Scala analysis: 542_M50
Miscellaneous tetrachord 68/57 * 19/18 * 18/17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 68/57 305.487393 2: 34/27 399.090407 septendecimal major third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 18/17 98.9546 Arabic lute index finger 1: 68/57 305.4874 2: 19/18 93.6030 undevicesimal semitone 3: 18/17 98.9546 Arabic lute index finger
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 19/18 93.603 cents undevicesimal semitone 1: 1 18/17 98.955 cents Arabic lute index finger 1: 1 68/57 305.487 cents 2: 1 19/17 192.558 cents quasi-meantone 2: 1 34/27 399.090 cents septendecimal major third 2: 1 24/19 404.442 cents smaller undevicesimal 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 : 305.5 399.1 498.0 305.5: 93.6 192.6 498.0 399.1: 99.0 404.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 93.6030 .. 305.4874 cents 408/361, 211.8844 cents 19/18, 93.6030 cents 2: 192.5576 .. 404.4420 cents 408/361, 211.8844 cents 1083/1156,-112.9298 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 19/18, 93.6030 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 68/57, 305.4874 cents Average / Smallest step : 1.773607 Largest / Average step : 1.840119 Largest / Smallest step : 3.263649 Median interval of one step : 18/17, 98.9546 cents, amount: 1 Least squares average step : 185.55737 cents, oct.: 556.67212 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1676-tone equal temperament with octave 4/3 degrees: 1028 1343 1676 Least number of segments generator : 839 of 249.320 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1057 of 314.101 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 : LSM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 93.60301 cents Scale diversity : 1.050810 Lumma stability : 0.375882 Lumma impropriety factor : 0.226746 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 : 324/323, 5.3516 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Length of longest subharmonic part : 2 at degree 1 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 211.8844 cents: 1 -- Rational properties -- Prime limit : 19 Odd number limit : 57 (O: 19 U: 57) Highest odd numerator or denominator: 57 Scale harmonicity : 0.013473 Average absolute harmonicity : 0.084788 Specific harmonicity : 0.063045 Fundamental : 1/513, -9.0028 octaves, 0.5100 Hz. Guide tone : 68, 6.0875 octaves, 17790.538 Hz. Exponens Consonantiae : 3.488400E+04, 15.09028 octaves Euler's gradus suavitatis : 43 Sum of Mann's harmonic distance : 96.5, average 32.16667 Mersenne's string divisions : 53375 Sum of van Prooijen's expressibility: 3.66436, average 1.22145 Sum of Tenney's harmonic distance : 7.63041, average 2.54347 Vogel's harmonic complexity : 29.66667 Wille's k value : 161 Wilson's harmonic complexity : 45 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 14.51164, average 2.41861 Lattice compactness (without 2's) : 11.78068, average 1.96345 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -3 ..-1 -1.66667 5 1 17: 0 .. 