Scala analysis: 442_D12
Diatonic tetrachord 22/21 * 9/8 * 112/99
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 22/21 80.537035 undecimal minor semitone 2: 33/28 284.447037 undecimal minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 112/99 213.5980 1: 22/21 80.5370 undecimal minor semitone 2: 9/8 203.9100 major whole tone 3: 112/99 213.5980
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 22/21 80.537 cents undecimal minor semitone 1: 1 9/8 203.910 cents major whole tone 1: 1 112/99 213.598 cents 2: 1 33/28 284.447 cents undecimal minor third 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 14/11 417.508 cents undecimal diminished fourth or major 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 : 80.5 284.4 498.0 80.5 : 203.9 417.5 498.0 284.4: 213.6 294.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.5370 .. 213.5980 cents 392/363, 133.0609 cents 22/21, 80.5370 cents 2: 284.4470 .. 417.5080 cents 392/363, 133.0609 cents 3267/3136, 70.8491 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 22/21, 80.5370 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 112/99, 213.5980 cents Average / Smallest step : 2.061350 Largest / Average step : 1.286618 Largest / Smallest step : 2.652171 Median interval of one step : 9/8, 203.9100 cents, amount: 1 Least squares average step : 153.11186 cents, oct.: 459.33559 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1849-tone equal temperament with octave 4/3 degrees: 299 1056 1849 Least number of segments generator : 925 of 249.157 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1444 of 388.955 cents and inv. generated superset size: 31 = 28 more = 1033.333% 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 70.84907 cents Scale diversity : 0.958160 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.465667 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 : 896/891, 9.6880 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best major thirds form a closed circle Best minor thirds form a closed circle 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% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 123.3730 cents: 1 -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 33 U: 99) Highest odd numerator or denominator: 33 Scale harmonicity : 0.026454 Average absolute harmonicity : 0.091861 Specific harmonicity : 0.109937 Fundamental : 1/84, -6.3923 octaves, 3.1146 Hz. Guide tone : 132, 7.0444 octaves, 34534.575 Hz. Exponens Consonantiae : 1.108800E+04, 13.43671 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 55.5, average 18.50000 Mersenne's string divisions : 18361 Sum of van Prooijen's expressibility: 3.31785, average 1.10595 Sum of Tenney's harmonic distance : 6.70950, average 2.23650 Vogel's harmonic complexity : 14.00000 Wille's k value : 49 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 16.90984, average 2.81831 Lattice compactness (without 2's) : 10.32780, average 1.72130 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.33333 5 3: -1 .. 1 -0.33333 3 1 7: -1 .. 0 -0.66667 2 11: 0 .. 1 0.66667 2 2 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 18 23| Scale is weakly epimorphic with val: <6 10 19 24| Scale is weakly epimorphic with val: <6 10 20 25| Scale is weakly epimorphic with val: <6 10 21 26| Scale is weakly epimorphic with val: <6 10 22 27| Scale is weakly epimorphic with val: <6 11 19 23| Scale is weakly epimorphic with val: <6 11 20 24| Scale is weakly epimorphic with val: <6 11 21 25| Scale is weakly epimorphic with val: <6 11 22 26| Scale is weakly epimorphic with val: <7 10 18 24| Scale is weakly epimorphic with val: <7 10 19 25| Scale is weakly epimorphic with val: <7 10 20 26| Scale is weakly epimorphic with val: <7 10 21 27| Scale is JI-epimorphic with val: <7 11 18 23| Scale is weakly epimorphic with val: <7 11 18 26| Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 11 19 27| Scale is JI-epimorphic with val: <7 11 20 25| = patent Scale is weakly epimorphic with val: <7 11 21 23| Scale is JI-epimorphic with val: <7 11 21 26| Scale is weakly epimorphic with val: <7 11 22 24| Scale is JI-epimorphic with val: <7 11 22 27| Scale is weakly epimorphic with val: <8 11 18 24| Scale is weakly epimorphic with val: <8 11 19 25| Scale is weakly epimorphic with val: <8 11 20 26| Scale is weakly epimorphic with val: <8 11 21 27|
FIT/MODE
3: 1 1 1 SP B ME I SD: 56.4819 c. M:-85.4780 c. 4: 1 1 2 P M ME S SD: 32.6018 c. M:-43.9742 c. 5: 1 2 2 SP M ME S SD: 13.7904 c. M:-19.0720 c. 7: 1 3 3 SP M DE S SD: 5.4207 c. M: 9.3877 c. 12: 2 5 5 SP M DE S SD: 3.7886 c. M:-6.0792 c. 19: 3 8 8 SP M DE S SD: 2.5015 c. M:-3.8948 c. 30: 5 12 13 SP T3 SD: 1.9182 c. M:-2.4705 c. 37: 6 15 16 SP T3 SD: 1.0319 c. M: 1.7728 c. 44: 7 18 19 SP T3 SD: 1.1326 c. M: 1.4669 c. 49: 8 20 21 SP T3 SD: 0.4566 c. M:-0.7764 c. 56: 9 23 24 SP T3 SD: 0.2981 c. M: 0.4941 c. 105: 17 43 45 SP T3 SD: 0.1038 c. M:-0.1501 c. 161: 26 66 69 SP T3 SD: 0.1066 c. M:-0.1501 c. 247: 40 101 106 SP T3 SD: 0.1048 c. M: 0.1379 c. 266: 43 109 114 SP T3 SD: 0.0880 c. M:-0.1501 c. 303: 49 124 130 SP T3 SD: 0.0490 c. M: 0.0847 c. 359: 58 147 154 SP T3 SD: 0.0504 c. M: 0.0729 c. 408: 66 167 175 SP T3 SD: 0.0219 c. M:-0.0291 c. 464: 75 190 199 SP T3 SD: 0.0198 c. M: 0.0341 c. 569: 92 233 244 SP T3 SD: 0.0155 c. M:-0.0251 c. 872: 141 357 374 SP T3 SD: 0.0080 c. M: 0.0131 c. 977: 158 400 419 SP T3 SD: 0.0046 c. M:-0.0066 c. 1441: 233 590 618 SP T3 SD: 0.0039 c. M: 0.0065 c. 1849: 299 757 793 SP T3 SD: 0.0023 c. M: 0.0038 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: 101.8667 cents 5 x 6:7 S SD: 45.0216 cents 6 x 7:8 S SD: 8.7881 cents 7 x 8:9 S SD: 41.2374 cents 8 x 9:11 SD: 48.2810 cents 9:10:11:12 H SD: 39.9178 cents 10:11:12:13 H SD: 33.3815 cents 11:12:13:15 SD: 26.7714 cents 12:13:14:16 S SD: 20.2129 cents 15:16:18:20 S SD: 14.7051 cents 16:17:19:21 SD: 12.9542 cents 17:18:20:23 SD: 10.4749 cents 18:19:21:24 SD: 7.3002 cents 21:22:25:28 SD: 5.7998 cents 38:40:45:51 SD: 5.4309 cents 39:41:46:52 SD: 2.0635 cents 45:47:53:60 SD: 1.7940 cents 84:88:99:112 SD: 0.0000 cents