Scala analysis: 405_D6
Diatonic tetrachord 34/33 * 77/68 * 8/7
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 34/33 51.682466 2: 7/6 266.870906 septimal minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 34/33 51.6825 2: 77/68 215.1884 3: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 34/33 51.682 cents 1: 1 77/68 215.188 cents 1: 1 8/7 231.174 cents septimal whole tone 2: 1 7/6 266.871 cents septimal minor third 2: 1 272/231 282.857 cents 2: 1 22/17 446.363 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 : 51.7 266.9 498.0 51.7 : 215.2 446.4 498.0 266.9: 231.2 282.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 51.6825 .. 231.1741 cents 132/119, 179.4916 cents 34/33, 51.6825 cents 2: 266.8709 .. 446.3625 cents 132/119, 179.4916 cents 49/48, 35.6968 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 34/33, 51.6825 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 3.212211 Largest / Average step : 1.392489 Largest / Smallest step : 4.472969 Median interval of one step : 77/68, 215.1884 cents, amount: 1 Least squares average step : 148.53995 cents, oct.: 445.61984 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1995-tone equal temperament with octave 4/3 degrees: 207 1069 1995 Least number of segments generator : 998 of 249.147 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1972 of 492.303 cents and inv. generated superset size: 137 = 134 more = 4566.667% 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 35.69681 cents Scale diversity : 0.696854 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.279215 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 : 544/539, 15.9857 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% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 163.5060 cents: 1 -- Rational properties -- Prime limit : 17 Odd number limit : 231 (O: 77 U: 231) Highest odd numerator or denominator: 33 Scale harmonicity : 0.015564 Average absolute harmonicity : 0.101733 Specific harmonicity : 0.082578 Fundamental : 1/66, -6.0444 octaves, 3.9640 Hz. Guide tone : 476, 8.8948 octaves, 124533.769 Hz. Exponens Consonantiae : 3.141600E+04, 14.93921 octaves Euler's gradus suavitatis : 38 Sum of Mann's harmonic distance : 43.5, average 14.50000 Mersenne's string divisions : 6097 Sum of van Prooijen's expressibility: 2.84073, average 0.94691 Sum of Tenney's harmonic distance : 5.75242, average 1.91747 Vogel's harmonic complexity : 17.00000 Wille's k value : 38 Wilson's harmonic complexity : 38 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 13.50820, average 2.25137 Lattice compactness (without 2's) : 8.29253, average 1.38209 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.66667 4 3: -1 ..-1 -1.00000 3 1 7: 0 .. 1 0.33333 1 1 11: -1 .. 0 -0.33333 1 17: 0 .. 1 0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 19 23 28| Scale is weakly epimorphic with val: <6 10 19 23 31| Scale is weakly epimorphic with val: <6 10 19 24 29| Scale is weakly epimorphic with val: <6 10 19 24 32| Scale is weakly epimorphic with val: <6 10 19 25 27| Scale is weakly epimorphic with val: <6 10 19 25 30| Scale is weakly epimorphic with val: <6 10 19 25 33| Scale is weakly epimorphic with val: <6 10 19 26 28| Scale is weakly epimorphic with val: <6 10 19 26 31| Scale is weakly epimorphic with val: <6 10 19 27 29| Scale is weakly epimorphic with val: <6 10 19 27 32| Scale is weakly epimorphic with val: <6 10 20 23 30| Scale is weakly epimorphic with val: <6 10 20 24 31| Scale is weakly epimorphic with val: <6 10 20 25 32| Scale is weakly epimorphic with val: <6 10 20 26 33| Scale is weakly epimorphic with val: <6 11 19 23 31| Scale is weakly epimorphic with val: <6 11 19 24 32| Scale is weakly epimorphic with val: <6 11 19 25 