Scala analysis: 558_M66
Miscellaneous tetrachord 13/12 * 55/52 * 64/55
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 13/12 138.572661 tridecimal 2/3-tone 2: 55/48 235.676655 undecimal semi-augmented whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 64/55 262.3683 1: 13/12 138.5727 tridecimal 2/3-tone 2: 55/52 97.1040 3: 64/55 262.3683
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 55/52 97.104 cents 1: 1 13/12 138.573 cents tridecimal 2/3-tone 1: 1 64/55 262.368 cents 2: 1 55/48 235.677 cents undecimal semi-augmented whole tone 2: 1 16/13 359.472 cents tridecimal neutral third 2: 1 208/165 400.941 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 : 138.6 235.7 498.0 138.6: 97.1 359.5 498.0 235.7: 262.4 400.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 97.1040 .. 262.3683 cents 3328/3025, 165.2643 cents 55/52, 97.1040 cents 2: 235.6767 .. 400.9410 cents 3328/3025, 165.2643 cents 3025/3072,-26.6917 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 55/52, 97.1040 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 64/55, 262.3683 cents Average / Smallest step : 1.709662 Largest / Average step : 1.580389 Largest / Smallest step : 2.701932 Median interval of one step : 13/12, 138.5727 cents, amount: 1 Least squares average step : 150.29007 cents, oct.: 450.87021 cents Scale is not proper Scale has trivalence property Scale is a mode of a 877-tone equal temperament with octave 4/3 degrees: 244 415 877 Least number of segments generator : 439 of 249.306 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 609 of 345.849 cents and inv. generated superset size: 32 = 29 more = 1066.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 26.69169 cents Scale diversity : 1.149415 Lumma stability : 0.389941 Lumma impropriety factor : 0.053593 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 : 3072/3025, 26.6917 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 : 13 Odd number limit : 165 (O: 55 U: 165) Highest odd numerator or denominator: 55 Scale harmonicity : 0.018050 Average absolute harmonicity : 0.094524 Specific harmonicity : 0.095120 Fundamental : 1/48, -5.5850 octaves, 5.4505 Hz. Guide tone : 2860, 11.4818 octaves, 748249.117 Hz. Exponens Consonantiae : 1.372800E+05, 17.06676 octaves Euler's gradus suavitatis : 35 Sum of Mann's harmonic distance : 67.5, average 22.50000 Mersenne's string divisions : 18025 Sum of van Prooijen's expressibility: 3.33143, average 1.11048 Sum of Tenney's harmonic distance : 6.69391, average 2.23130 Vogel's harmonic complexity : 12.33333 Wille's k value : 27 Wilson's harmonic complexity : 32 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 21.97773, average 3.66295 Lattice compactness (without 2's) : 8.29253, average 1.38209 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -1.33333 8 3: -1 ..-1 -1.00000 3 1 5: 0 .. 1 0.33333 1 11: 0 .. 1 0.33333 1 1 13: 0 .. 1 0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 15 23 25| Scale is weakly epimorphic with val: <6 10 16 25 25| Scale is weakly epimorphic with val: <6 10 17 24 25| Scale is weakly epimorphic with val: <6 10 18 23 25| Scale is weakly epimorphic with val: <6 10 19 25 25| Scale is weakly epimorphic with val: <6 11 15 23 25| Scale is weakly epimorphic with val: <6 11 15 23 28| Scale is weakly epimorphic with val: <6 11 15 25 26| Scale is weakly epimorphic with val: <6 11 16 24 26| Scale is weakly epimorphic with val: <6 11 17 23 26| Scale is weakly epimorphic with val: <6 11 17 26 26| Scale is weakly epimorphic with val: <6 11 18 25 26| Scale is weakly epimorphic with val: <6 11 19 24 26| Scale is weakly epimorphic with val: <7 10 15 25 27| Scale is weakly epimorphic with val: <7 10 15 26 26| Scale is weakly epimorphic with val: <7 10 15 26 29| Scale is weakly epimorphic with val: <7 10 16 24 27| Scale is weakly epimorphic with val: <7 10 16 25 26| Scale is weakly epimorphic with val: <7 10 16 25 29| Scale is weakly epimorphic with val: <7 10 16 27 27| Scale is weakly epimorphic with val: <7 10 17 23 27| Scale is weakly epimorphic with val: <7 10 17 24 26| Scale is weakly epimorphic with val: <7 10 17 24 29| Scale is weakly epimorphic with val: <7 10 17 26 27| Scale is weakly epimorphic with val: <7 10 18 23 26| Scale is weakly epimorphic with val: <7 10 18 23 29| Scale is weakly epimorphic with val: <7 10 18 25 27| Scale is weakly epimorphic with val: <7 10 19 24 27| Scale is weakly epimorphic with val: <7 