Scala analysis: xen15-chalmers-triadic-reversed-diamond-6-5-tetrachord
Tetrachord 10/9 * 27/25 * 10/9 of triadic reversed diamond for M=6/5, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 10/9 182.403712 minor whole tone 2: 6/5 315.641287 minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 10/9 182.4037 minor whole tone 2: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 3: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 2 10/9 182.404 cents minor whole tone 2: 2 6/5 315.641 cents minor third 2: 1 100/81 364.807 cents grave 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 : 182.4 315.6 498.0 182.4: 133.2 315.6 498.0 315.6: 182.4 364.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 133.2376 .. 182.4037 cents 250/243, 49.1661 cents 27/25, 133.2376 cents 2: 315.6413 .. 364.8074 cents 250/243, 49.1661 cents 27/25, 133.2376 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 27/25, 133.2376 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 10/9, 182.4037 cents Average / Smallest step : 1.246007 Largest / Average step : 1.098718 Largest / Smallest step : 1.369011 Median interval of one step : 10/9, 182.4037 cents, amount: 2 Most common interval of one step : 10/9, 182.4037 cents, amount: 2 Least squares average step : 164.84438 cents, oct.: 494.53313 cents Scale is strictly proper Scale has Myhill's property chromas: 250/243, 49.1661 cents and 6561/6250, 84.0714 cents, ratio: 1.709946 generators: 1 of 182.40371 cents and 2 of 315.64129 cents ET pair of linear temperament : 22&60 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 314-tone equal temperament with octave 4/3 degrees: 115 199 314 generators: 115 and 199 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABA Step pattern size order : LSL Scale is a Constant Structure, by a margin of 133.23757 cents Scale diversity : 1.214351 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.802563 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 : 250/243, 49.1661 cents Most common intervals : 10/9, 182.4037 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 1-2 -- Rational properties -- Prime limit : 5 Odd number limit : 81 (O: 27 U: 81) Highest odd numerator or denominator: 9 Scale harmonicity : 0.043860 Average absolute harmonicity : 0.130719 Specific harmonicity : 0.225140 Fundamental : 1/45, -5.4919 octaves, 5.8139 Hz. Guide tone : 60, 5.9069 octaves, 15697.534 Hz. Exponens Consonantiae : 2.700000E+03, 11.39874 octaves Euler's gradus suavitatis : 17 Sum of Mann's harmonic distance : 18.5, average 6.16667 Mersenne's string divisions : 1463 Sum of van Prooijen's expressibility: 2.13033, average 0.71011 Sum of Tenney's harmonic distance : 4.51055, average 1.50352 Vogel's harmonic complexity : 10.33333 Wille's k value : 13 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 14.20470, average 2.36745 Lattice compactness (without 2's) : 11.90611, average 1.98435 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.33333 4 3: -2 .. 1 -0.66667 4 1 5: -1 .. 1 0.00000 2 2 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is JI-epimorphic with val: <7 11 16| Scale is weakly epimorphic with val: <7 11 17| = patent Scale is weakly epimorphic with val: <7 11 19|
FIT/MODE
3: 1 1 1 SP B ME I SD: 13.3813 c. M: 16.3887 c. 8: 3 2 3 SP M ME I SD: 3.5625 c. M: 4.3632 c. 11: 4 3 4 SP M ME I SD: 1.0585 c. M: 1.2964 c. 19: 7 5 7 SP M DE I SD: 0.8872 c. M: 1.0866 c. 30: 11 8 11 SP M DE I SD: 0.1737 c. M: 0.2128 c. 41: 15 11 15 SP M DE I SD: 0.1569 c. M: 0.1921 c. 71: 26 19 26 SP M DE I SD: 0.0172 c. M: 0.0210 c. 172: 63 46 63 SP M DE I SD: 0.0161 c. M: 0.0197 c. 243: 89 65 89 SP M DE I SD: 0.0064 c. M: 0.0078 c. 314: 115 84 115 SP M DE I SD: 0.0011 c. M: 0.0013 c. 699: 256 187 256 SP M DE I SD: 0.0008 c. M: 0.0010 c. 1013: 371 271 371 SP M DE I SD: 0.0002 c. M: 0.0003 c. 1327: 486 355 486 SP M DE I SD: 0.0001 c. M: 0.0001 c. 2340: 857 626 857 SP M DE I SD: 0.0000 c. M: 0.0001 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: 70.6724 cents 5 x 6:7 S SD: 42.2336 cents 6 x 7:8 S SD: 24.3852 cents 7:8 x 9 S SD: 39.8203 cents 8:9:10:11 H SD: 30.3592 cents 9:10:11:12 H SD: 10.5889 cents 19:21:23:25 SD: 9.6488 cents 20:22:24:27 S SD: 9.2211 cents 24:27:29:32 SD: 8.2061 cents 25:28:30:33 SD: 7.4015 cents 26:29:31:35 SD: 7.0126 cents 30:33:36:40 S SD: 5.7998 cents 35:39:42:47 SD: 4.4250 cents 36:40:43:48 SD: 2.6779 cents 45:50:54:60 SD: 0.0000 cents