Scala analysis: 550_M58
Miscellaneous tetrachord 28/27 * 1024/945 * 1215/1024
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: 4096/3645 201.956281 narrow diminished third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 1215/1024 296.0887 wide augmented second 1: 28/27 62.9609 Archytas' 1/3-tone 2: 1024/945 138.9954 3: 1215/1024 296.0887 wide augmented second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 1024/945 138.995 cents 1: 1 1215/1024 296.089 cents wide augmented second 2: 1 4096/3645 201.956 cents narrow diminished third 2: 1 315/256 359.050 cents 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 : 63.0 202.0 498.0 63.0 : 139.0 435.1 498.0 202.0: 296.1 359.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 296.0887 cents 32805/28672, 233.1278 cents 28/27, 62.9609 cents 2: 201.9563 .. 435.0841 cents 32805/28672, 233.1278 cents 4194304/4428675,-94.1324 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 : 1215/1024, 296.0887 cents Average / Smallest step : 2.636795 Largest / Average step : 1.783506 Largest / Smallest step : 4.702739 Median interval of one step : 1024/945, 138.9954 cents, amount: 1 Least squares average step : 140.07203 cents, oct.: 420.21610 cents Scale is not proper Scale has trivalence property Scale is a mode of a 799-tone equal temperament with octave 4/3 degrees: 101 324 799 Least number of segments generator : 400 of 249.334 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 763 of 475.605 cents and inv. generated superset size: 26 = 23 more = 866.667% 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 62.96090 cents Scale diversity : 0.980519 Lumma stability : 0.252832 Lumma impropriety factor : 0.189004 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 : 28/27, 62.9609 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing 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 : 3645 (O: 1215 U: 3645) Highest odd numerator or denominator: 3645 Scale harmonicity : 0.022379 Average absolute harmonicity : 0.097550 Specific harmonicity : 0.114785 Fundamental : 1/3645, -11.8317 octaves, 0.0718 Hz. Guide tone : 28672, 14.8074 octaves, 7501328.208 Hz. Exponens Consonantiae : 1.045094E+08, 26.63906 octaves Euler's gradus suavitatis : 35 Sum of Mann's harmonic distance : 3901.5, average 1300.50000 Mersenne's string divisions : 2980285 Sum of van Prooijen's expressibility: 5.47018, average 1.82339 Sum of Tenney's harmonic distance : 11.13176, average 3.71059 Vogel's harmonic complexity : 19.00000 Wille's k value : 607 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 8 Triangular lattice diameter : 6 Lattice compactness : 43.42804, average 7.23801 Lattice compactness (without 2's) : 20.89675, average 3.48279 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 12 5.33333 16 3: -6 ..-1 -3.33333 10 1 5: -1 .. 0 -0.33333 1 1 7: 0 .. 1 0.33333 1 1 Average exponent except 2's :-10 / 3 =-3.33333 Average absolute exponent except 2's: 12 / 3 = 4.00000 Scale is weakly epimorphic with val: <6 10 17 21| Scale is weakly epimorphic with val: <7 10 16 19| Scale is weakly epimorphic with val: <7 10 19 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: <8 11 17 20|
FIT/MODE
3: 0 1 2 N G T3 SD: 41.8563 c. M: 62.9609 c. 5: 1 1 3 N M DE S SD: 21.2178 c. M:-36.6481 c. 6: 1 1 4 N M DE S SD: 23.7602 c. M: 35.9413 c. 7: 1 2 4 N T3 SD: 8.1467 c. M:-11.4916 c. 10: 1 3 6 N T3 SD: 7.7586 c. M: 13.1564 c. 15: 2 4 9 N T3 SD: 2.5408 c. M:-3.4451 c. 22: 3 6 13 N T3 SD: 3.0412 c. M:-4.9543 c. 25: 3 7 15 N T3 SD: 2.4296 c. M: 3.1955 c. 32: 4 9 19 N T3 SD: 0.4610 c. M: 0.7053 c. 47: 6 13 28 N T3 SD: 0.5055 c. M:-0.6193 c. 79: 10 22 47 N T3 SD: 0.1338 c. M: 0.2165 c. 111: 14 31 66 N T3 SD: 0.0875 c. M: 0.1444 c. 190: 24 53 113 N T3 SD: 0.0734 c. M: 0.1170 c. 301: 38 84 179 N T3 SD: 0.0718 c. M: 0.0909 c. 419: 53 117 249 N T3 SD: 0.0696 c. M:-0.1145 c. 466: 59 130 277 N T3 SD: 0.0603 c. M:-0.0963 c. 498: 63 139 296 N T3 SD: 0.0441 c. M:-0.0620 c. 577: 73 161 343 N T3 SD: 0.0320 c. M:-0.0500 c. 609: 77 170 362 N T3 SD: 0.0251 c. M:-0.0423 c. 688: 87 192 409 N T3 SD: 0.0130 c. M:-0.0186 c. 799: 101 223 475 N T3 SD: 0.0034 c. M:-0.0044 c. 1677: 212 468 997 N T3 SD: 0.0035 c. M: 0.0060 c. 2365: 299 660 1406 N T3 SD: 0.0032 c. M:-0.0055 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: 70.8149 cents 6 x 7:8 S SD: 32.4573 cents 7 x 8:9 S SD: 34.7050 cents 8 x 9:11 SD: 26.6544 cents 9 x 10:12 S SD: 9.7763 cents 10 x 11:13 SD: 28.6645 cents 11 x 12:15 S SD: 32.1999 cents 12 x 13:16 SD: 31.6918 cents 13:14:15:17 SD: 28.8585 cents 14:15:16:19 SD: 23.5297 cents 15:16:17:20 SD: 16.9821 cents 16:17:18:21 S SD: 16.7022 cents 17:18:19:23 SD: 14.9913 cents 18:19:20:24 S SD: 12.1163 cents 21:22:24:28 S SD: 11.3656 cents 22:23:25:29 SD: 10.3382 cents 23:24:26:31 SD: 7.9669 cents 24:25:27:32 SD: 2.6517 cents 57:59:64:76 SD: 1.1850 cents 81:84:91:108 SD: 0.1409 cents