33| Scale is weakly epimorphic with val: <6 11 20 23 27| Scale is weakly epimorphic with val: <6 11 20 23 30| Scale is weakly epimorphic with val: <6 11 20 23 33| Scale is weakly epimorphic with val: <6 11 20 24 28| Scale is weakly epimorphic with val: <6 11 20 24 31| Scale is weakly epimorphic with val: <6 11 20 25 29| Scale is weakly epimorphic with val: <6 11 20 25 32| Scale is weakly epimorphic with val: <6 11 20 26 27| Scale is weakly epimorphic with val: <6 11 20 26 30| Scale is weakly epimorphic with val: <6 11 20 26 33| Scale is weakly epimorphic with val: <6 11 20 27 28| Scale is weakly epimorphic with val: <6 11 20 27 31| Scale is weakly epimorphic with val: <6 11 22 23 31| Scale is weakly epimorphic with val: <6 11 22 24 32| Scale is weakly epimorphic with val: <6 11 22 25 33| Scale is weakly epimorphic with val: <7 10 19 23 29| Scale is weakly epimorphic with val: <7 10 19 24 30| Scale is weakly epimorphic with val: <7 10 19 25 31| Scale is weakly epimorphic with val: <7 10 19 26 32| Scale is weakly epimorphic with val: <7 10 19 27 33| Scale is weakly epimorphic with val: <7 10 20 23 28| Scale is weakly epimorphic with val: <7 10 20 23 31| Scale is weakly epimorphic with val: <7 10 20 24 29| Scale is weakly epimorphic with val: <7 10 20 24 32| Scale is weakly epimorphic with val: <7 10 20 25 27| Scale is weakly epimorphic with val: <7 10 20 25 30| Scale is weakly epimorphic with val: <7 10 20 25 33| Scale is weakly epimorphic with val: <7 10 20 26 28| Scale is weakly epimorphic with val: <7 10 20 26 31| Scale is weakly epimorphic with val: <7 10 20 27 29| Scale is weakly epimorphic with val: <7 10 20 27 32| Scale is weakly epimorphic with val: <7 10 22 23 29| Scale is weakly epimorphic with val: <7 10 22 24 30| Scale is weakly epimorphic with val: <7 10 22 25 31| Scale is weakly epimorphic with val: <7 10 22 26 32| Scale is weakly epimorphic with val: <7 10 22 27 33| Scale is weakly epimorphic with val: <7 11 19 23 29| Scale is weakly epimorphic with val: <7 11 19 23 32| Scale is weakly epimorphic with val: <7 11 19 24 27| Scale is weakly epimorphic with val: <7 11 19 24 30| Scale is weakly epimorphic with val: <7 11 19 24 33| Scale is weakly epimorphic with val: <7 11 19 25 28| Scale is weakly epimorphic with val: <7 11 19 25 31| Scale is weakly epimorphic with val: <7 11 19 26 29| Scale is weakly epimorphic with val: <7 11 19 26 32| Scale is weakly epimorphic with val: <7 11 19 27 27| Scale is weakly epimorphic with val: <7 11 19 27 30| Scale is weakly epimorphic with val: <7 11 19 27 33| Scale is JI-epimorphic with val: <7 11 20 23 28| Scale is weakly epimorphic with val: <7 11 20 23 31| Scale is JI-epimorphic with val: <7 11 20 24 29| Scale is weakly epimorphic with val: <7 11 20 24 32| Scale is weakly epimorphic with val: <7 11 20 25 27| Scale is JI-epimorphic with val: <7 11 20 25 30| = patent Scale is weakly epimorphic with val: <7 11 20 25 33| Scale is weakly epimorphic with val: <7 11 20 26 28| Scale is JI-epimorphic with val: <7 11 20 26 31| Scale is weakly epimorphic with val: <7 11 20 27 29| Scale is JI-epimorphic with val: <7 11 20 27 32| Scale is weakly epimorphic with val: <7 11 22 23 29| Scale is weakly epimorphic with val: <7 11 22 23 32| Scale is weakly epimorphic with val: <7 11 22 24 27| Scale is weakly epimorphic with val: <7 11 22 24 30| Scale is weakly epimorphic with val: <7 11 22 24 33| Scale is weakly epimorphic with val: <7 11 22 25 28| Scale is weakly epimorphic with val: <7 11 22 25 31| Scale is weakly epimorphic with val: <7 11 22 26 29| Scale is weakly epimorphic with val: <7 11 22 26 32| Scale is weakly epimorphic with val: <7 11 22 27 27| Scale is weakly epimorphic with val: <7 11 22 27 30| Scale is weakly epimorphic with val: <7 