Scala analysis: 544_M52
Miscellaneous tetrachord 256/243 * 243/229 * 229/192
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: 256/229 192.955454 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 229/192 305.0895 1: 256/243 90.2250 limma, Pythagorean minor second 2: 243/229 102.7305 3: 229/192 305.0895
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 256/243 90.225 cents limma, Pythagorean minor second 1: 1 243/229 102.730 cents 1: 1 229/192 305.090 cents 2: 1 256/229 192.955 cents 2: 1 916/729 395.315 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 : 90.2 193.0 498.0 90.2 : 102.7 407.8 498.0 193.0: 305.1 395.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 305.0895 cents 18549/16384, 214.8645 cents 256/243, 90.2250 cents 2: 192.9555 .. 407.8200 cents 18549/16384, 214.8645 cents 49152/52441,-112.1341 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 : 229/192, 305.0895 cents Average / Smallest step : 1.840011 Largest / Average step : 1.837723 Largest / Smallest step : 3.381430 Median interval of one step : 243/229, 102.7305 cents, amount: 1 Least squares average step : 140.73364 cents, oct.: 422.20091 cents Scale is not proper Scale has trivalence property Scale is a mode of a 955-tone equal temperament with octave 4/3 degrees: 173 370 955 Least number of segments generator : 478 of 249.283 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 564 of 294.133 cents and inv. generated superset size: 66 = 63 more = 2200.000% 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 : 1.055937 Lumma stability : 0.362317 Lumma impropriety factor : 0.225149 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 : 59049/58624, 12.5055 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 202.3591 cents: 2 -- Rational properties -- Prime limit : 229 Odd number limit : 729 (O: 243 U: 729) Highest odd numerator or denominator: 243 Scale harmonicity : 0.046875 Fundamental : 1/55647, -15.7640 octaves, 0.0047 Hz. Guide tone : 256, 8.0000 octaves, 66976.145 Hz. Exponens Consonantiae : 1.424563E+07, 23.76402 octaves Euler's gradus suavitatis : 247 Sum of Mann's harmonic distance : 495.5, average 165.16667 Mersenne's string divisions : 1694105 Sum of van Prooijen's expressibility: 5.22256, average 1.74085 Sum of Tenney's harmonic distance : 10.64110, average 3.54703 Vogel's harmonic complexity : 167.66667 Wille's k value : 9274 Wilson's harmonic complexity : 244 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 37.96391, average 6.32732 Lattice compactness (without 2's) : 16.00000, average 2.66667 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 2 .. 8 6.00000 18 3: -5 .. 0 -2.00000 6 2 229: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-7 / 3 =-2.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <7 11 57| = patent
FIT/MODE
3: 0 1 2 N G T3 SD: 54.3640 c. M: 90.2250 c. 4: 1 1 2 P M ME S SD: 37.9432 c. M:-56.0670 c. 5: 1 1 3 N M DE S SD: 6.5136 c. M:-9.3840 c. 16: 3 3 10 N M DE S SD: 4.0114 c. M: 6.1886 c. 18: 3 4 11 N T3 SD: 4.1882 c. M: 7.2175 c. 21: 4 4 13 N M DE S SD: 3.2624 c. M:-4.6407 c. 23: 4 5 14 N T3 SD: 2.3631 c. M: 3.6085 c. 28: 5 6 17 N T3 SD: 1.7299 c. M:-2.7051 c. 33: 6 7 20 N T3 SD: 1.8826 c. M:-3.2441 c. 34: 6 7 21 N T3 SD: 1.9861 c. M: 2.5265 c. 39: 7 8 24 N T3 SD: 0.9402 c. M: 1.3997 c. 44: 8 9 27 N T3 SD: 0.3595 c. M: 0.5290 c. 111: 20 23 68 N T3 SD: 0.2815 c. M: 0.4872 c. 116: 21 24 71 N T3 SD: 0.1496 c. M:-0.2517 c. 155: 28 32 95 N T3 SD: 0.1753 c. M: 0.2556 c. 160: 29 33 98 N T3 SD: 0.0339 c. M:-0.0457 c. 635: 115 131 389 N T3 SD: 0.0175 c. M: 0.0279 c. 795: 144 164 487 N T3 SD: 0.0077 c. M: 0.0131 c. 955: 173 197 585 N T3 SD: 0.0031 c. M:-0.0044 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: 74.4757 cents 6 x 7:8 S SD: 36.9577 cents 7 x 8:9 S SD: 36.8264 cents 8 x 9:11 SD: 27.1938 cents 9 x 10:12 S SD: 5.2759 cents 10 x 11:13 SD: 25.9925 cents 11 x 12:15 S SD: 28.7424 cents 12:13 x 16 SD: 24.1738 cents 14:15:16:19 SD: 19.0125 cents 15:16:17:20 SD: 10.6755 cents 17:18:19:23 SD: 8.9140 cents 18:19:20:24 S SD: 3.6931 cents 42:44:47:56 SD: 3.2828 cents 51:54:57:68 SD: 2.9129 cents 57:60:64:76 SD: 2.5697 cents 60:63:67:80 SD: 2.0229 cents 75:79:84:100 SD: 1.0848 cents 93:98:104:124 SD: 0.2424 cents 297:313:332:396 SD: 0.2071 cents 357:376:399:476 SD: 0.2014 cents 390:411:436:520 SD: 0.1921 cents 432:455:483:576 SD: 0.1612 cents 450:474:503:600 SD: 0.1112 cents 543:572:607:724 SD: 0.0540 cents