator: 323 Scale harmonicity : 0.009552 Average absolute harmonicity : 0.084353 Specific harmonicity : 0.048628 Fundamental : 1/31977, -14.9647 octaves, 0.0082 Hz. Guide tone : 336, 8.3923 octaves, 87906.190 Hz. Exponens Consonantiae : 1.074427E+07, 23.35706 octaves Euler's gradus suavitatis : 61 Sum of Mann's harmonic distance : 438.5, average 146.16667 Mersenne's string divisions : 973343 Sum of van Prooijen's expressibility: 4.98196, average 1.66065 Sum of Tenney's harmonic distance : 10.15958, average 3.38653 Vogel's harmonic complexity : 43.33333 Wille's k value : 5329 Wilson's harmonic complexity : 63 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 20.82510, average 3.47085 Lattice compactness (without 2's) : 13.29139, average 2.21523 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 3.33333 10 3: -2 .. 1 -0.66667 4 1 7: 0 .. 1 0.66667 2 11: -1 .. 0 -0.33333 1 1 17: -1 .. 0 -0.33333 1 19: -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 19 24 29 30| Scale is weakly epimorphic with val: <7 11 19 24 30 32| Scale is weakly epimorphic with val: <7 11 19 24 31 31| Scale is weakly epimorphic with val: <7 11 19 26 29 31| Scale is weakly epimorphic with val: <7 11 19 26 30 30| Scale is weakly epimorphic with val: <7 11 19 26 31 32| Scale is weakly epimorphic with val: <7 11 20 24 29 32| Scale is weakly epimorphic with val: <7 11 20 24 30 31| Scale is weakly epimorphic with val: <7 11 20 25 29 31| Scale is weakly epimorphic with val: <7 11 20 25 30 30| Scale is weakly epimorphic with val: <7 11 20 25 31 32| Scale is JI-epimorphic with val: <7 11 21 25 29 30| Scale is weakly epimorphic with val: <7 11 21 25 30 32| Scale is weakly epimorphic with val: <7 11 21 25 31 31| Scale is weakly epimorphic with val: <7 11 21 26 29 32| Scale is weakly epimorphic with val: <7 11 21 26 30 31|
FIT/MODE
3: 0 1 2 N G T3 SD: 48.0650 c. M: 68.3125 c. 5: 1 1 3 N M DE S SD: 19.8851 c. M:-31.2965 c. 6: 1 2 3 P T3 SD: 22.1423 c. M:-35.4245 c. 7: 1 2 4 N T3 SD: 1.6401 c. M:-2.8368 c. 30: 4 9 17 N T3 SD: 1.6902 c. M:-2.2215 c. 37: 5 11 21 N T3 SD: 1.1777 c. M:-1.7728 c. 44: 6 13 25 N T3 SD: 0.8774 c. M:-1.4669 c. 51: 7 15 29 N T3 SD: 0.7193 c. M:-1.2450 c. 58: 8 17 33 N T3 SD: 0.6598 c. M:-1.0766 c. 65: 9 19 37 N T3 SD: 0.6612 c. M:-0.9445 c. 72: 10 21 41 N T3 SD: 0.6935 c. M:-0.8604 c. 103: 14 30 59 N T3 SD: 0.6022 c. M: 0.8409 c. 110: 15 32 63 N T3 SD: 0.5141 c. M: 0.7969 c. 117: 16 34 67 N T3 SD: 0.4533 c. M: 0.7582 c. 124: 17 36 71 N T3 SD: 0.4183 c. M: 0.7239 c. 131: 18 38 75 N T3 SD: 0.4063 c. M: 0.6932 c. 138: 19 40 79 N T3 SD: 0.4124 c. M: 0.6657 c. 140: 19 41 80 N T3 SD: 0.4250 c. M: 0.7207 c. 145: 20 42 83 N T3 SD: 0.4311 c. M: 0.6408 c. 147: 20 43 84 N T3 SD: 0.3299 c. M: 0.5513 c. 154: 21 45 88 N T3 SD: 0.2452 c. M: 0.3973 c. 161: 22 47 92 N T3 SD: 0.1717 c. M: 0.2566 c. 168: 23 49 96 N T3 SD: 0.1138 c. M: 0.1501 c. 175: 24 51 100 N T3 SD: 0.0868 c. M: 0.1501 c. 233: 32 68 133 N T3 SD: 0.1032 c. M:-0.1553 c. 343: 47 100 196 N T3 SD: 0.0950 c. M: 0.1501 c. 357: 49 104 204 N T3 SD: 0.0907 c. M: 0.1501 c. 387: 53 113 221 N T3 SD: 0.0635 c. M: 0.1048 c. 394: 54 115 225 N T3 SD: 0.0351 c. M: 0.0525 c. 401: 55 117 229 N T3 SD: 0.0158 c. M:-0.0273 c. 576: 79 168 329 N T3 SD: 0.0155 c. M: 0.0266 c. 809: 111 236 462 N T3 SD: 0.0198 c. M:-0.0258 c. 970: 133 283 554 N T3 SD: 0.0139 c. M: 0.0238 c. 977: 134 285 558 N T3 SD: 0.0032 c. M: 0.0045 c. 2355: 323 687 1345 N T3 SD: 0.0019 c. M: 0.0031 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 x 11:13 SD: 32.7205 cents 11 x 12:15 S SD: 37.0059 cents 12:13:14:16 S SD: 29.3910 cents 13:14:15:17 SD: 25.5911 cents 14:15:16:19 SD: 20.7155 cents 15:16:17:20 SD: 14.5095 cents 18:19:20:24 S SD: 13.3861 cents 20:21:23:27 SD: 13.0296 cents 21:22:24:28 S SD: 7.1364 cents 23:24:26:31 SD: 6.5057 cents 24:25:27:32 SD: 3.3238 cents 45:47:51:60 SD: 2.5414 cents 54:56:61:72 SD: 1.9801 cents 69:72:78:92 SD: 1.8447 cents 75:78:85:100 SD: 1.0387 cents 99:103:112:132 SD: 0.0867 cents