11 22 27 33| Scale is weakly epimorphic with val: <7 12 20 23 31| Scale is weakly epimorphic with val: <7 12 20 24 32| Scale is weakly epimorphic with val: <7 12 20 25 33| Scale is weakly epimorphic with val: <7 12 22 23 29| Scale is weakly epimorphic with val: <7 12 22 23 32| Scale is weakly epimorphic with val: <7 12 22 24 27| Scale is weakly epimorphic with val: <7 12 22 24 30| Scale is weakly epimorphic with val: <7 12 22 24 33| Scale is weakly epimorphic with val: <7 12 22 25 28| Scale is weakly epimorphic with val: <7 12 22 25 31| Scale is weakly epimorphic with val: <7 12 22 26 29| Scale is weakly epimorphic with val: <7 12 22 26 32| Scale is weakly epimorphic with val: <7 12 22 27 27| Scale is weakly epimorphic with val: <7 12 22 27 30| Scale is weakly epimorphic with val: <7 12 22 27 33| Scale is weakly epimorphic with val: <8 11 20 23 29| Scale is weakly epimorphic with val: <8 11 20 24 30| Scale is weakly epimorphic with val: <8 11 20 25 31| Scale is weakly epimorphic with val: <8 11 20 26 32| Scale is weakly epimorphic with val: <8 11 20 27 33| Scale is weakly epimorphic with val: <8 11 22 23 27| Scale is weakly epimorphic with val: <8 11 22 23 30| Scale is weakly epimorphic with val: <8 11 22 23 33| Scale is weakly epimorphic with val: <8 11 22 24 28| Scale is weakly epimorphic with val: <8 11 22 24 31| Scale is weakly epimorphic with val: <8 11 22 25 29| Scale is weakly epimorphic with val: <8 11 22 25 32| Scale is weakly epimorphic with val: <8 11 22 26 27| Scale is weakly epimorphic with val: <8 11 22 26 30| Scale is weakly epimorphic with val: <8 11 22 26 33| Scale is weakly epimorphic with val: <8 11 22 27 28| Scale is weakly epimorphic with val: <8 11 22 27 31| Scale is weakly epimorphic with val: <8 12 19 23 30| Scale is weakly epimorphic with val: <8 12 19 24 31| Scale is weakly epimorphic with val: <8 12 19 25 32| Scale is weakly epimorphic with val: <8 12 19 26 33| Scale is weakly epimorphic with val: <8 12 22 23 30| Scale is weakly epimorphic with val: <8 12 22 24 31| Scale is weakly epimorphic with val: <8 12 22 25 32| Scale is weakly epimorphic with val: <8 12 22 26 33|
FIT/MODE
3: 0 1 2 N G T3 SD: 65.4293 c. M: 100.8559 c. 4: 0 2 2 P M DE S SD: 31.5681 c. M: 51.6825 c. 6: 1 2 3 P T3 SD: 20.8152 c. M:-31.3250 c. 7: 1 3 3 SP M DE S SD: 15.2006 c. M:-19.4668 c. 8: 1 3 4 P T3 SD: 11.9772 c. M: 17.8484 c. 9: 1 4 4 SP M DE S SD: 6.0501 c. M:-9.8208 c. 11: 1 5 5 SP M DE S SD: 4.6180 c. M: 6.4056 c. 17: 2 7 8 SP T3 SD: 4.3971 c. M:-6.9111 c. 19: 2 8 9 SP T3 SD: 2.7712 c. M: 4.7420 c. 28: 3 12 13 SP T3 SD: 0.9703 c. M:-1.6795 c. 39: 4 17 18 SP T3 SD: 0.8306 c. M:-1.3072 c. 58: 6 25 27 SP T3 SD: 0.4003 c. M: 0.6744 c. 86: 9 37 40 SP T3 SD: 0.3731 c. M: 0.4747 c. 97: 10 42 45 SP T3 SD: 0.2073 c. M: 0.3376 c. 125: 13 54 58 SP T3 SD: 0.0809 c. M:-0.1142 c. 222: 23 96 103 SP T3 SD: 0.0747 c. M:-0.0992 c. 280: 29 121 130 SP T3 SD: 0.0673 c. M: 0.0992 c. 308: 32 133 143 SP T3 SD: 0.0504 c. M:-0.0625 c. 405: 42 175 188 SP T3 SD: 0.0217 c. M: 0.0334 c. 530: 55 229 246 SP T3 SD: 0.0036 c. M:-0.0060 c. 1995: 207 862 926 SP T3 SD: 0.0033 c. M: 0.0056 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: 48.7680 cents 6 x 7:8 S SD: 0.0000 cents 7 x 8:9 S SD: 36.1882 cents 8 x 9:11 SD: 41.2374 cents 9 x 11:12 SD: 40.2685 cents 10 x 12:13 S SD: 32.7861 cents 12:13:14:16 S SD: 28.9634 cents 13:14:15:17 SD: 28.6086 cents 14:15:16:19 SD: 27.4968 cents 15:16:18:20 S SD: 25.7863 cents 16:17:19:21 SD: 22.4110 cents 17:18:20:23 SD: 18.5092 cents 18:19:21:24 SD: 13.9735 cents 22:23:26:29 SD: 13.0353 cents 23:24:27:31 SD: 10.2693 cents 24:25:28:32 SD: 6.3300 cents 29:30:34:39 SD: 6.1674 cents 30:31:35:40 SD: 1.6948 cents 36:37:42:48 SD: 1.4161 cents 66:68:77:88 SD: 0.0000 cents