Scala analysis: 561_M69
Miscellaneous tetrachord 28/27 * 81/70 * 10/9
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: 6/5 315.641287 minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 28/27 62.9609 Archytas' 1/3-tone 2: 81/70 252.6804 Al-Hwarizmi's lute middle finger 3: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 10/9 182.404 cents minor whole tone 1: 1 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 1 280/243 245.365 cents 2: 1 6/5 315.641 cents minor 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 : 63.0 315.6 498.0 63.0 : 252.7 435.1 498.0 315.6: 182.4 245.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 252.6804 cents 2187/1960, 189.7195 cents 28/27, 62.9609 cents 2: 245.3646 .. 435.0841 cents 2187/1960, 189.7195 cents 19600/19683,-7.3158 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 : 81/70, 252.6804 cents Average / Smallest step : 2.636795 Largest / Average step : 1.522033 Largest / Smallest step : 4.013290 Median interval of one step : 10/9, 182.4037 cents, amount: 1 Least squares average step : 156.31275 cents, oct.: 468.93824 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1155-tone equal temperament with octave 4/3 degrees: 146 732 1155 Least number of segments generator : 578 of 249.238 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 911 of 392.830 cents and inv. generated superset size: 30 = 27 more = 1000.000% 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 7.31577 cents Scale diversity : 0.896549 Lumma stability : 0.252832 Lumma impropriety factor : 0.014689 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 : 19683/19600, 7.3158 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% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 7 Odd number limit : 243 (O: 81 U: 243) Highest odd numerator or denominator: 27 Scale harmonicity : 0.034069 Average absolute harmonicity : 0.120973 Specific harmonicity : 0.174436 Fundamental : 1/135, -7.0768 octaves, 1.9380 Hz. Guide tone : 84, 6.3923 octaves, 21976.547 Hz. Exponens Consonantiae : 1.134000E+04, 13.46913 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 36.5, average 12.16667 Mersenne's string divisions : 385 Sum of van Prooijen's expressibility: 2.60746, average 0.86915 Sum of Tenney's harmonic distance : 5.43482, average 1.81161 Vogel's harmonic complexity : 13.33333 Wille's k value : 40 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 16.75423, average 2.79237 Lattice compactness (without 2's) : 14.29127, average 2.38188 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -3 .. 1 -1.00000 5 1 5: -1 .. 0 -0.33333 1 1 7: 0 .. 1 0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 15 21| Scale is weakly epimorphic with val: <6 10 18 21| Scale is weakly epimorphic with val: <7 10 15 19| Scale is weakly epimorphic with val: <7 10 18 19| Scale is JI-epimorphic with val: <7 11 16 20| Scale is weakly epimorphic with val: <7 11 17 18| Scale is weakly epimorphic with val: <7 11 17 21| Scale is weakly epimorphic with val: <7 11 19 20| Scale is weakly epimorphic with val: <7 12 16 20| Scale is weakly epimorphic with val: <8 11 15 20| Scale is weakly epimorphic with val: <8 11 16 18| Scale is weakly epimorphic with val: <8 11 16 21| Scale is weakly epimorphic with val: <8 11 18 20| Scale is weakly epimorphic with val: <8 12 17 19| Scale is weakly epimorphic with val: <8 12 17 22|
FIT/MODE
3: 0 2 1 N G T3 SD: 37.5618 c. M: 62.9609 c. 5: 1 2 2 SP M ME S SD: 23.2795 c. M:-36.6481 c. 6: 1 3 2 P T3 SD: 14.9494 c. M:-20.0466 c. 8: 1 4 3 P T3 SD: 2.5518 c. M: 4.3632 c. 25: 3 13 9 N T3 SD: 2.5734 c. M: 3.1955 c. 30: 4 15 11 P T3 SD: 1.9928 c. M:-3.4451 c. 33: 4 17 12 N T3 SD: 1.6731 c. M: 2.5918 c. 38: 5 19 14 P T3 SD: 1.6117 c. M:-2.5713 c. 41: 5 21 15 N T3 SD: 1.2886 c. M: 2.2237 c. 46: 6 23 17 P T3 SD: 1.5000 c. M:-2.0015 c. 47: 6 24 17 N T3 SD: 1.3528 c. M:-2.2598 c. 49: 6 25 18 N T3 SD: 1.1843 c. M: 1.9758 c. 55: 7 28 20 N T3 SD: 0.7880 c. M:-1.2964 c. 63: 8 32 23 N T3 SD: 0.3714 c. M:-0.5778 c. 71: 9 36 26 N T3 SD: 0.0998 c. M:-0.1716 c. 221: 28 112 81 N T3 SD: 0.1133 c. M:-0.1398 c. 292: 37 148 107 N T3 SD: 0.1026 c. M:-0.1475 c. 325: 41 165 119 N T3 SD: 0.0793 c. M: 0.1306 c. 333: 42 169 122 N T3 SD: 0.0910 c. M: 0.1444 c. 388: 49 197 142 N T3 SD: 0.0833 c. M:-0.1295 c. 396: 50 201 145 N T3 SD: 0.0495 c. M: 0.0764 c. 404: 51 205 148 N T3 SD: 0.0584 c. M: 0.0889 c. 467: 59 237 171 N T3 SD: 0.0306 c. M: 0.0387 c. 475: 60 241 174 N T3 SD: 0.0363 c. M: 0.0500 c. 538: 68 273 197 N T3 SD: 0.0207 c. M:-0.0341 c. 546: 69 277 200 N T3 SD: 0.0214 c. M: 0.0304 c. 609: 77 309 223 N T3 SD: 0.0197 c. M:-0.0326 c. 617: 78 313 226 N T3 SD: 0.0141 c. M: 0.0244 c. 688: 87 349 252 N T3 SD: 0.0157 c. M: 0.0197 c. 1084: 137 550 397 N T3 SD: 0.0093 c. M: 0.0161 c. 1155: 146 586 423 N T3 SD: 0.0031 c. M: 0.0046 c. 2381: 301 1208 872 N T3 SD: 0.0020 c. M:-0.0034 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: 70.6724 cents 5 x 6:7 S SD: 42.2336 cents 6 x 7:8 S SD: 24.3852 cents 7 x 8:9 S SD: 52.6754 cents 8 x 10:11 S SD: 44.2510 cents 9:10:11:12 H SD: 41.1983 cents 10:11:12:13 H SD: 37.0195 cents 11:12:13:15 SD: 33.1652 cents 12:13:14:16 S SD: 29.9920 cents 13:14:16:17 S SD: 28.5195 cents 14:15:17:19 SD: 22.4819 cents 15:16:18:20 S SD: 16.2568 cents 18:19:22:24 SD: 14.7123 cents 19:20:23:25 SD: 12.5703 cents 20:21:24:27 S SD: 10.1382 cents 21:22:25:28 SD: 7.4477 cents 24:25:29:32 SD: 4.7494 cents 30:31:36:40 SD: 2.0647 cents 54:56:65:72 SD: 1.7784 cents 75:78:90:100 SD: 1.6464 cents 81:84:97:108 SD: 1.1886 cents 105:109:126:140 SD: 0.5886 cents 135:140:162:180 SD: 0.0000 cents