Scala analysis: xen15-chalmers-triadic-reversed-diamond-11-9-tetrachord
Tetrachord 12/11 * 121/108 * 12/11 of triadic reversed diamond for M=11/9, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 12/11 150.637059 undecimal neutral second, 3/4-tone 2: 11/9 347.407941 undecimal neutral third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 12/11 150.6371 undecimal neutral second, 3/4-tone 2: 121/108 196.7709 3: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 121/108 196.771 cents 2: 1 144/121 301.274 cents two (undecimal neutral second, 3/4-tone) 2: 2 11/9 347.408 cents undecimal neutral 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 : 150.6 347.4 498.0 150.6: 196.8 347.4 498.0 347.4: 150.6 301.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.6371 .. 196.7709 cents 1331/1296, 46.1338 cents 12/11, 150.6371 cents 2: 301.2741 .. 347.4079 cents 1331/1296, 46.1338 cents 15552/14641, 104.5032 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 12/11, 150.6371 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 121/108, 196.7709 cents Average / Smallest step : 1.102086 Largest / Average step : 1.185260 Largest / Smallest step : 1.306258 Median interval of one step : 12/11, 150.6371 cents, amount: 2 Most common interval of one step : 12/11, 150.6371 cents, amount: 2 Least squares average step : 167.11342 cents, oct.: 501.34027 cents Scale is strictly proper Scale has Myhill's property chromas: 1331/1296, 46.1338 cents and 15552/14641, 104.5032 cents, ratio: 2.265219 generators: 1 of 150.63706 cents and 2 of 347.40794 cents ET pair of linear temperament : 20&66 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 367-tone equal temperament with octave 4/3 degrees: 111 256 367 generators: 111 and 256 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABA Step pattern size order : SLS Scale is a Constant Structure, by a margin of 104.50323 cents Scale diversity : 1.328004 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.814740 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 : 1331/1296, 46.1338 cents Most common intervals : 12/11, 150.6371 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 Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 1-2 -- Rational properties -- Prime limit : 11 Odd number limit : 121 (O: 121 U: 121) Highest odd numerator or denominator: 11 Scale harmonicity : 0.021569 Average absolute harmonicity : 0.100192 Specific harmonicity : 0.111298 Fundamental : 1/99, -6.6294 octaves, 2.6427 Hz. Guide tone : 132, 7.0444 octaves, 34534.575 Hz. Exponens Consonantiae : 1.306800E+04, 13.67375 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 25.0, average 8.33333 Mersenne's string divisions : 3220 Sum of van Prooijen's expressibility: 2.55991, average 0.85330 Sum of Tenney's harmonic distance : 5.19539, average 1.73180 Vogel's harmonic complexity : 16.33333 Wille's k value : 60 Wilson's harmonic complexity : 31 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 15.73029, average 2.62171 Lattice compactness (without 2's) : 11.90611, average 1.98435 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.33333 4 3: -2 .. 1 -0.66667 4 1 11: -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 weakly epimorphic with val: <7 11 23| Scale is JI-epimorphic with val: <7 11 24| Scale is weakly epimorphic with val: <7 11 26| Scale is weakly epimorphic with val: <7 11 27|
FIT/MODE
3: 1 1 1 SP B ME I SD: 12.5560 c. M: 15.3779 c. 7: 2 3 2 SP M ME I SD: 6.8083 c. M: 8.3385 c. 10: 3 4 3 SP M ME I SD: 0.9990 c. M: 1.2236 c. 23: 7 9 7 SP M DE I SD: 0.7690 c. M: 0.9419 c. 33: 10 13 10 SP M DE I SD: 0.2332 c. M: 0.2857 c. 43: 13 17 13 SP M DE I SD: 0.0533 c. M: 0.0653 c. 119: 36 47 36 SP M DE I SD: 0.0261 c. M: 0.0320 c. 162: 49 64 49 SP M DE I SD: 0.0050 c. M: 0.0062 c. 367: 111 145 111 SP M DE I SD: 0.0018 c. M: 0.0022 c. 529: 160 209 160 SP M DE I SD: 0.0003 c. M: 0.0004 c. 1425: 431 563 431 SP M DE I SD: 0.0002 c. M: 0.0003 c. 1954: 591 772 591 SP M DE I SD: 0.0001 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: 38.9058 cents 5 x 6:7 S SD: 45.1216 cents 6 x 7:8 S SD: 40.2685 cents 7:8 x 9 S SD: 51.1133 cents 8:9:10:11 H SD: 28.2640 cents 9:10:11:12 H SD: 10.5889 cents 21:23:26:28 SD: 7.7891 cents 22:24:27:29 SD: 7.0114 cents 23:25:28:31 SD: 6.9666 cents 31:34:38:41 SD: 5.8536 cents 32:35:39:43 SD: 5.0116 cents 33:36:40:44 S SD: 4.7891 cents 36:39:44:48 SD: 4.0215 cents 45:49:55:60 SD: 1.0697 cents 54:59:66:72 SD: 0.8899 cents 99:108:121:132 SD: 0.0000 cents