Scala analysis: xen15-chalmers-triadic-reversed-diamond-33-26-tetrachord
Tetrachord 104/99 * 3267/2704 * 104/99 of triadic reversed diamond for M=33/26, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 104/99 85.299718 2: 33/26 412.745281 tridecimal major third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 104/99 85.2997 1: 104/99 85.2997 2: 3267/2704 327.4456 3: 104/99 85.2997
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 104/99 85.300 cents 1: 1 3267/2704 327.446 cents 2: 1 10816/9801 170.599 cents 2: 2 33/26 412.745 cents tridecimal major third Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 85.3 412.7 498.0 85.3 : 327.4 412.7 498.0 412.7: 85.3 170.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 85.2997 .. 327.4456 cents 323433/281216, 242.1458 cents 104/99, 85.2997 cents 2: 170.5994 .. 412.7453 cents 323433/281216, 242.1458 cents 29246464/32019867,-156.8461 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 104/99, 85.2997 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 3267/2704, 327.4456 cents Average / Smallest step : 1.946255 Largest / Average step : 1.972385 Largest / Smallest step : 3.838765 Median interval of one step : 104/99, 85.2997 cents, amount: 2 Most common interval of one step : 104/99, 85.2997 cents, amount: 2 Least squares average step : 171.78038 cents, oct.: 515.34113 cents Scale is not proper Scale has Myhill's property chromas: 323433/281216, 242.1458 cents and 32019867/29246464, 156.8461 cents, ratio: 1.543843 generators: 1 of 85.29972 cents and 2 of 412.74528 cents ET pair of linear temperament : 70&292 Scale is distributional even Scale is a mode of a 181-tone equal temperament with octave 4/3 degrees: 31 150 181 generators: 31 and 150 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABA Step pattern size order : SLS Interval vector is [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ] Scale is a Constant Structure, by a margin of 85.29972 cents Scale diversity : 0.934209 Lumma stability : 0.342538 Lumma impropriety factor : 0.314924 Rothenberg efficiency : 0.888889 redundancy: 0.111111 Efficiency x scale size : 2.666667 Number of different interval sizes : 4 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 104/99, 85.2997 cents Most common intervals : 104/99, 85.2997 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 3 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 1-2 -- Rational properties -- Prime limit : 13 Odd number limit : 9801 (O: 3267 U: 9801) Highest odd numerator or denominator: 99 Scale harmonicity : 0.010791 Average absolute harmonicity : 0.085852 Specific harmonicity : 0.056601 Fundamental : 1/2574, -11.3298 octaves, 0.1016 Hz. Guide tone : 3432, 11.7448 octaves, 897898.940 Hz. Exponens Consonantiae : 8.833968E+06, 23.07463 octaves Euler's gradus suavitatis : 55 Sum of Mann's harmonic distance : 134.5, average 44.83333 Mersenne's string divisions : 11977 Sum of van Prooijen's expressibility: 3.99127, average 1.33042 Sum of Tenney's harmonic distance : 8.02534, average 2.67511 Vogel's harmonic complexity : 30.33333 Wille's k value : 1633 Wilson's harmonic complexity : 57 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 19.72660, average 3.28777 Lattice compactness (without 2's) : 13.48619, average 2.24770 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 1.33333 6 3: -2 .. 1 -0.66667 4 1 11: -1 .. 1 0.00000 2 13: -1 .. 1 0.00000 2 2 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is JI-epimorphic with val: <7 11 23 25| Scale is weakly epimorphic with val: <7 11 23 26| Scale is weakly epimorphic with val: <7 11 23 28| Scale is weakly epimorphic with val: <7 11 23 29| Scale is JI-epimorphic with val: <7 11 24 26| Scale is weakly epimorphic with val: <7 11 24 27| Scale is weakly epimorphic with val: <7 11 24 29| Scale is weakly epimorphic with val: <7 11 24 30| Scale is weakly epimorphic with val: <7 11 25 25| Scale is JI-epimorphic with val: <7 11 25 27| = patent Scale is weakly epimorphic with val: <7 11 25 28| Scale is weakly epimorphic with val: <7 11 25 30| Scale is weakly epimorphic with val: <7 11 26 26| Scale is JI-epimorphic with val: <7 11 26 28| Scale is weakly epimorphic with val: <7 11 26 29| Scale is weakly epimorphic with val: <7 11 27 27| Scale is JI-epimorphic with val: <7 11 27 29| Scale is weakly epimorphic with val: <7 11 27 30|
FIT/MODE
3: 0 2 1 N G T3 SD: 67.8012 c. M: 85.2997 c. 4: 1 2 1 P M ME I SD: 32.0161 c. M: 39.2115 c. 5: 1 3 1 N M DE I SD: 11.6835 c. M: 14.3093 c. 6: 1 4 1 N M DE I SD: 1.8716 c. M: 2.2922 c. 23: 4 15 4 N M DE I SD: 1.0752 c. M: 1.3168 c. 29: 5 19 5 N M DE I SD: 0.4655 c. M: 0.5701 c. 35: 6 23 6 N M DE I SD: 0.0649 c. M: 0.0794 c. 111: 19 73 19 N M DE I SD: 0.0398 c. M: 0.0488 c. 146: 25 96 25 N M DE I SD: 0.0147 c. M: 0.0180 c. 181: 31 119 31 N M DE I SD: 0.0007 c. M: 0.0008 c. 1775: 304 1167 304 N M DE I SD: 0.0006 c. M: 0.0007 c. 1956: 335 1286 335 N M DE I SD: 0.0005 c. M: 0.0006 c. 2137: 366 1405 366 N M DE I SD: 0.0004 c. M: 0.0005 c. 2318: 397 1524 397 N M DE I SD: 0.0003 c. M: 0.0004 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: 26.4316 cents 5 x 6:7 S SD: 64.3504 cents 6 x x 8 S SD: 0.0000 cents 7:8:9 x S SD: 73.7875 cents 8:9:10:11 H SD: 44.2280 cents 9:10:11:12 H SD: 39.0130 cents 10:11:13 x SD: 44.9234 cents 11:12:14:15 S SD: 25.3975 cents 12:13:15:16 SD: 19.8232 cents 13:14 x 17 SD: 27.2901 cents 14:15:18:19 S SD: 17.0089 cents 15:16:19:20 SD: 8.8875 cents 18:19:23:24 SD: 4.7603 cents 37:39:47:49 SD: 4.3953 cents 41:43:52:55 SD: 3.6589 cents 45:47:57:60 SD: 3.5370 cents 56:59:71:75 SD: 3.1348 cents 57:60:72:76 S SD: 3.0037 cents 59:62:75:79 SD: 2.6036 cents 60:63:76:80 SD: 1.1995 cents 78:82:99:104 SD: 0.4267 cents 216:227:274:288 SD: 0.3979 cents 219:230:278:292 SD: 0.1717 cents 297:312:377:396 SD: 0.0589 cents