Scala analysis: 540_M48
Miscellaneous tetrachord 256/243 * 243/230 * 115/96
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 256/243 90.224996 limma, Pythagorean minor second 2: 128/115 185.411939 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 115/96 312.6331 1: 256/243 90.2250 limma, Pythagorean minor second 2: 243/230 95.1869 3: 115/96 312.6331
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 256/243 90.225 cents limma, Pythagorean minor second 1: 1 243/230 95.187 cents 1: 1 115/96 312.633 cents 2: 1 128/115 185.412 cents 2: 1 920/729 402.858 cents 2: 1 81/64 407.820 cents Pythagorean major third 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 : 90.2 185.4 498.0 90.2 : 95.2 407.8 498.0 185.4: 312.6 402.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 312.6331 cents 9315/8192, 222.4081 cents 256/243, 90.2250 cents 2: 185.4119 .. 407.8200 cents 9315/8192, 222.4081 cents 12288/13225,-127.2211 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 256/243, 90.2250 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 115/96, 312.6331 cents Average / Smallest step : 1.840011 Largest / Average step : 1.883162 Largest / Smallest step : 3.465038 Median interval of one step : 243/230, 95.1869 cents, amount: 1 Least squares average step : 139.65599 cents, oct.: 418.96797 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1104-tone equal temperament with octave 4/3 degrees: 200 411 1104 Least number of segments generator : 553 of 249.474 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 715 of 322.556 cents and inv. generated superset size: 34 = 31 more = 1133.333% 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 90.22500 cents Scale diversity : 1.017568 Lumma stability : 0.362317 Lumma impropriety factor : 0.255441 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 : 59049/58880, 4.9619 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 217.4461 cents: 2 -- Rational properties -- Prime limit : 23 Odd number limit : 729 (O: 243 U: 729) Highest odd numerator or denominator: 243 Scale harmonicity : 0.014322 Average absolute harmonicity : 0.093061 Specific harmonicity : 0.073689 Fundamental : 1/27945, -14.7703 octaves, 0.0094 Hz. Guide tone : 256, 8.0000 octaves, 66976.145 Hz. Exponens Consonantiae : 7.153920E+06, 22.77030 octaves Euler's gradus suavitatis : 45 Sum of Mann's harmonic distance : 374.5, average 124.83333 Mersenne's string divisions : 848799 Sum of van Prooijen's expressibility: 4.92343, average 1.64114 Sum of Tenney's harmonic distance : 10.04094, average 3.34698 Vogel's harmonic complexity : 33.33333 Wille's k value : 4657 Wilson's harmonic complexity : 43 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 36.60559, average 6.10093 Lattice compactness (without 2's) : 18.34242, average 3.05707 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 8 5.66667 17 3: -5 .. 0 -2.00000 6 2 5: -1 .. 0 -0.33333 1 23: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-8 / 3 =-2.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is JI-epimorphic with val: <7 11 15 32| Scale is weakly epimorphic with val: <7 11 15 35| Scale is JI-epimorphic with val: <7 11 16 31| Scale is weakly epimorphic with val: <7 11 16 34| Scale is JI-epimorphic with val: <7 11 17 30| Scale is weakly epimorphic with val: <7 11 17 33| = patent Scale is weakly epimorphic with val: <7 11 17 36| Scale is weakly epimorphic with val: <7 11 18 32| Scale is weakly epimorphic with val: <7 11 18 35| Scale is weakly epimorphic with val: <7 11 19 31| Scale is weakly epimorphic with val: <7 11 19 34|
FIT/MODE
3: 0 1 2 N G T3 SD: 53.2816 c. M: 90.2250 c. 4: 1 1 2 P M ME S SD: 41.7207 c. M:-63.6106 c. 5: 1 1 3 N M DE S SD: 9.6379 c. M:-13.8061 c. 11: 2 2 7 N M DE S SD: 2.4925 c. M: 4.3047 c. 16: 3 3 10 N M DE S SD: 1.9842 c. M:-3.1584 c. 27: 5 5 17 N M DE S SD: 1.2815 c. M:-2.0056 c. 38: 7 7 24 N M DE S SD: 1.4146 c. M: 1.9217 c. 43: 8 8 27 N M DE S SD: 1.4066 c. M:-2.4345 c. 51: 9 10 32 N T3 SD: 1.3502 c. M: 2.3347 c. 56: 10 11 35 N T3 SD: 1.0795 c. M:-1.3549 c. 62: 11 12 39 N T3 SD: 1.1394 c. M: 1.8622 c. 67: 12 13 42 N T3 SD: 0.6397 c. M: 1.0229 c. 78: 14 15 49 N T3 SD: 0.5003 c. M: 0.8323 c. 83: 15 16 52 N T3 SD: 0.3710 c. M:-0.6049 c. 94: 17 18 59 N T3 SD: 0.0901 c. M: 0.1530 c. 204: 37 39 128 N T3 SD: 0.0990 c. M:-0.1342 c. 215: 39 41 135 N T3 SD: 0.0867 c. M:-0.1181 c. 298: 54 57 187 N T3 SD: 0.0603 c. M:-0.1015 c. 309: 56 59 194 N T3 SD: 0.0380 c. M: 0.0554 c. 403: 73 77 253 N T3 SD: 0.0210 c. M: 0.0354 c. 497: 90 95 312 N T3 SD: 0.0245 c. M: 0.0358 c. 607: 110 116 381 N T3 SD: 0.0215 c. M:-0.0303 c. 701: 127 134 440 N T3 SD: 0.0136 c. M:-0.0228 c. 1010: 183 193 634 N T3 SD: 0.0086 c. M:-0.0148 c. 1104: 200 211 693 N T3 SD: 0.0010 c. M:-0.0016 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: 77.6118 cents 6 x 7:8 S SD: 40.7295 cents 7 x 8:9 S SD: 38.9174 cents 8 x 9:11 SD: 28.1966 cents 9 x 10:12 S SD: 1.5041 cents 10 x 11:13 SD: 24.1746 cents 11 x 12:15 S SD: 26.0910 cents 12 x 13:16 SD: 23.4196 cents 13:14 x 17 SD: 25.3953 cents 14:15:16:19 SD: 20.7814 cents 15:16:17:20 SD: 12.6519 cents 16:17:18:21 S SD: 12.0300 cents 17:18:19:23 SD: 9.2258 cents 18:19:20:24 S SD: 1.5078 cents 96:101:107:128 SD: 1.1125 cents 114:120:127:152 SD: 0.6996 cents 132:139:147:176 SD: 0.4001 cents 150:158:167:200 SD: 0.1752 cents 168:177:187:224 SD: 0.0484 cents