Scala analysis: 246_C17
Chromatic tetrachord 27/25 * 25/24 * 32/27
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 27/25 133.237575 large limma, BP small semitone, Zarlino semitone 2: 9/8 203.910002 major whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 32/27 294.1350 Pythagorean minor third 1: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 2: 25/24 70.6724 classic chromatic semitone, minor chroma 3: 32/27 294.1350 Pythagorean minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 1 32/27 294.135 cents Pythagorean minor third 2: 1 9/8 203.910 cents major whole tone 2: 1 100/81 364.807 cents grave major third 2: 1 32/25 427.373 cents classic diminished fourth 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 : 133.2 203.9 498.0 133.2: 70.7 364.8 498.0 203.9: 294.1 427.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 294.1350 cents 256/225, 223.4626 cents 25/24, 70.6724 cents 2: 203.9100 .. 427.3726 cents 256/225, 223.4626 cents 243/256,-90.2250 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 25/24, 70.6724 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 32/27, 294.1350 cents Average / Smallest step : 2.349077 Largest / Average step : 1.771737 Largest / Smallest step : 4.161948 Median interval of one step : 27/25, 133.2376 cents, amount: 1 Least squares average step : 145.37090 cents, oct.: 436.11269 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1656-tone equal temperament with octave 4/3 degrees: 443 678 1656 Least number of segments generator : 829 of 249.323 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1475 of 443.609 cents and inv. generated superset size: 43 = 40 more = 1433.333% 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 70.67243 cents Scale diversity : 1.034060 Lumma stability : 0.283799 Lumma impropriety factor : 0.181158 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 : 648/625, 62.5651 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined -- Rational properties -- Prime limit : 5 Odd number limit : 81 (O: 27 U: 81) Highest odd numerator or denominator: 27 Scale harmonicity : 0.035129 Average absolute harmonicity : 0.127454 Specific harmonicity : 0.176340 Fundamental : 1/600, -9.2288 octaves, 0.4360 Hz. Guide tone : 108, 6.7549 octaves, 28255.561 Hz. Exponens Consonantiae : 6.480000E+04, 15.98371 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 38.0, average 12.66667 Mersenne's string divisions : 6188 Sum of van Prooijen's expressibility: 2.86273, average 0.95424 Sum of Tenney's harmonic distance : 5.76582, average 1.92194 Vogel's harmonic complexity : 16.33333 Wille's k value : 337 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 23.91876, average 3.98646 Lattice compactness (without 2's) : 16.31376, average 2.71896 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.33333 5 3: -1 .. 3 1.33333 6 2 5: -2 .. 0 -0.66667 2 1 Average exponent except 2's : 2 / 3 = 0.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <7 11 17| = patent Scale is weakly epimorphic with val: <7 12 16| Scale is weakly epimorphic with val: <7 12 19| Scale is weakly epimorphic with val: <8 11 15|
FIT/MODE
3: 1 0 2 N G T3 SD: 28.9274 c. M: 37.8950 c. 4: 1 1 2 P M ME S SD: 26.5285 c. M:-45.1125 c. 5: 1 1 3 N M DE S SD: 19.6035 c. M: 33.6286 c. 7: 2 1 4 N T3 SD: 7.5954 c. M:-9.5379 c. 12: 3 2 7 N T3 SD: 5.4520 c. M: 8.7263 c. Vietnamese tritonic 15: 4 2 9 N T3 SD: 2.7200 c. M: 4.6920 c. 22: 6 3 13 N T3 SD: 1.5000 c. M:-2.5929 c. 34: 9 5 20 N T3 SD: 1.0534 c. M: 1.4021 c. 49: 13 7 29 N T3 SD: 0.7324 c. M: 1.1032 c. 56: 15 8 33 N T3 SD: 0.3843 c. M:-0.6442 c. 71: 19 10 42 N T3 SD: 0.2800 c. M: 0.4832 c. 105: 28 15 62 N T3 SD: 0.2475 c. M: 0.4256 c. 127: 34 18 75 N T3 SD: 0.0568 c. M:-0.0973 c. 303: 81 43 179 N T3 SD: 0.0762 c. M: 0.0968 c. 325: 87 46 192 N T3 SD: 0.0735 c. M: 0.0947 c. 359: 96 51 212 N T3 SD: 0.0352 c. M: 0.0556 c. 430: 115 61 254 N T3 SD: 0.0410 c. M: 0.0590 c. 486: 130 69 287 N T3 SD: 0.0156 c. M:-0.0220 c. 613: 164 87 362 N T3 SD: 0.0126 c. M:-0.0203 c. 1043: 279 148 616 N T3 SD: 0.0098 c. M: 0.0124 c. 1170: 313 166 691 N T3 SD: 0.0055 c. M: 0.0095 c. 1656: 443 235 978 N T3 SD: 0.0026 c. M: 0.0045 c. 1783: 477 253 1053 N T3 SD: 0.0016 c. M:-0.0027 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: 70.0332 cents 6 x 7:8 S SD: 31.4805 cents 7 x 8:9 S SD: 34.3053 cents 8 x 9:11 SD: 26.6365 cents 9 x 10:12 S SD: 10.7531 cents 10:11 x 13 SD: 27.0660 cents 11:12 x 15 S SD: 21.3096 cents 12:13:14:16 S SD: 21.0622 cents 13:14:15:17 SD: 18.4863 cents 14:15:16:19 SD: 14.4244 cents 15:16:17:20 SD: 8.3384 cents 19 x 21:25 SD: 19.1360 cents 20:22:23:27 SD: 18.0108 cents 21:23:24:28 SD: 12.1641 cents 22:24:25:29 SD: 10.5249 cents 23:25:26:31 SD: 7.7708 cents 24:26:27:32 SD: 1.7784 cents 63:68:71:84 SD: 1.0720 cents 87:94:98:116 SD: 0.7764 cents 177:191:199:236 SD: 0.6040 cents 201:217:226:268 SD: 0.3835 cents 225:243:253:300 SD: 0.2850 cents 264:285:297:352 SD: 0.2429 cents 288:311:324:384 SD: 0.0742 cents 312:337:351:416 SD: 0.0685 cents 600:648:675:800 SD: 0.0000 cents