Scala analysis: 276_C19
Chromatic tetrachord 27/26 * 88/81 * 13/11
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 27/26 65.337341 tridecimal comma 2: 44/39 208.835280 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 13/11 289.2097 tridecimal minor third 1: 27/26 65.3373 tridecimal comma 2: 88/81 143.4979 2nd undecimal neutral second 3: 13/11 289.2097 tridecimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 27/26 65.337 cents tridecimal comma 1: 1 88/81 143.498 cents 2nd undecimal neutral second 1: 1 13/11 289.210 cents tridecimal minor third 2: 1 44/39 208.835 cents 2: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 2: 1 104/81 432.708 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 : 65.3 208.8 498.0 65.3 : 143.5 432.7 498.0 208.8: 289.2 354.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 65.3373 .. 289.2097 cents 338/297, 223.8724 cents 27/26, 65.3373 cents 2: 208.8353 .. 432.7077 cents 338/297, 223.8724 cents 484/507,-80.3744 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 27/26, 65.3373 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 13/11, 289.2097 cents Average / Smallest step : 2.540890 Largest / Average step : 1.742070 Largest / Smallest step : 4.426408 Median interval of one step : 88/81, 143.4979 cents, amount: 1 Least squares average step : 141.22449 cents, oct.: 423.67348 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2020-tone equal temperament with octave 4/3 degrees: 265 847 2020 Least number of segments generator : 1011 of 249.269 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1173 of 289.211 cents and inv. generated superset size: 47 = 44 more = 1566.667% 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 65.33734 cents Scale diversity : 1.001341 Lumma stability : 0.262375 Lumma impropriety factor : 0.161380 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 : 27/26, 65.3373 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 : 13 Odd number limit : 81 (O: 27 U: 81) Highest odd numerator or denominator: 39 Scale harmonicity : 0.018518 Average absolute harmonicity : 0.089535 Specific harmonicity : 0.084733 Fundamental : 1/78, -6.2854 octaves, 3.3542 Hz. Guide tone : 1188, 10.2143 octaves, 310811.172 Hz. Exponens Consonantiae : 9.266400E+04, 16.49972 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 71.5, average 23.83333 Mersenne's string divisions : 30793 Sum of van Prooijen's expressibility: 3.49955, average 1.16652 Sum of Tenney's harmonic distance : 7.16004, average 2.38668 Vogel's harmonic complexity : 14.00000 Wille's k value : 40 Wilson's harmonic complexity : 36 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 19.81070, average 3.30178 Lattice compactness (without 2's) : 15.55475, average 2.59246 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 1.00000 5 3: -1 .. 3 0.33333 5 1 11: 0 .. 1 0.33333 1 13: -1 .. 0 -0.66667 2 2 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <7 10 26 27| Scale is JI-epimorphic with val: <7 11 24 25| Scale is weakly epimorphic with val: <7 11 24 28| Scale is weakly epimorphic with val: <7 11 25 27| = patent Scale is weakly epimorphic with val: <7 11 25 30| Scale is weakly epimorphic with val: <7 11 27 28| Scale is weakly epimorphic with val: <7 12 25 26| Scale is weakly epimorphic with val: <8 11 25 27| Scale is weakly epimorphic with val: <8 12 23 25| Scale is weakly epimorphic with val: <8 12 25 26|
FIT/MODE
3: 0 1 2 N G T3 SD: 45.1019 c. M: 65.3373 c. 5: 1 1 3 N M DE S SD: 20.5511 c. M:-34.2717 c. 7: 1 2 4 N T3 SD: 4.2839 c. M:-5.8119 c. 22: 3 6 13 N T3 SD: 3.2939 c. M: 5.0896 c. 24: 3 7 14 N T3 SD: 1.9348 c. M: 3.0817 c. 31: 4 9 18 N T3 SD: 0.6199 c. M: 1.0735 c. 38: 5 11 22 N T3 SD: 0.5135 c. M:-0.8679 c. 69: 9 20 40 N T3 SD: 0.3553 c. M:-0.4880 c. 107: 14 31 62 N T3 SD: 0.3732 c. M:-0.6229 c. 122: 16 35 71 N T3 SD: 0.3675 c. M: 0.6361 c. 129: 17 37 75 N T3 SD: 0.2654 c. M: 0.3513 c. 160: 21 46 93 N T3 SD: 0.1620 c. M: 0.2789 c. 167: 22 48 97 N T3 SD: 0.1635 c. M:-0.2734 c. 191: 25 55 111 N T3 SD: 0.1580 c. M: 0.2300 c. 198: 26 57 115 N T3 SD: 0.0496 c. M:-0.0625 c. 427: 56 123 248 N T3 SD: 0.0327 c. M: 0.0529 c. 465: 61 134 270 N T3 SD: 0.0129 c. M:-0.0223 c. 663: 87 191 385 N T3 SD: 0.0099 c. M:-0.0170 c. 892: 117 257 518 N T3 SD: 0.0101 c. M: 0.0137 c. 1128: 148 325 655 N T3 SD: 0.0070 c. M:-0.0090 c. 1357: 178 391 788 N T3 SD: 0.0046 c. M: 0.0079 c. 1822: 239 525 1058 N T3 SD: 0.0046 c. M: 0.0065 c. 2020: 265 582 1173 N T3 SD: 0.0009 c. M: 0.0016 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: 68.0849 cents 6 x 7:8 S SD: 29.0178 cents 7 x 8:9 S SD: 33.4032 cents 8 x 9:11 SD: 26.7501 cents 9 x 10:12 S SD: 13.2158 cents 10 x 11:13 SD: 30.9932 cents 11 x 12:15 S SD: 35.0025 cents 12 x 14:16 S SD: 29.0178 cents 13:14:15:17 SD: 27.0962 cents 14:15:16:19 SD: 22.0236 cents 15:16:17:20 SD: 15.6845 cents 17:18:19:23 SD: 15.0328 cents 18:19:20:24 S SD: 12.8995 cents 21:22:24:28 S SD: 9.0065 cents 22:23:25:29 SD: 8.7056 cents 23:24:26:31 SD: 6.9249 cents 24:25:27:32 SD: 2.4203 cents 54:56:61:72 SD: 1.0760 cents 78:81:88:104 SD: 0.0000 cents