1 0.66667 2 1 19: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 27 28| Scale is weakly epimorphic with val: <6 10 27 31| Scale is weakly epimorphic with val: <6 10 27 34| Scale is weakly epimorphic with val: <6 11 30 32| Scale is weakly epimorphic with val: <7 10 28 29| Scale is weakly epimorphic with val: <7 10 31 32| Scale is weakly epimorphic with val: <7 11 27 28| Scale is weakly epimorphic with val: <7 11 27 31| Scale is weakly epimorphic with val: <7 11 27 34| Scale is JI-epimorphic with val: <7 11 28 30| Scale is weakly epimorphic with val: <7 11 28 33| Scale is weakly epimorphic with val: <7 11 30 31| = patent Scale is weakly epimorphic with val: <7 11 30 34| Scale is weakly epimorphic with val: <7 11 31 33| Scale is weakly epimorphic with val: <7 11 33 34| Scale is weakly epimorphic with val: <7 12 32 33| Scale is weakly epimorphic with val: <8 11 28 29| Scale is weakly epimorphic with val: <8 11 28 32| Scale is weakly epimorphic with val: <8 11 29 31| Scale is weakly epimorphic with val: <8 11 32 34| Scale is weakly epimorphic with val: <8 12 27 28| Scale is weakly epimorphic with val: <8 12 30 31| Scale is weakly epimorphic with val: <8 12 31 33| Scale is weakly epimorphic with val: <8 12 33 34|
FIT/MODE
3: 2 0 1 N G T3 SD: 41.6398 c. M: 67.0604 c. 4: 2 1 1 P M ME S SD: 35.7837 c. M: 56.4649 c. 5: 3 1 1 N M DE S SD: 3.8639 c. M: 6.6604 c. 16: 10 3 3 N M DE S SD: 4.6393 c. M:-5.7907 c. 21: 13 4 4 N M DE S SD: 2.8697 c. M:-4.0889 c. 26: 16 5 5 N M DE S SD: 1.9231 c. M:-3.1767 c. 31: 19 6 6 N M DE S SD: 1.4835 c. M:-2.5588 c. 36: 22 7 7 N M DE S SD: 1.3822 c. M:-2.1125 c. 41: 25 8 8 N M DE S SD: 1.4601 c. M: 1.8014 c. 49: 30 9 10 N T3 SD: 1.5850 c. M: 2.6872 c. 54: 33 10 11 N T3 SD: 1.5826 c. M: 2.4990 c. 55: 34 10 11 N T3 SD: 1.4334 c. M:-2.3950 c. 59: 36 11 12 N T3 SD: 1.6365 c. M: 2.3427 c. 60: 37 11 12 N T3 SD: 1.0196 c. M:-1.6404 c. 65: 40 12 13 N T3 SD: 0.6909 c. M:-1.0018 c. 70: 43 13 14 N T3 SD: 0.4600 c. M: 0.6544 c. 75: 46 14 15 N T3 SD: 0.3780 c. M: 0.6544 c. 96: 59 18 19 N T3 SD: 0.4124 c. M:-0.6028 c. 101: 62 19 20 N T3 SD: 0.2375 c. M:-0.3318 c. 106: 65 20 21 N T3 SD: 0.1715 c. M:-0.2853 c. 176: 108 33 35 N T3 SD: 0.0913 c. M:-0.1311 c. 181: 111 34 36 N T3 SD: 0.0684 c. M: 0.1041 c. 282: 173 53 56 N T3 SD: 0.0420 c. M:-0.0520 c. 463: 284 87 92 N T3 SD: 0.0073 c. M: 0.0090 c. 1213: 744 228 241 N T3 SD: 0.0053 c. M: 0.0088 c. 1676: 1028 315 333 N T3 SD: 0.0023 c. M: 0.0039 c. 2139: 1312 402 425 N T3 SD: 0.0016 c. M: 0.0025 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: 12.7767 cents 5:6 x 7 S SD: 42.5377 cents 6:7 x 8 S SD: 19.3082 cents 7:8:9 x S SD: 41.2856 cents 8 x 10:11 S SD: 27.3918 cents 9:11 x 12 SD: 20.9603 cents 10:12 x 13 S SD: 22.4959 cents 11:13:14:15 SD: 15.3400 cents 12:14:15:16 S SD: 13.5584 cents 13 x 16:17 SD: 25.9794 cents 14:17:18:19 SD: 18.7777 cents 15:18:19:20 S SD: 4.7866 cents 27:32:34:36 SD: 3.7841 cents 42:50:53:56 SD: 1.7145 cents 78:93:98:104 SD: 1.3472 cents 93:111:117:124 SD: 0.6123 cents 135:161:170:180 SD: 0.1886 cents 285:340:359:380 SD: 0.1786 cents 363:433:457:484 SD: 0.1568 cents 378:451:476:504 SD: 0.0673 cents 513:612:646:684 SD: 0.0000 cents