10 19 27 27| Scale is weakly epimorphic with val: <7 11 15 23 26| Scale is weakly epimorphic with val: <7 11 15 23 29| Scale is weakly epimorphic with val: <7 11 15 25 27| Scale is weakly epimorphic with val: <7 11 15 25 30| Scale is JI-epimorphic with val: <7 11 15 26 26| Scale is weakly epimorphic with val: <7 11 15 26 29| Scale is weakly epimorphic with val: <7 11 16 24 27| Scale is weakly epimorphic with val: <7 11 16 24 30| Scale is JI-epimorphic with val: <7 11 16 25 26| Scale is weakly epimorphic with val: <7 11 16 25 29| Scale is weakly epimorphic with val: <7 11 16 27 27| Scale is weakly epimorphic with val: <7 11 16 27 30| Scale is weakly epimorphic with val: <7 11 17 23 27| Scale is weakly epimorphic with val: <7 11 17 23 30| Scale is JI-epimorphic with val: <7 11 17 24 26| Scale is weakly epimorphic with val: <7 11 17 24 29| Scale is weakly epimorphic with val: <7 11 17 26 27| Scale is weakly epimorphic with val: <7 11 17 26 30| Scale is weakly epimorphic with val: <7 11 17 27 29| Scale is JI-epimorphic with val: <7 11 18 23 26| Scale is weakly epimorphic with val: <7 11 18 23 29| Scale is weakly epimorphic with val: <7 11 18 25 27| Scale is weakly epimorphic with val: <7 11 18 25 30| Scale is weakly epimorphic with val: <7 11 18 26 26| Scale is weakly epimorphic with val: <7 11 18 26 29| Scale is weakly epimorphic with val: <7 11 19 24 27| Scale is weakly epimorphic with val: <7 11 19 24 30| Scale is weakly epimorphic with val: <7 11 19 25 26| Scale is weakly epimorphic with val: <7 11 19 25 29| Scale is weakly epimorphic with val: <7 11 19 27 27| Scale is weakly epimorphic with val: <7 11 19 27 30| Scale is weakly epimorphic with val: <7 12 15 23 29| Scale is weakly epimorphic with val: <7 12 15 26 29| Scale is weakly epimorphic with val: <7 12 16 25 29| Scale is weakly epimorphic with val: <7 12 16 27 27| Scale is weakly epimorphic with val: <7 12 16 27 30| Scale is weakly epimorphic with val: <7 12 17 24 29| Scale is weakly epimorphic with val: <7 12 17 26 27| Scale is weakly epimorphic with val: <7 12 17 26 30| Scale is weakly epimorphic with val: <7 12 17 27 29| Scale is weakly epimorphic with val: <7 12 18 23 29| Scale is weakly epimorphic with val: <7 12 18 25 27| Scale is weakly epimorphic with val: <7 12 18 25 30| Scale is weakly epimorphic with val: <7 12 18 26 29| Scale is weakly epimorphic with val: <7 12 19 24 27| Scale is weakly epimorphic with val: <7 12 19 24 30| Scale is weakly epimorphic with val: <7 12 19 25 29| Scale is weakly epimorphic with val: <8 11 15 23 30| Scale is weakly epimorphic with val: <8 11 15 26 30| Scale is weakly epimorphic with val: <8 11 16 25 30| Scale is weakly epimorphic with val: <8 11 17 24 30| Scale is weakly epimorphic with val: <8 11 17 27 30| Scale is weakly epimorphic with val: <8 11 18 23 30| Scale is weakly epimorphic with val: <8 11 18 26 30| Scale is weakly epimorphic with val: <8 11 19 25 30| Scale is weakly epimorphic with val: <8 11 19 27 28|
FIT/MODE
3: 1 0 2 N G T3 SD: 43.2274 c. M: 69.6617 c. 4: 1 1 2 P M ME S SD: 11.1928 c. M: 14.0614 c. 10: 3 2 5 P T3 SD: 9.9270 c. M:-13.3458 c. 11: 3 2 6 N T3 SD: 5.5938 c. M: 9.2926 c. 15: 4 3 8 N T3 SD: 3.8203 c. M: 5.7607 c. 21: 6 4 11 N T3 SD: 2.3163 c. M:-3.7259 c. 25: 7 5 13 N T3 SD: 2.0193 c. M:-3.3849 c. 32: 9 6 17 N T3 SD: 1.5467 c. M: 2.2181 c. 36: 10 7 19 N T3 SD: 0.3111 c. M: 0.4887 c. 97: 27 19 51 N T3 SD: 0.2962 c. M:-0.5096 c. 129: 36 25 68 N T3 SD: 0.2592 c. M:-0.4166 c. 133: 37 26 70 N T3 SD: 0.1386 c. M:-0.2394 c. 169: 47 33 89 N T3 SD: 0.0608 c. M:-0.0843 c. 205: 57 40 108 N T3 SD: 0.0539 c. M: 0.0919 c. 374: 104 73 197 N T3 SD: 0.0485 c. M: 0.0789 c. 467: 130 91 246 N T3 SD: 0.0410 c. M:-0.0694 c. 503: 140 98 265 N T3 SD: 0.0304 c. M:-0.0482 c. 636: 177 124 335 N T3 SD: 0.0276 c. M:-0.0342 c. 672: 187 131 354 N T3 SD: 0.0121 c. M:-0.0202 c. 708: 197 138 373 N T3 SD: 0.0122 c. M: 0.0198 c. 877: 244 171 462 N T3 SD: 0.0035 c. M: 0.0060 c. 1549: 431 302 816 N T3 SD: 0.0034 c. M:-0.0054 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: 58.1572 cents 6 x 7:8 S SD: 15.5971 cents 7 x 8:9 S SD: 31.5608 cents 8 x 9:11 SD: 31.0126 cents 9:10 x 12 S SD: 21.9155 cents 10:11 x 13 SD: 25.5919 cents 11:12:13:15 SD: 22.4227 cents 12:13:14:16 S SD: 10.3981 cents 21:23:24:28 SD: 6.4830 cents 27:29:31:36 SD: 5.0886 cents 33:36:38:44 SD: 4.9316 cents 35:38:40:47 SD: 4.5528 cents 36:39:41:48 SD: 3.5081 cents 48:52:55:64 SD: 0.0000 cents