Scala analysis: 528_M36
Miscellaneous tetrachord 28/27 * 2187/1792 * 256/243
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/27 62.960904 Archytas' 1/3-tone 2: 81/64 407.820003 Pythagorean major third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 256/243 90.2250 limma, Pythagorean minor second 1: 28/27 62.9609 Archytas' 1/3-tone 2: 2187/1792 344.8591 3: 256/243 90.2250 limma, Pythagorean minor second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 256/243 90.225 cents limma, Pythagorean minor second 1: 1 2187/1792 344.859 cents 2: 1 7168/6561 153.186 cents 2: 1 81/64 407.820 cents Pythagorean major third 2: 1 9/7 435.084 cents septimal major third, BP 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 : 63.0 407.8 498.0 63.0 : 344.9 435.1 498.0 407.8: 90.2 153.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 344.8591 cents 59049/50176, 281.8982 cents 28/27, 62.9609 cents 2: 153.1859 .. 435.0841 cents 59049/50176, 281.8982 cents 12845056/14348907,-191.6732 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 2187/1792, 344.8591 cents Average / Smallest step : 2.636795 Largest / Average step : 2.077277 Largest / Smallest step : 5.477353 Median interval of one step : 256/243, 90.2250 cents, amount: 1 Least squares average step : 169.48114 cents, oct.: 508.44341 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1242-tone equal temperament with octave 4/3 degrees: 157 1017 1242 Least number of segments generator : 623 of 249.825 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 715 of 286.717 cents and inv. generated superset size: 72 = 69 more = 2400.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SLM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 62.96090 cents Scale diversity : 0.806450 Lumma stability : 0.252832 Lumma impropriety factor : 0.384851 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 : 64/63, 27.2641 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 7 Odd number limit : 6561 (O: 2187 U: 6561) Highest odd numerator or denominator: 81 Scale harmonicity : 0.027062 Average absolute harmonicity : 0.107860 Specific harmonicity : 0.138499 Fundamental : 1/1728, -10.7549 octaves, 0.1514 Hz. Guide tone : 2268, 11.1472 octaves, 593366.782 Hz. Exponens Consonantiae : 3.919104E+06, 21.90209 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 103.5, average 34.50000 Mersenne's string divisions : 11165 Sum of van Prooijen's expressibility: 3.81697, average 1.27232 Sum of Tenney's harmonic distance : 7.67237, average 2.55746 Vogel's harmonic complexity : 16.66667 Wille's k value : 1093 Wilson's harmonic complexity : 28 Rectangular lattice diameter : 8 Triangular lattice diameter : 7 Lattice compactness : 35.53596, average 5.92266 Lattice compactness (without 2's) : 22.46941, average 3.74490 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -6 .. 2 -0.66667 10 3: -3 .. 4 0.00000 8 2 7: 0 .. 1 0.33333 1 1 Average exponent except 2's : 1 / 3 = 0.33333 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <6 10 21| Scale is JI-epimorphic with val: <7 11 20| = patent
FIT/MODE
3: 0 2 1 N G T3 SD: 56.8864 c. M: 75.7900 c. 4: 0 3 1 N G T3 SD: 41.3909 c. M: 62.9609 c. 5: 1 3 1 N M DE I SD: 21.8414 c. M:-36.6481 c. 6: 1 4 1 N M DE I SD: 12.3012 c. M:-20.0466 c. 7: 1 5 1 N M DE I SD: 11.9852 c. M:-19.0757 c. 10: 1 7 2 N T3 SD: 9.3301 c. M: 13.1564 c. 15: 2 10 3 N T3 SD: 5.7714 c. M: 9.3840 c. 16: 2 11 3 N T3 SD: 1.8684 c. M: 3.1584 c. 33: 4 23 6 N T3 SD: 1.5084 c. M: 2.5918 c. 38: 5 26 7 N T3 SD: 1.7246 c. M:-2.5713 c. 39: 5 27 7 N T3 SD: 0.7040 c. M:-0.8910 c. 55: 7 38 10 N T3 SD: 0.3109 c. M:-0.4266 c. 94: 12 65 17 N T3 SD: 0.3683 c. M:-0.6193 c. 111: 14 77 20 N T3 SD: 0.2934 c. M:-0.4872 c. 127: 16 88 23 N T3 SD: 0.1252 c. M: 0.2151 c. 166: 21 115 30 N T3 SD: 0.1278 c. M:-0.2169 c. 182: 23 126 33 N T3 SD: 0.0477 c. M: 0.0799 c. 348: 44 241 63 N T3 SD: 0.0361 c. M:-0.0617 c. 475: 60 329 86 N T3 SD: 0.0419 c. M:-0.0526 c. 530: 67 367 96 N T3 SD: 0.0076 c. M:-0.0131 c. 712: 90 493 129 N T3 SD: 0.0070 c. M: 0.0107 c. 1242: 157 860 225 N T3 SD: 0.0021 c. M: 0.0035 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 5 x S SD: 21.5063 cents 5 x 6:7 S SD: 62.5132 cents 6 x x 8 S SD: 0.0000 cents 7:8:9 x S SD: 85.2042 cents 8:9:10:11 H SD: 50.7359 cents 9:10:11:12 H SD: 44.6171 cents 10:11 x 13 SD: 55.5293 cents 11:12:14:15 S SD: 32.1362 cents 12:13:15:16 SD: 26.2036 cents 14:15:18:19 S SD: 23.2677 cents 15:16:19:20 SD: 16.2637 cents 18:19:23:24 SD: 11.6077 cents 19:20:24:25 S SD: 11.5706 cents 21:22:27:28 SD: 10.8128 cents 22:23:28:29 SD: 8.7000 cents 23:24:29:31 SD: 7.5106 cents 26:27:33:35 SD: 5.8154 cents 27:28:34:36 SD: 2.9099 cents 30:31:38:40 SD: 2.1186 cents 57:59:72:76 SD: 1.5642 cents 87:90:110:116 SD: 1.5343 cents 102:106:129:136 SD: 1.2816 cents 105:109:133:140 SD: 0.7562 cents 132:137:167:176 SD: 0.5156 cents 135:140:171:180 SD: 0.4748 cents 162:168:205:216 SD: 0.0880 cents 459:476:581:612 SD: 0.0776 cents